A. Agarwal, R. K. Guntu, A. Banerjee, M. A. Gadhawe, N. Marwan:
A complex network approach to study the extreme precipitation patterns in a river basin, Chaos, 32, 013113 (2022). DOI:10.1063/5.0072520 » Abstract
The quantification of spatial propagation of extreme precipitation events is vital in water resources planning and disaster mitigation. However, quantifying these extreme events has always been challenging as many traditional methods are insufficient to capture the nonlinear interrelationships between extreme event time series. Therefore, it is crucial to develop suitable methods for analyzing the dynamics of extreme events over a river basin with a diverse climate and complicated topography. Over the last decade, complex network analysis emerged as a powerful tool to study the intricate spatiotemporal relationship between many variables in a compact way. In this study, we employ two nonlinear concepts of event synchronization and edit distance to investigate the extreme precipitation pattern in the Ganga river basin. We use the network degree to understand the spatial synchronization pattern of extreme rainfall and identify essential sites in the river basin with respect to potential prediction skills. The study also attempts to quantify the influence of precipitation seasonality and topography on extreme events. The findings of the study reveal that (1) the network degree is decreased in the southwest to northwest direction, (2) the timing of 50th percentile precipitation within a year influences the spatial distribution of degree, (3) the timing is inversely related to elevation, and (4) the lower elevation greatly influences connectivity of the sites. The study highlights that edit distance could be a promising alternative to analyze event-like data by incorporating event time and amplitude and constructing complex networks of climate extremes.
C. Boettner, G. Klinghammer, N. Boers, T. Westerhold, N. Marwan:
Early-Warning Signals For Cenozoic Climate Transitions, Quaternary Science Reviews, 270, 107177 (2021). DOI:10.1016/j.quascirev.2021.107177 » Abstract
Deep-time paleoclimatic records document large-scale shifts and perturbations in Earth's climate; during the Cenozoic in particular transitions have been recorded on time scales of 10 thousand to 1 million years. Bifurcations in the leading dynamical modes could be a key element driving these events. Such bifurcation-induced critical transitions are typically preceded by characteristic early-warning signals, for example in terms of rising standard deviation and lag-one autocorrelation. These early-warning signals are generated by a widening of the underlying basin of attraction when approaching the bifurcation, a phenomenon dubbed critical slowing down. The associated dynamical transitions should therefore be preceded by characteristic signals that can be detected by statistical methods. Here, we reveal the presence of significant early-warning signals prior to several climate events within a paleoclimate record spanning the last 66 million years - the Cenozoic Era. We computed standard deviation and lag-one autocorrelation of the CENOzoic Global Reference benthic foraminifer carbon and oxygen Isotope Dataset (CENOGRID), comprising two time series of deep sea carbonate isotope variations of 18O and 13C. We find significant early-warning signals for five out of nine previously identified Cenozoic paleoclimatic events in at least one of the two records, which can be considered as viable candidates for bifurcation-induced transitions to be analysed in follow-up studies. Our results suggest that some of the major climate events of the last 66 Ma were triggered by bifurcations in leading modes of variability, indicating bifurcations could be a key component of Earth's climate system deep-time evolution.
S. Gupta, Z. Su, N. Boers, J. Kurths, N. Marwan, F. Pappenberger:
Interconnection between the Indian and the East Asian summer monsoon: Spatial synchronization patterns of extreme rainfall events, International Journal of Climatology, 43(2), 1034–1049 (2023). DOI:10.1002/joc.7861 » Abstract
A deeper understanding of the intricate relationship between the two components of the Asian summer monsoon (ASM)—the Indian summer monsoon (ISM) and the East Asian summer monsoon (EASM)—is crucial to improve the subseasonal forecasting of extreme precipitation events. Using an innovative complex network-based approach, we identify two dominant synchronization pathways between ISM and EASM—a southern mode between the Arabian Sea and southeastern China occurring in June, and a northern mode between the core ISM zone and northern China which peaks in July—and their associated large-scale atmospheric circulation patterns. Furthermore, we discover that certain phases of the Madden–Julian oscillation and the lower frequency mode of the boreal summer intraseasonal oscillation (BSISO) seem to favour the overall synchronization of extreme rainfall events between ISM and EASM while the higher-frequency mode of the BSISO is likely to support the shifting between the modes of ISM–EASM connection.
S. Gupta, A. Banerjee, N. Marwan, D. Richardson, L. Magnusson, J. Kurths, F. Pappenberger:
Analysis of Spatially Coherent Forecast Error Structures, Quaterly Journal of the Royal Meteorological Socicety, 149(756), 2881–2894 (2023). DOI:10.1002/qj.4536 » Abstract
Understanding error properties is an essential part in numerical weather prediction. Predictable relationship between errors of different regions due to some underlying systematic or random process can give rise to correlated errors. Estimation of error correlation is crucial for improvement of forecasts. However, the size of the corresponding correlation matrix is larger than what is possible to represent on geographical maps in order to diagnose its full spatial variation. Here, we propose a complex network-based approach to analyse forecast error correlations which enables us to estimate the spatially varying component of the error. A quantitative study of the spatiotemporal coherent structures of medium-range forecast errors of different climate variables using network measures can reveal common sources of errors. Such an information is crucial especially in cases such as the outgoing long wave radiation in which errors are correlated across very long distances, indicating an underlying climate mechanism as the source of the error. We show that the spatial patterns of forecast error co-variability may not be the same as that of the corresponding climate variable itself, thereby implying that the mechanisms behind the correlated errors may be different from the climate processes responsible for the spatiotemporal interactions of the climate variable. Our results highlight the importance of diagnosing the full spatial variation of error correlations to understand the origin and propagation of forecast errors, and demonstrate complex networks to be a promising diagnostic tool in this regard.
M. Kemter, N. Marwan, G. Villarini, B. Merz:
Controls on Flood Trends Across the United States, Water Resources Research, 59(2), e2021WR031673 (2023). DOI:10.1029/2021WR031673 » Abstract
Trends in flood magnitudes vary across the conterminous USA (CONUS). There have been attempts to identify what controls these regionally varying trends, but these attempts were limited to certain—for example, climatic—variables or to smaller regions, using different methods and datasets each time. Here we attribute the trends in annual maximum streamflow for 4,390 gauging stations across the CONUS in the period 1960–2010, while using a novel combination of methods and an unprecedented variety of potential controlling variables to allow large-scale comparisons and minimize biases. Using process-based flood classification and complex networks, we find 10 distinct clusters of catchments with similar flood behavior. We compile a set of 31 hydro-climatological and land use variables as predictors for 10 separate Random Forest models, allowing us to find the main controls the flood magnitude trends for each cluster. By using Accumulated Local Effect plots, we can understand how these controls influence the trends in the flood magnitude. We show that hydro-climatologic changes and land use are of similar importance for flood magnitude trends across the CONUS. Static land use variables are more important than their trends, suggesting that land use is able to attenuate (forested areas) or amplify (urbanized areas) the effects of climatic changes on flood magnitudes. For some variables, we find opposing effects in different regions, showing that flood trend controls are highly dependent on regional characteristics and that our novel approach is necessary to attribute flood magnitude trends reliably at the continental scale while maintaining sensitivity to regional controls.
C. Nava-Fernandez, T. Braun, C. L. Pederson, B. Fox, A. Hartland, O. Kwiecien, S. N. Höpker, S. Bernasconi, M. Jaggi, J. Hellstrom, F. Gázquez, A. French, N. Marwan, A. Immenhauser, S. F. M. Breitenbach:
Mid-Holocene rainfall seasonality and ENSO dynamics over the south-western Pacific, The Depositional Record, 10(1), 176–194 (2024). DOI:10.1002/dep2.268 » Abstract
El Niño–Southern Oscillation dynamics affect global weather patterns, with regionally diverse hydrological responses posing critical societal challenges. The lack of seasonally resolved hydrological proxy reconstructions beyond the observational era limits our understanding of boundary conditions that drive and/or adjust El Niño–Southern Oscillation variability. Detailed reconstructions of past El Niño–Southern Oscillation dynamics can help modelling efforts, highlight impacts on disparate ecosystems and link to extreme events that affect populations from the tropics to high latitudes. Here, mid-Holocene El Niño–Southern Oscillation and hydrological changes are reconstructed in the south-west Pacific using a stalagmite from Niue Island, which represents the period 6.4–5.4 ka BP. Stable oxygen and carbon isotope ratios, trace elements and greyscale data from a U/Th-dated and layer counted stalagmite profile are combined to infer changes in local hydrology at sub-annual to multi-decadal timescales. Principal component analysis reveals seasonal-scale hydrological changes expressed as variations in stalagmite growth patterns and geochemical characteristics. Higher levels of host rock-derived elements (Sr/Ca and U/Ca) and higher δ18O and δ13C values are observed in dark, dense calcite laminae deposited during the dry season, whereas during the wet season, higher concentrations of soil-derived elements (Zn/Ca and Mn/Ca) and lower δ18O and δ13C values are recorded in pale, porous calcite laminae. The multi-proxy record from Niue shows seasonal cycles associated with hydrological changes controlled by the positioning and strength of the South Pacific Convergence Zone. Wavelet analysis of the greyscale record reveals that El Niño–Southern Oscillation was continuously active during the mid-Holocene, with two weaker intervals at 6–5.9 and 5.6–5.5 ka BP. El Niño–Southern Oscillation especially affects dry season rainfall dynamics, with increased cyclone activity that reduces hydrological seasonality during El Niño years.
I. Pavithran, V. R. Unni, A. Saha, A. J. Varghese, R. I. Sujith, N. Marwan, J. Kurths:
Predicting the Amplitude of Thermoacoustic Instability Using Universal Scaling Behaviour, ASME Turbo Expo 2021: Turbomachinery Technical Conference and Exposition, , GT2021-60074 (2021). DOI:10.1115/GT2021-60074 » Abstract
The complex interaction between the turbulent flow, combustion and the acoustic field in gas turbine engines often results in thermoacoustic instability that produces ruinously high-amplitude pressure oscillations. These self-sustained periodic oscillations may result in a sudden failure of engine components and associated electronics, and increased thermal and vibra-tional loads. Estimating the amplitude of the limit cycle oscillations (LCO) that are expected during thermoacoustic instability helps in devising strategies to mitigate and to limit the possible damages due to thermoacoustic instability. We propose two methodologies to estimate the amplitude using only the pressure measurements acquired during stable operation. First, we use the universal scaling relation of the amplitude of the dominant mode of oscillations with the Hurst exponent to predict the amplitude of the LCO. We also present a methodology to estimate the amplitudes of different modes of oscillations separately using spectral measures which quantify the sharpening of peaks in the amplitude spectrum. The scaling relation enables us to predict the peak amplitude at thermoacoustic instability, given the data during the safe operating condition. The accuracy of prediction is tested for both methods, using the data acquired from a laboratory-scale turbulent combustor. The estimates are in good agreement with the actual amplitudes.
I. Pavithran, V. R. Unni, A. Saha, A. J. Varghese, R. I. Sujith, N. Marwan, J. Kurths:
Predicting the Amplitude of Thermoacoustic Instability Using Universal Scaling Behaviour, Journal of Engineering for Gas Turbines and Power, 143(12), 121005 (2021). DOI:10.1115/1.4052059 » Abstract
The complex interaction between the turbulent flow, combustion and the acoustic field in gas turbine engines often results in thermoacoustic instability that produces ruinously high-amplitude pressure oscillations. These self-sustained periodic oscillations may result in a sudden failure of engine components and associated electronics, and increased thermal and vibra-tional loads. Estimating the amplitude of the limit cycle oscillations (LCO) that are expected during thermoacoustic instability helps in devising strategies to mitigate and to limit the possible damages due to thermoacoustic instability. We propose two methodologies to estimate the amplitude using only the pressure measurements acquired during stable operation. First, we use the universal scaling relation of the amplitude of the dominant mode of oscillations with the Hurst exponent to predict the amplitude of the LCO. We also present a methodology to estimate the amplitudes of different modes of oscillations separately using spectral measures which quantify the sharpening of peaks in the amplitude spectrum. The scaling relation enables us to predict the peak amplitude at thermoacoustic instability, given the data during the safe operating condition. The accuracy of prediction is tested for both methods, using the data acquired from a laboratory-scale turbulent combustor. The estimates are in good agreement with the actual amplitudes.
M. H. Trauth, N. Marwan:
Introduction-Time series analysis for Earth, climate and life interactions, Quaternary Science Reviews, 284, 107475 (2022). DOI:10.1016/j.quascirev.2022.107475 » Abstract
Introduction to the VSI Time Series Analysis for Earth, Climate and Life Interactions.
O. Afsar, U. Tirnakli, N. Marwan:
Recurrence Quantification Analysis at work: Quasi-periodicity based interpretation of gait force profiles for patients with Parkinson disease, Scientific Reports, 8, 9102 (2018). DOI:10.1038/s41598-018-27369-2 » Abstract
In this letter, making use of real gait force profiles of healthy and patient groups with Parkinson disease which have different disease severity in terms of Hoehn-Yahr stage, we calculate various heuristic complexity measures of the recurrence quantification analysis (RQA). Using this technique, we are able to evince that entropy, determinism and average diagonal line length (divergence) measures decrease (increases) with increasing disease severity. We also explain these tendencies using a theoretical model (based on the sine-circle map), so that we clearly relate them to decreasing degree of irrationality of the system as a course of gait's nature. This enables us to interpret the dynamics of normal/pathological gait and is expected to increase further applications of this technique on gait timings, gait force profiles and combinations of them with various physiological signals.
A. Agarwal, N. Marwan, U. Ozturk, R. Maheswaran:
Unfolding Community Structure in Rainfall Network of Germany Using Complex Network-Based Approach, In: Water Resources and Environmental Engineering II, Springer, Singapore, 179–193 (2018). DOI:10.1007/978-981-13-2038-5_17 » Abstract
Many natural systems can be represented as networks of dynamical units with a modular structure in the form of communities of densely interconnected nodes. Unfolding structure of such densely interconnected nodes in hydro-climatology is essential for reliable parameter transfer, model inter-comparison, prediction in ungauged basins, and estimating missing information. This study presents the application of complex network-based approach for regionalization of rainfall patterns in Germany. As a test case study, daily rainfall records observed at 1,229 rain gauges were selected throughout Germany. The rainfall data, when represented as a complex network using event synchronization, exhibits small-world and scale-free network topology which are a class of stable and efficient networks common in nature. In total, eight communities were identified using Louvain community detection algorithm. Each of the identified communities has a sufficient number of rain gauges which show distinct statistical and physical rainfall characteristics. The method used has wide application in most of the real systems which can be represented by network enabling to understand modular patterns through time series analysis.
A. Agarwal, N. Marwan, R. Maheswaran, B. Merz, J. Kurths:
Quantifying the roles of single stations within homogeneous regions using complex network analysis, Journal of Hydrology, 563, 802–810 (2018). DOI:10.1016/j.jhydrol.2018.06.050 » Abstract
Regionalization and pooling stations to form homogeneous regions or communities are essential for reliable parameter transfer, prediction in ungauged basins, and estimation of missing information. Over the years, several clustering methods have been proposed for regional analysis. Most of these methods are able to quantify the study region in terms of homogeneity but fail to provide microscopic information about the interaction between communities, as well as about each station within the communities. We propose a complex network-based approach to extract this valuable information and demonstrate the potential of our approach using a rainfall network constructed from the Indian gridded daily precipitation data. The communities were identified using the network-theoretical community detection algorithm for maximizing the modularity. Further, the grid points (nodes) were classified into universal roles according to their pattern of within- and between-community connections. The method thus yields zoomed-in details of individual rainfall grids within each community.
A. Agarwal, R. Maheswaran, N. Marwan, L. Caesar, J. Kurths:
Wavelet-based multiscale similarity measure for complex networks, The European Physical Journal B, 91(11), 296 (2018). DOI:10.1140/epjb/e2018-90460-6 » Abstract
In recent years, complex network analysis facilitated the identification of universal and unexpected patterns in complex climate systems. However, the analysis and representation of a multiscale complex relationship that exists in the global climate system are limited. A logical first step in addressing this issue is to construct multiple networks over different timescales. Therefore, we propose to apply the wavelet multiscale correlation (WMC) similarity measure, which is a combination of two state-of-the-art methods, viz. wavelet and Pearson's correlation, for investigating multiscale processes through complex networks. Firstly we decompose the data over different timescales using the wavelet approach and subsequently construct a corresponding network by Pearson's correlation. The proposed approach is illustrated and tested on two synthetics and one real-world example. The first synthetic case study shows the efficacy of the proposed approach to unravel scale-specific connections, which are often undiscovered at a single scale. The second synthetic case study illustrates that by dividing and constructing a separate network for each time window we can detect significant changes in the signal structure. The real-world example investigates the behavior of the global sea surface temperature (SST) network at different timescales. Intriguingly, we notice that spatial dependent structure in SST evolves temporally. Overall, the proposed measure has an immense potential to provide essential insights on understanding and extending complex multivariate process studies at multiple scales.
A. Agarwal, L. Caesar, N. Marwan, R. Maheswaran, B. Merz, J. Kurths:
Network-based identification and characterization of teleconnections on different scales, Scientific Reports, 9, 8808 (2019). DOI:10.1038/s41598-019-45423-5 » Abstract
Sea surface temperature (SST) patterns can – as surface climate forcing – affect weather and climate at large distances. One example is El Niño-Southern Oscillation (ENSO) that causes climate anomalies around the globe via teleconnections. Although several studies identified and characterized these teleconnections, our understanding of climate processes remains incomplete, since interactions and feedbacks are typically exhibited at unique or multiple temporal and spatial scales. This study characterizes the interactions between the cells of a global SST data set at different temporal and spatial scales using climate networks. These networks are constructed using wavelet multi-scale correlation that investigate the correlation between the SST time series at a range of scales allowing instantaneously deeper insights into the correlation patterns compared to traditional methods like empirical orthogonal functions or classical correlation analysis. This allows us to identify and visualise regions of – at a certain timescale – similarly evolving SSTs and distinguish them from those with long-range teleconnections to other ocean regions. Our findings re-confirm accepted knowledge about known highly linked SST patterns like ENSO and the Pacific Decadal Oscillation, but also suggest new insights into the characteristics and origins of long-range teleconnections like the connection between ENSO and Indian Ocean Dipole.
A. Agarwal, N. Marwan, R. Maheswaran, U. Ozturk, J. Kurths, B. Merz:
Optimal design of hydrometric station networks based on complex network analysis, Hydrology and Earth System Sciences, 24, 2235–2251 (2020). DOI:10.5194/hess-24-2235-2020 » Abstract
Hydrometric networks play a vital role in providing information for decision-making in water resource management. They should be set up optimally to provide as much information as possible that is as accurate as possible and, at the same time, be cost-effective. Although the design of hydrometric networks is a well-identified problem in hydrometeorology and has received considerable attention, there is still scope for further advancement. In this study, we use complex network analysis, defined as a collection of nodes interconnected by links, to propose a new measure that identifies critical nodes of station networks. The approach can support the design and redesign of hydrometric station networks. The science of complex networks is a relatively young field and has gained significant momentum over the last few years in different areas such as brain networks, social networks, technological networks, or climate networks. The identification of influential nodes in complex networks is an important field of research. We propose a new node-ranking measure the weighted degreebetweenness (WDB) measure to evaluate the importance of nodes in a network. It is compared to previously proposed measures used on synthetic sample networks and then applied to a real-world rain gauge network comprising 1229 stations across Germany to demonstrate its applicability. The proposed measure is evaluated using the decline rate of the network efficiency and the kriging error. The results suggest that WDB effectively quantifies the importance of rain gauges, although the benefits of the method need to be investigated in more detail.
A. Agarwal, P. Azais, L. Cifarelli, J. de Boer, D. Eroglu, G. Gebel, C. Hidalgo, D. Jamet, J. Kurths, F. Lefebvre-Joud, S. Linderoth, A. Loarte11, N. Marwan, N. Mingo, U. Ozturk, S. Perraud, R. Pitz-Paal, S. Poedts, T. Priem, B. Rech, M. Ripani, S. Sharma, T. Quoc Tran, H.-J. Wagner:
Physics for the environment and sustainable development, In: EPS Grand Challenges – Physics for Society in the Horizon 2050, Eds.: M. Sakellariadou and C.-E. Wulz and K. van Der Beek and F. Ritort and B. van Tiggelen and R. Assmann and G. Cerullo and L. Cifarelli and C. Hidalgo and F. Barbato and C. Beck and C. Rossel and L. van Dyck, IOP Publishing, Bristol, 6-1–6-132 (2024). DOI:10.1088/978-0-7503-6342-6ch6 » Abstract
Chapter 6 presents an introduction and sections on: earth system analysis from a nonlinear physics perspective; physics fields with relevance for energy technologies; towards green cities: the role of transport electrification; environmental safety; understanding and predicting space weather
D. Assaf, E. Amar, N. Marwan, Y. Neuman, M. Salai, E. Rath:
Dynamic Patterns of Expertise: The Case of Orthopedic Medical Diagnosis, PLoS ONE, 11(7), 1–12 (2016). DOI:10.1371/journal.pone.0158820 » Abstract
The aim of this study was to analyze dynamic patterns for scanning femoroacetabular impingement (FAI) radiographs in orthopedics, in order to better understand the nature of expertise in radiography. Seven orthopedics residents with at least two years of expertise and seven board-certified orthopedists participated in the study. The participants were asked to diagnose 15 anteroposterior (AP) pelvis radiographs of 15 surgical patients, diagnosed with FAI syndrome. Eye tracking data were recorded using the SMI desk-mounted tracker and were analyzed using advanced measures and methodologies, mainly recurrence quantification analysis. The expert orthopedists presented a less predictable pattern of scanning the radiographs although there was no difference between experts and non-experts in the deterministic nature of their scan path. In addition, the experts presented a higher percentage of correct areas of focus and more quickly made their first comparison between symmetric regions of the pelvis. We contribute to the understanding of experts' process of diagnosis by showing that experts are qualitatively different from residents in their scanning patterns. The dynamic pattern of scanning that characterizes the experts was found to have a more complex and less predictable signature, meaning that experts' scanning is simultaneously both structured (i.e. deterministic) and unpredictable.
Extreme events are defined as events that largely deviate from the nominal state of the system as observed in a time series. Due to the rarity and uncertainty of their occurrence, predicting extreme events has been challenging. In real life, some variables (passive variables) often encode significant information about the occurrence of extreme events manifested in another variable (active variable). For example, observables such as temperature, pressure, etc., act as passive variables in case of extreme precipitation events. These passive variables do not show any large excursion from the nominal condition yet carry the fingerprint of the extreme events. In this study, we propose a reservoir computation-based framework that can predict the preceding structure or pattern in the time evolution of the active variable that leads to an extreme event using information from the passive variable. An appropriate threshold height of events is a prerequisite for detecting extreme events and improving the skill of their prediction. We demonstrate that the magnitude of extreme events and the appearance of a coherent pattern before the arrival of the extreme event in a time series affect the prediction skill. Quantitatively, we confirm this using a metric describing the mean phase difference between the input time signals, which decreases when the magnitude of the extreme event is relatively higher, thereby increasing the predictability skill.
A. Banerjee, M. Kemter, B. Goswami, B. Merz, J. Kurths, N. Marwan:
Spatial coherence patterns of extreme winter precipitation in the U.S., Theoretical and Applied Climatology, 152, 385–395 (2023). DOI:10.1007/s00704-023-04393-5 » Abstract
Extreme precipitation events have a significant impact on life and property. The U.S. experiences huge economic losses due to severe floods caused by extreme precipitation. With the complex terrain of the region, it becomes increasingly important to understand the spatial variability of extreme precipitation to conduct a proper risk assessment of natural hazards such as floods. In this work, we use a complex network-based approach to identify distinct regions exhibiting spatially coherent precipitation patterns due to various underlying climate mechanisms. To quantify interactions between event series of different locations, we use a nonlinear similarity measure, called the edit-distance method, which considers not only the occurrence of the extreme events but also their intensity, while measuring similarity between two event series. Using network measures, namely, degree and betweenness centrality, we are able to identify the specific regions affected by the landfall of atmospheric rivers in addition to those where the extreme precipitation due to storm track activity is modulated by different mountain ranges such as the Rockies and the Appalachians. Our approach provides a comprehensive picture of the spatial patterns of extreme winter precipitation in the U.S. due to various climate processes despite its vast, complex topography.
P. beim Graben, A. Hutt, N. Marwan, C. Uhl, C. L. Webber, Jr.:
Editorial: Recurrence Analysis of Complex Systems Dynamics, Frontiers in Applied Mathematics and Statistics, 6, 33 (2020). DOI:10.3389/fams.2020.00033 » Abstract
In the last three decades, recurrence plot (RP) and quantification (RQA) techniques have become important research tools in the analysis of short, noisy, and non-stationary data. Theoretical work on RPs has reached considerable maturity, and the method's popularity in recent years continues to increase due to a large number of practical RP/RQA applications in diverse areas such as physiology, human cognition, engineering, or earth and climate sciences.
N. Boers, B. Bookhagen, N. Marwan, J. Kurths, J. Marengo:
Complex networks identify spatial patterns of extreme rainfall events of the South American Monsoon System, Geophysical Research Letters, 40(16), 4386–4392 (2013). DOI:10.1002/grl.50681 » Abstract
We investigate the spatial characteristics of extreme rainfall synchronicity of the South American Monsoon System (SAMS) by means of Complex Networks (CN). By introducing a new combination of CN measures and interpreting it in a climatic context, we investigate climatic linkages and classify the spatial characteristics of extreme rainfall synchronicity. Although our approach is based on only one variable (rainfall), it reveals the most important features of the SAMS, such as the main moisture pathways, areas with frequent development of Mesoscale Convective Systems (MCS), and the major convergence zones. In addition, our results reveal substantial differences between the spatial structures of rainfall synchronicity above the 90th and above the 95th percentiles. Most notably, events above the 95th percentile contribute stronger to MCS in the La Plata Basin.
N. Boers, A. Rheinwalt, B. Bookhagen, H. M. J. Barbosa, N. Marwan, J. Marengo, J. Kurths:
The South American rainfall dipole: A complex network analysis of extreme events, Geophysical Research Letters, 41(20), 7397–7405 (2014). DOI:10.1002/2014GL061829 » Abstract
Intraseasonal rainfall variability of the South American monsoon system is characterized by a pronounced dipole between southeastern South America and southeastern Brazil. Here we analyze the dynamical properties of extreme rainfall events associated with this dipole by combining a nonlinear synchronization measure with complex networks. We make the following main observations: (i) Our approach reveals the dominant synchronization pathways of extreme events for the two dipole phases, (ii) while extreme rainfall synchronization in the tropics is directly driven by the trade winds and their deflection by the Andes mountains, extreme rainfall propagation in the subtropics is mainly dictated by frontal systems, and (iii) the well-known rainfall dipole is, in fact, only the most prominent mode of an oscillatory pattern that extends over the entire continent. This provides further evidence that the influence of Rossby waves, which cause frontal systems over South America and impact large-scale circulation patterns, extends beyond the equator.
N. Boers, B. Bookhagen, H. M. J. Barbosa, N. Marwan, J. Kurths, J. A. Marengo:
Prediction of extreme floods in the eastern Central Andes based on a complex networks approach, Nature Communications, 5, 5199 (2014). DOI:10.1038/ncomms6199 » Abstract
Changing climatic conditions have led to a significant increase in the magnitude and frequency of extreme rainfall events in the Central Andes of South America. These events are spatially extensive and often result in substantial natural hazards for population, economy and ecology. Here we develop a general framework to predict extreme events by introducing the concept of network divergence on directed networks derived from a non-linear synchronization measure. We apply our method to real-time satellite-derived rainfall data and predict more than 60% (90% during El Ni no conditions) of rainfall events above the 99th percentile in the Central Andes. In addition to the societal benefits of predicting natural hazards, our study reveals a linkage between polar and tropical regimes as the responsible mechanism: the interplay of northward migrating frontal systems and a low-level wind channel from the western Amazon to the subtropics.
N. Boers, A. Rheinwalt, B. Bookhagen, N. Marwan, J. Kurths:
A Complex Network Approach to Investigate the Spatiotemporal Co-variability of Extreme Rainfall, In: Machine Learning and Data Mining Approaches to Climate Science, Eds.: V. Lakshmanan and E. Gilleland and A. McGovern and M. Tingley, Springer, Cham, 23–33 (2015). DOI:10.1007/978-3-319-17220-0_15 » Abstract
The analysis of spatial patterns of co-variability of extreme rainfall is challenging because traditional techniques based on principal component analysis of the covariance matrix only capture the first two statistical moments of the data distribution and are thus not suitable to analyze the behavior in the tails of the respective distributions. Here, we describe an alternative to these techniques which is based on the combination of a nonlinear synchronization measure and complex network theory. This approach allows to derive spatial patterns encoding the co-variability of extreme rainfall at different locations. By introducing suitable network measures, the methodology can be used to perform climatological analysis but also for statistical prediction of extreme rainfall events. We introduce the methodological framework and present applications to high-spatiotemporal resolution rainfall data (TRMM 3B42) over South America.
N. Boers, B. Bookhagen, J. Marengo, N. Marwan, J.-S. von Storch, J. Kurths:
Extreme rainfall of the South American monsoon system: A dataset comparison using complex networks, Journal of Climate, 28(3), 1031–1056 (2015). DOI:10.1175/JCLI-D-14-00340.1 » Abstract
In this study, the authors compare six different rainfall datasets for South America with a focus on their representation of extreme rainfall during the monsoon season (December-February): the gauge-calibrated TRMM 3B42 V7 satellite product; the near-real-time TRMM 3B42 V7 RT, the GPCP 1° daily (1DD) V1.2 satellite-gauge combination product, the Interim ECMWF Re-Analysis (ERA-Interim) product; output of a high-spatial-resolution run of the ECHAM6 global circulation model; and output of the regional climate model Eta. For the latter three, this study can be understood as a model evaluation. In addition to statistical values of local rainfall distributions, the authors focus on the spatial characteristics of extreme rainfall covariability. Since traditional approaches based on principal component analysis are not applicable in the context of extreme events, they apply and further develop methods based on complex network theory. This way, the authors uncover substantial differences in extreme rainfall patterns between the different datasets: (i) The three model-derived datasets yield very different results than the satellite-gauge combinations regarding the main climatological propagation pathways of extreme events as well as the main convergence zones of the monsoon system. (ii) Large discrepancies are found for the development of mesoscale convective systems in southeastern South America. (iii) Both TRMM datasets and ECHAM6 indicate a linkage of extreme rainfall events between the central Amazon basin and the eastern slopes of the central Andes, but this pattern is not reproduced by the remaining datasets. The authors' study suggests that none of the three model-derived datasets adequately captures extreme rainfall patterns in South America.
N. Boers, M. J. Barbosa, B. Bookhagen, J. A. Marengo, N. Marwan, J. Kurths:
Propagation of Strong Rainfall Events from Southeastern South America to the Central Andes, Journal of Climate, 28(19), 7641–7658 (2015). DOI:10.1175/JCLI-D-15-0137.1 » Abstract
Based on high-spatiotemporal-resolution data, the authors perform a climatological study of strong rainfall events propagating from southeastern South America to the eastern slopes of the central Andes during the monsoon season. These events account for up to 70% of total seasonal rainfall in these areas. They are of societal relevance because of associated natural hazards in the form of floods and landslides, and they form an intriguing climatic phenomenon, because they propagate against the direction of the low-level moisture flow from the tropics. The responsible synoptic mechanism is analyzed using suitable composites of the relevant atmospheric variables with high temporal resolution. The results suggest that the low-level inflow from the tropics, while important for maintaining sufficient moisture in the area of rainfall, does not initiate the formation of rainfall clusters. Instead, alternating low and high pressure anomalies in midlatitudes, which are associated with an eastward-moving Rossby wave train, in combination with the northwestern Argentinean low, create favorable pressure and wind conditions for frontogenesis and subsequent precipitation events propagating from southeastern South America toward the Bolivian Andes.
N. Boers, B. Bookhagen, N. Marwan, J. Kurths:
Spatiotemporal characteristics and synchronization of extreme rainfall in South America with focus on the Andes Mountain range, Climate Dynamics, 46(1), 601–617 (2016). DOI:10.1007/s00382-015-2601-6 » Abstract
The South American Andes are frequently exposed to intense rainfall events with varying moisture sources and precipitation-forming processes. In this study, we assess the spatiotemporal characteristics and geographical origins of rainfall over the South American continent. Using high-spatiotemporal resolution satellite data (TRMM 3B42 V7), we define four different types of rainfall events based on their (1) high magnitude, (2) long temporal extent, (3) large spatial extent, and (4) high magnitude, long temporal and large spatial extent combined. In a first step, we analyze the spatiotemporal characteristics of these events over the entire South American continent and integrate their impact for the main Andean hydrologic catchments. Our results indicate that events of type 1 make the overall highest contributions to total seasonal rainfall (up to 50%). However, each consecutive episode of the infrequent events of type 4 still accounts for up to 20% of total seasonal rainfall in the subtropical Argentinean plains. In a second step, we employ complex network theory to unravel possibly non-linear and long-ranged climatic linkages for these four event types on the high-elevation Altiplano-Puna Plateau as well as in the main river catchments along the foothills of the Andes. Our results suggest that one to two particularly large squall lines per season, originating from northern Brazil, indirectly trigger large, long-lasting thunderstorms on the Altiplano Plateau. In general, we observe that extreme rainfall in the catchments north of approximately 20°ree;S typically originates from the Amazon Basin, while extreme rainfall at the eastern Andean foothills south of 20°ree;S and the Puna Plateau originates from southeastern South America.
N. Boers, N. Marwan, H. M. J. Barbosa, J. Kurths:
A deforestation-induced tipping point for the South American monsoon system, Scientific Reports, 7, 41489 (2017). DOI:10.1038/srep41489 » Abstract
The Amazon rainforest has been proposed as a tipping element of the earth system, with the possibility of a dieback of the entire ecosystem due to deforestation only of parts of the rainforest. Possible physical mechanisms behind such a transition are still subject to ongoing debates. Here, we use a specifically designed model to analyse the nonlinear couplings between the Amazon rainforest and the atmospheric moisture transport from the Atlantic to the South American continent. These couplings are associated with a westward cascade of precipitation and evapotranspiration across the Amazon. We investigate impacts of deforestation on the South American monsoonal circulation with particular focus on a previously neglected positive feedback related to condensational latent heating over the rainforest, which strongly enhances atmospheric moisture inflow from the Atlantic. Our results indicate the existence of a tipping point. In our model setup, crossing the tipping point causes precipitation reductions of up to 40% in non-deforested parts of the western Amazon and regions further downstream. The responsible mechanism is the breakdown of the aforementioned feedback, which occurs when deforestation reduces transpiration to a point where the available atmospheric moisture does not suffice anymore to release the latent heat needed to maintain the feedback.
T. Braun, S. F. M. Breitenbach, V. Skiba, F. A. Lechleitner, E. E. Ray, L. M. Baldini, V. J. Polyak, J. U. L. Baldini, D. J. Kennett, K. M. Prufer, N. Marwan:
Decline in seasonal predictability potentially destabilized Classic Maya societies, Communications Earth & Environment, 4, 82 (2023). DOI:10.1038/s43247-023-00717-5 » Abstract News, Related news report, Article in P.M. History
Classic Maya populations living in peri-urban states were highly dependent on seasonally distributed rainfall for reliable surplus crop yields. Despite intense study of the potential impact of decadal to centennial-scale climatic changes on the demise of Classic Maya sociopolitical institutions (750-950 CE), its direct importance remains debated. We provide a detailed analysis of a precisely dated speleothem record from Yok Balum cave, Belize, that reflects local hydroclimatic changes at seasonal scale over the past 1600 years. We find that the initial disintegration of Maya sociopolitical institutions and population decline occurred in the context of a pronounced decrease in the predictability of seasonal rainfall and severe drought between 700 and 800 CE. The failure of Classic Maya societies to successfully adapt to volatile seasonal rainfall dynamics likely contributed to gradual but widespread processes of sociopolitical disintegration. We propose that the complex abandonment of Classic Maya population centers was not solely driven by protracted drought but also aggravated by year-to-year decreases in rainfall predictability, potentially caused by a regional reduction in coherent Intertropical Convergence Zone-driven rainfall.
S. F. M. Breitenbach, J. F. Adkins, H. Meyer, N. Marwan, K. K. Kumar, G. H. Haug:
Strong Influence of Water Vapor Source Dynamics on Stable Isotopes in Precipitation Observed in Southern Meghalaya, NE India, Earth and Planetary Science Letters, 292(1–2), 212–220 (2010). DOI:10.1016/j.epsl.2010.01.038 » Abstract
To calibrate δ18O time-series from speleothems in the eastern Indian summer monsoon (ISM) region of India, and to understand the moisture regime over the northern Bay of Bengal (BoB) we analyze the δ18O and δD of rainwater, collected in 2007 and 2008 near Cherrapunji, India. δD values range from +18.5‰ to -144.4‰, while δ18O varies between +0.8‰ and -18.8‰. The Local Meteoric Water Line (LMWL) is found to be indistinguishable from the Global Meteoric Water Line (GMWL). Late ISM (September-October) rainfall exhibits lowest δ18O and δD values, with little relationship to the local precipitation amount. There is a trend to lighter isotope values over the course of the ISM, but it does not correlate with the patterns of temperature and rainfall amount. δ18O and δD time-series have to be interpreted with caution in terms of the "amount effect" in this subtropical region. We find that the temporal trend in δ18O reflects increasing transport distance during the ISM, isotopic changes in the northern BoB surface waters during late ISM, and vapor re-equilibration with rain droplets. Using an isotope box model for surface ocean waters, we quantify the potential influence of river runoff on the isotopic composition of the seasonal freshwater plume in the northern BoB. Temporal variations in this source can contribute up to 25% of the observed changes in stable isotopes of precipitation in NE India. To delineate other moisture sources, we use backward trajectory computations and find a strong correlation between source region and isotopic composition. Palaeoclimatic stable isotope time-series from northeast Indian speleothems likely reflect changes in moisture source and transport pathway, as well as the isotopic composition of the BoB surface water, all of which in turn reflect ISM strength. Stalagmite records from the region can therefore be interpreted as integrated measures of the ISM strength.
S. Breitenbach, N. Marwan, G. Wibbelt:
Weißnasensyndrom in Nordamerika – Pilzbesiedlung in Europa, Nyctalus, 16(3), 172–179 (2011).
S. F. M. Breitenbach, K. Rehfeld, B. Goswami, J. U. L. Baldini, H. E. Ridley, D. Kennett, K. Prufer, V. V. Aquino, Y. Asmerom, V. J. Polyak, H. Cheng, J. Kurths, N. Marwan:
COnstructing Proxy-Record Age models (COPRA), Climate of the Past, 8, 1765–1779 (2012). DOI:10.5194/cp-8-1765-2012 » Abstract
Reliable age models are fundamental for any palaeoclimate reconstruction. Available interpolation procedures between age control points are often inadequately reported, and very few translate age uncertainties to proxy uncertainties. Most available modeling algorithms do not allow incorporation of layer counted intervals to improve the confidence limits of the age model in question.
We present a framework that allows detection and interactive handling of age reversals and hiatuses, depth-age modeling, and proxy-record reconstruction. Monte Carlo simulation and a translation procedure are used to assign a precise time scale to climate proxies and to translate dating uncertainties to uncertainties in the proxy values. The presented framework allows integration of incremental relative dating information to improve the final age model. The free software package COPRA1.0 facilitates easy interactive usage.
S. F. M. Breitenbach, F. A. Lechleitner, H. Meyer, G. Diengdoh, D. Mattey, N. Marwan:
Cave ventilation and rainfall signals in dripwater in a monsoonal setting – a monitoring study from NE India, Chemical Geology, 402, 111–124 (2015). DOI:10.1016/j.chemgeo.2015.03.011 » Abstract
Detailed monitoring of subterranean microclimatic and hydrological conditions can delineate factors influencing speleothem-based climate proxy data and helps in their interpretation. Multi-annual monitoring of water stable isotopes, air temperature, relative humidity, drip rates and PCO2 in surface, soil and cave air gives detailed insight into dripwater isotopes, temperature and ventilation dynamics in Mawmluh Cave, NE India.
Water isotopes vary seasonally in response to monsoonal rainfall. Most negative values are observed during late Indian Summer Monsoon (ISM), with a less than one-month lag between ISM rainfall and drip response. Two dry season and two less-well distinguishable wet season dynamic ventilation regimes are identified in Mawmluh Cave. Cave air temperatures higher than surface air result in chimney ventilation during dry season nights. Dry season days show reduced ventilation due to cool cave air relative to surface air and cold-air lake development. Both, high water flow and cooler-than-surface cave air temperatures result in air inflow during wet season nights. Wet season daytime ventilation is governed by river flow, but is prone to stagnation and development of cold air lakes. CO2 monitoring indicates that PCO2 levels vary at diurnal to annual scale. Mawmluh Cave seems to act as CO2 sink during part of the dry season. While very likely, additional data is needed to establish whether wet season cave air CO2 levels rise above atmospheric values. Drip behavior is highly nonlinear, related to effective recharge dynamics, and further complicated by human influence on the epikarst aquifer.
S. F. M. Breitenbach, B. Plessen, S. Waltgenbach, R. Tjallingii, J. Leonhardt, K. P. Jochum, H. Meyer, B. Goswami, N. Marwan, D. Scholz:
Holocene interaction of maritime and continental climate in Central Europe: New speleothem evidence from Central Germany, Global and Planetary Change, 176, 144–161 (2019). DOI:10.1016/j.gloplacha.2019.03.007 » Abstract
Central European climate is strongly influenced by North Atlantic (Westerlies) and Siberian High circulation patterns, which govern precipitation and temperature dynamics and induce heterogeneous climatic conditions, with distinct boundaries between climate zones. These climate boundaries are not stationary and shift geographically, depending on long-term atmospheric conditions. So far, little is known about past shifts of these climate boundaries and the local to regional environmental response prior to the instrumental era.
High resolution multi-proxy data (stable oxygen and carbon isotope ratios, S/Ca and Sr/Ca) from two Holocene stalagmites from Bleßberg Cave (Thuringia) are used here to differentiate local and pan-regional environmental and climatic conditions Central Germany through the Holocene. Carbon isotope and S/Ca and Sr/Ca ratios inform us on local Holocene environmental changes in and around the cave, while δ18O (when combined with independent records) serves as proxy for (pan-)regional atmospheric conditions.
The stable carbon isotope record suggests repeated changes in vegetation density (open vs. dense forest), and increasing forest cover in the late Holocene. Concurrently, decreasing S/Ca values indicate more effective sulfur retention in better developed soils, with a stabilization in the mid-Holocene. This goes in hand with changes in effective summer infiltration, reflected in the Sr/Ca profile. Highest Sr/Ca values between 4 ka and 1 ka BP indicate intensified prior calcite precipitation resulting from reduced effective moisture supply.
The region of Bleßberg Cave is sensitive to shifts of the boundary between maritime (Cfb) and continental (Dfb) climate and ideally suited to reconstruct past meridional shifts of this divide. We combined the Bleßberg Cave δ18O time series with δ18O data from Bunker Cave (western Germany) and a North Atlantic Oscillation (NAO) record from lake SS1220 (SW Greenland) to reconstruct the mean position of the Cfb-Dfb climate boundary. We further estimate the dynamic interplay of the North Atlantic Oscillation and the Siberian High and their influence on Central European climate. Repeated shifts of the Cfb-Dfb boundary over the last 4000 years might explain previously observed discrepancies between proxy records from Europe. Detailed correlation analyses reveal multi-centennial scale alternations of maritime and continental climate and, concurrently, waning and waxing influences of Siberian High and NAO on Central Europe.
S. Breitenbach, N. Marwan:
Die Bleßberghöhle – ein Glücksfall für die Klimaforschung, In: Nächster Halt: Bleßberghöhle, Thüringer Höhlenverein e. V., Suhl, 128 (2022). » Abstract
Höhlen stellen generell für die Wissenschaft ein wertvolles Archiv dar, aus dem vielfältige und interessante Erkenntnisse gewonnen werden können. So gehören sie inzwischen auch zu den bedeutendsten Klimaarchiven auf dem Festland (See- und Meeressedimente stellen andere wichtige Archive dar). Solange die Höhlensedimente und Sinter ungestört bleiben, können hydrologische und klimatische Bedingungen detailliert aufgezeichnet werden. Die Bleßberghöhle ist in diesem Zusammenhang ein ausgesprochener Glücksfall, da sie über viele Jahrtausende komplett verschlossen war und so vor äußeren Störungen bewahrt wurde. Sie ist in vielen Abschnitten mit verschiedensten Sinterformen geschmückt. Für die Rekonstruktion regionaler Klimaänderungen sind vor allem die Stalagmiten geeignet. Die wissenschaftliche Bearbeitung des aus der Bleßberghöhle gesammelten Materials ist ein langwieriger Prozess und noch lange nicht abgeschlossen. Zum gegenwärtigen Zeitpunkt können aber bereits erste interessante Aussagen gemacht werden, auf die wir hier nach einem kurzen allgemeinen Einblick in verschiedene Aspekte der Paläoklimaforschung eingehen wollen.
F. Brenner, N. Marwan, P. Hoffmann:
Climate impact on spreading of airborne infectious diseases, European Physical Journal – Special Topics, 226(9), 1845–1856 (2017). DOI:10.1140/epjst/e2017-70028-2 » Abstract
In this study we combined a wide range of data sets to simulate the outbreak of an airborne infectious disease that is directly transmitted from human to human. The basis is a complex network whose structures are inspired by global air traffic data (from openflights.org) containing information about airports, airport locations, direct flight connections and airplane types. Disease spreading inside every node is realized with a Susceptible-Exposed-Infected-Recovered (SEIR) compartmental model. Disease transmission rates in our model are depending on the climate environment and therefore vary in time and from node to node. To implement the correlation between water vapor pressure and influenza transmission rate [J. Shaman, M. Kohn, Proc. Natl. Acad. Sci. 106, 3243 (2009)], we use global available climate reanalysis data (WATCH-Forcing-Data-ERA-Interim, WFDEI). During our sensitivity analysis we found that disease spreading dynamics are strongly depending on network properties, the climatic environment of the epidemic outbreak location, and the season during the year in which the outbreak is happening.
F. Brenner, N. Marwan:
Change of influenza pandemics because of climate change: Complex network simulations, Revue d'Epidemiologie et de Sante Publique, 66, S424 (2018). DOI:10.1016/j.respe.2018.05.513 » Abstract
Introduction br>Airborne influenza virus transmission is depending on climate. Infected individuals are able to travel to any country in the world within one day. In this study we combine these two insights to investigate the influence of climate change on pandemic spreading patterns of airborne infectious diseases, like influenza. Well-known recent examples for pandemics are severe acute respiratory syndrome (SARS, 2002/2003) and H1N1 (Influenza A virus subtype, 2009), which have demonstrated the vulnerability of a strongly connected world. Methods
Our study is based on a complex network approach including the following datasets: – global air traffic data (from openflights.org) with information on airports, direct flight connections, and airplane types; – global population grid [from Socioeconomic Data and Applications Center (SEDAC), NASA]; –WATCH-Forcing-Data-ERA-Interim (WFDEI) climate reanalysis data (1980-2015) and RCP6.0 climate projection data (2016-2040): temperature, specific humidity, surface air pressure, water vapour pressure.
We use the dependency between water vapour pressure and influenza transmission rate to give every location around the globe a unique transmission rate time series from 1980 until 2040. Local disease development is simulated with a stochastic SEIR compartmental model. All individuals (including infectious ones) are able to migrate from location to location via air traffic to simulate global dissemination of the virus. Results ybr>Our results show which regions are most vulnerable to climate change in terms of influenza pandemics towards key target locations (defined by highest degree, highest population, highest betweenness centrality). Furthermore, we point out the influence of climate change on pandemics from 1980 until 2040. A significant trend in the pandemic rate of spreading can be seen on a global scale. Climate change causes an influenza pandemic to proceed 5 days slower (global average) in the year 2040 compared to the year 1980. This trend varies from country to country. For example, pandemics originating from Chad show an accelerated (6 days faster) spread. Conclusion
The presented results focus on the effect that climate change has on spreading patterns of airborne infectious diseases. The change from 1980 until 2040 of important influencing variables like population distribution, varying air traffic, vaccine research, hygiene, and healthcare are neglected to separate the impact of climate change.
A. Builes-Jaramillo, N. Marwan, G. Poveda, J. Kurths:
Nonlinear interactions between the Amazon River basin and the Tropical North Atlantic at interannual timescales, Climate Dynamics, 50(7–8), 2951–2969 (2018). DOI:10.1007/s00382-017-3785-8 » Abstract
We study the physical processes involved in the potential influence of Amazon (AM) hydroclimatology over the Tropical North Atlantic (TNA) Sea Surface Temperatures (SST) at interannual timescales, by analyzing time series of the precipitation index (P-E) over AM, as well as the surface atmospheric pressure gradient between both regions, and TNA SSTs. We use a recurrence joint probability based analysis that accounts for the lagged nonlinear dependency between time series, which also allows quantifying the statistical significance, based on a twin surrogates technique of the recurrence analysis. By means of such nonlinear dependence analysis we find that at interannual timescales AM hydrology influences future states of the TNA SSTs from 0 to 2 months later with a 90–95% statistical confidence. It also unveils the existence of two-way feedback mechanisms between the variables involved in the processes: (1) precipitation over AM leads the atmospheric pressure gradient between TNA and AM from 0 to 2 month lags, (2) the pressure gradient leads the trade zonal winds over the TNA from 0 to 3 months and from 7 to 12 months, (3) the zonal winds lead the SSTs from 0 to 3 months, and (4) the SSTs lead precipitation over AM by 1 month lag. The analyses were made for time series spanning from 1979 to 2008, and for extreme precipitation events in the AM during the years 1999, 2005, 2009 and 2010. We also evaluated the monthly mean conditions of the relevant variables during the extreme AM droughts of 1963, 1980, 1983, 1997, 1998, 2005, and 2010, and also during the floods of 1989, 1999, and 2009. Our results confirm that the Amazon River basin acts as a land surface-atmosphere bridge that links the Tropical Pacific and TNA SSTs at interannual timescales. The identified mutual interactions between TNA and AM are of paramount importance for a deeper understanding of AM hydroclimatology but also of a suite of oceanic and atmospheric phenomena over the TNA, including recently observed trends in SSTs, as well as future occurrences and impacts on tropical storms and hurricanes throughout the TNA region, but also on fires, droughts, deforestation and dieback of the tropical rain forest of the Amazon River basin.
S. Buschmann, P. Hoffmann, A. Agarwal, N. Marwan, T. Nocke:
GPU-based, interactive exploration of large spatio-temporal climate networks, Chaos, 33(4), 043129 (2023). DOI:10.1063/5.0131933 » Abstract
This paper introduces the Graphics Processing Unit (GPU)-based tool Geo-Temporal eXplorer (GTX), integrating a set of highly interactive techniques for visual analytics of large geo-referenced complex networks from the climate research domain. The visual exploration of these networks faces a multitude of challenges related to the geo-reference and the size of these networks with up to several million edges and the manifold types of such networks. In this paper, solutions for the interactive visual analysis for several distinct types of large complex networks will be discussed, in particular, time-dependent, multi-scale, and multi-layered ensemble networks. Custom-tailored for climate researchers, the GTX tool supports heterogeneous tasks based on interactive, GPU-based solutions for on-the-fly large network data processing, analysis, and visualization. These solutions are illustrated for two use cases: multi-scale climatic process and climate infection risk networks. This tool helps one to reduce the complexity of the highly interrelated climate information and unveils hidden and temporal links in the climate system, not available using standard and linear tools (such as empirical orthogonal function analysis).
S. De, S. Gupta, V. R. Unni, R. Ravindran, P. Kasthuri, N. Marwan, J. Kurths, R. I. Sujith:
Study of interaction and complete merging of binary cyclones using complex networks, Chaos, 33, 013129 (2023). DOI:10.1063/5.0101714 » Abstract AIP Scilight paper, News in Times of India
Cyclones are among the most hazardous extreme weather events on Earth. In certain scenarios, two co-rotating cyclones in close proximity to one another can drift closer and completely merge into a single cyclonic system. Identifying the dynamic transitions during such an interaction period of binary cyclones and predicting the complete merger (CM) event are challenging for weather forecasters. In this work, we suggest an innovative approach to understand the evolving vortical interactions between the cyclones during two such CM events (Noru–Kulap and Seroja–Odette) using time-evolving induced velocity-based unweighted directed networks. We find that network-based indicators, namely, in-degree and out-degree, quantify the changes in the interaction between the two cyclones and are excellent candidates to classify the interaction stages before a CM. The network indicators also help to identify the dominant cyclone during the period of interaction and quantify the variation of the strength of the dominating and merged cyclones. Finally, we show that the network measures also provide an early indication of the CM event well before its occurrence.
J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
The backbone of the climate network, Europhysics Letters, 87, 48007 (2009). DOI:10.1209/0295-5075/87/48007 » Abstract
We propose a method to reconstruct and analyze a complex network from data generated by a spatio-temporal dynamical system, relying on the nonlinear mutual information of time series analysis and betweenness centrality of the complex network theory. We show that this approach reveals a rich internal structure in complex climate networks constructed from reanalysis and model surface air temperature data. Our novel method uncovers peculiar wave-like structures of high-energy flow, that we relate to global surface ocean currents. This points to a ma jor role of the oceanic surface circulation in coupling and stabilizing the global temperature field in the long-term mean (140 years for the model run and 60 years for reanalysis data). We find that these results cannot be obtained using classical linear methods of multivariate data analysis, and have ensured their robustness by intensive significance testing.
J. F. Donges, R. V. Donner, K. Rehfeld, N. Marwan, M. H. Trauth, J. Kurths:
Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis, Nonlinear Processes in Geophysics, 18, 545–562 (2011). DOI:10.5194/npg-18-545-2011 » Abstract
The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks – a recently developed approach – are promising candidates for characterising the system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. In a first order approximation, the results of recurrence network analysis are invariant to changes in the age model and are not directly affected by non-equidistant sampling of the data. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. This suggests its application as a general exploratory tool of time series analysis complementing existing methods.
J. F. Donges, R. V. Donner, M. H. Trauth, N. Marwan, H. J. Schellnhuber, J. Kurths:
Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution, Proceedings of the National Academy of Sciences, 108(51), 20422–20427 (2011). DOI:10.1073/pnas.1117052108 » Abstract
Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35-3.15 Ma B.P.), (ii) Early Pleistocene (2.25-1.6 Ma B.P.), and (iii) Middle Pleistocene (1.1-0.7 Ma B.P.). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Middle Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa.
J. F. Donges, R. V. Donner, N. Marwan, S. F. M. Breitenbach, K. Rehfeld, J. Kurths:
Non-linear regime shifts in Holocene Asian monsoon variability: potential impacts on cultural change and migratory patterns, Climate of the Past, 11, 709–741 (2015). DOI:10.5194/cp-11-709-2015 » Abstract
The Asian monsoon system is an important tipping element in Earth's climate with a large impact on human societies in the past and present. In light of the potentially severe impacts of present and future anthropogenic climate change on Asian hydrology, it is vital to understand the forcing mechanisms of past climatic regime shifts in the Asian monsoon domain. Here we use novel recurrence network analysis techniques for detecting episodes with pronounced non-linear changes in Holocene Asian monsoon dynamics recorded in speleothems from caves distributed throughout the major branches of the Asian monsoon system. A newly developed multi-proxy methodology explicitly considers dating uncertainties with the COPRA (COnstructing Proxy Records from Age models) approach and allows for detection of continental-scale regime shifts in the complexity of monsoon dynamics. Several epochs are characterised by non-linear regime shifts in Asian monsoon variability, including the periods around 8.5-7.9, 5.7-5.0, 4.1-3.7, and 3.0-2.4 ka BP. The timing of these regime shifts is consistent with known episodes of Holocene rapid climate change (RCC) and high-latitude Bond events. Additionally, we observe a previously rarely reported non-linear regime shift around 7.3 ka BP, a timing that matches the typical 1.0-1.5 ky return intervals of Bond events. A detailed review of previously suggested links between Holocene climatic changes in the Asian monsoon domain and the archaeological record indicates that, in addition to previously considered longer-term changes in mean monsoon intensity and other climatic parameters, regime shifts in monsoon complexity might have played an important role as drivers of migration, pronounced cultural changes, and the collapse of ancient human societies.
R. Donner, S. Barbosa, J. Kurths, N. Marwan:
Understanding the Earth as a Complex System – recent advances in data analysis and modelling in Earth sciences, European Physical Journal – Special Topics, 174, 1–9 (2009). DOI:10.1140/epjst/e2009-01086-6 » Abstract
This topical issue collects contributions exemplifying the recent scientific progress in the development and application of data analysis methods and conceptual modelling for understanding the dynamics of the Earth as a complex dynamical system. The individual papers focus on different questions of present-day interest in Earth sciences and sustainability, which are often of paramount importance for mankind (recent and future climate change, occurrence of natural hazards, etc.). This editorial shall motivate the link between the different contributions from both topical and methodological perspectives. The holistic view on the Earth as a complex system is important for identifying mutual links between the individual subsystems and hence for improving the physical understanding of how these components interact with each other on various temporal as well as spatial scales and how the corresponding interactions determine the dynamics of the full system.
R. V. Donner, J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
Recurrence-Based Evolving Networks for Time Series Analysis of Complex Systems, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2010), Krakow(6165), 87–90 (2010). » Abstract
This paper presents a novel approach for analyzing the structural properties of time series from real-world complex systems by means of evolving complex networks. Starting from the concept of recurrences in phase space, the recurrence matrices corresponding to different parts of a time series are re-interpreted as the adjacency matrices of complex networks, which link different observations if the associated temporal evolution is sufficiently similar. We provide some illustrative examples demonstrating that the local properties of the resulting recurrence networks allow identifying dynamically invariant objects in the phase space of complex systems. Moreover, changes in the global network properties of evolving recurrence networks allow identifying time intervals containing dynamical transitions, which is exemplified for some financial time series.
R. V. Donner, J. H. Feldhoff, J. F. Donges, N. Marwan, J. Kurths:
Multivariate extensions of recurrence networks reveal geometric signatures of coupling between nonlinear systems, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2014), Luzern, 321–324 (2014). » Abstract
Recurrence networks have recently proven their great potential for characterizing important properties of dynamical systems. However, in the real-world such systems typically do not evolve completely isolated from each other, but exhibit mutual interactions with their neighborhood. Here, we extend the recent view on isolated systems towards an coupled network approach to interacting sys- tems. Specifically, we illustrate how to modify the concept of recurrence networks for studying dynamical interrelationships between two or more coupled nonlinear dynamical systems exclusively based on their attractors' geometric structures in phase space.
W. Duesing, N. Berner, A. L. Deino, V. Foerster, K. H. Kraemer, N. Marwan, M. H. Trauth:
Multiband Wavelet Age Modeling for a 293 m ( 600 kyr) Sediment Core From Chew Bahir Basin, Southern Ethiopian Rift, Frontiers in Earth Sciences, 9, 594047 (2021). DOI:10.3389/feart.2021.594047 » Abstract
The use of cyclostratigraphy to reconstruct the timing of deposition of lacustrine deposits requires sophisticated tuning techniques that can accommodate continuous long-term changes in sedimentation rates. However, most tuning methods use stationary filters that are unable to take into account such long-term variations in accumulation rates. To overcome this problem we present herein a new multiband wavelet age modeling (MUBAWA) technique that is particularly suitable for such situations and demonstrate its use on a 293 m composite core from the Chew Bahir basin, southern Ethiopian rift. In contrast to traditional tuning methods, which use a single, defined bandpass filter, the new method uses an adaptive bandpass filter that adapts to changes in continuous spatial frequency evolution paths in a wavelet power spectrum, within which the wavelength varies considerably along the length of the core due to continuous changes in long-term sedimentation rates. We first applied the MUBAWA technique to a synthetic data set before then using it to establish an age model for the approximately 293 m long composite core from the Chew Bahir basin. For this we used the 2nd principal component of color reflectance values from the sediment, which showed distinct cycles with wavelengths of 1015 and of 40 m that were probably a result of the influence of orbital cycles. We used six independent 40Ar/39Ar ages from volcanic ash layers within the core to determine an approximate spatial frequency range for the orbital signal. Our results demonstrate that the new wavelet-based age modeling technique can significantly increase the accuracy of tuned age models.
N. Ekhtiari, A. Agarwal, N. Marwan, R. V. Donner:
Disentangling the multi-scale effects of sea-surface temperatures on global precipitation: A coupled networks approach, Chaos, 29, 063116 (2019). DOI:10.1063/1.5095565 » Abstract AIP Scilight paper
The oceans and atmosphere interact via a multiplicity of feedback mechanisms, shaping to a large extent the global climate and its variability. To deepen our knowledge of the global climate system, characterizing and investigating this interdependence is an important task of contemporary research. However, our present understanding of the underlying large-scale processes is greatly limited due to the manifold interactions between essential climatic variables at different temporal scales. To address this problem, we here propose to extend the application of complex network techniques to capture the interdependence between global fields of sea-surface temperature (SST) and precipitation (P) at multiple temporal scales. For this purpose, we combine time-scale decomposition by means of a discrete wavelet transform with the concept of coupled climate network analysis. Our results demonstrate the potential of the proposed approach to unravel the scale-specific interdependences between atmosphere and ocean and, thus, shed light on the emerging multiscale processes inherent to the climate system, which traditionally remain undiscovered when investigating the system only at the native resolution of existing climate data sets. Moreover, we show how the relevant spatial interdependence structures between SST and P evolve across time-scales. Most notably, the strongest mutual correlations between SST and P at annual scale (8-16 months) concentrate mainly over the Pacific Ocean, while the corresponding spatial patterns progressively disappear when moving toward longer time-scales.
D. Eroglu, F. H. McRobie, I. Ozken, T. Stemler, K.-H. Wyrwoll, S. F. M. Breitenbach, N. Marwan, J. Kurths:
See-saw relationship of the Holocene East Asian-Australian summer monsoon, Nature Communications, 7, 12929 (2016). DOI:10.1038/ncomms12929 » Abstract
The East Asian-Indonesian-Australian summer monsoon (EAIASM) links the Earth's hemispheres and provides a heat source that drives global circulation. At seasonal and inter-seasonal timescales, the summer monsoon of one hemisphere is linked via outflows from the winter monsoon of the opposing hemisphere. Long-term phase relationships between the East Asian summer monsoon (EASM) and the Indonesian-Australian summer monsoon (IASM) are poorly understood, raising questions of long-term adjustments to future greenhouse-triggered climate change and whether these changes could 'lock in' possible IASM and EASM phase relationships in a region dependent on monsoonal rainfall. Here we show that a newly developed nonlinear time series analysis technique allows confident identification of strong versus weak monsoon phases at millennial to sub-centennial timescales. We find a see-saw relationship over the last 9,000 years – with strong and weak monsoons opposingly phased and triggered by solar variations. Our results provide insights into centennial- to millennial-scale relationships within the wider EAIASM regime.
A. Facchini, C. Mocenni, N. Marwan, A. Vicino, E. B. P. Tiezzi:
Nonlinear time series analysis of dissolved oxygen in the Orbetello Lagoon (Italy), Ecological Modelling, 203(3–4), 339–348 (2007). DOI:10.1016/j.ecolmodel.2006.12.001 » Abstract
In this paper, a nonlinear time series analysis of data representing dissolved oxygen collected in the Lagoon of Orbetello (Grosseto, Italy) is performed. A first biological inspection of the data shows that the coastal area is highly eutrophic and subject to unexpected phenomena, like anoxic and distrophic crises. We use the recurrence plots and the recurrence quantification analysis to show that, even if the time series are short and strongly nonstationary, it is possible to characterize the oscillations of dissolved oxygen and the oxygen crises in terms of nonlinear dynamical systems.
M. L. Fischer, P. M. Munz, A. Asrat, V. Foerster, S. Kaboth-Bahr, N. Marwan, F. Schaebitz, W. Schwanghart, M. H. Trauth:
Spatio-temporal variations of climate along possible African-Arabian routes of H. sapiens expansion, Quaternary Science Advances, 14, 100174 (2024). DOI:10.1016/j.qsa.2024.100174 » Abstract
Eastern Africa and Arabia were major hominin hotspots and critical crossroads for migrating towards Asia during the late Pleistocene. To decipher the role of spatiotemporal environmental change on human occupation and migration patterns, we remeasured the marine core from Meteor Site KL 15 in the Gulf of Aden and reanalyzed its data together with the aridity index from ICDP Site Chew Bahir in eastern Africa and the wet-dry index from ODP Site 967 in the eastern Mediterranean Sea using linear and nonlinear time series analysis. These analyses show major changes in the spatiotemporal paleoclimate dynamics at 400 and 150 ka BP (thousand years before 1950), presumably driven by changes in the amplitude of the orbital eccentricity. From 400 to 150 ka BP, eastern Africa and Arabia show synchronized wet-dry shifts, which changed drastically at 150 ka BP. After 150 ka BP, an overall trend to dry climate states is observable, and the hydroclimate dynamics between eastern Africa and Arabia are negatively correlated. Those spatio-temporal variations and interrelationships of climate potentially influenced the availability of spatial links for human expansion along those vertices. We observe positively correlated network links during the supposed out-of-Africa migration phases of H. sapiens. Furthermore, our data do not suggest hominin occupation phases during specific time intervals of humid or stable climates but provide evidence of the so far underestimated potential role of climate predictability as an important factor of hominin ecological competitiveness.
J. Fohlmeister, N. Sekhon, A. Columbu, G. Vettoretti, N. Weitzel, K. Rehfeld, C. Veiga-Pires, M. Ben-Yami, N. Marwan, N. Boers:
Global reorganization of atmospheric circulation during Dansgaard–Oeschger cycles, Proceedings of the National Academy of Sciences, 120(36), e2302283120 (2023). DOI:10.1073/pnas.2302283120 » Abstract PIK News
Ice core records from Greenland provide evidence for multiple abrupt cold–warm–cold events recurring at millennial time scales during the last glacial interval. Although climate variations resembling Dansgaard–Oeschger (DO) oscillations have been identified in climate archives across the globe, our understanding of the climate and ecosystem impacts of the Greenland warming events in lower latitudes remains incomplete. Here, we investigate the influence of DO-cold-to-warm transitions on the global atmospheric circulation pattern. We comprehensively analyze δ18O changes during DO transitions in a globally distributed dataset of speleothems and set those in context with simulations of a comprehensive high-resolution climate model featuring internal millennial-scale variations of similar magnitude. Across the globe, speleothem δ18O signals and model results indicate consistent large-scale changes in precipitation amount, moisture source, or seasonality of precipitation associated with the DO transitions, in agreement with northward shifts of the Hadley circulation. Furthermore, we identify a decreasing trend in the amplitude of DO transitions with increasing distances from the North Atlantic region. This provides quantitative observational evidence for previous suggestions of the North Atlantic region being the focal point for these archetypes of past abrupt climate changes.
J. S. A. E. Fouda, W. Koepf, N. Marwan, J. Kurths, T. Penzel:
Complexity from ordinal pattern positioned slopes (COPPS), Chaos, Solitons & Fractals, 181, 114708 (2024). DOI:10.1016/j.chaos.2024.114708 » Abstract
Measuring complexity allows to characterize complex systems. Existing techniques are limited to simultaneously measure complexity from short length data sets, detect transitions and periodic dynamics. This paper presents an approach based on ordinal pattern positioned slopes (OPPS). It considers exclusively OPPS group occurrences to compute the complexity from OPPS (COPPS) as the average number of patterns and applies to short data series. The COPPS measure was successfully applied to simulation data for measuring complexity, detecting transition phases and regular dynamics, distinguishing between chaotic and stochastic dynamics; and to real-world data for detecting arrhythmia ECG beats.
Z. Gao, X. Zhang, N. Jin, R. V. Donner, N. Marwan, J. Kurths:
Recurrence networks from multivariate signals for uncovering dynamic transitions of horizontal oil-water stratified flows, Europhysics Letters, 103(5), 50004 (2013). DOI:10.1209/0295-5075/103/50004 » Abstract
Characterizing the mechanism of drop formation at the interface of horizontal oil-water stratified flows is a fundamental problem eliciting a great deal of attention from different disciplines. We experimentally and theoretically investigate the formation and transition of horizontal oil-water stratified flows. We design a new multi-sector conductance sensor and measure multivariate signals from two different stratified flow patterns. Using the Adaptive Optimal Kernel Time-Frequency Representation (AOK TFR) we first characterize the flow behavior from an energy and frequency point of view. Then, we infer multivariate recurrence networks from the experimental data and investigate the cross-transitivity for each constructed network. We find that the cross-transitivity allows quantitatively uncovering the flow behavior when the stratified flow evolves from a stable state to an unstable one and recovers deeper insights into the mechanism governing the formation of droplets at the interface of stratified flows, a task that existing methods based on AOK TFR fail to work. These findings present a first step towards an improved understanding of the dynamic mechanism leading to the transition of horizontal oil-water stratified flows from a complex-network perspective.
Z. Gao, X. Zhang, N. Jin, N. Marwan, J. Kurths:
Multivariate recurrence network analysis for characterizing horizontal oil-water two-phase flow, Physical Review E, 88, 032910 (2013). DOI:10.1103/PhysRevE.88.032910 » Abstract
Characterizing complex patterns arising from horizontal oil-water two-phase flows is a contemporary and challenging problem of paramount importance. We design a new multi-sector conductance sensor and systematically carry out horizontal oil-water two-phase flow experiments for measuring multivariate signals of different flow patterns. We then infer multivariate recurrence networks from these experimental data and investigate local cross-network properties for each constructed network. Our results demonstrate that cross-clustering coefficient from a multivariate recurrence network is very sensitive to transitions among different flow patterns and recovers quantitative insights into the flow behavior underlying horizontal oil-water flows. These properties render multivariate recurrence networks particularly powerful for investigating a horizontal oil-water two-phase flow system and its complex interacting components from a network perspective.
A. Giesche, D. A. Hodell, C. A. Petrie, G. H. Haug, J. F. Adkins, B. Plessen, N. Marwan, H. J. Bradbury, A. Hartland, A. D. French:
Recurring summer and winter droughts from 4.2-3.97 thousand years ago in north India, Communications Earth & Environment, 4, 103 (2023). DOI:10.1038/s43247-023-00763-z » Abstract
The 4.2-kiloyear event has been described as a global megadrought that transformed multiple Bronze Age complex societies, including the Indus Civilization, located in a sensitive transition zone with a bimodal (summer and winter) rainfall regime. Here we reconstruct changes in summer and winter rainfall from trace elements and oxygen, carbon, and calcium isotopes of a speleothem from Dharamjali Cave in the Himalaya spanning 4.2–3.1 thousand years ago. We find a 230-year period of increased summer and winter drought frequency between 4.2 and 3.97 thousand years ago, with multi-decadal aridity events centered on 4.19, 4.11, and 4.02 thousand years ago. The sub-annually resolved record puts seasonal variability on a human decision-making timescale, and shows that repeated intensely dry periods spanned multiple generations. The record highlights the deficits in winter and summer rainfall during the urban phase of the Indus Civilization, which prompted adaptation through flexible, self-reliant, and drought-resistant agricultural strategies.
V. Godavarthi, S. A. Pawar, V. R. Unni, R. I. Sujith, N. Marwan, J. Kurths:
Coupled interaction between unsteady flame dynamics and acoustic field in a turbulent combustor, Chaos, 28, 113111 (2018). DOI:10.1063/1.5052210 » Abstract
Thermoacoustic instability is a result of the positive feedback between the acoustic pressure and the unsteady heat release rate fluctuations in a combustor. We apply the framework of the synchronization theory to study the coupled behavior of these oscillations during the transition to thermoacoustic instability in a turbulent bluff-body stabilized gas-fired combustor. Furthermore, we characterize this complex behavior using recurrence plots and recurrence networks. We mainly found that the correlation of probability of recurrence (CPR), the joint probability of recurrence (JPR), the determinism (DET), and the recurrence rate (RR) of the joint recurrence matrix aid in detecting the synchronization transitions in this thermoacoustic system. We noticed that CPR and DET can uncover the occurrence of phase synchronization state, whereas JPR and RR can be used as indices to identify the occurrence of generalized synchronization (GS) state in the system. We applied measures derived from joint and cross recurrence networks and observed that the joint recurrence network measures, transitivity ratio, and joint transitivity are useful to detect GS. Furthermore, we use the directional property of the network measure, namely, cross transitivity to analyze the type of coupling existing between the acoustic field (dot p') and the heat release rate (dot q') fluctuations. We discover a possible asymmetric bidirectional coupling between dot q' and dot p', wherein dot q' is observed to exert a stronger influence on dot p' than vice versa.
V. Godavarthi, P. Kasthuri, S. Mondal, R. I. Sujith, N. Marwan, J. Kurths:
Synchronization transition from chaos to limit cycle oscillations when a locally coupled chaotic oscillator grid is coupled globally to another chaotic oscillator, Chaos, 30, 033121 (2020). DOI:10.1063/1.5134821 » Abstract
Some physical systems with interacting chaotic subunits, when synchronized, exhibit a dynamical transition from chaos to limit cycle oscillations via intermittency such as during the onset of oscillatory instabilities that occur due to feedback between various subsystems in turbulent flows. We depict such a transition from chaos to limit cycle oscillations via intermittency when a grid of chaotic oscillators is coupled diffusively with a dissimilar chaotic oscillator. Toward this purpose, we demonstrate the occurrence of such a transition to limit cycle oscillations in a grid of locally coupled non-identical Rössler oscillators bidirectionally coupled with a chaotic Van der Pol oscillator. Further, we report the existence of symmetry breaking phenomena such as chimera states and solitary states during this transition from desynchronized chaos to synchronized periodicity. We also identify the temporal route for such a synchronization transition from desynchronized chaos to generalized synchronization via intermittent phase synchronization followed by chaotic synchronization and phase synchronization. Further, we report the loss of multifractality and loss of scale-free behavior in the time series of the chaotic Van der Pol oscillator and the mean field time series of the Rössler system. Such behavior has been observed during the onset of oscillatory instabilities in thermoacoustic, aeroelastic, and aeroacoustic systems. This model can be used to perform inexpensive numerical control experiments to suppress synchronization and thereby to mitigate unwanted oscillations in physical systems.
B. Goswami, N. Marwan, G. Feulner, J. Kurths:
How do global temperature drivers influence each other? – A network perspective using recurrences, European Physical Journal – Special Topics, 222, 861–873 (2013). DOI:10.1140/epjst/e2013-01889-8 » Abstract
We investigate a network of influences connected to global mean temperature. Considering various climatic factors known to influence global mean temperature, we evaluate not only the impacts of these factors on temperature but also the directed dependencies among the factors themselves. Based on an existing recurrence-based connectivity measure, we propose a new and more general measure that quantifies the level of dependence between two time series based on joint recurrences at a chosen time delay. The measures estimated in the analysis are tested for statistical significance using twin surrogates. We find, in accordance with earlier studies, the major drivers for global mean temperature to be greenhouse gases, ENSO, volcanic activity, and solar irradiance. We further uncover a feedback between temperature and ENSO. Our results demonstrate the need to involve multiple, delayed interactions within the drivers of temperature in order to develop a more thorough picture of global temperature variations.
B. Goswami, J. Heitzig, K. Rehfeld, N. Marwan, A. Anoop, S. Prasad, J. Kurths:
Estimation of sedimentary proxy records together with associated uncertainty, Nonlinear Processes in Geophysics, 21, 1093–1111 (2014). DOI:10.5194/npg-21-1093-2014 » Abstract
Sedimentary proxy records constitute a significant portion of the recorded evidence that allows us to investigate paleoclimatic conditions and variability. However, uncertainties in the dating of proxy archives limit our ability to fix the timing of past events and interpret proxy record intercomparisons. While there are various age-modeling approaches to improve the estimation of the age-depth relations of archives, relatively little focus has been placed on the propagation of the age (and radiocarbon calibration) uncertainties into the final proxy record.
We present a generic Bayesian framework to estimate proxy records along with their associated uncertainty, starting with the radiometric age-depth and proxy–depth measurements, and a radiometric calibration curve if required. We provide analytical expressions for the posterior proxy probability distributions at any given calendar age, from which the expected proxy values and their uncertainty can be estimated. We illustrate our method using two synthetic data sets and then use it to construct the proxy records for groundwater inflow and surface erosion from Lonar lake in central India.
Our analysis reveals interrelations between the uncertainty of the proxy record over time and the variance of proxies along the depth of the archive. For the Lonar lake proxies, we show that, rather than the age uncertainties, it is the proxy variance combined with calibration uncertainty that accounts for most of the final uncertainty. We represent the proxy records as probability distributions on a precise, error-free timescale that makes further time series analyses and intercomparisons of proxies relatively simple and clear. Our approach provides a coherent understanding of age uncertainties within sedimentary proxy records that involve radiometric dating. It can be potentially used within existing age modeling structures to bring forth a reliable and consistent framework for proxy record estimation.
B. Goswami, P. Schultz, B. Heinze, N. Marwan, B. Bodirsky, H. Lotze-Campen, J. Kurths:
Inferring interdependencies from short time series, Indian Academy of Sciences Conference Series, 1(1), 51–60 (2017). DOI:10.29195/iascs.01.01.0021 » Abstract
Complex networks provide an invaluable framework for the study of interlinked dynamical systems. In many cases, such networks are constructed from observed time series by first estimating the interdependencies between pairs of datasets. However, most of the classic and state-of-the-art interdependence estimation techniques require sufficiently long time series for their successful application. In this study, we present a modification of the inner composition alignment approach (IOTA), correspondingly termed mIOTA, and review its advantages. Using two coupled auto-regressive stochastic processes, we demonstrate the discriminating power of mIOTA and show that it outperforms standard interdependence measures. We then use mIOTA to derive econo-climatic networks of interdependencies between economic indicators and climatic variability for Sub-Saharan Africa (AFR) and South Asia including India (SAS). Our analysis uncovers that crop production in AFR is strongly interdependent with the regional rainfall. While the gross domestic product (GDP) as an economic indicator in AFR is independent of climatic factors, we find that precipitation in the SAS influences the regional GDP, likely reflecting the influence of the summer monsoons. The differences in the interdependence structures between AFR and SAS reflect an underlying structural difference in their overall economies, as well as their agricultural sectors.
K. Guhathakurta, N. Marwan, B. Bhattacharya, A. R. Chowdhury:
Understanding the Interrelationship Between Commodity and Stock Indices Daily Movement Using ACE and Recurrence Analysis, In: Translational Recurrences – From Mathematical Theory to Real-World Applications, 103, Eds.: N. Marwan and M. A. Riley and A. Giuliani and C. L. Webber, Jr., Springer, Cham, 211–230 (2014). DOI:10.1007/978-3-319-09531-8_13 » Abstract
The relationship between the temporal evolution of the commodity market and the stock market has long term implications for policy makers, and particularly in the case of emerging markets, the economy as a whole. We analyze the complex dynamics of the daily variation of two indices of stock and commodity exchange respectively of India. To understand whether there is any difference between emerging markets and developed markets in terms of a dynamic correlation between the two market indices, we also examine the complex dynamics of stock and commodity indices of the US market. We compare the daily variation of the commodity and stock prices in the two countries separately. For this purpose we have considered commodity India along with Dow Jones Industrial Average (DJIA) and Dow Jones-AIG Commodity (DJ-AIGCI) indices for stock and commodities, USA, from June 2005 to August 2008. To analyse the dynamics of the time variation of the indices we use a set of analytical methods based on recurrence plots. Our studies show that the dynamics of the Indian stock and commodity exchanges have a lagged correlation while those of US market have a lead correlation and a weaker correlation.
T. Haselhoff, T. Braun, A. Fiebig, J. Hornberg, B. T. Lawrence, N. Marwan, S. Moebus:
Complex networks for analyzing the urban acoustic environment, Ecological Informatics, 78, 102326 (2023). DOI:10.1016/j.ecoinf.2023.102326 » Abstract
The urban acoustic environment (AE) provides comprehensive acoustic information related to the diverse systems of urban areas, such as traffic, the built environment, or biodiversity. The decreasing cost of acoustic sensors and rapid growth of storage space and computational power have fostered the collection of large amounts of acoustical data to be processed. However, despite the extensive information that is recorded by modern acoustic sensors, few approaches are established to capture the rich complex dynamics embedded in the time-frequency domain of the urban AE. Quantitative methods need to account for this complexity, while effectively reducing the high dimensionality of acoustic features within the data. Therefore, we introduce complex networks as a tool for analyzing the complex structure of large-scale urban AE data. We present a framework to construct networks based on frequency correlation matrices (FCMs). FCMs have shown to be a promising tool to depict environment specific interrelationships between consecutive power spectra. Accordingly, we show the capabilities of complex networks for the quantification of these interrelationships and thus, to characterize different urban AEs.
We demonstrate the scope of the proposed method, using one of the world's most extensive longitudinal audio datasets, considering 3-min audio recordings (n
J. Hlinka, D. Hartman, N. Jajcay, M. Vejmelka, R. Donner, N. Marwan, J. Kurths, M. Paluš:
Regional and inter-regional effects in evolving climate networks, Nonlinear Processes in Geophysics, 21, 451–462 (2014). DOI:10.5194/npg-21-451-2014 » Abstract
Complicated systems composed of many interacting subsystems are frequently studied as complex networks. In the simplest approach, a given real-world system is represented by an undirected graph composed of nodes standing for the subsystems and non-oriented unweighted edges for interactions present among the nodes; the characteristic properties of the graph are subsequently studied and related to the system's behaviour. More detailed graph models may include edge weights, orientations or multiple types of links; potential time-dependency of edges is conveniently captured in so-called evolving networks. Recently, it has been shown that an evolving climate network can be used to disentangle different types of El Niño episodes described in the literature. The time evolution of several graph characteristics has been compared with the intervals of El Niño and La Niña episodes. In this study we identify the sources of the evolving network characteristics by considering a reduced-dimensionality description of the climate system using network nodes given by rotated principal component analysis. The time evolution of structures in local intra-component networks is studied and compared to evolving inter-component connectivity.
N. Itoh, N. Marwan:
An extended singular spectrum transformation (SST) for the investigation of Kenyan precipitation data, Nonlinear Processes in Geophysics, 20, 467–481 (2013). DOI:10.5194/npg-20-467-2013 » Abstract
In this paper a change-point detection method is proposed by extending the singular spectrum transformation (SST) developed as one of the capabilities of singular spectrum analysis (SSA). The method uncovers change points related with trends and periodicities. The potential of the proposed method is demonstrated by analysing simple model time series including linear functions and sine functions as well as real world data (precipitation data in Kenya). A statistical test of the results is proposed based on a Monte Carlo simulation with surrogate methods. As a result, the successful estimation of change points as inherent properties in the representative time series of both trend and harmonics is shown. With regards to the application, we find change points in the precipitation data of Kenyan towns (Nakuru, Naivasha, Narok, and Kisumu) which coincide with the variability of the Indian Ocean Dipole (IOD) suggesting its impact of extreme climate in East Africa.
P. Kasthuri, A. Krishnan, R. Gejji, W. Anderson, N. Marwan, J. Kurths, R. I. Sujith:
Investigation into the coherence of flame intensity oscillations in a model multi-element rocket combustor using complex networks, Physics of Fluids, 34(3), 034107 (2022). DOI:10.1063/5.0080874 » Abstract
Capturing the complex spatiotemporal flame dynamics inside a rocket combustor is essential to validate high-fidelity simulations for developing high-performance rocket engines. Utilizing tools from a complex network theory, we construct positively and negatively correlated weighted networks from methylidyne (CH*) chemiluminescence intensity oscillations for different dynamical states observed during the transition to thermoacoustic instability (TAI) in a subscale multi-element rocket combustor. We find that the distribution of network measures quantitatively captures the extent of coherence in the flame dynamics. We discover that regions with highly correlated flame intensity oscillations tend to connect with other regions exhibiting highly correlated flame intensity oscillations. This phenomenon, known as assortative mixing, leads to a core group (a cluster) in the flow-field that acts as a “reservoir” for coherent flame intensity oscillations. Spatiotemporal features described in this study can be used to understand the self-excited flame response during the transition to TAI and validate high-fidelity simulations essential for developing high-performance rocket engines.
M. Kemter, B. Merz, N. Marwan, S. Vorogushyn, G. Blöschl:
Joint Trends in Flood Magnitudes and Spatial Extents Across Europe, Geophysical Research Letters, 47(7), e2020GL087464 (2020). DOI:10.1029/2020GL087464 » Abstract
The magnitudes of river floods in Europe have been observed to change, but their alignment with changes in the spatial coverage or extent of individual floods has not been clear. We analyze flood magnitudes and extents for 3,872 hydrometric stations across Europe over the past five decades and classify each flood based on antecedent weather conditions. We find positive correlations between flood magnitudes and extents for 95% of the stations. In central Europe and the British Isles, the association of increasing trends in magnitudes and extents is due to a magnitudeextent correlation of precipitation and soil moisture along with a shift in the flood generating processes. The alignment of trends in flood magnitudes and extents highlights the increasing importance of transnational flood risk management.
D. J. Kennett, S. F. M. Breitenbach, V. V. Aquino, Y. Asmerom, J. Awe, J. U. L. Baldini, P. Bartlein, B. J. Culleton, C. Ebert, C. Jazwa, M. J. Macri, N. Marwan, V. Polyak, K. M. Prufer, H. E. Ridley, H. Sodemann, B. Winterhalder, G. H. Haug:
Development and Disintegration of Maya Political Systems in Response to Climate Change, Science, 338(6108), 788–791 (2012). DOI:10.1126/science.1226299 » Abstract
The role of climate change in the development and demise of Classic Maya civilization (300 to 1000 C.E.) remains controversial because of the absence of well-dated climate and archaeological sequences. We present a precisely dated subannual climate record for the past 2000 years from Yok Balum Cave, Belize. From comparison of this record with historical events compiled from well-dated stone monuments, we propose that anomalously high rainfall favored unprecedented population expansion and the proliferation of political centers between 440 and 660 C.E. This was followed by a drying trend between 660 and 1000 C.E. that triggered the balkanization of polities, increased warfare, and the asynchronous disintegration of polities, followed by population collapse in the context of an extended drought between 1020 and 1100 C.E.
D. J. Kennett, I. Hajdas, B. J. Culleton, S. Belmecheri, S. Martin, H. Neff, J. Awe, H. V. Graham, K. H. Freeman, L. Newsom, D. L. Lentz, F. S. Anselmetti, M. Robinson, Norbert Marwan, J. Southon, D. A. Hodell, G. H. Haug:
Correlating the Ancient Maya and Modern European Calendars with High-Precision AMS 14C Dating, Scientific Reports, 3, 1597 (2013). DOI:10.1038/srep01597 » Abstract
The reasons for the development and collapse of Maya civilization remain controversial and historical events carved on stone monuments throughout this region provide a remarkable source of data about the rise and fall of these complex polities. Use of these records depends on correlating the Maya and European calendars so that they can be compared with climate and environmental datasets. Correlation constants can vary up to 1000 years and remain controversial. We report a series of high-resolution AMS 14C dates on a wooden lintel collected from the Classic Period city of Tikal bearing Maya calendar dates. The radiocarbon dates were calibrated using a Bayesian statistical model and indicate that the dates were carved on the lintel between AD 658-696. This strongly supports the Goodman-Martínez-Thompson (GMT) correlation and the hypothesis that climate change played an important role in the development and demise of this complex civilization.
D. J. Kennett, N. Marwan:
Climatic volatility, agricultural uncertainty, and the formation, consolidation and breakdown of preindustrial agrarian states, Philosophical Transactions of the Royal Society A, 373(2055), 20140458 (2015). DOI:10.1098/rsta.2014.0458 » Abstract
The episodic formation, consolidation and breakdown of preindustrial states occurred in multiple contexts worldwide during the last 5000 years and are contingent upon interacting endogenous economic, demographic and political mechanisms. In some instances, there is support for climate change stimulating integration or inducing sociopolitical fragmentation in these complex systems. Here, we build upon this paradigm and introduce the hypothesis that stable climatic conditions favour the formation of agrarian states, while persistently volatile climatic conditions can contribute to the episodic collapse of these complex societies. It is generally recognized that agrarian economies underwrite preindustrial state-level societies. In these contexts, the economic uncertainty associated with highly volatile climatic regimes makes it difficult for individuals or institutions to determine the costs and benefits of one agricultural strategy over another. We argue that this fosters sociopolitical instability and decentralization. As a first test of this hypothesis, we examine the historical dynamics of state formation and decline in the Mexican and Andean highlands within the last 2000 years. The available data in these regions are consistent with the hypothesis that the formation and consolidation of regional polities and empires is favoured in stable climatic regimes and that political decentralization can be stimulated and perpetuated by highly volatile climatic conditions.
D. J. Kennett, M. Masson, C. Peraza Lope, S. Serafin, R. J. George, T. C. Spencer, J. A. Hoggarth, B. J. Culleton, T. K. Harper, K. M. Prufer, S. Milbrath, B. W. Russell, E. Uc González, W. C. McCool, V. V. Aquino, E. H. Paris, J. H. Curtis, N. Marwan, M. Zhang, Y. Asmerom, V. J. Polyak, S. A. Carolin, D. H. James, A. J. Mason, G. M. Henderson, M. Brenner, J. U. L. Baldini, S. F. M. Breitenbach, D. A. Hodell:
Drought-Induced Civil Conflict Among the Ancient Maya, Nature Communications, 13, 3911 (2022). DOI:10.1038/s41467-022-31522-x » Abstract Radio Feature
The influence of climate change on civil conflict and societal instability in the premodern world is a subject of much debate, in part because of the limited temporal or disciplinary scope of case studies. We present a transdisciplinary case study that combines archeological, historical, and paleoclimate datasets to explore the dynamic, shifting relationships among climate change, civil conflict, and political collapse at Mayapan, the largest Postclassic Maya capital of the Yucatán Peninsula in the thirteenth and fourteenth centuries CE. Multiple data sources indicate that civil conflict increased significantly and generalized linear modeling correlates strife in the city with drought conditions between 1400 and 1450 cal. CE. We argue that prolonged drought escalated rival factional tensions, but subsequent adaptations reveal regional-scale resiliency, ensuring that Maya political and economic structures endured until European contact in the early sixteenth century CE.
C. Komalapriya, M. C. Romano, M. Thiel, N. Marwan, J. Kurths, I. Z. Kiss, J. L. Hudson:
An automated algorithm for the generation of dynamically reconstructed trajectories, Chaos, 20(1), 013107 (2010). DOI:10.1063/1.3279680 » Abstract
The lack of long enough data sets is a major problem in the study of many real world systems. As it has been recently shown [C. Komalapriya, M. Thiel, M. C. Romano, N. Marwan, U. Schwarz, and J. Kurths, Phys. Rev. E 78, 066217 (2008)], this problem can be overcome in the case of ergodic systems if an ensemble of short trajectories is available, from which dynamically reconstructed trajectories can be generated. However, this method has some disadvantages which hinder its applicability, such as the need for estimation of optimal parameters. Here, we propose a substantially improved algorithm that overcomes the problems encountered by the former one, allowing its automatic application. Furthermore, we show that the new algorithm not only reproduces the short term but also the long term dynamics of the system under study, in contrast to the former algorithm. To exemplify the potential of the new algorithm, we apply it to experimental data from electrochemical oscillators and also to analyze the well-known problem of transient chaotic trajectories.
K. H. Kraemer, G. Datseris, J. Kurths, I. Z. Kiss, J. L. Ocampo-Espindola, N. Marwan:
A unified and automated approach to attractor reconstruction, New Journal of Physics, 23, 033017 (2021). DOI:10.1088/1367-2630/abe336 » Abstract
We present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data from chaotic chemical oscillators.
A. Krishnan, R. Manikandan, P. R. Midhun, K. V. Reeja, V. R. Unni, R. I. Sujith, N. Marwan, J. Kurths:
Mitigation of oscillatory instability in turbulent reactive flows: A novel approach using complex networks, Europhysics Letters, 128(1), 14003 (2019). DOI:10.1209/0295-5075/128/14003 » Abstract
We present a novel and an efficient way to mitigate oscillatory instability in turbulent reactive flows. First, we construct weighted spatial correlation networks from the velocity field obtained from high-speed particle image velocimetry. Using network measures, we identify the optimal location for implementing passive control strategies. By injecting micro-jets at this optimal location, we are able to reduce the amplitude of the pressure oscillations to a value comparable to what is observed during the state of stable operation. This approach opens up new avenues to control oscillatory instabilities in turbulent flows.
A. Krishnan, R. I. Sujith, N. Marwan, J. Kurths:
On the emergence of large clusters of acoustic power sources at the onset of thermoacoustic instability in a turbulent combustor, Journal of Fluid Mechanics, 874, 455–482 (2019). DOI:10.1017/jfm.2019.429 » Abstract
In turbulent combustors, the transition from stable combustion (i.e. combustion noise) to thermoacoustic instability occurs via intermittency. During stable combustion, the acoustic power production happens in a spatially incoherent manner. In contrast, during thermoacoustic instability, the acoustic power production happens in a spatially coherent manner. In the present study, we investigate the spatiotemporal dynamics of acoustic power sources during the intermittency route to thermoacoustic instability using complex network theory. To that end, we perform simultaneous acoustic pressure measurement, high-speed chemiluminescence imaging and particle image velocimetry in a backward-facing step combustor with a bluff body stabilized flame at different equivalence ratios. We examine the spatiotemporal dynamics of acoustic power sources by constructing time-varying spatial networks during the different dynamical states of combustor operation. We show that as the turbulent combustor transits from combustion noise to thermoacoustic instability via intermittency, small fragments of acoustic power sources, observed during combustion noise, nucleate, coalesce and grow in size to form large clusters at the onset of thermoacoustic instability. This nucleation, coalescence and growth of small clusters of acoustic power sources occurs during the growth of pressure oscillations during intermittency. In contrast, during the decay of pressure oscillations during intermittency, these large clusters of acoustic power sources disintegrate into small ones. We use network measures such as the link density, the number of components and the size of the largest component to quantify the spatiotemporal dynamics of acoustic power sources as the turbulent combustor transits from combustion noise to thermoacoustic instability via intermittency.
A. Krishnan, R.I. Sujith, N. Marwan, J. Kurths:
Suppression of thermoacoustic instability by targeting the hubs of the turbulent networks in a bluff body stabilized combustor, Journal of Fluid Mechanics, 916, A20 (2021). DOI:10.1017/jfm.2021.166 » Abstract
In the present study, we quantify the vorticity interactions in a bluff body stabilized turbulent combustor during the transition from combustion noise to thermoacoustic instability via intermittency using complex networks. To that end, we perform simultaneous acoustic pressure, high-speed particle image velocimetry (PIV) and high-speed chemiluminescence measurements during the occurrence of combustion noise, intermittency and thermoacoustic instability. Based on the BiotSavart law, we construct time-varying weighted spatial networks from the flow fields during these different regimes of combustor operation. We uncover that the turbulent networks display weighted scale-free behaviour intermittently during the different regimes of combustor operation, with the strong vortical structures acting as the hubs. Further, we discover two optimal locations for injecting steady air jets to successfully suppress the thermoacoustic oscillations. The amplitude of the acoustic pressure fluctuations of the suppressed state is comparable to that during the occurrence of combustion noise. However, the weighted scale-free network topology during the suppressed state is not as dominant as compared with the state of combustion noise.
R. Kumar Guntu, P. Kumar Yeditha, M. Rathinasamy, M. Perc, N. Marwan, J. Kurths, A. Agarwal:
Wavelet entropy-based evaluation of intrinsic predictability of time series, Chaos, 30, 033117 (2020). DOI:10.1063/1.5145005 » Abstract
Intrinsic predictability is imperative to quantify inherent information contained in a time series and assists in evaluating the performance of different forecasting methods to get the best possible prediction. Model forecasting performance is the measure of the probability of success. Nevertheless, model performance or the model does not provide understanding for improvement in prediction. Intuitively, intrinsic predictability delivers the highest level of predictability for a time series and informative in unfolding whether the system is unpredictable or the chosen model is a poor choice. We introduce a novel measure, the Wavelet Entropy Energy Measure (WEEM), based on wavelet transformation and information entropy for quantification of intrinsic predictability of time series. To investigate the efficiency and reliability of the proposed measure, model forecast performance was evaluated via a wavelet networks approach. The proposed measure uses the wavelet energy distribution of a time series at different scales and compares it with the wavelet energy distribution of white noise to quantify a time series as deterministic or random. We test the WEEM using a wide variety of time series ranging from deterministic, non-stationary, and ones contaminated with white noise with different noise-signal ratios. Furthermore, a relationship is developed between the WEEM and NashSutcliffe Efficiency, one of the widely known measures of forecast performance. The reliability of WEEM is demonstrated by exploring the relationship to logistic map and real-world data.
J. Kurths, N. Marwan, N. Wessel:
Recurrence Plot Based Measures of Complexity to Predict Life-Threatening Cardiac Arrhythmias, Proceedings ECCTD 03, Krakow (2003). » Abstract
We present recently introduced new recurrence plot based measures of complexity and illustrate their potential with applications to the logistic map and heart rate variability data. These new measures make the identification of chaos-chaos transitions possible and identify laminar states. The application to the heart rate variability data detects and quantifies the laminar phases before a life-threatening cardiac arrhythmia occurs; thereby facilitating a prediction of such an event.
J. Kurths, J. F. Donges, N. Marwan, Y. Zou:
Dynamics on Complex Networks with Time Varying Topology, In: Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2010), Krakow(6175), 2 (2010). » Abstract
A challenging task is to understand the implications of such network structures on the functional organization of the brain activities. This is studied here basing on dynamical complex networks. We investigate synchronization dynamics on the cortico-cortical network of the cat by modelling each node (cortical area) of the network with a sub-network of interacting excitable neurons. We find that the network displays clustered synchronization behaviour and the dynamical clusters coincide with the topological community structures observed in the anatomical network. Our results provide insights into the relationship between the global organization and the functional specialization of the brain cortex. This approach of a network of networks seems to be of general importance, especially for spreading of diseases or opinion formation in human societies or socio-economic dynamics. Therefore, we next study a network of networks with time varying topology for modelling epidemic spreading. We find qualitatively different behaviour there in dependence on the changes of the topology.
J. Kurths, N. Marwan, M. Riedl, S. Schinkel:
Complex Synchronization and Recurrence Analyses – are such Nonlinear Techniques Useful for Brain Oscillation Studies?, Biomedical Engineering/ Biomedizinische Technik, 57, 386 (2012). DOI:10.1515/bmt-2012-4537 » Abstract
Biological systems are typically composed of several subsystems which interact via several feedbacks. They are, therefore, typical examples of complex systems which are able to self- organization and complex structure formation even for rather weak changes of parameters or environment.
Basing on modern measurement techniques, such systems can be quantified by multivariate time series. To interpret these records and to understand basic properties of the underlying complex dynamics, it is, however, necessary to apply methods from Nonlinear Dynamics and Complex Systems Theory. Note that linear techniques, such as spectral and correlation analysis, can uncover only linear structures.
We present some modern nonlinear analysis techniques, apply them to multivariate biosignals and discuss their potentials resp. limits in comparison with well-known linear methods. We especially discuss two main approaches: i) synchronization analysis of even weakly coupled subsystems, and ii) quantification of (complex) recurrence properties.
The corresponding techniques will be applied to understand the implications of such network structures on the functional organization of the brain activities. We investigate synchronization dynamics on the cortico-cortical network of mammals and find that the network displays clustered synchronization behaviour and the dynamical clusters coincide with the topological community structures observed in the corresponding anatomical network. Next, we aim at investigating how graph theoretical approaches can help to discover systematic and task- dependent differences in high-level cognitive processes such as language perception. We will show that such an approach is feasible and that the results coincide well with the findings from neuroimaging studies.
J. Kurths, J. Donges, R. Donner, N. Malik, N. Marwan, H. Schultz, Y. Zou:
Network of Networks and the Climate System, IEICE Proceedings Series, 1, 170 (2012). DOI:10.15248/proc.1.170 » Abstract
Network of networks is a new direction in complex systems science. One can find such networks in various fields, such as infrastructure (power grids etc.), human brain or Earth system. Basic properties and new characteristics, such as cross-degree, or cross-betweenness will be discussed. This allows us to quantify the structural role of single vertices or whole sub-networks with respect to the interaction of a pair of subnetworks on local, mesoscopic, and global topological scales. Next, we consider an inverse problem: Is there a backbone-like structure underlying the climate system? For this we propose a method to reconstruct and analyze a complex network from data generated by a spatio-temporal dynamical system. This technique is then applied to 3-dimensional data of the climate system. We interpret different heights in the atmosphere as different networks and the whole as a network of networks. This approach enables us to uncover relations to global circulation patterns in oceans and atmosphere. The global scale view on climate networks offers promising new perspectives for detecting dynamical structures based on nonlinear physical processes in the climate system. This concept is applied to Indian Monsoon data in order to characterize the regional occurrence of strong rain events and its impact on predictability.
J. Kurths, J. Heitzig, N. Marwan:
Approaching cooperation via complexity, In: Global Cooperation and the Human Factor in International Relations, Eds.: D. Messner and S. Weinlich, Routledge, Oxon, 153–180 (2016). » Abstract
A universal experience of our society is the increasing complexity of our life. Technological progress is the fundament of an increased connectivity around the world, of rapid growth of knowledge and understanding about the mechanisms affecting our world and the major challenges we are facing (international conflicts, limited resources, climate change, population growth), but also of a growing quality of life. Whereas on the one hand cooperation is one of the key ingredients to form complex behaviour, on the other hand the increasing complexity in our daily life calls for cooperation in order to manage specific problems but also makes cooperation more and more difficult. In this chapter, we will therefore first give an introduction into complex systems science, highlighting how cooperation and other interaction between systems in general can lead to complexity due to feedbacks, and then focus more specifically on systems of cooperating humans and show how complexity arises there and discuss its implications.
J. Kurths, A. Agarwal, R. Shukla, N. Marwan, M. Rathinasamy, L. Caesar, R. Krishnan, B. Merz:
Unravelling the spatial diversity of Indian precipitation teleconnections via a non-linear multi-scale approach, Nonlinear Processes in Geophysics, 26(3), 251–266 (2019). DOI:10.5194/npg-26-251-2019 » Abstract Paper of the month at NPG
A better understanding of precipitation dynamics in the Indian subcontinent is required since India's society depends heavily on reliable monsoon forecasts. We introduce a non-linear, multiscale approach, based on wavelets and event synchronization, for unravelling teleconnection influences on precipitation. We consider those climate patterns with the highest relevance for Indian precipitation. Our results suggest significant influences which are not well captured by only the wavelet coherence analysis, the state-of-the-art method in understanding linkages at multiple timescales. We find substantial variation across India and across timescales. In particular, El Niño-Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD) mainly influence precipitation in the south-east at interannual and decadal scales, respectively, whereas the North Atlantic Oscillation (NAO) has a strong connection to precipitation, particularly in the northern regions. The effect of the Pacific Decadal Oscillation (PDO) stretches across the whole country, whereas the Atlantic Multidecadal Oscillation (AMO) influences precipitation particularly in the central arid and semi-arid regions. The proposed method provides a powerful approach for capturing the dynamics of precipitation and, hence, helps improve precipitation forecasting.
O. Kwiecien, T. Braun, C. F. Brunello, P. Faulkner, N. Hausmann, G. Helle, J. A. Hoggarth, M. Ionita, C. Jazwa, S. Kelmelis, N. Marwan, C. Nava-Fernandez, C. Nehme, T. Opel, J. L. Oster, A. Percsoiu, C. Petrie, K. Prufer, S. M. Saarni, A. Wolf, S. F. M. Breitenbach:
What we talk about when we talk about seasonality – A transdisciplinary review, Earth-Science Reviews, 225, 103843 (2022). DOI:10.1016/j.earscirev.2021.103843 » Abstract
The role of seasonality is indisputable in climate and ecosystem dynamics. Seasonal temperature and precipitation variability are of vital importance for the availability of food, water, shelter, migration routes, and raw materials. Thus, understanding past climatic and environmental changes at seasonal scale is equally important for unearthing the history and for predicting the future of human societies under global warming scenarios. Alas, in palaeoenvironmental research, the term ‘seasonality change’ is often used liberally without scrutiny or explanation as to which seasonal parameter has changed and how.
Here we provide fundamentals of climate seasonality and break it down into external (insolation changes) and internal (atmospheric CO2 concentration) forcing, and regional and local and modulating factors (continentality, altitude, large-scale atmospheric circulation patterns). Further, we present a brief overview of the archives with potentially annual/seasonal resolution (historical and instrumental records, marine invertebrate growth increments, stalagmites, tree rings, lake sediments, permafrost, cave ice, and ice cores) and discuss archive-specific challenges and opportunities, and how these limit or foster the use of specific archives in archaeological research.
Next, we address the need for adequate data-quality checks, involving both archive-specific nature (e.g., limited sampling resolution or seasonal sampling bias) and analytical uncertainties. To this end, we present a broad spectrum of carefully selected statistical methods which can be applied to analyze annually- and seasonally-resolved time series. We close the manuscript by proposing a framework for transparent communication of seasonality-related research across different communities.
F. A. Lechleitner, J. U. L. Baldini, S. F. M. Breitenbach, J. Fohlmeister, C. McIntyre, B. Goswami, R. A. Jamieson, T. S. van der Voort, K. Prufer, N. Marwan, B. J. Culleton, D. J. Kennett, Y. Asmerom, V. Polyak, T. I. Eglinton:
Hydrological and climatological controls on radiocarbon concentrations in a tropical stalagmite, Geochimica et Cosmochimica Acta, 194, 233–252 (2016). DOI:10.1016/j.gca.2016.08.039 » Abstract
Precisely-dated stalagmites are increasingly important archives for the reconstruction of terrestrial paleoclimate at very high temporal resolution. In-depth understanding of local conditions at the cave site and of the processes driving stalagmite deposition is of paramount importance for interpreting proxy signals incorporated in stalagmite carbonate. Here we present a sub-decadally resolved dead carbon fraction (DCF) record for a stalagmite from Yok Balum Cave (southern Belize). The record is coupled to parallel stable carbon isotope (δ13C) and U/Ca measurements, as well as radiocarbon (14C) measurements from soils overlying the cave system. Using a karst carbon cycle model we disentangle the importance of soil and karst processes on stalagmite DCF incorporation, revealing a dominant host rock dissolution control on total DCF. Covariation between DCF, δ13C, and U/Ca indicates that karst processes are a common driver of all three parameters, suggesting possible use of δ13C and trace element ratios to independently quantify DCF variability. A statistically significant multi-decadal lag of variable length exists between DCF and reconstructed solar activity, suggesting that solar activity influenced regional precipitation in Mesoamerica over the past 1500 years, but that the relationship was non-static. Although the precise nature of the observed lag is unclear, solar-induced changes in North Atlantic oceanic and atmospheric dynamics may play a role.
F. A. Lechleitner, S. F. M. Breitenbach, H. Cheng, B. Plessen, K. Rehfeld, B. Goswami, N. Marwan, D. Eroglu, J. Adkins, G. Haug:
Climatic and in-cave influences on δ18O and δ13C in a stalagmite from northeastern India through the last deglaciation, Quaternary Research, 88(3), 458–471 (2017). DOI:10.1017/qua.2017.72 » Abstract
Northeastern (NE) India experiences extraordinarily pronounced seasonal climate, governed by the Indian summer monsoon (ISM). The vulnerability of this region to floods and droughts calls for detailed and highly resolved paleoclimate reconstructions to assess the recurrence rate and driving factors of ISM changes. We use stable oxygen and carbon isotope ratios (δ18O and δ13C) from stalagmite MAW-6 from Mawmluh Cave to infer climate and environmental conditions in NE India over the last deglaciation (16-6ka). We interpret stalagmite δ18O as reflecting ISM strength, whereas δ13C appears to be driven by local hydroclimate conditions. Pronounced shifts in ISM strength over the deglaciation are apparent from the δ18O record, similarly to other records from monsoonal Asia. The ISM is weaker during the late glacial (LG) period and the Younger Dryas, and stronger during the Bølling-Allerød and Holocene. Local conditions inferred from the δ13C record appear to have changed less substantially over time, possibly related to the masking effect of changing precipitation seasonality. Time series analysis of the δ18O record reveals more chaotic conditions during the late glacial and higher predictability during the Holocene, likely related to the strengthening of the seasonal recurrence of the ISM with the onset of the Holocene.
F. A. Lechleitner, S. F. M. Breitenbach, K. Rehfeld, H. E. Ridley, Y. Asmerom, K. M. Prufer, N. Marwan, B. Goswami, D. J. Kennett, V. V. Aquino, V. Polyak, G. H. Haug, T. I. Eglinton, J. U. L. Baldini:
Tropical rainfall over the last two millennia: evidence for a low-latitude hydrologic seesaw, Scientific Reports, 7, 45809 (2017). DOI:10.1038/srep45809 » Abstract
The presence of a low- to mid-latitude interhemispheric hydrologic seesaw is apparent over orbital and glacial-interglacial timescales, but its existence over the most recent past remains unclear. Here we investigate, based on climate proxy reconstructions from both hemispheres, the inter-hemispherical phasing of the Intertropical Convergence Zone (ITCZ) and the low- to mid-latitude teleconnections in the Northern Hemisphere over the past 2000 years. A clear feature is a persistent southward shift of the ITCZ during the Little Ice Age until the beginning of the 19th Century. Strong covariation between our new composite ITCZ-stack and North Atlantic Oscillation (NAO) records reveals a tight coupling between these two synoptic weather and climate phenomena over decadal-to-centennial timescales. This relationship becomes most apparent when comparing two precisely dated, high-resolution paleorainfall records from Belize and Scotland, indicating that the low- to mid-latitude teleconnection was also active over annual-decadal timescales. It is likely a combination of external forcing, i.e., solar and volcanic, and internal feedbacks, that drives the synchronous ITCZ and NAO shifts via energy flux perturbations in the tropics.
N. Malik, N. Marwan, J. Kurths:
Spatial structures and directionalities in Monsoonal precipitation over South Asia, Nonlinear Processes in Geophysics, 17(5), 371–381 (2010). DOI:10.5194/npg-17-371-2010 » Abstract
Precipitation during the monsoon season over the Indian subcontinent occurs in form of enormously complex spatiotemporal patterns due to the underlying dynamics of atmospheric circulation and varying topography. Employing methods from nonlinear time series analysis, we study spatial structures of the rainfall field during the summer monsoon and identify principle regions where the dynamics of monsoonal rainfall is more coherent or homogenous. Moreover, we estimate the time delay patterns of rain events. Here we present an analysis of two separate high resolution gridded data sets of daily rainfall covering the Indian subcontinent. Using the method of event synchronization (ES), we estimate regions where heavy rain events during monsoon happen in some lag synchronised form. Further using the delay behaviour of rainfall events, we estimate the directionalities related to the progress of such type of rainfall events. The Active (break) phase of a monsoon is characterised by an increase(decrease) of rainfall over certain regions of the Indian subcontinent. We show that our method is able to identify regions of such coherent rainfall activity.
N. Malik, B. Bookhagen, N. Marwan, J. Kurths:
Analysis of spatial and temporal extreme monsoonal rainfall over South Asia using complex networks, Climate Dynamics, 39(3–4), 971–987 (2012). DOI:10.1007/s00382-011-1156-4 » Abstract
We present a detailed analysis of summer monsoon rainfall over the Indian peninsular using nonlinear spatial correlations. This analysis is carried out employing the tools of complex networks and a measure of nonlinear correlation for point processes such as rainfall, called event synchronization. This study provides valuable insights into the spatial organization, scales, and structure of the 90th and 94th percentile rainfall events during the Indian summer monsoon (June–September). We furthermore analyse the influence of different critical synoptic atmospheric systems and the impact of the steep Himalayan topography on rainfall patterns. The presented method not only helps us in visualising the structure of the extreme-event rainfall fields, but also identifies the water vapor pathways and decadal-scale moisture sinks over the region. Furthermore a simple scheme based on complex networks is presented to decipher the spatial intricacies and temporal evolution of monsoonal rainfall patterns over the last 6 decades.
N. Malik, Y. Zou, N. Marwan, J. Kurths:
Dynamical regimes and transitions in Plio-Pleistocene Asian monsoon, Europhysics Letters, 97(4), 40009 (2012). DOI:10.1209/0295-5075/97/40009 » Abstract
We propose a novel approach based on the fluctuation of similarity to identify regimes of distinct dynamical complexity in short time series. A statistical test is developed to estimate the significance of the identified transitions. Our method is verified by uncovering bifurcation structures in several paradigmatic models, providing more complex transitions compared with traditional Lyapunov exponents. In a real-world situation, we apply this method to identify millennial-scale dynamical transitions in Plio-Pleistocene proxy records of the South Asian summer monsoon system. We infer that many of these transitions are induced by the external forcing of the solar insolation and are also affected by internal forcing on Monsoonal dynamics, i.e., the glaciation cycles of the Northern Hemisphere and the onset of the Walker circulation.
N. Malik, N. Marwan, Y. Zou, P. J. Mucha, J. Kurths:
Fluctuation of similarity to detect transitions between distinct dynamical regimes in short time series, Physical Review E, 89, 062908 (2014). DOI:10.1103/PhysRevE.89.062908 » Abstract
A method to identify distinct dynamical regimes and transitions between those regimes in a short univariate time series was recently introduced [N. Malik et al., Europhys. Lett. 97, 40009 (2012)], employing the computation of fluctuations in a measure of nonlinear similarity based on local recurrence properties. In this work, we describe the details of the analytical relationships between this newly introduced measure and the well-known concepts of attractor dimensions and Lyapunov exponents. We show that the new measure has linear dependence on the effective dimension of the attractor and it measures the variations in the sum of the Lyapunov spectrum. To illustrate the practical usefulness of the method, we identify various types of dynamical transitions in different nonlinear models. We present testbed examples for the new method's robustness against noise and missing values in the time series. We also use this method to analyze time series of social dynamics, specifically an analysis of the US crime record time series from 1975 to 1993. Using this method, we find that dynamical complexity in robberies was influenced by the unemployment rate until the late 1980s. We have also observed a dynamical transition in homicide and robbery rates in the late 1980s and early 1990s, leading to increase in the dynamical complexity of these rates.
N. Marwan, M. H. Trauth, M. Vuille, J. Kurths:
Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods, Climate Dynamics, 21(3–4), 317–326 (2003). DOI:10.1007/s00382-003-0335-3 » Abstract
Higher variability in rainfall and river discharge could be of major importance in landslide generation in the north-western Argentine Andes. Annual layered (varved) deposits of a landslide dammed lake in the Santa Maria Basin (26°S, 66°W) with an age of 30,000 14C years provide an archive of precipitation variability during this time. The comparison of these data with present-day rainfall observations tests the hypothesis that increased rainfall variability played a major role in landslide generation. A potential cause of such variability is the El Niño/ Southern Oscillation (ENSO). The causal link between ENSO and local rainfall is quantified by using a new method of nonlinear data analysis, the quantitative analysis of cross recurrence plots (CRP). This method seeks similarities in the dynamics of two different processes, such as an ocean-atmosphere oscillation and local rainfall. Our analysis reveals significant similarities in the statistics of both modern and palaeo-precipitation data. The similarities in the data suggest that an ENSO-like influence on local rainfall was present at around 30,000 14C years ago. Increased rainfall, which was inferred from a lake balance modeling in a previous study, together with ENSO-like cyclicities could help to explain the clustering of landslides at around 30,000 14C years ago.
N. Marwan, A. Meinke:
Extended recurrence plot analysis and its application to ERP data, International Journal of Bifurcation and Chaos, 14(2), 761–771 (2004). DOI:10.1142/S0218127404009454 » Abstract
We present new measures of complexity and their application to event related potential data. The new measures base on structures of recurrence plots and makes the identification of chaos-chaos transitions possible. The application of these measures to data from single-trials of the Oddball experiment can identify laminar states therein. This offers a new way of analyzing event-related activity on a single-trial basis.
N. Marwan:
Nonlinear Time-Series Analysis, In: MATLAB Recipes for Earth Sciences (1. edition), Eds.: M. H. Trauth, Springer, Berlin, Heidelberg, ISBN: 3-540-27983-0, 106–118 (2006). DOI:10.1007/3-540-27984-9_5
N. Marwan:
Nonlinear Time-Series Analysis, In: MATLAB Recipes for Earth Sciences (2. edition), Eds.: M. H. Trauth, Springer, Berlin, Heidelberg, ISBN: 978-3-540-72748-4, 119–132 (2007). DOI:10.1007/978-3-540-72749-1_5 » Abstract
Time-series analysis aims to understand the temporal behavior of one of several variablesy(t). Examples are the investigation of long-term records of mountain uplift, sea-level fluctuations, orbitally-induced insolation variations and their influence on the ice-age cycles, millenium-scale variations of the atmosphere-ocean system, the effect of the El Niño/Southern Oscillation on tropical rainfall and sedimentation (Fig. 5.1) and tidal influences on nobel gas emissions of bore holes. The temporal structure of a sequence of events can be random, clustered, cyclic or chaotic. Time-series analysis provides various tools to detect these temporal structures. The understanding of the underlying process that produced the observed data allows us to predict future values of the variable. We use the Signal Processing and Wavelet Toolbox, which contain all necessary routines for time-series analysis.
N. Marwan, A. Groth, J. Kurths:
Quantification of Order Patterns Recurrence Plots of Event Related Potentials, Chaos and Complexity Letters, 2(2/3), 301–314 (2007). » Abstract
We study an innovative modification of recurrence plots defining the recurrence by the local ordinal structure of a time series. In this paper we demonstrate that in comparison to a recently developed approach this concept improves the analyis of event related activity on a single trial basis.
N. Marwan, J. Kurths, P. Saparin, J. S. Thomsen:
Measuring Changes of 3D Structures in High-resolution μCT Images of Trabecular Bone, In: BIOSIGNALS 2008 – Proceedings of the 1st International Conference on Bio-inspired Systems and Signal Processing, 2, 425–430 (2008). » Abstract
The appearances of pathological changes of bone can be various. Determination of apparent bone mineral density is commonly used for diagnosing bone pathological conditions. However, in the last years the structural changes of trabecular bone have received more attention because bone densitometry alone cannot explain all variation in bone strength. The rapid progress in high resolution 3D micro Computed Tomography (μCT) imaging facilitates the development of new 3D measures of complexity for assessing the spatial architecture of trabecular bone. We have developed a novel approach which is based on 3D complexity measures in order to quantify spatial geometrical properties of bone architecture. These measures evaluate different aspects of organization and complexity of trabecular bone, such as complexity of its surface, node complexity, or local surface curvature. In order to quantify the differences in the trabecular bone architecture at different stages of osteoporotic bone loss, the developed complexity measures were applied to 3D data sets acquired by μCT from human proximal tibiae and lumbar vertebrae. The results obtained by the complexity measures were compared with results provided by static histomorphometry. We have found clear relationships between the proposed measures and different aspects of bone architecture assessed by the histomorphometry.
N. Marwan, J. F. Donges, A. Radebach, J. Runge, J. Kurths:
Evolving Climate Networks, In: Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2010), Krakow(6163), 3–6 (2010). » Abstract
We propose a method to reconstruct and analyse an evolving complex network from data generated by a spatio-temporal dynamical system. We study reanalysis surface air temperature data by different complex network measures. This approach reveals a rich internal structure in complex climate networks and allows to study the stability of the climate network and the impacts of teleconnections (e.g., El Niño/ Southern Oscillation). Moreover, the betweenness analyis uncovers peculiar wave-like structures of high information flow, that can be related to global surface ocean currents.
N. Marwan:
Nonlinear Time-Series Analysis, In: MATLAB Recipes for Earth Sciences (3. edition), Eds.: M. H. Trauth, Springer, Berlin, Heidelberg, ISBN: 978-3-642-44716-7, 146–160 (2010). DOI:10.1007/978-3-642-12762-5_5 » Abstract
Time-series analysis aims to investigate the temporal behavior of one of several variables x(t). Examples include the investigation of long-term records of mountain uplift , sea-level fluctuations, orbitally-induced insolation variations and their influence on the ice-age cycles, millenium-scale variations in the atmosphere-ocean system, the effect of the El Niño/Southern Oscillation on tropical rainfall and sedimentation (Fig. 5.1) and tidal influences on noble gas emissions from bore holes. The temporal pattern of a sequence of events can be random, clustered, cyclic or chaotic. Time-series analysis provides various tools with which to detect these temporal patterns. Understanding the underlying processes that produced the observed data allows us to predict future values of the variable. We use the Signal Processing and Wavelet Toolboxes, which contain all the necessary routines for time-series analysis.
N. Marwan, N. Wessel, H. Stepan, J. Kurths:
Recurrence based complex network analysis of cardiovascular variability data to predict pre-eclampsia, Proceedings of the Biosignal Conference 2010 Berlin, 1–4 (2010). » Abstract
Pre-eclampsia in pregnancy is a serious disease with high risk of fetal and maternal morbidity. The usual positive predictive value is 20–30%. Including cardiovascular variability, it has been recently shown that this predictive power can be improved. Here we propose a novel approach for analysing time series of systolic and diastolic blood pressure as well as heart rate variability measured in the 20th week of gestation in order to predict pre-eclampsia. For this aim, we identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. We demonstrate the potential of the complex network measures for a further improvement of the positive predictive value of pre-eclampsia.
N. Marwan, N. Wessel, H. Stepan, J. Kurths:
Recurrence Based Complex Network Analysis of Cardiovascular Variability Data to Predict Pre-Eclampsia, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2010), Krakow(6170), 585–588 (2010). » Abstract
We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. We illustrate similarities and differences between the recurrence quantification analysis and the complex network analysis. By using the logistic map, we demonstrate the potential of the complex network measures for the detection of different dynamical regimes. Pre-eclampsia in pregnancy is a serious disease with high risk of fetal and maternal morbidity. The usual positive predictive value is 20–30%. Including heart rate variability, it has been recently shown that this predictive power can be improved. In order to predict pre-eclampsia, we are analysing time series of systolic and diastolic blood pressure as well as heart rate variability measured in the 20th week of gestation.. We demonstrate the potential of the complex network measures for a further improvement of the positive predictive value of pre-eclampsia.
N. Marwan, Y. Zou, N. Wessel, M. Riedl, J. Kurths:
Estimating coupling directions in the cardio-respiratory system using recurrence properties, Philosophical Transactions of the Royal Society A, 371(1997), 20110624 (2013). DOI:10.1098/rsta.2011.0624 » Abstract
The asymmetry of coupling between complex systems can be studied by conditional probabilities of recurrence, which can be estimated by joint recurrence plots. This approach is applied for the first time on experimental data: time series of the human cardiorespiratory system in order to investigate the couplings between heart rate, mean arterial blood pressure and respiration. We find that the respiratory system couples towards the heart rate, and the heart rate towards the mean arterial blood pressure. However, our analysis could not detect a clear coupling direction between the mean arterial blood pressure and respiration.
N. Marwan:
Nonlinear Time-Series Analysis, In: MATLAB Recipes for Earth Sciences (4. edition), Eds.: M. H. Trauth, Springer, Berlin, Heidelberg, ISBN: 978-3-662-50033-0, 195–213 (2015). DOI:10.1007/978-3-662-46244-7_5 » Abstract
Time-series analysis aims to investigate the temporal behavior of a variable x(t). Examples include the investigation of long-term records of mountain uplift, sea-level fluctuations, orbitally-induced insolation variations and their influence on the ice-age cycles, millennium-scale variations in the atmosphere-ocean system, the effect of the El Nino/Southern Oscillation on tropical rainfall and sedimentation (Fig. 5.1), and tidal influences on noble gas emissions from bore holes. The temporal pattern of a sequence of events can be random, clustered, cyclic, or chaotic. Time-series analysis provides various tools with which to detect these temporal patterns. Understanding the underlying processes that produced the observed data allows us to predict future values of the variable.
N. Marwan, J. Kurths:
Complex network based techniques to identify extreme events and (sudden) transitions in spatio-temporal systems, Chaos, 25, 097609 (2015). DOI:10.1063/1.4916924 » Abstract
We present here two promising techniques for the application of the complex network approach to continuous spatio-temporal systems that have been developed in the last decade and show large potential for future application and development of complex systems analysis. First, we discuss the transforming of a time series from such systems to a complex network. The natural approach is to calculate the recurrence matrix and interpret such as the adjacency matrix of an associated complex network, called recurrence network. Using complex network measures, such as transitivity coefficient, we demonstrate that this approach is very efficient for identifying qualitative transitions in observational data, e.g., when analyzing paleoclimate regime transitions. Second, we demonstrate the use of directed spatial networks constructed from spatio-temporal measurements of such systems that can be derived from the synchronized-in-time occurrence of extreme events in different spatial regions. Although there are many possibilities to investigate such spatial networks, we present here the new measure of network divergence and how it can be used to develop a prediction scheme of extreme rainfall events.
N. Marwan, S. Foerster, J. Kurths:
Analysing spatially extended high-dimensional dynamics by recurrence plots, Physics Letters A, 379, 894–900 (2015). DOI:10.1016/j.physleta.2015.01.013 » Abstract
Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply this method on spatially extended chaos, such as derived from the Lorenz96 model and show that the recurrence plot based measures can qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analyzing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world.
N. Marwan, D. Eroglu, I. Ozken, T. Stemler, K.-H. Wyrwoll, J. Kurths:
Regime Change Detection in Irregularly Sampled Time Series, In: Advances in Nonlinear Geosciences, Eds.: A. A. Tsonis, Springer International, Cham, Switzerland, ISBN: 978-3-319-58895-7, 357–368 (2018). DOI:10.1007/978-3-319-58895-7_18 » Abstract
Irregular sampling is a common problem in palaeoclimate studies. We propose a method that provides regularly sampled time series and at the same time a difference filtering of the data. The differences between successive time instances are derived by a transformation costs procedure. A subsequent recurrence analysis is used to investigate regime transitions. This approach is applied on speleothem-based palaeoclimate proxy data from the Indonesian-Australian monsoon region. We can clearly identify Heinrich events in the palaeoclimate as characteristic changes in dynamics.
N. Marwan, C. L. Webber, Jr., E. E. N. Macau, R. L. Viana:
Introduction to focus issue: Recurrence quantification analysis for understanding complex systems, Chaos, 28(8), 085601 (2018). DOI:10.1063/1.5050929 » Abstract
In 1987, recurrence plots were first introduced by Eckmann, Oliffson-Kamphorst, and Ruelle as a simple graphical tool to visualize basic dynamical characteristics of time series.1 This present Focus Issue is dedicated to the 30th anniversary of recurrence plots and constitutes a unique collection of diverse papers on advanced recurrence plots, their extensions and ramifications, as well as their broad applications and utility. In the last three decades, an analytical framework based on recurrence plots has been developed, demonstrating an unanticipated but huge potential stemming from the original conceptualizations.2,3 In its brief history, thousands of recurrence publications over numerous disciplines spanning these three decades have permeated the scientific literature. In addition, regular scientific meetings continue to attract and recruit new members to the "recurrence community" indicating lively growth and expansion into new disciplines of inquiry. For example, our most recent meeting in Brazil at the Escola Politénica Universidade De S ao Paulo (August 23-25, 2017) focused on disciplines of engineering, earth science, and life and social sciences.
N. Marwan:
Nonlinear Time-Series Analysis, In: MATLAB Recipes for Earth Sciences (5. edition), Eds.: M. H. Trauth, Springer Nature Switzerland, Cham, ISBN: 978-3-030-38440-1, 237–257 (2021). DOI:10.1007/978-3-030-38441-8_5 » Abstract
Time-series analysis, introduced in this chapter, is used to investigate the temporal behavior of a variable. Sections 5.2–5.6 introduces methods of Fourier-based spectral analysis. An technique for analyzing unevenly-spaced data is explained in Sect. 5.7. Section 5.8 introduces the wavelet power spectrum, which is able to map temporal variations in the spectra in a similar way to the method demonstrated in Sect. 5.6. Section 5.9 then introduces methods to detect, and to remove, abrupt transitions within time series. Section 5.10 presents methods used to align stratigraphic sequences. This chapter then closes (Sect. 5.11) with an overview of nonlinear techniques, with special attention to recurrence plots.
N. Marwan, J. F. Donges, R. V. Donner, D. Eroglu:
Nonlinear time series analysis of palaeoclimate proxy records, Quaternary Science Reviews, 274, 107245 (2021). DOI:10.1016/j.quascirev.2021.107245 » Abstract
Identifying and characterising dynamical regime shifts, critical transitions or potential tipping points in palaeoclimate time series is relevant for improving the understanding of often highly nonlinear Earth system dynamics. Beyond linear changes in time series properties such as mean, variance, or trend, these nonlinear regime shifts can manifest as changes in signal predictability, regularity, complexity, or higher-order stochastic properties such as multi-stability. In recent years, several classes of methods have been put forward to study these critical transitions in time series data that are based on concepts from nonlinear dynamics, complex systems science, information theory, and stochastic analysis. These include approaches such as phase space-based recurrence plots and recurrence networks, visibility graphs, order pattern-based entropies, and stochastic modelling. Here, we review and compare in detail several prominent methods from these fields by applying them to the same set of marine palaeoclimate proxy records of African climate variations during the past 5 million years. Applying these methods, we observe notable nonlinear transitions in palaeoclimate dynamics in these marine proxy records and discuss them in the context of important climate events and regimes such as phases of intensified Walker circulation, marine isotope stage M2, the onset of northern hemisphere glaciation and the mid-Pleistocene transition. We find that the studied approaches complement each other by allowing us to point out distinct aspects of dynamical regime shifts in palaeoclimate time series. We also detect significant correlations of these nonlinear regime shift indicators with variations of Earth's orbit, suggesting the latter as potential triggers of nonlinear transitions in palaeoclimate. Overall, the presented study underlines the potentials of nonlinear time series analysis approaches to provide complementary information on dynamical regime shifts in palaeoclimate and their driving processes that cannot be revealed by linear statistics or eyeball inspection of the data alone.
N. Marwan:
Nichtlineare Zeitreihenanalyse, In: MATLAB-Rezepte für die Geowissenschaften (1. edition), Eds.: M. H. Trauth, Springer Spektrum, Berlin, Heidelberg, ISBN: 978-3-662-64356-3, 254–274 (2022). DOI:10.1007/978-3-662-64357-0_5 » Abstract
Die in Kap. 5 vorgestellte Zeitreihenanalyse wird zur Untersuchung des zeitlichen Verhaltens einer Variablen verwendet. In den Abschn. 5.2–5.6 werden Methoden der Fourier-basierten Spektralanalyse vorgestellt. Eine alternative Technik zur Analyse von Daten mit ungleichmäßigen Abständen wird in Abschn. 5.7 erläutert. In Abschn. 5.8 wird das sehr populäre Wavelet-Spektrum vorgestellt, das in der Lage ist, zeitliche Variationen in den Spektren auf ähnliche Weise abzubilden wie die in Abschn. 5.6 demonstrierte Methode. In Abschn. 5.9 werden dann Methoden vorgestellt, mit denen abrupte Übergänge in der zentralen Tendenz und der Streuung innerhalb von Zeitreihen erkannt und entfernt werden können. Abschn. 5.10 stellt Methoden vor, mit denen stratigraphische Sequenzen abgeglichen werden können. Dieses Kapitel schließt dann (Abschn. 5.11) mit einem Überblick über nichtlineare Techniken, mit besonderem Augenmerk auf Rekurrenzplots.
N. Marwan:
Nonlinear Time-Series Analysis, In: Python Recipes for Earth Sciences (1. edition), Eds.: M. H. Trauth, Springer Nature Switzerland, Cham, ISBN: 978-3-031-07718-0, 192–212 (2022). DOI:10.1007/978-3-031-07719-7_5 » Abstract
Time series analysis is used to investigate the temporal behavior of a variable x(t). Examples include investigations into long-term records of mountain uplift, sea-level fluctuations, orbitally induced insolation variations (and their influence on the ice-age cycles), millennium-scale variations in the atmosphere–ocean system, the effect of the El Niño/Southern Oscillation on tropical rainfall and sedimentation (Fig. 5.1), and tidal influences on noble gas emissions from bore holes. The temporal pattern of a sequence of events can be random, clustered, cyclic, or chaotic.
N. Marwan, T. Braun:
Power spectral estimate for discrete data, Chaos, 33(5), 053118 (2023). DOI:10.1063/5.0143224 » Abstract
The identification of cycles in periodic signals is a ubiquitous problem in time series analysis. Many real-world data sets only record a signal as a series of discrete events or symbols. In some cases, only a sequence of (non-equidistant) times can be assessed. Many of these signals are furthermore corrupted by noise and offer a limited number of samples, e.g., cardiac signals, astronomical light curves, stock market data, or extreme weather events.
We propose a novel method that provides a power spectral estimate for discrete data. The edit distance is a distance measure that allows to quantify similarities between non-equidistant event sequences of unequal lengths. However, its potential to quantify the frequency content of discrete signals has so far remained unexplored. We define a measure of serial dependence based on the edit distance which can be transformed into a power spectral estimate (EDSPEC), analogously to the Wiener-Khinchin theorem for continuous signals.
The proposed method is applied to a variety of discrete paradigmatic signals representing random, correlated, chaotic, and periodic occurrences of events. It is effective at detecting periodic cycles even in the presence of noise and for short event series. Finally, we apply the EDSPEC method to a novel catalogue of European atmospheric rivers (ARs). ARs are narrow filaments of extensive water vapor transport in the lower troposphere and can cause hazardous extreme precipitation events. Using the EDSPEC method, we conduct the first spectral analysis of European ARs, uncovering seasonal and multi-annual cycles along different spatial domains. The proposed method opens new research avenues in studying of periodic discrete signals in complex real-world systems.
N. Marwan, C. L. Webber, Jr., A. Rysak:
Editorial: Special Issue "Trends in recurrence analysis of dynamical systems", European Physical Journal – Special Topics, 232(1), 1–3 (2023). DOI:10.1140/epjs/s11734-023-00766-z » Abstract
More than a decade has passed since the publication of the special issue “20 Years of Recurrence Plots: Perspectives for a Multi-purpose Tool of Nonlinear Data Analysis” in the European Physical Journal—Special Topics. The hope for further developments inspired by the interesting contributions in this special issue was fully realized. We see an amazing development in the field of recurrence plots (RPs), recurrence quantification analysis (RQA), and recurrence networks. Recurrence analysis is not just one method; it has emerged as an entire framework with many extensions, special recurrence definitions, and specifically designed methods and tools. It has found spreading applications in diverse and growing scientific fields. Recurrence analysis has become a widely accepted concept, even referred to in studies that are actually not using it as a method, but rather using it as a reference or alternative tool. It continues to be an active area of research and development today. An attempt to provide an overview of the most significant technical developments of this recurrence-plot-based framework in the past decade is included in this special issue.
N. Marwan:
Nichtlineare Zeitreihenanalyse, In: Python-Rezepte für die Geowissenschaften (1. edition), Eds.: M. H. Trauth, Springer Spektrum, Berlin, Heidelberg, ISBN: 978-3-662-68117-6, 204–226 (2024). DOI:10.1007/978-3-662-68118-3_5 » Abstract
Zeitreihenanalyse wird verwendet, um das zeitliche Verhalten einer Variablen x(t) zu untersuchen. Beispiele sind Untersuchungen von Langzeitdaten zur Gebirgshebung, Schwankungen des Meeresspiegels, durch die Umlaufbahn induzierte Schwankungen der Sonneneinstrahlung (und deren Einfluss auf die Eiszeitalter), tausendjährige Variationen im Atmosphären-Ozean-System, die Auswirkung der El Niño-Southern Oscillation auf tropischen Niederschlag und Sedimentation (Abb. 5.1), und Gezeiten-Einflüsse auf Edelgasemissionen aus Bohrlöchern. Das zeitliche Muster einer Ereignissequenz kann zufällig, geclustert, zyklisch oder chaotisch sein.
W. C. McCool, B. F. Codding, K. B. Vernon, K. M. Wilson, P. M. Yaworsky, N. Marwan, D. J. Kennett:
Climate change-induced population pressure drives high rates of lethal violence in the Prehispanic central Andes, Proceedings of the National Academy of Sciences, 119(17), e2117556119 (2022). DOI:10.1073/pnas.2117556119 » Abstract
Understanding the influence of climate change and population pressure on human conflict remains a critically important topic in the social sciences. Long-term records that evaluate these dynamics across multiple centuries and outside the range of modern climatic variation are especially capable of elucidating the relative effect of—and the interaction between—climate and demography. This is crucial given that climate change may structure population growth and carrying capacity, while both climate and population influence per capita resource availability. This study couples paleoclimatic and demographic data with osteological evaluations of lethal trauma from 149 directly accelerator mass spectrometry 14C-dated individuals from the Nasca highland region of Peru. Multiple local and supraregional precipitation proxies are combined with a summed probability distribution of 149 14C dates to estimate population dynamics during a 700-y study window. Counter to previous findings, our analysis reveals a precipitous increase in violent deaths associated with a period of productive and stable climate, but volatile population dynamics. We conclude that favorable local climate conditions fostered population growth that put pressure on the marginal and highly circumscribed resource base, resulting in violent resource competition that manifested in over 450 y of internecine warfare. These findings help support a general theory of intergroup violence, indicating that relative resource scarcity—whether driven by reduced resource abundance or increased competition—can lead to violence in subsistence societies when the outcome is lower per capita resource availability.
P. Menzel, B. Gaye, P. K. Mishra, A. Anoop, N. Basavaiah, N. Marwan, B. Plessen, S. Prasad, N. Riedel, M. Stebich, M. G. Wiesner:
Linking Holocene drying trends from Lonar Lake in monsoonal central India to North Atlantic cooling events, Palaeogeography, Palaeoclimatology, Palaeoecology, 410, 164–178 (2014). DOI:10.1016/j.palaeo.2014.05.044 » Abstract
We present the results of biogeochemical and mineralogical analyses on a sediment core that covers the Holocene sedimentation history of the climatically sensitive, closed, saline, and alkaline Lonar Lake in the core monsoon zone in central India. We compare our results of C/N ratios, stable carbon and nitrogen isotopes, grain-size, as well as amino acid derived degradation proxies with climatically sensitive proxies of other records from South Asia and the North Atlantic region. The comparison reveals some more or less contemporaneous climate shifts. At Lonar Lake, a general long term climate transition from wet conditions during the early Holocene to drier conditions during the late Holocene, delineating the insolation curve, can be reconstructed. In addition to the previously identified periods of prolonged drought during 4.6-3.9 and 2.0-0.6 cal ka that have been attributed to temperature changes in the Indo Pacific Warm Pool, several additional phases of shorter term climate alteration superimposed upon the general climate trend can be identified. These correlate with cold phases in the North Atlantic region. The most pronounced climate deteriorations indicated by our data occurred during 6.2-5.2, 4.6-3.9, and 2.0-0.6 cal ka BP. The strong dry phase between 4.6 and 3.9 cal ka BP at Lonar Lake corroborates the hypothesis that severe climate deterioration contributed to the decline of the Indus Civilisation about 3.9 ka BP.
P. K. Mishra, S. Prasad, N. Marwan, A. Anoop, R. Krishnan, B. Gaye, N. Basavaiah, M. Stebich, P. Menzel, N. Riedel:
Contrasting pattern of hydrological changes during the past two millennia from central and northern India: Regional climate differences or anthropogenic impact?, Global and Planetary Change, 161, 97–107 (2018). DOI:10.1016/j.gloplacha.2017.12.005 » Abstract
High resolution reconstructions of the India Summer Monsoon (ISM) are essential to identify regionally different patterns of climate change and refine predictive models. We find opposing trends of hydrological proxies between northern (Sahiya cave stalagmite) and central India (Lonar Lake) between 100 and 1300 CE with the strongest anti-correlation between 810 and 1300 CE. The apparently contradictory data raise the question if these are related to widely different regional precipitation patterns or reflect human influence in/around the Lonar Lake. By comparing multiproxy data with historical records, we demonstrate that only the organic proxies show evidence of anthropogenic impact. However, evaporite data (mineralogy and δ18O) are indicative of precipitation/evaporation (P/E) into the Lonar Lake. Back-trajectories of air-mass circulation over northern and central India show that the relative contribution of the Bay of Bengal (BoB) branch of the ISM is crucial for determining the δ18O of carbonate proxies only in north India, whereas central India is affected significantly by the Arabian Sea (AS) branch of the ISM. We conclude that the δ18O of evaporative carbonates in the Lonar Lake reflects P/E and, in the interval under consideration, is not influenced by source water changes. The opposing trend between central and northern India can be explained by (i) persistent multidecadal droughts over central India between 810 and 1300 CE that provided an effective mechanism for strengthening sub-tropical westerly winds resulting in enhancement of wintertime (non-monsoonal) rainfall over northern parts of the Indian subcontinent, and/or (ii) increased moisture influx to northern India from the depleted BoB source waters.
V. Mitra, A. Sarma, M. S. Janaki, A. N. Sekar Iyengar, B. Sarma, N. Marwan, J. Kurths, P. K. Shaw, D. Saha, S. Ghosh:
Order to chaos transition studies in a DC glow discharge plasma by using recurrence quantification analysis, Chaos, Solitons & Fractals, 69, 285–293 (2014). DOI:10.1016/j.chaos.2014.10.005 » Abstract
Recurrence quantification analysis (RQA) is used to study dynamical systems and to identify the underlying physics when a system exhibits a transition due to changes in some control parameter. The tendency of reoccurrence of different states after certain interval reflects and reveals the hidden patterns of a complex time series data. The present work involves the study of the floating potential fluctuations of a glow discharge plasma obtained by using a Langmuir probe. Determinism, entropy and Lmax are important measures of RQA that show an increasing and decreasing trend with variation in the values of discharge voltages and indicate an order-chaos transition in the dynamics of the fluctuations. Statistical analysis techniques represented by skewness and kurtosis are also supportive of a similar phenomenon occurring in the system.
V. Mitra, B. Sarma, A. Sarma, M. S. Janaki, A. N. Sekar Iyengar, N. Marwan, J. Kurths:
Investigation of complexity dynamics in a DC glow discharge magnetized plasma using recurrence quantification analysis, Physics of Plasmas, 23(6), 062312 (2016). DOI:10.1063/1.4953903 » Abstract
Recurrence is an ubiquitous feature which provides deep insights into the dynamics of real dynamical systems. A suitable tool for investigating recurrences is recurrence quantification analysis (RQA). It allows, e.g., the detection of regime transitions with respect to varying control parameters. We investigate the complexity of different coexisting nonlinear dynamical regimes of the plasma floating potential fluctuations at different magnetic fields and discharge voltages by using recurrence quantification variables, in particular, DET, Lmax, and Entropy. The recurrence analysis reveals that the predictability of the system strongly depends on discharge voltage. Furthermore, the persistent behaviour of the plasma time series is characterized by the Detrended fluctuation analysis technique to explore the complexity in terms of long range correlation. The enhancement of the discharge voltage at constant magnetic field increases the nonlinear correlations; hence, the complexity of the system decreases, which corroborates the RQA analysis.
C. Nava-Fernandez, A. Hartland, F. Gázquez, O. Kwiecien, N. Marwan, B. Fox, J. Hellstrom, A. Pearson, B. Ward, A. French, D. A. Hodell, A. Immenhauser, S. F. M. Breitenbach:
Pacific climate reflected in Waipuna Cave dripwater hydrochemistry, Hydrology and Earth System Sciences, 24, 3361–3380 (2020). DOI:10.5194/hess-24-3361-2020 » Abstract
Cave microclimatic and geochemical monitoring is vitally important for correct interpretations of proxy time series from speleothems with regard to past climatic and environmental dynamics. We present results of a comprehensive cave monitoring programme in Waipuna Cave in the North Island of New Zealand, a region that is strongly influenced by the southern Westerlies and the El NiñoSouthern Oscillation (ENSO). This study aims to characterise the response of the Waipuna Cave hydrological system to atmospheric circulation dynamics in the southwestern Pacific region in order to secure the quality of ongoing palaeo-environmental reconstructions from this cave.
Cave air and water temperatures, drip rates, and CO2, concentration were measured, and samples for water isotopes (δ18O, δD, d-excess, 17Oexcess) and elemental ratios (Mg/Ca, Sr/Ca), were collected continuously and/or at monthly intervals from 10 drip sites inside Waipuna Cave for a period of ca. 3 years. These datasets were compared to surface air temperature, rainfall, and potential evaporation from nearby meteorological stations to test the degree of signal transfer and expression of surface environmental conditions in Waipuna Cave hydrochemistry.
Based on the drip response dynamics to rainfall and other characteristics we identify three hydrological pathways in Waipuna Cave: diffuse flow, combined flow, and fracture flow. Dripwater isotopes do not reflect seasonal variability, but show higher values during severe drought. Dripwater δ18O values display limited variability and reflect the mean isotopic signature of precipitation, testifying to rapid and thorough buffering in the epikarst. Mg/Ca and Sr/Ca ratios in dripwaters are predominantly controlled by prior calcite precipitation (PCP). Prior calcite precipitation is strongest during austral summer (DecemberFebruary), reflecting drier conditions and lack of effective infiltration, and is weakest during the wet austral winter (JulySeptember). The Sr/Ca ratio is particularly sensitive to ENSO conditions due to the interplay of congruent/incongruent host rock dissolution, which manifests itself in lower Sr/Ca in above-average warmer and wetter (La Niña-like) conditions. Our microclimatic observations at Waipuna Cave provide valuable baseline for perceptive interpretation of speleothem proxy records aiming at reconstructing the past expression of Pacific climate modes.
Y. Neuman, N. Marwan, D. Livshitz:
The Complexity of Advice-Giving, Complexity, 15(2), 28–30 (2009). DOI:10.1002/cplx.20270 » Abstract
Advice-giving about personal problems is a common form of human interaction. However, an open question is whether there is an abstract and general logic that explains how advice-giving works. In this study, we addressed this question from the perspective of dynamical systems. We measured the non-linear dynamics of advice-giving by using Recurrent Quantification Analysis. Analyzing 600 texts of request for advice and the advice given, our results uncover a typical logic of advice-giving, and suggest that advice-giving may be understood as a dynamic manipulation of perspective-taking.
Y. Neuman, N. Marwan, Y. Cohen:
Change in the Embedding Dimension as an Indicator of an Approaching Transition, PLoS ONE, 9(6), e101014 (2014). DOI:10.1371/journal.pone.0101014 » Abstract
Predicting a transition point in behavioral data should take into account the complexity of the signal being influenced by contextual factors. In this paper, we propose to analyze changes in the embedding dimension as contextual information indicating a proceeding transitive point, called OPtimal Embedding tRANsition Detection (OPERAND). Three texts were processed and translated to time-series of emotional polarity. It was found that changes in the embedding dimension proceeded transition points in the data. These preliminary results encourage further research into changes in the embedding dimension as generic markers of an approaching transition point.
Y. Neuman, N. Marwan, D. M. Unger:
Dinner is ready! Studying the dynamics and semiotics of dinner, Semiotica, 202, 555–569 (2014). DOI:10.1515/sem-2014-0039 » Abstract
Dinner, as the main meal in the West, is a symbolically laden practice. In this paper, we seek to better understand the cultural meaning of dinner by using a unique combination of a sophisticated quantitative methodology for studying non-linear dynamics and a careful interpretative cultural semiotic analysis. By using the Corpus of Historical American English, we retrieved the words significantly collocated with "Dinner" along 200 years. Using joint recurrence analysis, we have identified the words that synchronize with each other in a non-linear fashion and used them for constructing a representation of Dinner's semiotic field. By analyzing the graph, it was found that "Soup" is the main concept associated with the practice of Dinner along 200 years. The meaning of this finding is interpreted by proposing a semiotic explanation pointing to the "surplus" of soup in the semio-sphere of the Western culture.
E. J. Ngamga, S. Bialonski, N. Marwan, J. Kurths, C. Geier, K. Lehnertz:
Evaluation of selected recurrence measures in discriminating pre-ictal and inter-ictal periods from epileptic EEG data, Physics Letters A, 380(16), 1419–1425 (2016). DOI:10.1016/j.physleta.2016.02.024 » Abstract
We investigate the suitability of selected measures of complexity based on recurrence quantification analysis and recurrence networks for an identification of pre-seizure states in multi-day, multi-channel, invasive electroencephalographic recordings from five epilepsy patients. We employ several statistical techniques to avoid spurious findings due to various influencing factors and due to multiple comparisons and observe precursory structures in three patients. Our findings indicate a high congruence among measures in identifying seizure precursors and emphasize the current notion of seizure generation in large-scale epileptic networks. A final judgment of the suitability for field studies, however, requires evaluation on a larger database.
A. M. Nkomidio, E. J. Ngamga, B. R. N. Nbendjo, J. Kurths, N. Marwan:
Recurrence-Based Synchronization Analysis of Weakly Coupled Bursting Neurons Under External ELF Fields, Entropy, 24(2), 235 (2022). DOI:10.3390/e24020235 » Abstract
We investigate the response characteristics of a two-dimensional neuron model exposed to an externally applied extremely low frequency (ELF) sinusoidal electric field and the synchronization of neurons weakly coupled with gap junction. We find, by numerical simulations, that neurons can exhibit different spiking patterns, which are well observed in the structure of the recurrence plot (RP). We further study the synchronization between weakly coupled neurons in chaotic regimes under the influence of a weak ELF electric field. In general, detecting the phases of chaotic spiky signals is not easy by using standard methods. Recurrence analysis provides a reliable tool for defining phases even for noncoherent regimes or spiky signals. Recurrence-based synchronization analysis reveals that, even in the range of weak coupling, phase synchronization of the coupled neurons occurs and, by adding an ELF electric field, this synchronization increases depending on the amplitude of the externally applied ELF electric field. We further suggest a novel measure for RP-based phase synchronization analysis, which better takes into account the probabilities of recurrences.
U. Ozturk, N. Marwan, O. Korup, H. Saito, A. Agarwal, M. J. Grossman, M. Zaiki, J. Kurths:
Complex networks for tracking extreme rainfall during typhoons, Chaos, 28(7), 075301 (2018). DOI:10.1063/1.5004480 » Abstract
Reconciling the paths of extreme rainfall with those of typhoons remains difficult despite advanced forecasting techniques. We use complex networks defined by a nonlinear synchronization measure termed event synchronization to track extreme rainfall over the Japanese islands. Directed networks objectively record patterns of heavy rain brought by frontal storms and typhoons, but mask out contributions of local convective storms. We propose a radial ranks method to show that paths of extreme rainfall in the typhoon season (August-November, ASON) follow the overall southwest-northeast motion of typhoons and mean rainfall gradient of Japan. The associated eye-of-the-typhoon tracks deviate notably, and may thus distort estimates of heavy typhoon rainfall. We mainly found that the lower spread of rainfall tracks in ASON may enable better hindcasting than for westerly-fed frontal storms in June and July.
U. Ozturk, N. Marwan, S. Specht, O. Korup, J. Jensen:
A new centennial sea-level record for Antalya, eastern Mediterranean, Journal of Geophysical Research, 123(7), 4503–4517 (2018). DOI:10.1029/2018JC013906 » Abstract
Quantitative estimates of sea-level rise in the Mediterranean Basin become increasingly accurate thanks to detailed satellite monitoring. However, such measuring campaigns cover several years to decades, while longer-term sea-level records are rare for the Mediterranean. We used a data archaeological approach to re-analyze monthly mean sea-level data of the Antalya-I (1935-1977) tide gauge to fill this gap. We checked the accuracy and reliability of these data before merging them with the more recent records of the Antalya-II (1985-2009) tide gauge, accounting for an 8-year hiatus. We obtain a composite time series of monthly and annual mean sea levels spanning some 75 years, providing the longest record for the Eastern Mediterranean Basin, and thus an essential tool for studying the region's recent sea-level trends. We estimate a relative mean sea-level rise of 2.2 ± 0.5 mm/yr between 1935 and 2008, with an annual variability (expressed here as the standard deviation of the residuals, σresiduals
U. Ozturk, N. Malik, K. Cheung, N. Marwan, J. Kurths:
A network-based comparative study of extreme tropical and frontal storm rainfall over Japan, Climate Dynamics, 53(1–2), 521–532 (2019). DOI:10.1007/s00382-018-4597-1 » Abstract
Frequent and intense rainfall events demand innovative techniques to better predict the extreme rainfall dynamics. This task requires essentially the assessment of the basic types of atmospheric processes that trigger extreme rainfall, and then to examine the differences between those processes, which may help to identify key patterns to improve predictive algorithms. We employ tools from network theory to compare the spatial features of extreme rainfall over the Japanese archipelago and surrounding areas caused by two atmospheric processes: the Baiu front, which occurs mainly in June and July (JJ), and the tropical storms from August to November (ASON). We infer from complex networks of satellite-derived rainfall data, which are based on the nonlinear correlation measure of event synchronization. We compare the spatial scales involved in both systems and identify different regions which receive rainfall due to the large spatial scale of the Baiu and tropical storm systems. We observed that the spatial scales involved in the Baiu driven rainfall extremes, including the synoptic processes behind the frontal development, are larger than tropical storms, which even have long tracks during extratropical transitions. We further delineate regions of coherent rainfall during the two seasons based on network communities, identifying the horizontal (east-west) rainfall bands during JJ over the Japanese archipelago, while during ASON these bands align with the island arc of Japan.
I. Pavithran, V. R. Unni, A. J. Varghese, R. I. Sujith, A. Saha, N. Marwan, J. Kurths:
Universality in the emergence of oscillatory instabilities in turbulent flows, Europhysics Letters, 129(2), 24004 (2020). DOI:10.1209/0295-5075/129/24004 » Abstract
Self-organization driven by feedback between subsystems is ubiquitous in turbulent fluid mechanical systems. This self-organization manifests as emergence of oscillatory instabilities and is often studied in different system-specific frameworks. We uncover the existence of a universal scaling behaviour during self-organization in turbulent flows leading to oscillatory instability. Our experiments show that the spectral amplitude of the dominant mode of oscillations scales with the Hurst exponent of a fluctuating state variable following an inverse power law relation. Interestingly, we observe the same power law behaviour with a constant exponent near −2 across various turbulent systems such as aeroacoustic, thermoacoustic and aeroelastic systems.
I. Pavithran, V. R. Unni, A. J. Varghese, D. Premraj, R. I. Sujith, C. Vijayan, A. Saha, N. Marwan, J. Kurths:
Universality in spectral condensation, Scientific Reports, 10, 17405 (2020). DOI:10.1038/s41598-020-73956-7 » Abstract
Self-organization is the spontaneous formation of spatial, temporal, or spatiotemporal patterns in complex systems far from equilibrium. During such self-organization, energy distributed in a broadband of frequencies gets condensed into a dominant mode, analogous to a condensation phenomenon. We call this phenomenon spectral condensation and study its occurrence in fluid mechanical, optical and electronic systems. We define a set of spectral measures to quantify this condensation spanning several dynamical systems. Further, we uncover an inverse power law behaviour of spectral measures with the power corresponding to the dominant peak in the power spectrum in all the aforementioned systems.
S. Prasad, N. Marwan, D. Eroglu, B. Goswami, P. K. Mishra, B. Gaye, A. Anoop, N. Basavaiah, M. Stebich, A. Jehangir:
Holocene climate forcings and lacustrine regime shifts in the Indian summer monsoon realm, Earth Surface Processes and Landforms, 45(15), 3842–3853 (2020). DOI:10.1002/esp.5004 » Abstract
Extreme climate events have been identified both in meteorological and long‐term proxy records from the Indian summer monsoon (ISM) realm. However, the potential of palaeoclimate data for understanding mechanisms triggering climate extremes over long time scales has not been fully exploited. A distinction between proxies indicating climate change, environment, and ecosystem shift is crucial for enabling a comparison with forcing mechanisms (e.g. El‐Niño Southern Oscillation). In this study we decouple these factors using data analysis techniques [multiplex recurrence network (MRN) and principal component analyses (PCA)] on multiproxy data from two lakes located in different climate regions – Lonar Lake (ISM dominated) and the high‐altitude Tso Moriri Lake (ISM and westerlies influenced). Our results indicate that (i) MRN analysis, an indicator of changing environmental conditions, is associated with droughts in regions with a single climate driver but provides ambiguous results in regions with multiple climate/environmental drivers; (ii) the lacustrine ecosystem was ‘less sensitive’ to forcings during the early Holocene wetter periods; (iii) archives in climate zones with a single climate driver were most sensitive to regime shifts; (iv) data analyses are successful in identifying the timing of onset of climate change, and distinguishing between extrinsic and intrinsic (lacustrine) regime shifts by comparison with forcing mechanisms. Our results enable development of conceptual models to explain links between forcings and regional climate change that can be tested in climate models to provide an improved understanding of the ISM dynamics and their impact on ecosystems.
G. M. Ramírez Ávila, A. Gapelyuk, N. Marwan, H. Stepan, J. Kurths, T. Walther, N. Wessel:
Classifying healthy women and preeclamptic patients from cardiovascular data using recurrence and complex network methods, Autonomic Neuroscience, 178(1–2), 103–110 (2013). DOI:10.1016/j.autneu.2013.05.003 » Abstract
It is urgently aimed in prenatal medicine to identify pregnancies, which develop life-threatening preeclampsia prior to the manifestation of the disease. Here, we use recurrence-based methods to distinguish such pregnancies already in the second trimester, using the following cardiovascular time series: the variability of heart rate and systolic and diastolic blood pressures. We perform recurrence quantification analysis (RQA), in addition to a novel approach, ε-recurrence networks, applied to a phase space constructed by means of these time series. We examine all possible coupling structures in a phase space constructed with the above-mentioned biosignals. Several measures including recurrence rate, determinism, laminarity, trapping time, and longest diagonal and vertical lines for the recurrence quantification analysis and average path length, mean coreness, global clustering coefficient, assortativity, and scale local transitivity dimension for the network measures are considered as parameters for our analysis. With these quantities, we perform a quadratic discriminant analysis that allows us to classify healthy pregnancies and upcoming preeclamptic patients with a sensitivity of 91.7% and a specificity of 45.8% in the case of RQA and 91.7% and 68% when using ε-recurrence networks, respectively.
G. M. Ramírez Ávila, A. Gapelyuk, N. Marwan, T. Walther, H. Stepan, J. Kurths, N. Wessel:
Classification of cardiovascular time series based on different coupling structures using recurrence networks analysis, Philosophical Transactions of the Royal Society A, 371(1997), 20110623 (2013). DOI:10.1098/rsta.2011.0623 » Abstract
We analyse cardiovascular time series with the aim of performing early prediction of preeclampsia (PE), a pregnancy-specific disorder causing maternal and foetal morbidity and mortality. The analysis is made using a novel approach, namely the ε-recurrence networks applied to a phase space constructed by means of the time series of the variabilities of the heart rate and the blood pressure (systolic and diastolic). All the possible coupling structures among these variables are considered for the analysis. Network measures such as average path length, mean coreness, global clustering coefficient and scale-local transitivity dimension are computed and constitute the parameters for the subsequent quadratic discriminant analysis. This allows us to predict PE with a sensitivity of 91.7 per cent and a specificity of 68.1 per cent, thus validating the use of this method for classifying healthy and preeclamptic patients.
M. Rathinasamy, A. Agarwal, B. Sivakumar, N. Marwan, J. Kurths:
Wavelet analysis of precipitation extremes over India and teleconnections to climate indices, Stochastic Environmental Research and Risk Assessment, 33(11–12), 2053–2069 (2019). DOI:10.1007/s00477-019-01738-3 » Abstract
Precipitation patterns and extremes are significantly influenced by various climatic factors and large-scale atmospheric circulation patterns. This study uses wavelet coherence analysis to detect significant interannual and interdecadal oscillations in monthly precipitation extremes across India and their teleconnections to three prominent climate indices, namely, Niño 3.4, Pacific Decadal Oscillation, and Indian Ocean Dipole (IOD). Further, partial wavelet coherence analysis is used to estimate the standalone relationship between the climate indices and precipitation after removing the effect of interdependency. The wavelet analysis of monthly precipitation extremes at 30 different locations across India reveals that (a) interannual (2-8 years) and interdecadal (8-32 years) oscillations are statistically significant, and (b) the oscillations vary in both time and space. The results from the partial wavelet coherence analysis reveal that Niño 3.4 and IOD are the significant drivers of Indian precipitation at interannual and interdecadal scales. Intriguingly, the study also confirms that the strength of influence of large-scale atmospheric circulation patterns on Indian precipitation extremes varies with spatial physiography of the region.
K. Rehfeld, N. Marwan, J. Heitzig, J. Kurths:
Comparison of correlation analysis techniques for irregularly sampled time series, Nonlinear Processes in Geophysics, 18(3), 389–404 (2011). DOI:10.5194/npg-18-389-2011 » Abstract
Geoscientific measurements often provide time series with irregular time sampling, requiring either data reconstruction (interpolation) or sophisticated methods to handle irregular sampling. We compare the linear interpolation technique and different approaches for analyzing the correlation functions and persistence of irregularly sampled time series, as Lomb-Scargle Fourier transformation and kernel-based methods. In a thorough benchmark test we investigate the performance of these techniques.
All methods have comparable root mean square errors (RMSEs) for low skewness of the inter-observation time distribution. For high skewness, very irregular data, interpolation bias and RMSE increase strongly. We find a 40% lower RMSE for the lag-1 autocorrelation function (ACF) for the Gaussian kernel method vs. the linear interpolation scheme, in the analysis of highly irregular time series. For the cross correlation function (CCF) the RMSE is then lower by 60%. The application of the Lomb-Scargle technique gave results comparable to the kernel methods for the univariate, but poorer results in the bivariate case. Especially the high-frequency components of the signal, where classical methods show a strong bias in ACF and CCF magnitude, are preserved when using the kernel methods.
We illustrate the performances of interpolation vs. Gaussian kernel method by applying both to paleo-data from four locations, reflecting late Holocene Asian monsoon variability as derived from speleothem delta(18)O measurements. Cross correlation results are similar for both methods, which we attribute to the long time scales of the common variability. The persistence time (memory) is strongly overestimated when using the standard, interpolation-based, approach. Hence, the Gaussian kernel is a reliable and more robust estimator with significant advantages compared to other techniques and suitable for large scale application to paleo-data.
K. Rehfeld, N. Marwan, S. F. M. Breitenbach, J. Kurths:
Late Holocene Asian summer monsoon dynamics from small but complex networks of paleoclimate data, Climate Dynamics, 41(1), 3–19 (2013). DOI:10.1007/s00382-012-1448-3 » Abstract
Internal variability of the Asian monsoon system and the relationship amongst its sub-systems, the Indian and East Asian Summer Monsoon, are not sufficiently understood to predict its responses to a future warming climate. Past environmental variability is recorded in Palaeoclimate proxy data. In the Asian monsoon domain many records are available, e.g. from stalagmites, tree-rings or sediment cores. They have to be interpreted in the context of each other, but visual comparison is insufficient. Heterogeneous growth rates lead to uneven temporal sampling. Therefore, computing correlation values is difficult because standard methods require co-eval observation times, and sampling-dependent bias effects may occur. Climate networks are tools to extract system dynamics from observed time series, and to investigate Earth system dynamics in a spatio-temporal context. We establish paleoclimate networks to compare paleoclimate records within a spatially extended domain. Our approach is based on adapted linear and nonlinear association measures that are more efficient than interpolation-based measures in the presence of inter-sampling time variability. Based on this new method we investigate Asian Summer Monsoon dynamics for the late Holocene, focusing on the Medieval Warm Period (MWP), the Little Ice Age (LIA), and the recent period of warming in East Asia. We find a strong Indian Summer Monsoon (ISM) influence on the East Asian Summer Monsoon during the MWP. During the cold LIA, the ISM circulation was weaker and did not extend as far east. The most recent period of warming yields network results that could indicate a currently ongoing transition phase towards a stronger ISM penetration into China. We find that we could not have come to these conclusions using visual comparison of the data and conclude that paleoclimate networks have great potential to study the variability of climate subsystems in space and time.
A. Rheinwalt, B. Goswami, N. Boers, J. Heitzig, N. Marwan, R. Krishnan, J. Kurths:
Teleconnections in Climate Networks: A Network-of-Networks Approach to Investigate the Influence of Sea Surface Temperature Variability on Monsoon Systems, In: Machine Learning and Data Mining Approaches to Climate Science, Eds.: V. Lakshmanan and E. Gilleland and A. McGovern and M. Tingley, Springer, Cham, 23–33 (2015). DOI:10.1007/978-3-319-17220-0_3 » Abstract
We analyze large-scale interdependencies between sea surface temperature (SST) and rainfall variability. We propose a novel climate network construction scheme which we call teleconnection climate networks (TCN). On account of this analysis, gridded SST and rainfall data sets are coarse grained by merging grid points that are dynamically similar to each other. The resulting clusters of time series are taken as the nodes of the TCN. The SST and rainfall systems are investigated as two separate climate networks, and teleconnections within the individual climate networks are studied with special focus on dipolar patterns. Our analysis reveals a pronounced rainfall dipole between Southeast Asia and the Afghanistan-Pakistan region, and we discuss the influences of Pacific SST anomalies on this dipole.
A. Rheinwalt, N. Boers, N. Marwan, J. Kurths, P. Hoffmann, F.-W. Gerstengarbe, P. Werner:
Non-linear time series analysis of precipitation events using regional climate networks for Germany, Climate Dynamics, 46(3), 1066–1074 (2016). DOI:10.1007/s00382-015-2632-z » Abstract
Synchronous occurrences of heavy rainfall events and the study of their relation in time and space are of large socio-economical relevance, for instance for the agricultural and insurance sectors, but also for the general well-being of the population. In this study, the spatial synchronization structure is analyzed as a regional climate network constructed from precipitation event series. The similarity between event series is determined by the number of synchronous occurrences. We propose a novel standardization of this number that results in synchronization scores which are not biased by the number of events in the respective time series. Additionally, we introduce a new version of the network measure directionality that measures the spatial directionality of weighted links by also taking account of the effects of the spatial embedding of the network. This measure provides an estimate of heavy precipitation isochrones by pointing out directions along which rainfall events synchronize. We propose a climatological interpretation of this measure in terms of propagating fronts or event traces and confirm it for Germany by comparing our results to known atmospheric circulation patterns.
H. E. Ridley, Y. Asmerom, J. U. L. Baldini, S. F. M. Breitenbach, V. V. Aquino, K. M. Prufer, B. J. Culleton, V. Polyak, F. A. Lechleitner, D. J. Kennett, M. Zhangm, N. Marwan, C. G. Macpherson, L. M. Baldini, T. Xiao, J. L. Peterkin, J. Awe, G. H. Haug:
Aerosol forcing of the position of the intertropical convergence zone since ad 1550, Nature Geoscience, 8, 195–200 (2015). DOI:10.1038/ngeo2353 » Abstract
The position of the intertropical convergence zone is an important control on the distribution of low-latitude precipitation. Its position is largely controlled by hemisphere temperature contrasts1, 2. The release of aerosols by human activities may have resulted in a southward shift of the intertropical convergence zone since the early 1900s (refs 1, 3, 4, 5, 6) by muting the warming of the Northern Hemisphere relative to the Southern Hemisphere over this interval1, 7, 8, but this proposed shift remains equivocal. Here we reconstruct monthly rainfall over Belize for the past 456 years from variations in the carbon isotope composition of a well-dated, monthly resolved speleothem. We identify an unprecedented drying trend since ad 1850 that indicates a southward displacement of the intertropical convergence zone. This drying coincides with increasing aerosol emissions in the Northern Hemisphere and also marks a breakdown in the relationship between Northern Hemisphere temperatures and the position of the intertropical convergence zone observed earlier in the record. We also identify nine short-lived drying events since ad 1550 each following a large volcanic eruption in the Northern Hemisphere. We conclude that anthropogenic aerosol emissions have led to a reduction of rainfall in the northern tropics during the twentieth century, and suggest that geographic changes in aerosol emissions should be considered when assessing potential future rainfall shifts in the tropics.
N. Riedel, D. Q. Fuller, N. Marwan, C. Poretschkin, N. Basavaiah, P. Menzel, J. Ratnam, S. Prasad, D. Sachse, M. Sankaran, S. Sarkar, M. Stebich:
Monsoon forced evolution of savanna and the spread of agro-pastoralism in peninsular India, Scientific Reports, 11, 9032 (2021). DOI:10.1038/s41598-021-88550-8 » Abstract
An unresolved issue in the vegetation ecology of the Indian subcontinent is whether its savannas, characterized by relatively open formations of deciduous trees in C4-grass dominated understories, are natural or anthropogenic. Historically, these ecosystems have widely been regarded as anthropogenic-derived, degraded descendants of deciduous forests. Despite recent work showing that modern savannas in the subcontinent fall within established bioclimatic envelopes of extant savannas elsewhere, the debate persists, at least in part because the regions where savannas occur also have a long history of human presence and habitat modification. Here we show for the first time, using multiple proxies for vegetation, climate and disturbances from high-resolution, well-dated lake sediments from Lonar Crater in peninsular India, that neither anthropogenic impact nor fire regime shifts, but monsoon weakening during the past 6.0 kyr cal. BP, drove the expansion of savanna at the expense of forests in peninsular India. Our results provide unambiguous evidence for a climate-induced origin and spread of the modern savannas of peninsular India at around the mid-Holocene. We further propose that this savannization preceded and drove the introduction of agriculture and development of sedentism in this region, rather than vice-versa as has often been assumed.
M. Rusconi, A. Zaikin, N. Marwan, J. Kurths:
Effect of Stochastic Resonance on Bone Loss in Osteopenic Conditions, Physical Review Letters, 100(12), 128101 (2008). DOI:10.1103/PhysRevLett.100.128101 » Abstract
We investigate the effect of noise on the remodelling process of the inner spongy part of the trabecular bone. Recently, a new noise-induced phenomenon in bone formation has been reported experimentally. We propose the first conceptual model for this finding, explained by the stochastic resonance effect, and provide a theoretical basis for the development of new countermeasures for bone degeneration in long space flights, which currently has dramatic consequences on return to standard gravity. These results may also be applicable on Earth for patients under osteopenic conditions.
H. D. Salas, G. Poveda, O. J. Mesa, N. Marwan:
Generalized Synchronization Between ENSO and Hydrological Variables in Colombia: A Recurrence Quantification Approach, Frontiers in Applied Mathematics and Statistics, 6, 3 (2020). DOI:10.3389/fams.2020.00003 » Abstract
We use Recurrence Quantification Analysis (RQA) to study features of Generalized Synchronization (GS) between El Niño-Southern Oscillation (ENSO) and monthly hydrological anomalies (HyAns) of rainfall and streamflows in Colombia. To that end, we check the sensitivity of the RQA concerning diverse HyAns estimation methods, which constitutes a fundamental procedure for any climatological analysis at inter-annual timescales. In general, the GS and its sensitivity to HyAns methods are quantified by means of time-lagged joint recurrence analysis. Then, we link the GS results with the dynamics of major physical mechanisms that modulate Colombia's hydroclimatology, including the Caribbean, the CHOCO and the Orinoco Low-Level Jets (LLJs), and the Cross-Equatorial Flow (CEF) over northwestern Amazonia (southern Colombia). Our findings show that RQA exhibits significant differences depending on the HyAns methods. GS results are similar for the HyAns methods with variable annual cycle but the time-lags seem to be sensitive. On the other hand, our results make evident that HyAns in the Pacific, Caribbean, and Andean regions of Colombia exhibit strong (weak) GS with the ENSO signal during La Niña (El Niño), when hydrological anomalies are positive (negative). Results from the GS analysis allow us to identify spatial patterns of non-linear dependence between ENSO and the Colombian's climatology. The mentioned moisture transport sources constitute the interdependence mechanism and contribute to explain hydrological anomalies in Colombia during the phases of ENSO. During La Niña (El Niño), GS is strong (weak) for the Caribbean and the CHOCO LLJs whereas GS is moderate (strong) for the Orinoco LLJ. Moreover, moisture advection by the Caribbean and CHOCO LLJs exhibit synchrony with HyAns at 0–2 (2–4) months-lags over north-western Colombia and the Orinoco LLJ moisture advection synchronizes with HyAns at similar month-lags over the Amazon region of Colombia. Furthermore, our results suggest a strong (weak) GS between negative (positive) Sea Surface Temperatures (SST) anomalies in the Eastern Pacific and rainfall anomalies in Colombia. In contrast, GS is strong (weak) for positive (negative) SST anomalies in the Central Pacific. Our GS results contribute to advance our understanding on the regional effects of both phases of ENSO in Colombia, whose socio-economical, environmental and ecological impacts cannot be overstated. This work provides a novel approach that reveals new insights into the impact of ENSO on northern South America.
M. Sales, M. Mugnaine, J. D. Szezech, R. L. Viana, I. L. Caldas, N. Marwan, J. Kurths:
Stickiness and recurrence plots: An entropy-based approach, Chaos, 33(3), 033140 (2023). DOI:10.1063/5.0140613 » Abstract
The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of the recurrence plots (RPs), namely, the entropy of the distribution of the recurrence times (estimated from the RP), to characterize the dynamics of a typical quasi-integrable Hamiltonian system with coexisting regular and chaotic regions. We show that the recurrence time entropy (RTE) is positively correlated to the largest Lyapunov exponent, with a high correlation coefficient. We obtain a multi-modal distribution of the finite-time RTE and find that each mode corresponds to the motion around islands of different hierarchical levels.
S. Schinkel, N. Marwan, J. Kurths:
Order patterns recurrence plots in the anaylsis of ERP data, Cognitive Neurodynamics, 1(4), 317–325 (2007). DOI:10.1007/s11571-007-9023-z » Abstract
Recurrence quantification analysis (RQA) is an established tool for data analysis in various behavioural sciences. In this article we present a refined notion of RQA based on order patterns. The use of order patterns is commonplace in time series analysis. Exploiting this concept in combination with recurrence plots (RP) and their quantification (RQA) allows for advances in contemporary EEG research, specifically in the analysis of event related potentials (ERP), as the method is known to be robust against non-stationary data. The use of order patterns recurrence plots (OPRPs) on EEG data recorded during a language processing experiment exemplifies the potentials of the method. We could show that the application of RQA to ERP data allows for a considerable reduction of the number of trials required in ERP research while still maintaining statistical validity.
S. Schinkel, N. Marwan, J. Kurths:
Brain signal analysis based on recurrences, Journal of Physiology-Paris, 103(6), 315–323 (2009). DOI:10.1016/j.jphysparis.2009.05.007 » Abstract
The EEG is one of the most commonly used tools in brain research. Though of high relevance in research, the data obtained is very noisy and nonstationary. In the present article we investigate the applicability of a nonlinear data analysis method, the recurrence quantification analysis (RQA), to such data. The method solely rests on the natural property of recurrence which is a phenomenon inherent to complex systems, such as the brain. We show that this method is indeed suitable for the analysis of EEG data and that it might improve contemporary EEG analysis.
T. Semeraro, A. Luvisi, A. O. Lillo, R. Aretano, R. Buccolieri, N. Marwan:
Recurrence Analysis of Vegetation Indices for Highlighting the Ecosystem Response to Drought Events: An Application to the Amazon Forest, Remote Sensing, 12(6), 907 (2020). DOI:10.3390/rs12060907 » Abstract
Forests are important in sequestering CO2 and therefore play a significant role in climate change. However, the CO2 cycle is conditioned by drought events that alter the rate of photosynthesis, which is the principal physiological action of plants in transforming CO2 into biological energy. This study applied recurrence quantification analysis (RQA) to describe the evolution of photosynthesis-related indices to highlight disturbance alterations produced by the Atlantic Multidecadal Oscillation (AMO, years 2005 and 2010) and the El Niño-Southern Oscillation (ENSO, year 2015) in the Amazon forest. The analysis was carried out using Moderate Resolution Imaging Spectroradiometer (MODIS) images to build time series of the enhanced vegetation index (EVI), the normalized difference water index (NDWI), and the land surface temperature (LST) covering the period 2001–2018. The results did not show significant variations produced by AMO throughout the study area, while a disruption due to the global warming phase linked to the extreme ENSO event occurred, and the forest was able to recover. In addition, spatial differences in the response of the forest to the ENSO event were found. These findings show that the application of RQA to the time series of vegetation indices supports the evaluation of the forest ecosystem response to disruptive events. This approach provides information on the capacity of the forest to recover after a disruptive event and, therefore is useful to estimate the resilience of this particular ecosystem.
T. Semeraro, R. Buccolieri, M. Vergine, L. De Bellis, A. Luvisi, R. Emmanuel, N. Marwan:
Analysis of the Olive groves destructions by Xylella fastidosa bacterium effect on the Land Surface Temperature in Salento detected using Satellite Images, Forests, 12, 1266 (2021). DOI:10.3390/f12091266 » Abstract Editor's choice article
Agricultural activities are a major cause of land cover changes that simplifies the landscape pattern replacing natural vegetation with cultivated determinging effects on local and global climate changes. The strong specializations of agricultural productions can lead to extensive monoculture farmingwith a low biodiversity which may involve low landscape resilience against disturbances events. This is the case of Salento peninsula, in the Apulia region (Italy), where the Xylella fastidiosa bacterium causes mass death of olive trees, many of them in monumental olive groves. Therefore, the historical land cover that characterized the landscape is currently in a transition phase and can strongly affect climate conditions. This study aims to analyze the effect of X. fastidiosa on local climate change due to the mass destruction of olive groves. Data of land surface temperature (LST) detected by Landsat 8 and MODIS satellite images are used as a proxy of the microclimate mitigation ecosystem services linked at the evolution of the land cover. Moreover, the recurrence quantification analysis is applied to study the LST evolution. The analysis showed that olive groves are less capable of the forest class to mitigate the LST, but they are more capable than arable lands, above all in the summertime, when the air temperature is the highest. Furthermore, the recurrence analysis shows that X. fastidiosa is rapidly changing the LST of the olive groves into values comparable to those of arable land, with a difference in LST reduced to less than a third to six years from the identification of the bacterium in Apulia. Failure to restore the initial environmental conditions can be connected with the slow progress of the uprooting of infected plants and their replacement, probably due to the attempt to save the historical aspect of the landscape and find solutions to avoid the uprooting of diseased plants. This suggests how the social and economic components of the social-ecological systems have to be more flexible to phytosanitary epidemics and adapt to ecological processes, which cannot always be easily controlled, to produce more resilient landscapes and avoid unwanted transformations.
D. V. Senthilkumar, N. Marwan, J. Kurths:
Recurrence Network Approach to a Phase Space of a Time-Delay System, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2010), Krakow(6166), 83–86 (2010). » Abstract
An interesting potential approach for nonlinear time series analysis by exploiting the analogy between the recurrence matrix, representing the recurrences in phase space, and the adjacency matrix of a complex network to characterize and analyze the dynamical transitions in the phase space of complex systems is being emerging. In this work, we present our preliminary results by applying this method to a high dimensional phase space of a time-delay system.
M. Singh, R. Krishnan, B. Goswami, A. D. Choudhury, P. Swapna, R. Vellore, A. G. Prajeesh, N. Sandeep, C. Venkataraman, R. V. Donner, N. Marwan, J. Kurths:
Fingerprint of volcanic forcing on the ENSO–Indian monsoon coupling, Science Advances, 6, eaba8164 (2020). DOI:10.1126/sciadv.aba8164 » Abstract
Coupling of the El Niño–Southern Oscillation (ENSO) and Indian monsoon (IM) is central to seasonal summer monsoon rainfall predictions over the Indian subcontinent, although a nonstationary relationship between the two nonlinear phenomena can limit seasonal predictability. Radiative effects of volcanic aerosols injected into the stratosphere during large volcanic eruptions (LVEs) tend to alter ENSO evolution; however, their impact on ENSO-IM coupling remains unclear. Here, we investigate how LVEs influence the nonlinear behavior of the ENSO and IM dynamical systems using historical data, 25 paleoclimate reconstructions, last-millennium climate simulations, large-ensemble targeted climate sensitivity experiments, and advanced analysis techniques. Our findings show that LVEs promote a significantly enhanced phase-synchronization of the ENSO and IM oscillations, due to an increase in the angular frequency of ENSO. The results also shed innovative insights into the physical mechanism underlying the LVE-induced enhancement of ENSO-IM coupling and strengthen the prospects for improved seasonal monsoon predictions.
V. Skiba, C. Spötl, M. Trüssel, A. Schröder-Ritzrau, B. Schröder, N. Frank, R. Eichstädter, R. Tjallingii, N. Marwan, X. Zhang, J. Fohlmeister:
Millennial-scale climate variability in the Northern Hemisphere influenced glacier dynamics in the Alps around 250,000 years ago, Communications Earth & Environment, 4, 426 (2023). DOI:10.1038/s43247-023-01083-y » Abstract
Mountain glaciers are sensitive recorders of natural and human-induced climate change. Therefore, it is imperative to obtain a comprehensive understanding of the interplay between climate and glacier response on both short and long timescales. Here we present an analysis of oxygen and carbon isotope data from speleothems formed mainly below a glacier-covered catchment in the Alps 300,000 to 200,000 years ago. Isotope-enabled climate model simulations reveal that δ18O of precipitation in the Alps was higher by approximately 1 ‰ during interstadials compared to stadials. This agrees with interstadial-stadial amplitudes of our new speleothem-based estimate after correcting for cave-internal effects. We propose that the variability of these cave-internal effects offers a unique tool for reconstructing long-term dynamics of warm-based Alpine palaeoglaciers. Our data thereby suggests a close link between North Atlantic interstadial-stadial variability and the meltwater dynamics of Alpine glaciers during Marine Isotope Stage 8 and 7d.
V. Skiba, G. Jouvet, N. Marwan, C. Spötle, J. Fohlmeister:
Speleothem growth and stable carbon isotopes as proxies of the presence and thermodynamical state of glaciers compared to modelled glacier evolution in the Alps, Quaternary Science Reviews, 322, 108403 (2023). DOI:10.1016/j.quascirev.2023.108403 » Abstract
In recent years, glacier modelling proved to be an essential tool for simulating Quaternary glacier evolution in the European Alps. Yet, only sparse empirical data mostly concentrated around the Last Glacial Maximum (LGM) is available to validate these simulations. On the other hand, speleothems from the Alps are a widespread palaeoclimate archive. They provide stable carbon isotope records, which can inform about soil and vegetation conditions above a cave site but also potentially about the lack of soil during times of glacier coverage. In addition, speleothem growth in cold, high-elevation cave sites during glacials are a strong indicator of temperatures in the soil-karst-cave system above the freezing point, which is only likely to occur if the cave is covered by a warm-based glacier.
Here we use existing speleothem data (growth histories and stable carbon isotopes) from Alpine caves to infer soil coverage (i.e. glacier absence) and thermodynamical states of the glaciers during the last glacial cycle and to statistically assess the compatibility with modelled glacier reconstructions. We compare data from multiple cave sites located at different elevations (870–2512 m a.s.l.) with recent glacier evolution simulations. We find a general agreement between speleothem-derived soil presence or absence and modelled glacier coverage. However, speleothem data provide evidence of surface temperatures above freezing point if covered by a glacier, which is not fully reproduced by the simulations. Our work demonstrates the unique value of speleothem-based reconstructions as proxies to assess the performance of palaeo-ice flow models in a transient manner, whereas only maximum glacier state was considered before due to lack of data.
D. A. Smirnov, S. F. M. Breitenbach, G. Feulner, F. A. Lechleitner, K. M. Prufer, J. U. L. Baldini, N. Marwan, J. Kurths:
A regime shift in the Sun–Climate connection with the end of the Medieval Climate Anomaly, Scientific Reports, 7, 11131 (2017). DOI:10.1038/s41598-017-11340-8 » Abstract
Understanding the influence of changes in solar activity on Earth's climate and distinguishing it from other forcings, such as volcanic activity, remains a major challenge for palaeoclimatology. This problem is best approached by investigating how these variables influenced past climate conditions as recorded in high precision paleoclimate archives. In particular, determining if the climate system response to these forcings changes through time is critical. Here we use the Wiener-Granger causality approach along with well-established cross-correlation analysis to investigate the causal relationship between solar activity, volcanic forcing, and climate as reflected in well-established Intertropical Convergence Zone (ITCZ) rainfall proxy records from Yok Balum Cave, southern Belize. Our analysis reveals a consistent influence of volcanic activity on regional Central American climate over the last two millennia. However, the coupling between solar variability and local climate varied with time, with a regime shift around 1000-1300 CE after which the solar-climate coupling weakened considerably.
S. Spiegel, N. Marwan:
Time and Again: Time Series Mining via Recurrence Quantification Analysis, Lecture Notes in Computer Science, 9853, 258–262 (2016). DOI:10.1007/978-3-319-46131-1_30 » Abstract
Recurrence quantification analysis (RQA) was developed in order to quantify differently appearing recurrence plots (RPs) based on their small-scale structures, which generally indicate the number and duration of recurrences in a dynamical system. Although RQA measures are traditionally employed in analyzing complex systems and identifying transitions, recent work has shown that they can also be used for pairwise dissimilarity comparisons of time series. We explain why RQA is not only a modern method for nonlinear data analysis but also is a very promising technique for various time series mining tasks.
V. Stolbova, P. Martin, B. Bookhagen, N. Marwan, J. Kurths:
Topology and seasonal evolution of the network of extreme precipitation over the Indian subcontinent and Sri Lanka, Nonlinear Processes in Geophysics, 21, 901–917 (2014). DOI:10.5194/npg-21-901-2014 » Abstract
This paper employs a complex network approach to determine the topology and evolution of the network of extreme precipitation that governs the organization of extreme rainfall before, during, and after the Indian Summer Monsoon (ISM) season. We construct networks of extreme rainfall events during the ISM (June-September), post-monsoon (October-December), and pre-monsoon (March-May) periods from satellite-derived (Tropical Rainfall Measurement Mission, TRMM) and rain-gauge interpolated (Asian Precipitation Highly Resolved Observational Data Integration Towards the Evaluation of Water Resources, APHRODITE) data sets. The structure of the networks is determined by the level of synchronization of extreme rainfall events between different grid cells throughout the Indian subcontinent. Through the analysis of various complex-network metrics, we describe typical repetitive patterns in North Pakistan (NP), the Eastern Ghats (EG), and the Tibetan Plateau (TP). These patterns appear during the pre-monsoon season, evolve during the ISM, and disappear during the post-monsoon season. These are important meteorological features that need further attention and that may be useful in ISM timing and strength prediction.
B. G. Straiotto, N. Marwan, D. C. James, P. J. Seeley:
Recurrence analysis discriminates martial art movement patterns, European Physical Journal – Special Topics, 232, 151–159 (2023). DOI:10.1140/epjs/s11734-022-00684-6 » Abstract
We aimed to determine whether the combined application of principal components and recurrence quantification analyses might serve to discriminate both spatial and temporal differences between backwards-forwards movement patterns. Elite (n
A. Syta, J. Czarnigowski, P. Jaklinski, N. Marwan:
Detection and identification of cylinder misfire in small aircraft engine in different operating conditions by linear and non-linear properties of frequency components, Measurement, 223, 113763 (2023). DOI:10.1016/j.measurement.2023.113763 » Abstract
We suggest an approach for detecting and identifying ignition failure on a internal combustion engine used in aviation through the analysis of vibration time series. The research is carried out at the experimental stage, where time series of vibrations are collected from sensors installed in various parts of the facility at various rotational speeds and various operating conditions (no failure/failure of a selected piston). The time series were decomposed into periodic components centered around dominant frequencies. Data with greater dimensionality was statistically described using linear and non-linear indicators in short time windows, and labeled accordingly. Instead of examining the statistical significance of the characteristics of individual groups, machine learning classification methods were used, which allowed to distinguish the operating state of the engine (damaged/undamaged), and also to identify a specific unfired cylinder. The use of non-linear indicators allowed us to obtain 100% classification accuracy with a small number of samples.
I. B. Tagne Nkounga, N. Marwan, F. M. Moukam Kakmeni, R. Yamapi, J. Kurths:
Adaptive resonance and control of chaos in a new memristive generalized FitzHugh-Nagumo bursting model, Chaos, 33, 103106 (2023). DOI:10.1063/5.0166691 » Abstract
In a new memristive generalized FitzHugh–Nagumo bursting model, adaptive resonance (AR), in which the neuron system’s response to a varied stimulus can be improved by the ideal intensity of adaptation currents, is examined. We discovered that, in the absence of electromagnetic induction, there is signal detection at the greatest resonance peak of AR using the harmonic balance approach. For electromagnetic induction’s minor impacts, this peak of the AR is optimized, whereas for its larger effects, it disappears. We demonstrate dependency on adaption strength as a bifurcation parameter, the presence of period-doubling, and chaotic motion regulated and even annihilated by the increase in electromagnetic induction using bifurcation diagrams and Lyapunov exponents at specific resonance frequencies. The suggested system shows the propagation of localized excitations as chaotic or periodic modulated wave packets that resemble breathing structures. By using a quantitative recurrence-based analysis, it is possible to examine these plausible dynamics in the structures of the recurrence plot beyond the time series and phase portraits. Analytical and numerical analyses are qualitatively consistent.
I. B. Tagne Nkounga, N. Marwan, R. Yamapi, J. Kurths:
Recurrence-based analysis and controlling switching between synchronous silence and bursting states of coupled generalized FitzHugh-Nagumo models driven by an external sinusoidal current, Nonlinear Dynamics, , (in press). DOI:10.1007/s11071-024-09456-4 » Abstract
M. H. Trauth, B. Bookhagen, N. Marwan, M. R. Strecker:
Multiple landslide clusters record Quaternary climate changes in the northwestern Argentine Andes, Palaeogeography, Palaeoclimatology, Palaeoecology, 194(1–3), 109–121 (2003). DOI:10.1016/S0031-0182(03)00273-6 » Abstract
The chronology of multiple landslide deposits and related lake sediments in the semi-arid eastern Argentine Cordillera suggests that major mass movements cluster in two time periods during the Quaternary, i.e. between 40 and 25 and after 5 14C kyr BP. These clusters may correspond to the Minchin (maximum at around 28-27 14C kyr BP) and Titicaca wet periods (after 3.9 14C kyr BP). The more humid conditions apparently caused enhanced landsliding in this environment. In contrast, no landslide-related damming and associated lake sediments occurred during the Coipasa (11.5-10 14C yr BP) and Tauca wet periods (14.5-11 14C yr BP). The two clusters at 40-25 and after 5 14C kyr BP may correspond to periods where the El Niño-Southern Oscillation (ENSO) and Tropical Atlantic Sea Surface Temperature Variability (TAV) were active. This, however, was not the case during the Coipasa and Tauca wet periods. Lake-balance modelling of a landslide-dammed lake suggests a 10-15% increase in precipitation and a 3-4°C decrease in temperature at ~30 14C kyr BP as compared to the present. In addition, time-series analysis reveals a strong ENSO and TAV during that time. The landslide clusters in northwestern Argentina are therefore best explained by periods of more humid and more variable climates.
M. H. Trauth, A. Asrat, W. Duesing, V. Foerster, K. H. Kraemer, N. Marwan, M. A. Maslin, F. Schäbitz:
Classifying past climate change in the Chew Bahir basin, southern Ethiopia, using recurrence quantification analysis, Climate Dynamics, 53(5), 2557–2572 (2019). DOI:10.1007/s00382-019-04641-3 » Abstract
The Chew Bahir Drilling Project (CBDP) aims to test possible linkages between climate and evolution in Africa through the analysis of sediment cores that have recorded environmental changes in the Chew Bahir basin. In this statistical project we consider the Chew Bahir palaeolake to be a dynamical system consisting of interactions between its different components, such as the waterbody, the sediment beneath lake, and the organisms living within and around the lake. Recurrence is a common feature of such dynamical systems, with recurring patterns in the state of the system reflecting typical influences. Identifying and defining these influences contributes significantly to our understanding of the dynamics of the system. Different recurring changes in precipitation, evaporation, and wind speed in the Chew Bahir basin could result in similar (but not identical) conditions in the lake (e.g., depth and area of the lake, alkalinity and salinity of the lake water, species assemblages in the water body, and diagenesis in the sediments). Recurrence plots (RPs) are graphic displays of such recurring states within a system. Measures of complexity were subsequently introduced to complement the visual inspection of recurrence plots, and provide quantitative descriptions for use in recurrence quantification analysis (RQA). We present and discuss herein results from an RQA on the environmental record from six short (< 17 m) sediment cores collected during the CBDP, spanning the last 45 kyrs. The different types of variability and transitions in these records were classified to improve our understanding of the response of the biosphere to climate change, and especially the response of humans in the area.
M. H. Trauth, A. Asrat, A. S. Cohen, W. Duesing, V. Foerster, S. Kaboth-Bahr, K. H. Kraemer, H. F. Lamb, N. Marwan, M. A. Maslin, F. Schäbitz:
Recurring types of variability and transitions in the ~620 kyr record of climate change from the Chew Bahir basin, southern Ethiopia, Quaternary Science Reviews, 266, 106777 (2021). DOI:10.1016/j.quascirev.2020.106777 » Abstract
The Chew Bahir Drilling Project (CBDP) aims to test possible linkages between climate and hominin evolution in Africa through the analysis of sediment cores that have recorded environmental changes in the Chew Bahir basin (CHB). In this statistical project we used recurrence plots (RPs) together with a recurrence quantification analysis (RQA) to distinguish two types of variability and transitions in the Chew Bahir aridity record and compare them with the ODP Site 967 wetness index from the eastern Mediterranean. The first type of variability is one of slow variations with cycles of ∼20 kyr, reminiscent of the Earth’s precession cycle, and subharmonics of this orbital cycle. In addition to these cyclical wet-dry fluctuations in the area, extreme events often occur, i.e. short wet or dry episodes, lasting for several centuries or even millennia, and rapid transitions between these wet and dry episodes. The second type of variability is characterized by relatively low variation on orbital time scales, but significant century-millennium-scale variations with progressively increasing frequencies. Within this type of variability there are extremely fast transitions between dry and wet within a few decades or years, in contrast to those within Type 1 with transitions over several hundreds of years. Type 1 variability probably reflects the influence of precessional forcing in the lower latitudes at times with maximum values of the long (400 kyr) eccentricity cycle of the Earth’s orbit around the sun, with the tendency towards extreme events. Type 2 variability seems to be linked with minimum values of this cycle. There does not seem to be a systematic correlation between Type 1 or Type 2 variability with atmospheric CO2 concentration. The different types of variability and the transitions between those types had important effects on the availability of water, and could have transformed eastern Africa’s environment considerably, which would have had important implications for the shaping of the habitat of H. sapiens and the direct ancestors of this species.
L. Tupikina, K. Rehfeld, N. Molkenthin, V. Stolbova, N. Marwan, J. Kurths:
Characterizing the evolution of climate networks, Nonlinear Processes in Geophysics, 21, 705–711 (2014). DOI:10.5194/npg-21-705-2014 » Abstract
Complex network theory has been successfully applied to understand the structural and functional topology of many dynamical systems from nature, society and technology. Many properties of these systems change over time, and, consequently, networks reconstructed from them will, too. However, although static and temporally changing networks have been studied extensively, methods to quantify their robustness as they evolve in time are lacking. In this paper we develop a theory to investigate how networks are changing within time based on the quantitative analysis of dissimilarities in the network structure.
Our main result is the common component evolution function (CCEF) which characterizes network development over time. To test our approach we apply it to several model systems, Erdőnyi networks, analytically derived flow-based networks, and transient simulations from the START model for which we control the change of single parameters over time. Then we construct annual climate networks from NCEP/NCAR reanalysis data for the Asian monsoon domain for the time period of 1970-2011 CE and use the CCEF to characterize the temporal evolution in this region. While this real-world CCEF displays a high degree of network persistence over large time lags, there are distinct time periods when common links break down. This phasing of these events coincides with years of strong El Niño/Southern Oscillation phenomena, confirming previous studies. The proposed method can be applied for any type of evolving network where the link but not the node set is changing, and may be particularly useful to characterize nonstationary evolving systems using complex networks.
L. Tupikina, N. Molkenthin, C. López, E. Hernández-García, N. Marwan, J. Kurths:
Correlation Networks from Flows. The Case of Forced and Time-Dependent Advection-Diffusion Dynamics, PLoS ONE, 11(4), e0153703 (2016). DOI:10.1371/journal.pone.0153703 » Abstract
Complex network theory provides an elegant and powerful framework to statistically investigate different types of systems such as society, brain or the structure of local and long-range dynamical interrelationships in the climate system. Network links in climate networks typically imply information, mass or energy exchange. However, the specific connection between oceanic or atmospheric flows and the climate networku2019s structure is still unclear. We propose a theoretical approach for verifying relations between the correlation matrix and the climate network measures, generalizing previous studies and overcoming the restriction to stationary flows. Our methods are developed for correlations of a scalar quantity (temperature, for example) which satisfies an advection-diffusion dynamics in the presence of forcing and dissipation. Our approach reveals that correlation networks are not sensitive to steady sources and sinks and the profound impact of the signal decay rate on the network topology. We illustrate our results with calculations of degree and clustering for a meandering flow resembling a geophysical ocean jet.
V. R. Unni, A. Krishnan, R. Manikandan, N. B. George, R. I. Sujith, N. Marwan, J. Kurths:
On the emergence of critical regions at the onset of thermoacoustic instability in a turbulent combustor, Chaos, 28(6), 063125 (2018). DOI:10.1063/1.5028159 » Abstract
We use complex network theory to investigate the dynamical transition from stable operation to thermoacoustic instability via intermittency in a turbulent combustor with a bluff body stabilized flame. A spatial network is constructed, representing each of these three dynamical regimes of combustor operation, based on the correlation between time series of local velocity obtained from particle image velocimetry. Network centrality measures enable us to identify critical regions of the flow field during combustion noise, intermittency, and thermoacoustic instability. We find that during combustion noise, the bluff body wake turns out to be the critical region that determines the dynamics of the combustor. As the turbulent combustor transitions to thermoacoustic instability, during intermittency, the wake of the bluff body loses its significance in determining the flow dynamics and the region on top of the bluff body emerges as the most critical region in determining the flow dynamics during thermoacoustic instability. The knowledge about this critical region of the reactive flow field can help us devise optimal control strategies to evade thermoacoustic instability.
Emergence of order from chaos is a common sight in nature. Synchronous flashing of fireflies, Mexican wave in a football stadium, triggering of riots, collective behaviour of a school of fish or a swarm of birds, emergence of consciousness from the interplay of millions of neurons, and the evolution of life are some of the examples seen in nature. Formation of convection cells, pattern formation in the BelousovâZhabotinsky reaction, and the emergence of coherent vortices in a turbulent flow are examples of order emerging from disorder in fluid systems. An important fluid dynamic system exhibiting the emergence of order from disorder is a combustor, which houses a confined turbulent reactive flow. During normal operation, the reactive flow field exhibits incoherent turbulent fluctuations. However, under certain operational conditions, the flow field reorganizes, and a spatially ordered periodic behavior emerges. During this dynamic regime known as thermoacoustic instability, the acoustic field inside the combustor exhibits dangerous large amplitude oscillations. In this paper, using complex spatial networks, we characterize the spatial dynamics of the combustor during the stable operation (chaotic oscillations), the thermoacoustic instability (limit cycle oscillations), and the transition regime from stable operation to thermoacoustic instability known as intermittency. Further, using network measures, we identify the critical regions of the reactive flow field that influences the dynamics of the reactive flow field during thermoacoustic instability.
S. M. Vallejo-Bernal, F. Wolf, N. Boers, D. Traxl, N. Marwan, J. Kurths:
The role of atmospheric rivers in the distribution of heavy precipitation events over North America, Hydrology and Earth System Sciences, 27(4), 2645–2660 (2023). DOI:10.5194/hess-27-2645-2023 » Abstract
Atmospheric rivers (ARs) are filaments of extensive water vapor transport in the lower troposphere that play a crucial role in the distribution of freshwater but can also cause natural and economic damage by facilitating heavy precipitation. Here, we investigate the large-scale spatiotemporal synchronization patterns of heavy precipitation events (HPEs) over the western coast and the continental regions of North America (NA), during the period from 1979 to 2018. In particular, we use event synchronization and a complex network approach incorporating varying delays to examine the temporal evolution of spatial patterns of HPEs in the aftermath of land-falling ARs. For that, we employ the SIO-R1 catalog of ARs that landfall on the western coast of NA, ranked in terms of intensity and persistence on an AR-strength scale which varies from level AR1 to AR5, along with daily precipitation estimates from ERA5 with a 0.25° spatial resolution. Our analysis reveals a cascade of synchronized HPEs, triggered by ARs of level AR3 or higher. On the first 3 d after an AR makes landfall, HPEs mostly occur and synchronize along the western coast of NA. In the subsequent days, moisture can be transported to central and eastern Canada and cause synchronized but delayed HPEs there. Furthermore, we confirm the robustness of our findings with an additional AR catalog based on a different AR detection method. Finally, analyzing the anomalies of integrated water vapor transport, geopotential height, upper-level meridional wind, and precipitation, we find atmospheric circulation patterns that are consistent with the spatiotemporal evolution of the synchronized HPEs. Revealing the role of ARs in the precipitation patterns over NA will lead to a better understanding of inland HPEs and the effects that changing climate dynamics will have on precipitation occurrence and consequent impacts in the context of a warming atmosphere.
T. Vantuch, I. Zelinka, A. Adamatzky, N. Marwan:
Phase Transitions in Swarm Optimization Algorithms, Lecture Notes in Computer Science, 10867, 204–216 (2018). DOI:10.1007/978-3-319-92435-9_15 » Abstract
Natural systems often exhibit chaotic behavior in their space-time evolution. Systems transiting between chaos and order manifest a potential to compute, as shown with cellular automata and artificial neural networks. We demonstrate that swarms optimisation algorithms also exhibit transitions from chaos, analogous to motion of gas molecules, when particles explore solution space disorderly, to order, when particles follow a leader, similar to molecules propagating along diffusion gradients in liquid solutions of reagents. We analyse these 'phase-like' transitions in swarm optimization algorithms using recurrence quantification analysis and Lempel-Ziv complexity estimation. We demonstrate that converging and non-converging iterations of the optimization algorithms are statistically different in a view of applied chaos, complexity and predictability estimating indicators.
T. Vantuch, I. Zelinka, A. Adamatzky, N. Marwan:
Perturbations and phase transitions in swarm optimization algorithms, Natural Computing, 18(3), 579–591 (2019). DOI:10.1007/s11047-019-09741-x » Abstract
Natural systems often exhibit chaotic behavior in their space-time evolution. Systems transiting between chaos and order manifest a potential to compute, as shown with cellular automata and artificial neural networks. We demonstrate that swarm optimization algorithms also exhibit transitions from chaos, analogous to a motion of gas molecules, when particles explore solution space disorderly, to order, when particles follow a leader, similar to molecules propagating along diffusion gradients in liquid solutions of reagents. We analyze these 'phase-like' transitions in swarm optimization algorithms using recurrence quantification analysis and Lempel-Ziv complexity estimation. We demonstrate that converging iterations of the optimization algorithms are statistically different from non-converging ones in a view of applied chaos, complexity and predictability estimating indicators. An identification of a key factor responsible for the intensity of their phase transition is the main contribution of this paper. We examined an optimization as a process with three variable factors – an algorithm, number generator and optimization function. More than 9000 executions of the optimization algorithm revealed that the nature of an applied algorithm itself is the main source of the phase transitions. Some of the algorithms exhibit larger transition-shifting behavior while others perform rather transition-steady computing. These findings might be important for future extensions of these algorithms.
J. Wassmer, B. Merz, N. Marwan:
Resilience of transportation infrastructure networks to road failures, Chaos, 34, 013124 (2024). DOI:10.1063/5.0165839 » Abstract
Anthropogenic climate change drives extreme weather events, leading to significant consequences for both society and the environment. This includes damage to road infrastructure, causing disruptions in transportation, obstructing access to emergency services, and hindering humanitarian organizations after natural disasters. In this study, we develop a novel method for analyzing the impacts of natural hazards on transportation networks rooted in the gravity model of travel, offering a fresh perspective to assess the repercussions of natural hazards on transportation network stability. Applying this approach to the Ahr valley flood of 2021, we discovered that the destruction of bridges and roads caused major bottlenecks, affecting areas considerably distant from the flood’s epicenter. Furthermore, the flood-induced damage to the infrastructure also increased the response time of emergency vehicles, severely impeding the accessibility of emergency services. Our findings highlight the need for targeted road repair and reinforcement, with a focus on maintaining traffic flow for emergency responses. This research provides a new perspective that can aid in prioritizing transportation network resilience measures to reduce the economic and social costs of future extreme weather events.
D. Wendi, B. Merz, N. Marwan:
Assessing Hydrograph Similarity and Rare Runoff Dynamics by Cross Recurrence Plots, Water Resources Research, 55(6), 4704–4726 (2019). DOI:10.1029/2018WR024111 » Abstract
This paper introduces a novel measure to assess similarity between event hydrographs. It is based on Cross Recurrence Plots and Recurrence Quantification Analysis which have recently gained attention in a range of disciplines when dealing with complex systems. The method attempts to quantify the event runoff dynamics and is based on the time delay embedded phase space representation of discharge hydrographs. A phase space trajectory is reconstructed from the event hydrograph, and pairs of hydrographs are compared to each other based on the distance of their phase space trajectories. Time delay embedding allows considering the multi-dimensional relationships between different points in time within the event. Hence, the temporal succession of discharge values is taken into account, such as the impact of the initial conditions on the runoff event. We provide an introduction to Cross Recurrence Plots and discuss their parameterization. An application example based on flood time series demonstrates how the method can be used to measure the similarity or dissimilarity of events, and how it can be used to detect events with rare runoff dynamics. It is argued that this methods provides a more comprehensive approach to quantify hydrograph similarity compared to conventional hydrological signatures.
D. Wendi, B. Merz, N. Marwan:
Novel Quantification Method for Hydrograph Similarity, In: Advances in Hydroinformatics. Springer Water, Eds.: P. Gourbesville and G. Caignaert, Springer, Singapore, 727–734 (2020). DOI:10.1007/978-981-15-5436-0_56 » Abstract
We propose an additional elaborate hydrological signature index to quantify similarity (and dissimilarity) between recurring flood dynamics and between observation and model simulation as implied by their phase space trajectories. These phase space trajectories are reconstructed from their corresponding hydrographs (i.e., event time series) using Taken’s time delay embedding method. This reconstructed phase space allows multi-dimensional relationship between observation points (i.e., at different time of the event) to be analyzed. Such approach considers the relationships of set of magnitude points in their unique time sequence that are relevant to the complex temporal cascading processes in flood. In a simpler terms, the new index considers the characteristics shape dynamics of a hydrograph and optionally the antecedent discharge conditions that may implicitly cascade to the subsequent rainfall-runoff event and cause an extreme or unusual hydrograph shape. This new similarity index can be used to comprehensively assess the recurrence of extreme event characteristics, change of flood dynamics, shift of seasonality, and as additional metric or objective function to evaluate and calibrate hydrological and hydraulics models.
N. Wessel, N. Marwan, U. Meyerfeldt, A. Schirdewan, J. Kurths:
Recurrence quantification analysis to characterise the heart rate variability before the onset of ventricular tachycardia, Lecture Notes in Computer Science, 2199, 295–301 (2001). DOI:10.1007/3-540-45497-7_45 » Abstract
Ventricular tachycardia or fibrillation (VT) as fatal cardiac arrhythmias are the main factors triggering sudden cardiac death. The objective of this recurrence quantification analysis approach is to find early signs of sustained VT in patients with an implanted cardioverter-defibrillator (ICD). These devices are able to safeguard patients by returning their hearts to a normal rhythm via strong defibrillatory shocks; additionally, they are able to store at least 1000 beat-to-beat intervals immediately before the onset of a life-threatening arrhythmia. We study these 1000 beat-to-beat intervals of 63 chronic heart failure ICD patients before the onset of a life-threatening arrhythmia and at a control time, i.e. without VT event. We find that no linear parameter shows significant differences in heart rate variability between the VT and the control time series. However, the results of the recurrence quantification analysis are promising for this classification task.
N. Wessel, N. Marwan, A. Schirdewan, J. Kurths:
Beat-to-beat Complexity Analysis Before the Onset of Ventricular Tachycardia, Proceedings of the IEEE Conference on Computers in Cardiology, Thessaloniki, 2003, IEEE Computer Society Press, 477–480 (2003). DOI:10.1109/CIC.2003.1291196 » Abstract
We present recently introduced new recurrence plot based measures of complexity and illustrate their potential with applications to the logistic map and heart rate variability data. These new measures make the identification of chaos-chaos transitions possible and identify laminar states. The application to the heart rate variability data detects and quantifies the laminar phases before a life-threatening cardiac arrhythmia occurs; thereby facilitating a possible prediction of such an event. A comparison to the previous applied methods from symbolic dynamics and the finite-time growths rates is given.
N. Wessel, A. Suhrbier, M. Riedl, N. Marwan, H. Malberg, G. Bretthauer, T. Penzel, J. Kurths:
Detection of time-delayed interactions in biosignals using symbolic coupling traces, Europhysics Letters, 87, 10004 (2009). DOI:10.1209/0295-5075/87/10004 » Abstract
Directional coupling analysis of bivariate time series is an important subject of current research. In this letter, a method based on symbolic dynamics for the detection of time-delayed coupling is presented. The symbolic coupling traces, defined as the symmetric and diametric traces of the bivariate word distribution allow for the quantification of coupling and are compared with established methods like mutual information and cross recurrence analysis. The symbolic coupling traces method is applied to model systems and cardiological data which demonstrate its advantages especially for nonstationary data.
N. Wessel, A. Suhrbier, M. Riedl, N. Marwan, H. Malberg, G. Bretthauer, T. Penzel, J. Kurths:
Symbolic coupling traces for causality analysis of cardiovascular control, Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC 2011)(6091468), 5935–5938 (2011). DOI:10.1109/IEMBS.2011.6091468 » Abstract
Directional coupling analysis of time series is an important subject of current research. In this paper, a method based on symbolic dynamics for the detection of time-delayed coupling in biosignals is presented. The symbolic coupling traces, defined as the symmetric and diametric traces of the bivariate word distribution, allow for a more reliable quantification of coupling and are compared with established methods like mutual information and cross recurrence analysis. The symbolic coupling traces method is applied to appropriate model systems and cardiological data which demonstrate its advantages especially for nonstationary and noisy data. Moreover, the method of symbolic coupling traces is used to analyze and quantify time-delayed coupling of cardiovascular measurements during different sleep stages. Significant different regulatory mechanisms are detected not only between the deep sleep and the other sleep stages but also between healthy subjects and patients. The proposed method may help to indicate pathological changes in cardiovascular regulation and also effects of continuous positive airway pressure therapy on the cardiovascular system.
N. Wessel, N. Marwan, J. F. Krämer, J. Kurths:
TOCSY – Toolboxes for modelling of dynamical systems and time series, Biomedical Engineering/ Biomedizinische Technik, 58, 4180 (2013). DOI:10.1515/bmt-2013-4180 » Abstract
With Toolboxes for Complex Systems we provide a compilation of innovative methods for modern nonlinear data analysis and modelling. These methods were developed during scientific research in the Interdisciplinary Center for Dynamics of Complex Systems Potsdam, the Humboldt-Universität zu Berlin and the Potsdam Institute for Climate Impact Research (PIK). It provides analysis tools for recurrence quantification analysis, nonlinear regression analysis, innovative filtering and processing of physiological data, coupling direction estimations, wavelet spectrum and coherence analysis, time series graph estimation and more.
T. Westerhold, N. Marwan, A. J. Drury, D. Liebrand, C. Agnini, E. Anagnostou, J. S. K. Barnet, S. M. Bohaty, D. De Vleeschouwer, F. Florindo, T. Frederichs, D. A. Hodell, A. E. Holbourn, D. Kroon, V. Lauretano, K. Littler, L. J. Lourens, M. Lyle, H. Pälike, U. Röhl, J. Tian, R. H. Wilkens, P. A. Wilson, J. C. Zachos:
An astronomically dated record of Earth's climate and its predictability over the last 66 million years, Science, 369(6509), 1383–1387 (2020). DOI:10.1126/science.aba6853 » Abstract
Much of our understanding of Earth’s past climate comes from the measurement of oxygen and carbon isotope variations in deep-sea benthic foraminifera. Yet, long intervals in existing records lack the temporal resolution and age control needed to thoroughly categorize climate states of the Cenozoic era and to study their dynamics. Here, we present a new, highly resolved, astronomically dated, continuous composite of benthic foraminifer isotope records developed in our laboratories. Four climate states – Hothouse, Warmhouse, Coolhouse, Icehouse – are identified on the basis of their distinctive response to astronomical forcing depending on greenhouse gas concentrations and polar ice sheet volume. Statistical analysis of the nonlinear behavior encoded in our record reveals the key role that polar ice volume plays in the predictability of Cenozoic climate dynamics.
L. Yang, E. Song, S. Ding, R. J. Brown, N. Marwan, X. Ma:
Analysis of the dynamic characteristics of combustion instabilities in a pre-mixed lean-burn natural gas engine, Applied Energy, 183(1), 746–759 (2016). DOI:10.1016/j.apenergy.2016.09.037 » Abstract
The cyclic combustion instabilities in a pre-mixed lean-burn natural gas engine have been studied. Using non-linear embedding theory, recurrence plots (RPs) and recurrence qualification analysis (RQA), the hidden rhythms and dynamic complexity of a combustion system in high dimensional phase space for each gas injection timing (GIT) have been examined, and the possible source of combustion instabilities has been identified based on 3-D computational fluid dynamics (CFD) simulation. The results reveal that for lower engine load, with the decrease of mixture concentration, the combustion instability and complexity of combustion system become more sensitive to the variation of GITs. Richer mixture and earlier (GIT < 30°CA ATDC) or delayed (GIT, 90°CA ATDC) gas injection will lead to more stable combustion, regular oscillatory and low complexity of combustion system, while leaner mixture together with the medium GITs (from 30 to 90°CA ATDC) easily leads to increase of combustion fluctuations, time irreversibility and dynamic complexity of combustion system. When GITs are changed, the combustion instabilities of pre-mixed lean-burn natural gas engines are from in-cylinder unreasonable stratification of mixture concentration and turbulent motion.
Y. X. Yang, Z. Gao, X. M. Wang, Y. L. Li, J. W. Han, N. Marwan, J. Kurths:
A recurrence quantification analysis-based channel-frequency convolutional neural network for emotion recognition from EEG, Chaos, 28(8), 085724 (2018). DOI:10.1063/1.5023857 » Abstract
Constructing a reliable and stable emotion recognition system is a critical but challenging issue for realizing an intelligent human-machine interaction. In this study, we contribute a novel channel-frequency convolutional neural network (CFCNN), combined with recurrence quantification analysis (RQA), for the robust recognition of electroencephalogram (EEG) signals collected from different emotion states. We employ movie clips as the stimuli to induce happiness, sadness, and fear emotions and simultaneously measure the corresponding EEG signals. Then the entropy measures, obtained from the RQA operation on EEG signals of different frequency bands, are fed into the novel CFCNN. The results indicate that our system can provide a high emotion recognition accuracy of 92.24% and a relatively excellent stability as well as a satisfactory Kappa value of 0.884, rendering our system particularly useful for the emotion recognition task. Meanwhile, we compare the performance of the entropy measures, extracted from each frequency band, in distinguishing the three emotion states. We mainly find that emotional features extracted from the gamma band present a considerably higher classification accuracy of 90.51% and a Kappa value of 0.858, proving the high relation between emotional process and gamma frequency band.
L.-P. Yang, T. A. Bodisco, A. Zare, N. Marwan, T. Chu-Van, R. J. Brown:
Analysis of the nonlinear dynamics of inter-cycle combustion variations in an ethanol fumigation-diesel dual-fuel engine, Nonlinear Dynamics, 95(3), 2555–2574 (2019). DOI:10.1007/s11071-018-4708-x » Abstract
The nonlinear dynamics of a combustion system in a modern common-rail dual-fuel engine has been studied. Using nonlinear dynamic data analysis (phase space reconstruction, recurrence plots, recurrence qualification analysis and wavelet analysis), the effect of ethanol fumigation on the dynamic behaviour of a combustion system has been examined at an engine speed of 2000 rpm with engine load rates of 50%, 75% and 100% and ethanol substitutions up to 40% (by energy) in 10% increments for each engine load. The results show that the introduction of ethanol has a significant effect on inter-cycle combustion variation (ICV) and the dynamics of the combustion system for all of the studied engine loads. For pure diesel mode and lower ethanol substitutions, the ICV mainly exhibits multiscale dynamics: strongly periodic and/or intermittent fluctuations. As the ethanol substitution is increased, the combustion process gradually transfers to more persistent low-frequency variations. At different engine loads, we can observe the bands with the strongest spectral power density that persist over the entire 4000 engine cycles. Compared to high engine loads (75% and 100%), the dynamics of the combustion system at a medium engine load (50%) was more sensitive to the introduction of ethanol. At higher ethanol substitutions, the increased ICV and the complexity of the combustion system at the medium load are attributable to the enhanced cooling caused by the excessive ethanol evaporation, while the low-frequency large-scale combustion fluctuations for the higher engine loads are likely caused by cyclic excitation oscillation during the transition of the combustion mode.
Y. Yang, Z. Gao, Y. Li, Q. Cai, N. Marwan, J. Kurths:
A Complex Network-Based Broad Learning System for Detecting Driver Fatigue From EEG Signals, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 51(9), (2021). DOI:10.1109/TSMC.2019.2956022 » Abstract
Driver fatigue detection is of great significance for guaranteeing traffic safety and further reducing economic as well as societal loss. In this article, a novel complex network (CN) based broad learning system (CNBLS) is proposed to realize an electroencephalogram (EEG)-based fatigue detection. First, a simulated driving experiment was conducted to obtain EEG recordings in alert and fatigue state. Then, the CN theory is applied to facilitate the broad learning system (BLS) for realizing an EEG-based fatigue detection. The results demonstrate that the proposed CNBLS can accurately differentiate the fatigue state from an alert state with high stability. In addition, the performances of the four existing methods are compared with the results of the proposed method. The results indicate that the proposed method outperforms these existing methods. In comparison to directly using EEG signals as the input of BLS, CNBLS can sharply improve the detection results. These results demonstrate that it is feasible to apply BLS in classifying EEG signals by means of CN theory. Also, the proposed method enriches the EEG analysis methods.
J. P. Zbilut, A. Giuliani, A. Colosimo, J. C. Mitchell, M. Colafranceschi, N. Marwan, V. N. Uversky, C. L. Webber, Jr.:
Charge and Hydrophobicity Patterning along the Sequence Predicts the Folding Mechanism and Aggregation of Proteins: A Computational Approach, Journal of Proteome Research, 3, 1243–1253 (2004). DOI:10.1021/pr049883+ » Abstract
The presence of partially folded intermediates along the folding funnel of proteins has been suggested to be a signature of potentially aggregating systems. Many studies have concluded that metastable, highly flexible intermediates are the basic elements of the aggregation process. In a previous paper, we demonstrated how the choice between aggregation and folding behavior was influenced by hydrophobicity distribution patterning along the sequence, as quantified by recurrence quantification analysis (RQA) of the Myiazawa-Jernigan coded primary structures. In the present paper, we tried to unify the "partially folded intermediate" and "hydrophobicity/charge" models of protein aggregation verifying the ability of an empirical relation, developed for rationalizing the effect of different mutations on aggregation propensity of acyl-phosphatase and based on the combination of hydrophobicity RQA and charge descriptors, to discriminate in a statistically significant way two different protein populations: (a) proteins that fold by a process passing by partially folded intermediates and (b) proteins that do not present partially folded intermediates.
J. P. Zbilut, J. C. Mitchell, A. Giuliani, N. Marwan, C. L. Webber, Jr.:
Singular Hydrophobicity Patterns and Net Charge: A Mesoscopic Principle for Protein Aggregation/Folding, Physica A, 343, 348–358 (2004). DOI:10.1016/j.physa.2004.05.081 » Abstract
A statistical model describing the propensity for protein aggregation is presented. Only amino acid hydrophobicity values and calculated net charge are used for the model. The combined effects of hydrophobic patterns as computed by the signal analysis technique, recurrence quantification, plus calculated net charge were included in a function emphasizing the effect of singular hydrophobic patches which were found to be statistically significant for predicting aggregation propensity as quantified by fluorescence studies obtained from the literature. These results suggest preliminary evidence for a mesoscopic principle for protein folding/aggregation.
J. P. Zbilut, J. C. Mitchell, A. Giuliani, A. Colosimo, N. Marwan, M. Colafranceschi, C. L. Webber, Jr.:
Aggregation propensity of proteins quantified by hydrophobicity, Rapporti ISTISAN – Proceedings of the International meeting "Complexity in the living: a problem-oriented approach", Rome, 2004, 05/20, 136–151 (2005). » Abstract
(Introduction:) It has been well appreciated that the native state fold of proteins is in some way dependent upon the physico-chemical properties of their amino acid sequence, most notably, hydrophobicity. More recently it has been recognized that the actual folding process is of a stochastic nature, and also includes the possibility of forming aggregates that ultimately can be physiologically harmful. A growing body of evidence suggests that this involves partially or completely unfolded proteins. Yet, what factors specifically promote the formation of aggregates as opposed to native folds under relatively normal conditions remain undecided.
N. V. Zolotova, D. I. Ponyavin, N. Marwan, J. Kurths:
Long-term asymmetry in the wings of the butterfly diagram, Astronomy & Astrophysics, 505, 197–201 (2009). DOI:10.1051/0004-6361/200811430 » Abstract
Aims Sunspot distribution in the northern and southern solar hemispheres exibit striking synchronous behaviour on the scale of a Schwabe cycle. However, sometimes the bilateral symmetry of the Butterfly diagram relative to the solar equatorial plane breaks down. The investigation of this phenomenon is important to explaining the almost-periodic behaviour of solar cycles.
Methods We use cross-recurrence plots for the study of the time-varying phase asymmetry of the northern and southern hemisphere and compare our results with the latitudinal distribution of the sunspots.
Results We observe a long-term persistence of phase leading in one of the hemispheres, which lasts almost 4 solar cycles and probably corresponds to the Gleissberg cycle. Long-term variations in the hemispheric-leading do not demonstrate clear periodicity but are strongly anti-correlated with the long-term variations in the magnetic equator.
Y. Zou, R. Donner, N. Marwan, M. Small, J. Kurths:
Long-term changes in the north-south asymmetry of solar activity: a nonlinear dynamics characterization using visibility graphs, Nonlinear Processes in Geophysics, 21, 1113–1126 (2014). DOI:10.5194/npg-21-1113-2014 » Abstract
Solar activity is characterized by complex dynamics superimposed onto an almost periodic, approximately 11-year cycle. One of its main features is the presence of a marked, time-varying hemispheric asymmetry, the deeper reasons for which have not yet been completely uncovered. Traditionally, this asymmetry has been studied by considering amplitude and phase differences. Here, we use visibility graphs, a novel tool of nonlinear time series analysis, to obtain complementary information on hemispheric asymmetries in dynamical properties. Our analysis provides deep insights into the potential and limitations of this method, revealing a complex interplay between factors relating to statistical and dynamical properties, i.e., effects due to the probability distribution and the regularity of observed fluctuations. We demonstrate that temporal changes in the hemispheric predominance of the graph properties lag those directly associated with the total hemispheric sunspot areas. Our findings open a new dynamical perspective on studying the north-south sunspot asymmetry, which is to be further explored in future work.
G. Zurlini, N. Marwan, T. Semeraro, K. B. Jones, R. Aretano, M. R. Pasimeni, D. Valente, C. Mulder, I. Petrosillo:
Investigating landscape phase transitions in Mediterranean rangelands by recurrence analysis, Landscape Ecology, 33(9), 1617–1631 (2018). DOI:10.1007/s10980-018-0693-1 » Abstract
Context Socio-ecological landscapes typically characterized by non-linear dynamics in space and time are difficult to be analyzed using standard quantitative methods, due to multiple processes interacting on different spatial and temporal scales. This poses a challenge to the identification of appropriate approaches for analyzing time series that can evaluate system properties of landscape dynamics in the face of disturbances, such as uncontrolled fires.
Objective The purpose is the application of non-linear methods such as recurrence quantification analysis (RQA) to landscape ecology. The examples concern the time series of burnt and unburnt Mediterranean rangelands, to highlight potential and limits of RQA.
Methods We used RQA together with joint recurrence analysis (JRA) to compare the evolutionary behavior of different land uses.
Results Time series of forests and grasslands in rangelands present both periodic and chaotic components with a rather similar behavior after the fire and clear transitions from less to more regular/predictable dynamics/succession. Results highlight the impacts of fire, the recovery capacity of land covers to pre-burnt levels, and the decay of synchronization towards the previous regime associated with vegetation secondary succession consistent with early successional species.
Conclusions RQA and JRA with their set of indices (recurrence rate: RR, laminarity: LAM, determinism: DET, and divergence: DIV) can represent new sensitive measures that may monitor the adaptive capacity and the resilience of landscapes. However, future applications are needed to standardize the analysis by strengthening the accuracy of this approach in describing the ongoing transformations of natural and man-managed landscapes.
V. Mitra, H. Prakash, I. Solomon, M. Megalingam, A. N. Sekar Iyengar, N. Marwan, J. Kurths, A. Sarma, B. Sarma:
Mixed mode oscillations in presence of inverted fireball in an excitable DC glow discharge magnetized plasma, Physics of Plasmas, 24(2), 022307 (2017). DOI:10.1063/1.4976320 » Abstract
The typical phenomena of mixed mode oscillations and their associated nonlinear behaviors have been investigated in collisionless magnetized plasma oscillations in a DC glow discharge plasma system. Plasma is produced between a cylindrical mesh grid and a constricted anode. A spherical mesh grid of 80% optical transparency is kept inside a cylindrical grid to produce an inverted fireball. Three Langmuir probes are kept in the ambient plasma to measure the floating potential fluctuations at different positions of the chamber. It has been observed that under certain conditions of discharge voltages and magnetic fields, the mixed mode oscillation phenomena (MMOs) appears, and it shows a sequential alteration with the variation of the magnetic fields and probe positions. Low frequency instability has been observed consistently in various experimental conditions. The mechanisms of the low frequency instabilities along with the origin of the MMOs have been qualitatively explained. Extensive linear and nonlinear analysis using techniques such as fast Fourier transform, recurrence quantification analysis, and the well-known statistical computing, skewness, and kurtosis are carried out to explore the complex dynamics of the MMO appearing in the plasma oscillations under various discharge conditions and external magnetic fields.
Basics
O. Afsar, D. Eroglu, N. Marwan, J. Kurths:
Scaling behaviour for recurrence-based measures at the edge of chaos, Europhysics Letters, 112(1), 10005 (2015). DOI:10.1209/0295-5075/112/10005 » Abstract
The study of phase transitions with critical exponents has helped to understand fundamental physical mechanisms. Dynamical systems which go to chaos via period doublings show an equivalent behavior during transitions between different dynamical regimes that can be expressed by critical exponents, known as the Huberman-Rudnick scaling law. This universal law is well studied, e.g., with respect to the Lyapunov exponents. Recurrence plots and related recurrence quantification analysis are popular tools to investigate the regime transitions in dynamical systems. However, the measures are mostly heuristically defined and lack clear theoretical justification. In this letter we link a selection of these heuristical measures with theory by numerically studying their scaling behavior when approaching a phase transition point. We find a promising similarity between the critical exponents to those of the Huberman-Rudnick scaling law, suggesting that the considered measures are able to indicate dynamical phase transition even from the theoretical point of view.
A. Agarwal, N. Marwan, M. Rathinasamy, B. Merz, J. Kurths:
Multi-scale event synchronization analysis for unravelling climate processes: A wavelet-based approach, Nonlinear Processes in Geophysics, 24, 599–611 (2017). DOI:10.5194/npg-24-599-2017 » Abstract
The temporal dynamics of climate processes are spread across different timescales and, as such, the study of these processes at only one selected timescale might not reveal the complete mechanisms and interactions within and between the (sub-)processes. To capture the non-linear interactions between climatic events, the method of event synchronization has found increasing attention recently. The main drawback with the present estimation of event synchronization is its restriction to analysing the time series at one reference timescale only. The study of event synchronization at multiple scales would be of great interest to comprehend the dynamics of the investigated climate processes. In this paper, the wavelet-based multi-scale event synchronization (MSES) method is proposed by combining the wavelet transform and event synchronization. Wavelets are used extensively to comprehend multi-scale processes and the dynamics of processes across various timescales. The proposed method allows the study of spatio-temporal patterns across different timescales. The method is tested on synthetic and real-world time series in order to check its replicability and applicability. The results indicate that MSES is able to capture relationships that exist between processes at different timescales.
N. Antary, M. H. Trauth, N. Marwan:
Interpolation and sampling effects on recurrence quantification measures, Chaos, 33, 103105 (2023). DOI:10.1063/5.0167413 » Abstract
The recurrence plot and the recurrence quantification analysis (RQA) are well-established methods for the analysis of data from complex systems. They provide important insights into the nature of the dynamics, periodicity, regime changes, and many more. These methods are used in different fields of research, such as finance, engineering, life, and earth science. To use them, the data have usually to be uniformly sampled, posing difficulties in investigations that provide non-uniformly sampled data, as typical in medical data (e.g., heart-beat based measurements), paleoclimate archives (such as sediment cores or stalagmites), or astrophysics (supernova or pulsar observations). One frequently used solution is interpolation to generate uniform time series. However, this p
C. Bandt, A. Groth, N. Marwan, M. C. Romano, M. Thiel, M. Rosenblum, J. Kurths:
Analysis of Bivariate Coupling by Means of Recurrence, In: Mathematical Methods in Time Series Analysis and Digital Image Processing, Eds.: R. Dahlhaus and J. Kurths and P. Maas and J. Timmer, Springer, Berlin, Heidelberg, ISBN: 978-3-540-75631-6, 153–182 (2008). DOI:10.1007/978-3-540-75632-3_5 » Abstract
In the analysis of coupled systems, various techniques have been developed to model and detect dependencies from observed bivariate time series. Most well-founded methods, like Granger-causality and partial coherence, are based on the theory of linear systems: on correlation functions, spectra and vector autoregressive processes. In this paper we discuss a nonlinear approach using recurrence.
Recurrence, which intuitively means the repeated occurrence of a very similar situation, is a basic notion in dynamical systems. The classical theorem of Poincar?e says that for every dynamical system with an invariant probability measure P, almost every point in a set B will eventually return to B. Moreover, for ergodic systems the mean recurrence time is 1/P(B). Details of recurrence patterns were studied when chaotic systems came into the focus of research, and it turned out that they are linked to Lyapunov exponents, generalized entropies, the correlation sum, and generalized dimensions.
Our goal here is to develop methods for time series which typically contain a few hundreds or thousands of values and which need not come from a stationary source. While Poincaré's theorem holds for stationary stochastic processes, and linear methods require stationarity at least for suficiently large windows, recurrence methods need less stationarity. We outline different concepts of recurrence by specifying different classes of sets B. Then we visualize recurrence and define recurrence parameters similar to autocorrelation.
We are going to apply recurrence to the analysis of bivariate data. The basic idea is that coupled systems show similar recurrence patterns. We can study joint recurrences as well as cross-recurrence. We shall see that bothapproaches have their benefits and drawbacks.
Model systems of coupled oscillators form a test bed for analysis of bivariate time series since the corresponding differential equations involve a parameter which precisely defines the degree of coupling. Changing the parameter we can switch to phase synchronization and generalized synchronization. The approaches of cross- and joint recurrence are compared for several models. In view of possible experimental requirements, recurrence is studied on ordinal scale as well as on metric scale. Several quantities for the description of synchronization are derived and illustrated. Finally, two different applications to EEG data will be presented.
The identification of recurrences at various timescales in extreme event-like time series is challenging because of the rare occurrence of events which are separated by large temporal gaps. Most of the existing time series analysis techniques cannot be used to analyze an extreme event-like time series in its unaltered form. The study of the system dynamics by reconstruction of the phase space using the standard delay embedding method is not directly applicable to event-like time series as it assumes a Euclidean notion of distance between states in the phase space. The edit distance method is a novel approach that uses the point-process nature of events. We propose a modification of edit distance to analyze the dynamics of extreme event-like time series by incorporating a nonlinear function which takes into account the sparse distribution of extreme events and utilizes the physical significance of their temporal pattern. We apply the modified edit distance method to event-like data generated from point process as well as flood event series constructed from discharge data of the Mississippi River in the USA and compute their recurrence plots. From the recurrence analysis, we are able to quantify the deterministic properties of extreme event-like data. We also show that there is a significant serial dependency in the flood time series by using the random shuffle surrogate method.
N. Boers, J. Kurths, N. Marwan:
Complex systems approaches for Earth system data analysis, Journal of Physics: Complexity, 2(1), 011001 (2021). DOI:10.1088/2632-072X/abd8db » Abstract
Complex systems can, to a first approximation, be characterized by the fact that their dynamics emerging at the macroscopic level cannot be easily explained from the microscopic dynamics of the individual constituents of the system. This property of complex systems can be identified in virtually all natural systems surrounding us, but also in many social, economic, and technological systems. The defining characteristics of complex systems imply that their dynamics can often only be captured from the analysis of simulated or observed data. Here, we summarize recent advances in nonlinear data analysis of both simulated and real-world complex systems, with a focus on recurrence analysis for the investigation of individual or small sets of time series, and complex networks for the analysis of possibly very large, spatiotemporal datasets. We review and explain the recent success of these two key concepts of complexity science with an emphasis on applications for the analysis of geoscientific and in particular (palaeo-) climate data. In particular, we present several prominent examples where challenging problems in Earth system and climate science have been successfully addressed using recurrence analysis and complex networks. We outline several open questions for future lines of research in the direction of data-based complex system analysis, again with a focus on applications in the Earth sciences, and suggest possible combinations with suitable machine learning approaches. Beyond Earth system analysis, these methods have proven valuable also in many other scientific disciplines, such as neuroscience, physiology, epidemics, or engineering.
C. Brandt, N. Marwan:
Difference recurrence plots for structural inspection using guided ultrasonic waves – A new approach for evaluation of small signal differences, European Physical Journal – Special Topics, 232, 69–81 (2023). DOI:10.1140/epjs/s11734-022-00701-8 » Abstract
We propose a novel recurrence plot-based approach, the difference recurrence plot (DRP), to detect small deviations between measurements. By using a prototypical model system, we demonstrate the potential of DRPs and the difference to alternative measures, such as Pearson correlation, spectral analysis, or cross and joint recurrence analysis. Real-world data comes from an application of guided ultrasonic waves for structural health monitoring to detect damages in a composite plate. The specific challenge for this damage detection is to differentiate between defects and the influence of temperature. We show that DRPs are suited in the following sense: DRPs of two time series that derive from measurements at different temperatures hold practically full recurrence, whereas DRPs of one time series from a measurement without and one time series with defect show a hugely reduced recurrence rate.
T. Braun, V. R. Unni, R. I. Sujith, J. Kurths, N. Marwan:
Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure, Nonlinear Dynamics, 104, 3955-3973 (2021). DOI:10.1007/s11071-021-06457-5 » Abstract
We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot-based analysis for different paradigmatic systems and nonlinear empirical data in order to demonstrate the ability of our method to detect dynamical transitions ranging across different temporal scales. It succeeds to distinguish states of varying dynamical complexity in the presence of noise and non-stationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and geometric features beyond linear structures in the recurrence plot can be accounted for. This makes lacunarity more broadly applicable as a recurrence quantification measure. Lacunarity is usually interpreted as a measure of heterogeneity or translational invariance of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogeneity in the temporal recurrence patterns at all relevant time scales. We demonstrate the potential of the proposed method when applied to empirical data, namely time series of acoustic pressure fluctuations from a turbulent combustor. Recurrence lacunarity captures both the rich variability in dynamical complexity of acoustic pressure fluctuations and shifting time scales encoded in the recurrence plots. Furthermore, it contributes to a better distinction between stable operation and near blowout states of combustors.
T. Braun, C. N. Fernandez, D. Eroglu, A. Hartland, S. F. M. Breitenbach, N. Marwan:
Sampling rate-corrected analysis of irregularly sampled time series, Physical Review E, 105, 024206 (2022). DOI:10.1103/PhysRevE.105.024206 » Abstract
The analysis of irregularly sampled time series remains a challenging task requiring methods that account for continuous and abrupt changes of sampling resolution without introducing additional biases. The edit distance is an effective metric to quantitatively compare time series segments of unequal length by computing the cost of transforming one segment into the other. We show that transformation costs generally exhibit a nontrivial relationship with local sampling rate. If the sampling resolution undergoes strong variations, this effect impedes unbiased comparison between different time episodes. We study the impact of this effect on recurrence quantification analysis, a framework that is well suited for identifying regime shifts in nonlinear time series. A constrained randomization approach is put forward to correct for the biased recurrence quantification measures. This strategy involves the generation of a type of time series and time axis surrogates which we call sampling-rate-constrained (SRC) surrogates. We demonstrate the effectiveness of the proposed approach with a synthetic example and an irregularly sampled speleothem proxy record from Niue island in the central tropical Pacific. Application of the proposed correction scheme identifies a spurious transition that is solely imposed by an abrupt shift in sampling rate and uncovers periods of reduced seasonal rainfall predictability associated with enhanced El Niño-Southern Oscillation and tropical cyclone activity.
T. Braun, K. H. Kraemer, N. Marwan:
Recurrence flow measure of nonlinear dependence, European Physical Journal – Special Topics, 232, 57–67 (2023). DOI:10.1140/epjs/s11734-022-00687-3 » Abstract
Couplings in complex real-world systems are often nonlinear and scale dependent. In many cases, it is crucial to consider a multitude of interlinked variables and the strengths of their correlations to adequately fathom the dynamics of a high-dimensional nonlinear system. We propose a recurrence-based dependence measure that quantifies the relationship between multiple time series based on the predictability of their joint evolution. The statistical analysis of recurrence plots (RPs) is a powerful framework in nonlinear time series analysis that has proven to be effective in addressing many fundamental problems, e.g., regime shift detection and identification of couplings. The recurrence flow through an RP exploits artifacts in the formation of diagonal lines, a structure in RPs that reflects periods of predictable dynamics. Using time-delayed variables of a deterministic uni-/multivariate system, lagged dependencies with potentially many time scales can be captured by the recurrence flow measure. Given an RP, no parameters are required for its computation. We showcase the scope of the method for quantifying lagged nonlinear correlations and put a focus on the delay selection problem in time-delay embedding which is often used for attractor reconstruction. The recurrence flow measure of dependence helps to identify non-uniform delays and appears as a promising foundation for a recurrence-based state space reconstruction algorithm.
J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
Complex networks in climate dynamics – Comparing linear and nonlinear network construction methods, European Physical Journal – Special Topics, 174, 157–179 (2009). DOI:10.1140/epjst/e2009-01098-2 » Abstract
Complex network theory provides a powerful framework to statistically investigate the topology of local and non-local statistical interrelationships, i.e. teleconnections, in the climate system. Climate networks constructed from the same global climatological data set using the linear Pearson correlation coefficient or the nonlinear mutual information as a measure of dynamical similarity between regions, are compared systematically on local, mesoscopic and global topological scales. A high degree of similarity is observed on the local and mesoscopic topological scales for surface air temperature fields taken from AOGCM and reanalysis data sets. We find larger differences on the global scale, particularly in the betweenness centrality field. The global scale view on climate networks obtained using mutual information offers promising new perspectives for detecting network structures based on nonlinear physical processes in the climate system.
J. F. Donges, H. C. H. Schultz, N. Marwan, Y. Zou, J. Kurths:
Investigating the topology of interacting networks – Theory and application to coupled climate subnetworks, European Physical Journal B, 84, 635–651 (2011). DOI:10.1140/epjb/e2011-10795-8 » Abstract
Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales. Climate networks have recently been shown to be a powerful tool for the analysis of climatological data.
Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the elds of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere's three-dimensional geopotential height eld uncovers known as well as interesting novel features of the atmosphere's vertical stratication and general circulation. Specically, the new measure "cross-betweenness" identies regions which are particularly important for mediating vertical wind eld interactions. The promising results obtained by following the coupled climate subnetwork approach present a rst step towards an improved understanding of the Earth system and its complex interacting components from a network perspective.
J. F. Donges, I. Petrova, A. Loew, N. Marwan, J. Kurths:
How complex climate networks complement eigen techniques for the statistical analysis of climatological data, Climate Dynamics, 45(9), 2407–2424 (2015). DOI:10.1007/s00382-015-2479-3 » Abstract
Eigen techniques such as empirical orthogonal function (EOF) or coupled pattern (CP)/maximum covariance analysis have been frequently used for detecting patterns in multivariate climatological data sets. Recently, statistical methods originating from the theory of complex networks have been employed for the very same purpose of spatio-temporal analysis. This climate network (CN) analysis is usually based on the same set of similarity matrices as is used in classical EOF or CP analysis, e.g., the correlation matrix of a single climatological field or the cross-correlation matrix between two distinct climatological fields. In this study, formal relationships as well as conceptual differences between both eigen and network approaches are derived and illustrated using global precipitation, evaporation and surface air temperature data sets. These results allow us to pinpoint that CN analysis can complement classical eigen techniques and provides additional information on the higher-order structure of statistical interrelationships in climatological data. Hence, CNs are a valuable supplement to the statistical toolbox of the climatologist, particularly for making sense out of very large data sets such as those generated by satellite observations and climate model intercomparison exercises.
This paper presents a new approach for analysing the structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network, which links different points in time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques the new approach has important conceptual advantages, and can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases. It has been demonstrated here that there are fundamental relationships between many topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related to the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis.
R. V. Donner, Y. Zou, J. F. Donges, N. Marwan, J. Kurths:
Ambiguities in recurrence-based complex network representations of time series, Physical Review E, 81, 015101(R) (2010). DOI:10.1103/PhysRevE.81.015101 » Abstract
Recently, different approaches have been proposed for studying basic properties of time series from a complex network perspective. In this work, the corresponding potentials and limitations of networks based on recurrences in phase space are investigated in some detail. We discuss the main requirements that permit a feasible system-theoretic interpretation of network topology in terms of dynamically invariant phase space properties. Possible artifacts induced by disregarding these requirements are pointed out and systematically studied. Finally, a rigorous interpretation of the clustering coefficient and the betweenness centrality in terms of invariant objects is proposed.
R. V. Donner, J. Heitzig, J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
The Geometry of Chaotic Dynamics – A Complex Network Perspective, European Physical Journal B, 84, 653–672 (2011). DOI:10.1140/epjb/e2011-10899-1 » Abstract
Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques, recurrence-based concepts and prominently ε-recurrence networks, most faithfully represent the geometrical fine structure of the attractors underlying chaotic (and less interestingly non-chaotic) time series. In this paper we demonstrate that the well known graph theoretical properties local clustering coefficient and global (network) transitivity can meaningfully be exploited to define two new local and two new global measures of dimension in phase space: local upper and lower clustering dimension as well as global upper and lower transitivity dimension. Rigorous analytical as well as numerical results for self-similar sets and simple chaotic model systems suggest that these measures are well-behaved in most non-pathological situations and that they can be estimated reasonably well using ε-recurrence networks constructed from relatively short time series. Moreover, we study the relationship between clustering and transitivity dimensions on the one hand, and traditional measures like pointwise dimension or local Lyapunov dimension on the other hand. We also provide further evidence that the local clustering coefficients, or equivalently the local clustering dimensions, are useful for identifying unstable periodic orbits and other dynamically invariant objects from time series. Our results demonstrate that ε-recurrence networks exhibit an important link between dynamical systems and graph theory.
R. V. Donner, M. Small, J. F. Donges, N. Marwan, Y. Zou, R. Xiang, J. Kurths:
Recurrence-based time series analysis by means of complex network methods, International Journal of Bifurcation and Chaos, 21(4), 1019–1046 (2011). DOI:10.1142/S0218127411029021 » Abstract
Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide complementary information about structural features of dynamical systems that substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) methods.
ESA MAP team AO-99-030:
Assessment of Bone Structure and its Changes in Microgravity, In: SP-1290 "Microgravity Applications Programme: Successful Teaming of Science and Industry", Eds.: A. Wilson, ESA publications division, ESTEC, Noordwijk, ISBN: 92-9092-971-5, 282–305 (2005).
D. Eroglu, N. Marwan, S. Prasad, J. Kurths:
Finding recurrence networks' threshold adaptively for a specific time series, Nonlinear Processes in Geophysics, 21, 1085–1092 (2014). DOI:10.5194/npg-21-1085-2014 » Abstract
Recurrence-plot-based recurrence networks are an approach used to analyze time series using a complex networks theory. In both approaches – recurrence plots and recurrence networks –, a threshold to identify recurrent states is required. The selection of the threshold is important in order to avoid bias of the recurrence network results. In this paper, we propose a novel method to choose a recurrence threshold adaptively. We show a comparison between the constant threshold and adaptive threshold cases to study period-chaos and even period-period transitions in the dynamics of a prototypical model system. This novel method is then used to identify climate transitions from a lake sediment record.
D. Eroglu, T. K. D. Peron, N. Marwan, F. A. Rodrigues, L. d. F. Costa, M. Sebek, I. Z. Kiss, J. Kurths:
Entropy of weighted recurrence plots, Physical Review E, 90, 042919 (2014). DOI:10.1103/PhysRevE.90.042919 » Abstract
The Shannon entropy of a time series is a standard measure to assess the complexity of a dynamical process and can be used to quantify transitions between different dynamical regimes. An alternative way of quantifying complexity is based on state recurrences, such as those available in recurrence quantification analysis. Although varying definitions for recurrence-based entropies have been suggested so far, for some cases they reveal inconsistent results. Here we suggest a method based on weighted recurrence plots and show that the associated Shannon entropy is positively correlated with the largest Lyapunov exponent. We demonstrate the potential on a prototypical example as well as on experimental data of a chemical experiment.
D. Eroglu, N. Marwan, M. Stebich, J. Kurths:
Multiplex recurrence networks, Physical Review E, 97, 012312 (2018). DOI:10.1103/PhysRevE.97.012312 » Abstract
We have introduced a multiplex recurrence network approach by combining recurrence networks with the multiplex network approach in order to investigate multivariate time series. The potential use of this approach is demonstrated on coupled map lattices and a typical example from palaeobotany research. In both examples, topological changes in the multiplex recurrence networks allow for the detection of regime changes in their dynamics. The method goes beyond classical interpretation of pollen records by considering the vegetation as a whole and using the intrinsic similarity in the dynamics of the different regional vegetation elements. We find that the different vegetation types behave more similarly when one environmental factor acts as the dominant driving force.
J. H. Feldhoff, R. V. Donner, J. F. Donges, N. Marwan, J. Kurths:
Geometric detection of coupling directions by means of inter-system recurrence networks, Physics Letters A, 376(46), 3504–3513 (2012). DOI:10.1016/j.physleta.2012.10.008 » Abstract
We introduce a geometric method for identifying the couplingdirection between two dynamical systems based on a bivariate extension of recurrencenetwork analysis. Global characteristics of the resulting inter-systemrecurrencenetworks provide a correct discrimination for weakly coupled Rössler oscillators not yet displaying generalised synchronisation. Investigating two real-world palaeoclimate time series representing the variability of the Asian monsoon over the last 10,000 years, we observe indications for a considerable influence of the Indian summer monsoon on climate in Eastern China rather than vice versa. The proposed approach can be directly extended to studying K>2 coupled subsystems.
J. H. Feldhoff, R. V. Donner, J. F. Donges, N. Marwan, J. Kurths:
Geometric signature of complex synchronisation scenarios, Europhysics Letters, 102(3), 30007 (2013). DOI:10.1209/0295-5075/102/30007 » Abstract
Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the coupling strength often leads to qualitative changes in the dynamics exhibiting different types of synchronisation. Here, we study the geometric signatures of coupling along with the onset of generalised synchronisation (GS) between two coupled chaotic oscillators by mapping the systems' individual as well as joint recurrences in phase space to a complex network. For a paradigmatic continuous-time model system, we show that the transitivity properties of the resulting joint recurrence networks display distinct variations associated with changes in the structural similarity between different parts of the considered trajectories. They therefore provide a useful new indicator for the emergence of GS.
Z. Gao, Y. Yang, W. Dang, Q. Cai, Z. Wang, N. Marwan, S. Boccaletti, J. Kurths:
Reconstructing multi-mode networks from multivariate time series, Europhysics Letters, 19(5), 50008 (2017). DOI:10.1209/0295-5075/119/50008 » Abstract
Unveiling the dynamics hidden in multivariate time series is a task of the utmost importance in a broad variety of areas in physics. We here propose a method that leads to the construction of a novel functional network, a multi-mode weighted graph combined with an empirical mode decomposition, and to the realization of multi-information fusion of multivariate time series. The method is illustrated in a couple of successful applications (a multi-phase flow and an epileptic electro-encephalogram), which demonstrate its powerfulness in revealing the dynamical behaviors underlying the transitions of different flow patterns, and enabling to differentiate brain states of seizure and non-seizure.
B. Goswami, G. Ambika, N. Marwan, J. Kurths:
On interrelations of recurrences and connectivity trends between stock indices, Physica A, 391, 4364–4376 (2012). DOI:10.1016/j.physa.2012.04.018 » Abstract
Financial data has been extensively studied for correlations using Pearson's cross-correlation coefficient ρ as the point of departure. We employ an estimator based on recurrence plots – the Correlation of Probability of Recurrence (CPR) – to analyze connections between nine stock indices spread worldwide. We suggest a slight modification of the CPR approach in order to get more robust results. We examine trends in CPR for an approximately 19-month window moved along the time series and compare them to ρ. Binning CPR into three levels of connectedness: strong, moderate and weak, we extract the trends in number of connections in each bin over time. We also look at the behavior of CPR during the Dot-Com bubble by shifting the time series to align their peaks. CPR mainly uncovers that the markets move in and out of periods of strong connectivity erratically, instead of moving monotonously towards increasing global connectivity. This is in contrast to ρ, which gives a picture of ever increasing correlation. CPR also exhibits that time shifted markets have high connectivity around the Dot-Com bubble of 2000. We use significance tests using Twin Surrogates to interpret all the measures estimated in the study.
B. Goswami, N. Boers, A. Rheinwalt, N. Marwan, J. Heitzig, S. F. M. Breitenbach, J. Kurths:
Abrupt transitions in time series with uncertainties, Nature Communications, 9, 48 (2018). DOI:10.1038/s41467-017-02456-6 » Abstract
Identifying abrupt transitions is a key question in various disciplines. Existing transition detection methods, however, do not rigorously account for time series uncertainties, often neglecting them altogether or assuming them to be independent and qualitatively similar. Here, we introduce a novel approach suited to handle uncertainties by representing the time series as a time-ordered sequence of probability density functions. We show how to detect abrupt transitions in such a sequence using the community structure of networks representing probabilities of recurrence. Using our approach, we detect transitions in global stock indices related to well-known periods of politico-economic volatility. We further uncover transitions in the El Niño-Southern Oscillation which coincide with periods of phase locking with the Pacific Decadal Oscillation. Finally, we provide for the first time an 'uncertainty-aware' framework which validates the hypothesis that ice-rafting events in the North Atlantic during the Holocene were synchronous with a weakened Asian summer monsoon.
J. Heitzig, J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
Node-weighted measures for complex networks with spatially embedded, sampled, or differently sized nodes, European Physical Journal B, 85(1), 38 (1–22) (2012). DOI:10.1140/epjb/e2011-20678-7 » Abstract
When network and graph theory are used in the study of complex systems, a typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or infinite region or set of objects of interest. The selection procedure, e.g., formation of a subset or some kind of discretization or aggregation, typically results in individual nodes of the studied network representing quite differently sized parts of the domain of interest. This heterogeneity may induce substantial bias and artifacts in derived network statistics. To avoid this bias, we propose an axiomatic scheme based on the idea of node splitting invariance to derive consistently weighted variants of various commonly used statistical network measures. The practical relevance and applicability of our approach is demonstrated for a number of example networks from different fields of research, and is shown to be of fundamental importance in particular in the study of spatially embedded functional networks derived from time series as studied in, e.g., neuroscience and climatology.
Y. Hirata, T. Stemler, D. Eroglu, N. Marwan:
Prediction of flow dynamics using point processes, Chaos, 28, 011101 (2018). DOI:10.1063/1.5016219 » Abstract
Describing a time series parsimoniously is the first step to study the underlying dynamics. For a time-discrete system, a generating partition provides a compact description such that a time series and a symbolic sequence are one-to-one. But, for a time-continuous system, such a compact description does not have a solid basis. Here, we propose to describe a time-continuous time series using a local cross section and the times when the orbit crosses the local cross section. We show that if such a series of crossing times and some past observations are given, we can predict the system's dynamics with fine accuracy. This reconstructability neither depends strongly on the size nor the placement of the local cross section if we have a sufficiently long database. We demonstrate the proposed method using the Lorenz model as well as the actual measurement of wind speed.
J. Hlinka, D. Hartman, M. Vejmelka, J. Runge, N. Marwan, J. Kurths, M. Paluš:
Reliability of Inference of Directed Climate Networks Using Conditional Mutual Information, Entropy, 15(6), 2023–2045 (2013). DOI:10.3390/e15062023 » Abstract
Across geosciences, many investigated phenomena relate to specific complex systems consisting of intricately intertwined interacting subsystems. Such dynamical complex systems can be represented by a directed graph, where each link denotes an existence of a causal relation, or information exchange between the nodes. For geophysical systems such as global climate, these relations are commonly not theoretically known but estimated from recorded data using causality analysis methods. These include bivariate nonlinear methods based on information theory and their linear counterpart. The trade-off between the valuable sensitivity of nonlinear methods to more general interactions and the potentially higher numerical reliability of linear methods may affect inference regarding structure and variability of climate networks. We investigate the reliability of directed climate networks detected by selected methods and parameter settings, using a stationarized model of dimensionality-reduced surface air temperature data from reanalysis of 60-year global climate records. Overall, all studied bivariate causality methods provided reproducible estimates of climate causality networks, with the linear approximation showing higher reliability than the investigated nonlinear methods. On the example dataset, optimizing the investigated nonlinear methods with respect to reliability increased the similarity of the detected networks to their linear counterparts, supporting the particular hypothesis of the near-linearity of the surface air temperature reanalysis data.
P. Köthur, C. Witt, M. Sips, N. Marwan S. Schinkel, D. Dransch:
Visual Analytics for Correlation-Based Comparison of Time Series Ensembles, Computer Graphics Forum, 34(3), 411–420 (2015). DOI:10.1111/cgf.12653 » Abstract
An established approach to studying interrelations between two non-stationary time series is to compute the 'windowed' cross-correlation (WCC). The time series are divided into intervals and the cross-correlation between corresponding intervals is calculated. The outcome is a matrix that describes the correlation between two time series for different intervals and varying time lags. This important technique can only be used to compare two single time series. However, many applications require the comparison of ensembles of time series. Therefore, we propose a visual analytics approach that extends the WCC to support a correlation-based comparison of two ensembles of time series. We compute the pairwise WCC between all time series from the two ensembles, which results in hundreds of thousands of WCC matrices. Statistical measures are used to derive a concise description of the time-varying correlations between the ensembles as well as the uncertainty of the correlation values. We further introduce a visually scalable overview visualization of the computed correlation and uncertainty information. These components are combined with multiple linked views into a visual analytics system to support configuration of the WCC as well as detailed analysis of correlation patterns between two ensembles. Two use cases from very different domains, cognitive science and paleoclimatology, demonstrate the utility of our approach.
P. Kasthuri, I. Pavithran, A. Krishnan, S. A. Pawar, R. I. Sujith, R. Gejji, W. Anderson, N. Marwan, J. Kurths:
Recurrence analysis of slow–fast systems, Chaos, 30, 063152 (2020). DOI:10.1063/1.5144630 » Abstract
Many complex systems exhibit periodic oscillations comprising slow–fast timescales. In such slow–fast systems, the slow and fast timescales compete to determine the dynamics. In this study, we perform a recurrence analysis on simulated signals from paradigmatic model systems as well as signals obtained from experiments, each of which exhibit slow–fast oscillations. We find that slow–fast systems exhibit characteristic patterns along the diagonal lines in the corresponding recurrence plot (RP). We discern that the hairpin trajectories in the phase space lead to the formation of line segments perpendicular to the diagonal line in the RP for a periodic signal. Next, we compute the recurrence networks (RNs) of these slow–fast systems and uncover that they contain additional features such as clustering and protrusions on top of the closed-ring structure. We show that slow–fast systems and single timescale systems can be distinguished by computing the distance between consecutive state points on the phase space trajectory and the degree of the nodes in the RNs. Such a recurrence analysis substantially strengthens our understanding of slow–fast systems, which do not have any accepted functional forms.
C. Komalapriya, M. Thiel, M. C. Romano, N. Marwan, U. Schwarz, J. Kurths:
Reconstruction of a system's dynamics from short trajectories, Physical Review E, 78, 066217 (2008). DOI:10.1103/PhysRevE.78.066217 » Abstract
Long data sets are one of the prime requirements of time series analysis techniques to unravel the dynamics of an underlying system. However, acquiring long data sets is often not possible. In this paper, we address the question of whether it is still possible to understand the complete dynamics of a system if only short (but many) time series are observed. The key idea is to generate a single long time series from these short segments using the concept of recurrences in phase space. This long time series is constructed so as to exhibit a dynamics similar to that of a long time series obtained from the corresponding underlying system.
K. H. Kraemer, R. V. Donner, J. Heitzig, N. Marwan:
Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions, Chaos, 28(8), 085720 (2018). DOI:10.1063/1.5024914 » Abstract
The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors in the studied system's state space reconstructed by means of time-delay embedding as the key characteristic that should guide the corresponding choice for obtaining an adequate resolution of a recurrence plot. Specifically, we present an empirical description of the distance distribution, focusing on characteristic changes of its shape with increasing embedding dimension. Our results suggest that selecting the recurrence threshold according to a fixed percentile of this distribution reduces the dependence of recurrence characteristics on the embedding dimension in comparison with other commonly used threshold selection methods. Numerical investigations on some paradigmatic model systems with time-dependent parameters support these empirical findings.
K. H. Kraemer, N. Marwan:
Border effect corrections for diagonal line based recurrence quantification analysis measures, Physics Letters A, 383(34), 125977 (2019). DOI:10.1016/j.physleta.2019.125977 » Abstract
Recurrence Quantification Analysis (RQA) defines a number of quantifiers, which base upon diagonal line structures in the recurrence plot (RP). Due to the finite size of an RP, these lines can be cut by the borders of the RP and, thus, bias the length distribution of diagonal lines and, consequently, the line based RQA measures. In this letter we investigate the impact of the mentioned border effects and of the thickening of diagonal lines in an RP (caused by tangential motion) on the estimation of the diagonal line length distribution, quantified by its entropy. Although a relation to the Lyapunov spectrum is theoretically expected, the mentioned entropy yields contradictory results in many studies. Here we summarize correction schemes for both, the border effects and the tangential motion and systematically compare them to methods from the literature. We show that these corrections lead to the expected behavior of the diagonal line length entropy, in particular meaning zero values in case of a regular motion and positive values for chaotic motion. Moreover, we test these methods under noisy conditions, in order to supply practical tools for applied statistical research.
K. H. Kraemer, F. Hellmann, M. Anvari, J. Kurths, N. Marwan:
Spike spectra for recurrences, Entropy, 24(11), 1689 (2022). DOI:10.3390/e24111689 » Abstract
In recurrence analysis, the τ-recurrence rate encodes the periods of the cycles of the underlying high-dimensional time series. It, thus, plays a similar role to the autocorrelation for scalar time-series in encoding temporal correlations. However, its Fourier decomposition does not have a clean interpretation. Thus, there is no satisfactory analogue to the power spectrum in recurrence analysis. We introduce a novel way to decompose the τ-recurrence rate using an over-complete basis of Dirac combs together with a sparsity regularization. We show that this decomposition, the inter-spike spectrum, naturally provides an analogue to the power spectrum for recurrence analysis in the sense that it reveals the dominant periodicities of the underlying time series. We show that the inter-spike spectrum correctly identifies patterns and transitions in the underlying system in a wide variety of examples and is robust to measurement noise.
K. H. Kraemer, M. Gelbrecht, I. Pavithran, R. I. Sujith, N. Marwan:
Optimal state space reconstruction via Monte Carlo Decision Tree Search, Nonlinear Dynamics, 108, 1525–1545 (2022). DOI:10.1007/s11071-022-07280-2 » Abstract
A novel idea for an optimal time delay state space reconstruction from uni- and multivariate time series is presented. The entire embedding process is considered as a game, in which each move corresponds to an embedding cycle and is subject to an evaluation through an objective function. This way the embedding procedure can be modeled as a tree, in which each leaf holds a specific value of the objective function. By using a Monte Carlo ansatz the proposed algorithm populates the tree with many leafs by computing different possible embedding paths and the final embedding is chosen as that particular path, which ends at the leaf with the lowest achieved value of the objective function. The method aims to prevent getting stuck in a local minimum of the objective function and can be used in a modular way, enabling practitioners to choose a statistic for possible delays in each embedding cycle as well as a suitable objective function themselves. The proposed method guarantees the optimization of the chosen objective function over the parameter space of the delay embedding as long as the tree is sampled sufficiently. As a proof of concept, we demonstrate the superiority of the proposed method over the classical time delay embedding methods using a variety of application examples. We compare recurrence plot based statistics inferred from reconstructions of a Lorenz-96 system and highlight an improved forecast accuracy for map-like model data as well as for palaeoclimate isotope time series. Finally we utilize state space reconstruction for the detection of causality and its strength between observables of a gas turbine type thermoacoustic combustor.
A. Kulkarni, N. Marwan, L. Parrott, R. Proulx, C. L. Webber, Jr.:
Recurrence plots at the crossroad between theory and application, International Journal of Bifurcation and Chaos, 21(4), 997–1001 (2011). DOI:10.1142/S0218127411029057 » Abstract
Researchers in different subject areas are tackling similar questions that require a complex systems approach: Can we develop indicators that serve as warning signals for impending regime shifts or critical thresholds in the system behavior? What is the characteristic observation scale that allows for an optimal description of the system dynamics in space and time? How can the resilience (return time to equilibrium) and stability (resistance to external forcing) of a system subjected to disturbance regimes be quantified? Can we derive generalities on how natural and man-made systems develop in time? Amongst interacting units of the system, which ones are the keystones for its global functioning? In this context, recurrence plots are useful tools as they provide a common language for the study of complex systems.
G. Ladeira, N. Marwan, J.-B. Destro-Filho, C. D. Ramos, G. Lima:
Frequency spectrum recurrence analysis, Scientific Reports, 10, 21241 (2020). DOI:10.1038/s41598-020-77903-4 » Abstract
In this paper, we present the new frequency spectrum recurrence analysis technique by means of electro-encephalon signals (EES) analyses. The technique is suitable for time series analysis with noise and disturbances. EES were collected, and alpha waves of the occipital region were analysed by comparing the signals from participants in two states, eyes open and eyes closed. Firstly, EES were characterized and analysed by means of techniques already known to compare with the results of the innovative technique that we present here. We verified that, standard recurrence quantification analysis by means of EES time series cannot statistically distinguish the two states. However, the new frequency spectrum recurrence quantification exhibit quantitatively whether the participants have their eyes open or closed. In sequence, new quantifiers are created for analysing the recurrence concentration on frequency bands. These analyses show that EES with similar frequency spectrum have different recurrence levels revealing different behaviours of the nervous system. The technique can be used to deepen the study on depression, stress, concentration level and other neurological issues and also can be used in any complex system.
N. Marwan:
Untersuchung der Klimavariabilität in NW Argentinien mit Hilfe der quantitativen Analyse von Recurrence Plots, Diploma Thesis, Dresden University of Technology (1999). » Abstract
Nonlinear time series analysis is used to compare the impact of climate oscillations in the Pacific (El Niño/Southern Oscillation) and in the Atlantic (Tropical Atlantic Dipole) on present and past rainfall variations in NW Argentina. Past rainfall variations have been reconstructed from 30,000 years old varved lake sediments. In the analysis the methods of Recurrence Plot, Cross Recurrence Plot and Recurrence Quantification Analysis are applied. Similarities between the dynamics of climate oscillations and recent and past precipitation are detected. In addition these very new methods are studied by application to known examples and models.
N. Marwan, M. Thiel, N. R. Nowaczyk:
Cross Recurrence Plot Based Synchronization of Time Series, Nonlinear Processes in Geophysics, 9(3/4), 325–331 (2002). DOI:10.5194/npg-9-325-2002 » Abstract
The method of recurrence plots is extended to the cross recurrence plots (CRP) which, among others, enables the study of synchronization or time differences in two time series. This is emphasized in a distorted main diagonal in the cross recurrence plot, the line of synchronization (LOS). A non-parametrical fit of this LOS can be used to rescale the time axis of the two data series (whereby one of them is compressed or stretched) so that they are synchronized. An application of this method to geophysical sediment core data illustrates its suitability for real data. The rock magnetic data of two different sediment cores from the Makarov Basin can be adjusted to each other by using this method, so that they are comparable.
N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths:
Recurrence Plot Based Measures of Complexity and its Application to Heart Rate Variability Data, Physical Review E, 66(2), 026702 (2002). DOI:10.1103/PhysRevE.66.026702 » Abstract recommended work
The knowledge of transitions between regular, laminar or chaotic behaviors is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods that, however, require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart-rate-variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e., chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our measures to the heart-rate-variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia occurs thereby facilitating a prediction of such an event. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.
N. Marwan, J. Kurths:
Nonlinear analysis of bivariate data with cross recurrence plots, Physics Letters A, 302(5–6), 299–307 (2002). DOI:10.1016/S0375-9601(02)01170-2 » Abstract recommended work
We use the extension of the method of recurrence plots to cross recurrence plots (CRP) which enables a nonlinear analysis of bivariate data. To quantify CRPs, we develop further three measures of complexity mainly basing on diagonal structures in CRPs. The CRP analysis of prototypical model systems with nonlinear interactions demonstrates that this technique enables to find these nonlinear interrelations from bivariate time series, whereas linear correlation tests do not. Applying the CRP analysis to climatological data, we find a complex relationship between rainfall and El Ni? data.
N. Marwan:
Encounters With Neighbours – Current Developments Of Concepts Based On Recurrence Plots And Their Applications, PhD Thesis, ISBN: 3-00-012347-4 (2003). URN:nbn:de:kobv:517-0000856 » Abstract
In this work, different aspects and applications of the recurrence plot analysis are presented. First, a comprehensive overview of recurrence plots and their quantification possibilities is given. New measures of complexity are defined by using geometrical structures of recurrence plots. These measures are capable to find chaos-chaos transitions in processes. Furthermore, a bivariate extension to cross recurrence plots is studied. Cross recurrence plots exhibit characteristic structures which can be used for the study of differences between two processes or for the alignment and search for matching sequences of two data series. The selected applications of the introduced techniques to various kind of data demonstrate their ability. Analysis of recurrence plots can be adopted to the specific problem and thus opens a wide field of potential applications.
Regarding the quantification of recurrence plots, chaos-chaos transitions can be found in heart rate variability data before the onset of life threatening cardiac arrhythmias. This may be of importance for the therapy of such cardiac arrhythmias. The quantification of recurrence plots allows to study transitions in brain during cognitive experiments on the base of single trials. Traditionally, for the finding of these transitions the averaging of a collection of single trials is needed.
Using cross recurrence plots, the existence of an El Niño/Southern Oscillation-like oscillation is traced in northwestern Argentina 34,000 yrs. ago. In further applications to geological data, cross recurrence plots are used for time scale alignment of different borehole data and for dating a geological profile with a reference data set. Additional examples from molecular biology and speech recognition emphasize the suitability of cross recurrence plots.
N. Marwan, J. Kurths:
Cross Recurrence Plots and Their Applications, In: Mathematical Physics Research at the Cutting Edge, Eds.: C. V. Benton, Nova Science Publishers, Hauppauge, ISBN: 1-59033-939-8, 101–139 (2004). » Abstract
Cross recurrence plots are a new tool for the nonlinear data analysis. They exhibit characteristic structures which can be used for the study of differences between two processes or for the alignment and search for matching sequences of two data series, even in the case when cross-correlation techniques fails or when the data are nonstationary. Selected applications of the introduced techniques to various kind of data demonstrate their potential.
N. Marwan, J. Kurths, P. Saparin, J. S. Thomsen:
A New Quantitative Approach for Measuring Changes of 3D Structures in Trabecular Bone, In: Proc. 3rd European Congress "Achievements in Space Medicine into Healthcare Practice and Industry", Berlin, 315–323 (2005). » Abstract
A novel approach which is based on 3D complexity measures was developed in order to quantify the spatial geometrical properties of trabecular bone. These non-destructive measures are able to evaluate different aspects of the organization and complexity of the architecture of trabecular bone, such as complexity of its surface, node complexity, or trabecular bone surface curvature. Their application to 3D μCT images of human proximal tibiae of various osteoporotic stages illustrates the abilities of these measures. The outcome of the bone architecture evaluation by the complexity measures was compared with and validated by the results provided by traditional 2D static histomorphometry. Finally, it can be concluded that this new approach, which was originally designed for quantification of microgravity induced bone loss can be directly applied for diagnosing pathological changes in bone structure in patients as well as to monitor the progress of medical treatment regimens.
N. Marwan, P. Saparin, J. S. Thomsen, J. Kurths:
An Innovative Approach for the Assessment of 3D Structures in Trabecular Bone, Journal of Gravitational Physiology, 12(1), 127–128 (2005). » Abstract
A series of new structural measures of complexity were introduced in order to quantify the micro-architecture of trabecular bone from 3D micro Computed Tomography (μCT) data sets. The application of these measures on μCT data acquired from proximal tibia and lumbar vertebra illustrates their ability to quantify structures in trabecular bone.
N. Marwan, J. Kurths:
Line structures in recurrence plots, Physics Letters A, 336(4–5), 349–357 (2005). DOI:10.1016/j.physleta.2004.12.056 » Abstract recommended work
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the phase-space trajectory. This provides us a better understanding of the structures occurring in recurrence plots. The relationship between the time-scales and line structures are of practical importance in cross recurrence plots. Using this relationship within cross recurrence plots, the time-scales of differently sampled or time-transformed measurements can be adjusted. An application to geophysical measurements illustrates the capability of this method for the adjustment of time-scales in different measurements.
N. Marwan, P. Saparin, J. Kurths:
Generalisation of Recurrence Plot Analysis for Spatial Data, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2005), Brugge, Bruges, Belgium, 630–633 (2005). » Abstract
The method of recurrence plots and algorithms for their quantification are extended to analyse spatial data thus allowing to study recurrent structures in 2D images. To verify its capabilities, the method is tested on prototypical 2D models. Next, the developed approach is applied to assess the bone structure from CT images of human proximal tibia. It is found that the spatial structures in trabecular bone become more self-similar during the bone loss in osteoporosis.
N. Marwan, P. Saparin, J. Kurths, W. Gowin:
3D measures of complexity for the assessment of complex trabecular bone structures, Rapporti ISTISAN – Proceedings of the International meeting "Complexity in the living: a problem-oriented approach", Rome, 2004, 05/20, 53–58 (2005). » Abstract
(Introduction:) For the assessment of bone stage (e.g. regarding different osteoporotic stages), usually the bone mineral density (BMD) is measured. However, this measurement does not contain any information about the structures inside the bone (Figure 1). Recent work emphasized the importance of analysing the structural changes of trabecular bone (1, 2). Different approaches for the study of trabecular bone were successfully introduced for 2D image analysis, as measures of complexity based on symbolic dynamics. The new available 3D bone images (CT-data) challenge the development of new 3D measures of complexity, which are able to assess structural changes in trabecular bone. We consider here new developments of 3D measures based on spatial correlation and geometrical properties: Moran's I Index and Shape Index. Histomorphometrical measures are used for comparison with the "golden standard" of investigation of trabecular bone.
N. Marwan, P. Saparin, J. Kurths:
Measures of complexity for 3D image analysis of trabecular bone, European Physical Journal – Special Topics, 143(1), 109–116 (2007). DOI:10.1140/epjst/e2007-00078-x » Abstract
Based on fractal properties and spatial auto-correlation, the measures of complexity lacunarity, Moran's I and Geary's C index are defined for 3D image analysis. Their abilities to investigate translational invariance, characteristic length scales, spatial correlation and shapes of 3D micro-structures are demonstrated on proto-typical examples. Finally, using these measures of complexity, 3D images of trabecular bone are analysed. The main findings are that the complexity of the trabecular structure decreases and the plate-like shapes of the trabeculae change to mainly rod-like shapes during bone loss. These results and the proposed measures could have a great impact for medicine and for space exploration.
N. Marwan, J. Kurths, P. Saparin:
Generalised Recurrence Plot Analysis for Spatial Data, Physics Letters A, 360(4–5), 545–551 (2007). DOI:10.1016/j.physleta.2006.08.058 » Abstract
Recurrence plot based methods are highly efficient and widely accepted tools for the investigation of time series or one-dimensional data. We present an extension of the recurrence plots and their quantifications in order to study recurrent structures in higher-dimensional spatial data. The capability of this extension is illustrated on prototypical 2D models. Next, the tested and proved approach is applied to assess the bone structure from CT images of human proximal tibia. We find that the spatial structures in trabecular bone become more recurrent during the bone loss in osteoporosis.
N. Marwan, M. C. Romano, M. Thiel, J. Kurths:
Recurrence Plots for the Analysis of Complex Systems, Physics Reports, 438(5–6), 237–329 (2007). DOI:10.1016/j.physrep.2006.11.001 » Abstract recommended work
Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis called recurrence plot was introduced in the late 1980's. This report is a comprehensive overview covering recurrence based methods and their applications with an emphasis on recent developments. After a brief outline of the theory of recurrences, the basic idea of the recurrence plot with its variations is presented. This includes the quantification of recurrence plots, like the recurrence quantification analysis, which is highly effective to detect, e. g., transitions in the dynamics of systems from time series. A main point is how to link recurrences to dynamical invariants and unstable periodic orbits. This and further evidence suggest that recurrences contain all relevant information about a system's behaviour. As the respective phase spaces of two systems change due to coupling, recurrence plots allow studying and quantifying their interaction. This fact also provides us with a sensitive tool for the study of synchronisation of complex systems. In the last part of the report several applications of recurrence plots in economy, physiology, neuroscience, earth sciences, astrophysics and engineering are shown. The aim of this work is to provide the readers with the know how for the application of recurrence plot based methods in their own field of research. We therefore detail the analysis of data and indicate possible difficulties and pitfalls.
N. Marwan, A. Facchini, M. Thiel, J. P. Zbilut, H. Kantz:
20 Years of Recurrence Plots: Perspectives for a Multi-purpose Tool of Nonlinear Data Analysis, European Physical Journal – Special Topics, 164(1), 1–2 (2008). DOI:10.1140/epjst/e2008-00828-2 » Abstract
Recurrence plot based methods are modern tools of nonlinear data analysis (especially time and spatial series) and have been proven to be very successful especially in analysing short, noisy and nonstationary data. The year, 2007, witnessed the 20th anniversary of the introduction of recurrence plots by J.-P. Eckmann in 1987. Since then, significant progress has been made in the areas of data analysis by means of recurrences. Recurrence Plots (RPs) have found applications in such diverse fields as life sciences, astrophysics, earth sciences, meteorology, biochemistry and finance. Theoretical results show how closely RPs are linked to dynamical invariants like entropies and dimensions. Moreover, they are successful tools for synchronisation analysis and advanced surrogate tests.
N. Marwan:
A Historical Review of Recurrence Plots, European Physical Journal – Special Topics, 164(1), 3–12 (2008). DOI:10.1140/epjst/e2008-00829-1 » Abstract
In the last two decades recurrence plots (RPs) were introduced in many different scientific disciplines. It turned out how powerful this method is. After introducing approaches of quantification of RPs and by the study of relationships between RPs and fundamental properties of dynamical systems, this method attracted even more attention. After 20 years of RPs it is time to summarise this development in a historical context.
N. Marwan, S. Schinkel, J. Kurths:
Significance for a recurrence based transition analysis, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA2008), Budapest, Hungary, 412–415 (2008). » Abstract
The recurrence of states is a fundamental behaviour of dynamical systems. As a modern technique of nonlinear data analysis, the recurrence plot visualises and analyses the recurrence structure. Its quantification (recurrence quantification analysis, RQA) allows us to detect transitions in the system's dynamics. In the last decade, RPs and RQA have become popular in many scientific fields. However, a sufficient significance test was not yet developed. We propose a statistical test for the RQA which is based on bootstrapping of the characteristic small scale structures in the recurrence plot. Using this test we can present confidence bounds for the detected transitions and, hence, get a more reliable result. We demonstrate the new technique on marine dust records from the Atlantic which were used to infer climate changes in Africa for the last 4 millennia.
N. Marwan, J. Kurths:
Comment on "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" by Rohde et al. [Physica D 237 (2008) 619–629], Physica D, 238(16), 1711–1715 (2009). DOI:10.1016/j.physd.2009.04.018 » Abstract
In the recent article "Stochastic analysis of recurrence plots with applications to the detection of deterministic signals" (Physica D 237 (2008) 619-629), Rohde et al. stated that the performance of RQA in order to detect deterministic signals would be below traditional and well-known detectors. However, we have concerns about such a general statement. Based on our own studies we cannot confirm their conclusions. Our findings suggest that the measures of complexity provided by RQA are useful detectors outperforming well-known traditional detectors, in particular for the detection of signals of complex systems, with phase differences or signals modified due to the measurement process.
Nevertheless, we have also clearly assert that an uncritical application of RQA may lead to wrong conclusions.
N. Marwan, J. Kurths, J. S. Thomsen, D. Felsenberg, P. Saparin:
Three dimensional quantification of structures in trabecular bone using measures of complexity, Physical Review E, 79(2), 021903 (2009). DOI:10.1103/PhysRevE.79.021903 » Abstract
The study of pathological changes of bone is an important task in diagnostic procedures of patients with metabolic bone diseases such as osteoporosis as well as in monitoring the health state of astronauts during long-term space flights. The recent availability of high resolution 3D imaging of bone challenges the development of data analysis techniques able to assess changes of the 3D micro-architecture of trabecular bone. We introduce a novel approach based on spatial geometrical properties and define new structural measures of complexity for 3D image analysis. These measures evaluate different aspects of organisation and complexity of 3D structures, such as complexity of its surface or shape variability. We apply these measures to 3D data acquired by high resolution micro-computed tomography (mCT) from human proximal tibiae and lumbar vertebrae at different stages of osteoporotic bone loss. The outcome is compared to the results of conventional static histomorphometry and exhibits clear relationships between the analysed geometrical features of trabecular bone and loss of bone density, but also indicate that the new measures reveal additional information about the structural composition of bone, which were not revealed by the static histomorphometry. Finally, we have studied the dependency of the developed measures of complexity on the spatial resolution of the mCT data sets.
N. Marwan, J. F. Donges, Y. Zou, R. V. Donner, J. Kurths:
Complex network approach for recurrence analysis of time series, Physics Letters A, 373(46), 4246–4254 (2009). DOI:10.1016/j.physleta.2009.09.042 » Abstract
We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. By using the logistic map, we illustrate the potential of these complex network measures for the detection of dynamical transitions. Finally, we apply the proposed approach to a marine palaeo-climate record and identify the subtle changes to the climate regime.
N. Marwan:
How to avoid potential pitfalls in recurrence plot based data analysis, International Journal of Bifurcation and Chaos, 21(4), 1003–1017 (2011). DOI:10.1142/S0218127411029008 » Abstract
Recurrence plots and recurrence quantification analysis have become popular in the last two decades. Recurrence based methods have on the one hand a deep foundation in the theory of dynamical systems and are on the other hand powerful tools for the investigation of a variety of problems. The increasing interest encompasses the growing risk of misuse and uncritical application of these methods. Therefore, we point out potential problems and pitfalls related to different aspects of the application of recurrence plots and recurrence quantification analysis.
N. Marwan, G. Beller, D. Felsenberg, P. Saparin, J. Kurths:
Quantifying changes in the spatial structure of trabecular bone, International Journal of Bifurcation and Chaos, 22(2), 1250027-1–12 (2012). DOI:10.1142/S0218127412500277 » Abstract
We apply recently introduced measures of complexity for the structural quantification of distal tibial bone. For the first time, we are able to investigate the temporal structural alteration of trabecular bone. Based on four patients, we show how the bone may alter due to temporal immobilization.
N. Marwan, S. Schinkel, J. Kurths:
Recurrence plots 25 years later – Gaining confidence in dynamical transitions, Europhysics Letters, 101, 20007 (2013). DOI:10.1209/0295-5075/101/20007 » Abstract
Recurrence-plot-based time series analysis is widely used to study changes and transitions in the dynamics of a system or temporal deviations from its overall dynamical regime. However, most studies do not discuss the significance of the detected variations in the recurrence quantification measures. In this letter we propose a novel method to add a confidence measure to the recurrence quantification analysis. We show how this approach can be used to study significant changes in dynamical systems due to a change in control parameters, chaos-order as well as chaos- chaos transitions. Finally we study and discuss climate transitions by analysing a marine proxy record for past sea surface temperature.
This paper is dedicated to the 25th anniversary of the introduction of recurrence plots
N. Marwan, M. A. Riley, A. Giuliani, C. L. Webber, Jr.:
Translational Recurrences – From Mathematical Theory to Real-World Applications, 103, Springer, Cham, ISBN: 978-3-319-09530-1, 230 (2014). DOI:10.1007/978-3-319-09531-8 » Abstract
This book features 13 papers presented at the Fifth International Symposium on Recurrence Plots, held August 2013 in Chicago, IL. It examines recent applications and developments in recurrence plots and recurrence quantification analysis (RQA) with special emphasis on biological and cognitive systems and the analysis of coupled systems using cross-recurrence methods.
Readers will discover new applications and insights into a range of systems provided by recurrence plot analysis and new theoretical and mathematical developments in recurrence plots. Recurrence plot based analysis is a powerful tool that operates on real-world complex systems that are nonlinear, non-stationary, noisy, of any statistical distribution, free of any particular model type, and not particularly long. Quantitative analyses promote the detection of system state changes, synchronized dynamical regimes, or classification of system states.
The book will be of interest to an interdisciplinary audience of recurrence plot users and researchers interested in time series analysis of complex systems in general.
N. Marwan, J. H. Feldhoff, R. V. Donner, J. F. Donges, J. Kurths:
Detection of coupling directions with intersystem recurrence networks, Proceedings of the International Symposium on Nonlinear Theory and its Applications (NOLTA 2012), 1, 231–234 (2014). DOI:10.15248/proc.1.231 » Abstract
We describe and apply a novel concept for inferring coupling directions between dynamical systems based on geometric properties in phase space reconstructed from time series. The approach combines the recently introduced techniques for (1) studying interacting networks and (2) construction of complex networks from time series by their recurrence structure: we extend the approach of cross-recurrence between two systems towards an inter-system recurrence network and apply measures for studying interacting networks on it. These measures allow us to examine the emergence of typical geometric signatures in the driven relative to those of the driving system and vice versa, and, therefore, reveal signs of coupling directions. We demonstrate this concept by investigating the coupling between parts of the Asian monsoon system as seen from a palaeo-climate perspective.
N. Marwan, C. L. Webber, Jr.:
Mathematical and Computational Foundations of Recurrence Quantifications, In: Recurrence Quantification Analysis – Theory and Best Practices, Eds.: C. L. Webber, Jr. and N. Marwan, Springer, Cham, 3–43 (2015). DOI:10.1007/978-3-319-07155-8_1 » Abstract
Real-world systems possess deterministic trajectories, phase singularities and noise. Dynamic trajectories have been studied in temporal and frequency domains, but these are linear approaches. Basic to the field of nonlinear dynamics is the representation of trajectories in phase space. A variety of nonlinear tools such as the Lyapunov exponent, Kolmogorov-Sinai entropy, correlation dimension, etc. have successfully characterized trajectories in phase space, provided the systems studied were stationary in time. Ubiquitous in nature, however, are systems that are nonlinear and nonstationary, existing in noisy environments all of which are assumption breaking to otherwise powerful linear tools. What has been unfolding over the last quarter of a century, however, is the timely discovery and practical demonstration that the recurrences of system trajectories in phase space can provide important clues to the system designs from which they derive. In this chapter we will introduce the basics of recurrence plots (RP) and their quantification analysis (RQA). We will begin by summarizing the concept of phase space reconstructions. Then we will provide the mathematical underpinnings of recurrence plots followed by the details of recurrence quantifications. Finally, we will discuss computational approaches that have been implemented to make recurrence strategies feasible and useful. As computers become faster and computer languages advance, younger generations of researchers will be stimulated and encouraged to capture nonlinear recurrence patterns and quantification in even better formats. This particular branch of nonlinear dynamics remains wide open for the definition of new recurrence variables and new applications untouched to date.
N. Marwan:
Recurrence Plot Techniques for the Investigation of Recurring Phenomena in the System Earth, Habilitation Thesis, ISBN: 978-3-00-064508-2 (2019). DOI:10.25932/publishup-44197 » Abstract
The habilitation deals with the numerical analysis of the recurrence properties of geological and climatic processes. The recurrence of states of dynamical processes can be analysed with recurrence plots and various recurrence quantification options. In the present work, the meaning of the structures and information contained in recurrence plots are examined and described. New developments have led to extensions that can be used to describe the recurring patterns in both space and time. Other important developments include recurrence plot-based approaches to identify abrupt changes in the system's dynamics, to detect and investigate external influences on the dynamics of a system, the couplings between different systems, as well as a combination of recurrence plots with the methodology of complex networks. Typical problems in geoscientific data analysis, such as irregular sampling and uncertainties, are tackled by specific modifications and additions. The development of a significance test allows the statistical evaluation of quantitative recurrence analysis, especially for the identification of dynamical transitions. Finally, an overview of typical pitfalls that can occur when applying recurrence-based methods is given and guidelines on how to avoid such pitfalls are discussed. In addition to the methodological aspects, the application potential especially for geoscientific research questions is discussed, such as the identification and analysis of transitions in past climates, the study of the influence of external factors to ecological or climatic systems, or the analysis of landuse dynamics based on remote sensing data.
N. Marwan, K. H. Kraemer:
Trends in recurrence analysis of dynamical systems, European Physical Journal – Special Topics, 232, 5–27 (2023). DOI:10.1140/epjs/s11734-022-00739-8 » Abstract
The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot-based data analysis and to widen its application potential. We will give a brief overview about important and innovative developments, such as computational improvements, alternative recurrence definitions (event-like, multiscale, heterogeneous, and spatio-temporal recurrences) and ideas for parameter selection, theoretical considerations of recurrence quantification measures, new recurrence quantifiers (e.g. for transition detection and causality detection), and correction schemes. New perspectives have recently been opened by combining recurrence plots with machine learning. We finally show open questions and perspectives for futures directions of methodical research.
N. Marwan:
Challenges and perspectives in recurrence analyses of event time series, Frontiers in Applied Mathematics and Statistics, 9, 1129105 (2023). DOI:10.3389/fams.2023.1129105 » Abstract
The analysis of event time series is in general challenging. Most time series analysis tools are limited for the analysis of this kind of data. Recurrence analysis, a powerful concept from nonlinear time series analysis, provides several opportunities to work with event data and even for the most challenging task of comparing event time series with continuous time series. Here, the basic concept is introduced, the challenges are discussed, and the future perspectives are summarised.
P. J. Menck, J. Heitzig, N. Marwan, J. Kurths:
How basin stability complements the linear-stability paradigm, Nature Physics, 9(2), 89–92 (2013). DOI:10.1038/nphys2516 » Abstract
The human brain, power grids, arrays of coupled lasers and the Amazon rainforest are all characterized by multistability. The likelihood that these systems will remain in the most desirable of their many stable states depends on their stability against significant perturbations, particularly in a state space populated by undesirable states. Here we claim that the traditional linearization-based approach to stability is too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of the basin of attraction. Basin stability is non-local, nonlinear and easily applicable, even to high-dimensional systems. It provides a long-sought-after explanation for the surprisingly regular topologies of neural networks and power grids, which have eluded theoretical description based solely on linear stability. We anticipate that basin stability will provide a powerful tool for complex systems studies, including the assessment of multistable climatic tipping elements.
N. Molkenthin, K. Rehfeld, N. Marwan, J. Kurths:
Networks from Flows – From Dynamics to Topology, Scientific Reports, 4(4119), 1–5 (2014). DOI:10.1038/srep04119 » Abstract
Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure. However the relationship between the underlying atmospheric or oceanic flow's dynamics and the estimated network measures have remained largely unclear. We bridge this crucial gap in a bottom-up approach and define a continuous analytical analogue of Pearson correlation networks for advection-diffusion dynamics on a background flow. Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks. The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness mark transition zones in the flow rather than, as previously thought, the propagation of dynamical information.
N. Molkenthin, H. Kutza, L. Tupikina, N. Marwan, J. F. Donges, U. Feudel, J. Kurths, R. V. Donner:
Edge anisotropy and the geometric perspective on flow networks, Chaos, 27, 035802 (2017). DOI:10.1063/1.4971785 » Abstract
Spatial networks have recently attracted great interest in various fields of research. While the traditional network-theoretic viewpoint is commonly restricted to their topological characteristics (often disregarding the existing spatial constraints), this work takes a geometric perspective, which considers vertices and edges as objects in a metric space and quantifies the corresponding spatial distribution and alignment. For this purpose, we introduce the concept of edge anisotropy and define a class of measures characterizing the spatial directedness of connections. Specifically, we demonstrate that the local anisotropy of edges incident to a given vertex provides useful information about the local geometry of geophysical flows based on networks constructed from spatio-temporal data, which is complementary to topological characteristics of the same flow networks. Taken both structural and geometric viewpoints together can thus assist the identification of underlying flow structures from observations of scalar variables.
Complex networks have recently attracted a rising interest for studying dynamical patterns in geophysical flows such as in the atmosphere and ocean. For this purpose, two distinct approaches have been proposed based on either (i) correlations between values of a certain variable measured at different parts of the flow domain (correlation-based flow networks) or (ii) transition probabilities of passively advected tracers between different parts of the fluid domain (Lagrangian flow networks). So far, the investigations on both types of flow networks have mostly addressed classical topological network characteristics, disregarding the fact that such networks are naturally embedded in some physical space and, hence, have intrinsic restrictions to their structural organization. In this paper, we introduce a novel concept to obtain a complementary geometric characterization of the local network patterns based on the anisotropy of edge orientations. For two prototypical model systems of different complexity, we demonstrate that the geometric characterization of correlation-based flow networks derived from scalar observables can actually provide additional and useful information contributing to the identification of the underlying flow patterns that are often not directly accessible. In this spirit, the proposed approach provides a prospective diagnostic tool for geophysical as well as technological flows.
D. Mukhin, A. Hannachi, T. Braun, N. Marwan:
Revealing recurrent regimes of mid-latitude atmospheric variability using novel machine learning method, Chaos, 32(11), 113105 (2022). DOI:10.1063/5.0109889 » Abstract Featured article: https://aip.scitation.org/doi/10.1063/10.0016505
The low-frequency variability of the extratropical atmosphere involves hemispheric-scale recurring, often persistent, states known as teleconnection patterns or regimes, which can have a profound impact on predictability on intra-seasonal and longer timescales. However, reliable data-driven identification and dynamical representation of such states are still challenging problems in modeling the dynamics of the atmosphere. We present a new method, which allows us both to detect recurring regimes of atmospheric variability and to obtain dynamical variables serving as an embedding for these regimes. The method combines two approaches from nonlinear data analysis: partitioning a network of recurrent states with studying its properties by the recurrence quantification analysis and the kernel principal component analysis. We apply the method to study teleconnection patterns in a quasi-geostrophical model of atmospheric circulation over the extratropical hemisphere as well as to reanalysis data of geopotential height anomalies in the mid-latitudes of the Northern Hemisphere atmosphere in the winter seasons from 1981 to the present. It is shown that the detected regimes as well as the obtained set of dynamical variables explain large-scale weather patterns, which are associated, in particular, with severe winters over Eurasia and North America. The method presented opens prospects for improving empirical modeling and long-term forecasting of large-scale atmospheric circulation regimes.
E. J. Ngamga, D. V. Senthilkumar, A. Prasad, P. Parmananda, N. Marwan, J. Kurths:
Distinguishing dynamics using recurrence-time statistics, Physical Review E, 85(2), 026217 (2012). DOI:10.1103/PhysRevE.85.026217 » Abstract
The probability densities of the mean recurrence time, which is the average time needed for a system to recur to a previously visited neighborhood, are investigated in various dynamical regimes and are found to be in agreement with those of the finite-time Lyapunov exponents. The important advantages of the former ones are that they are easy to estimate and that comparable short time series are sufficient. Asymmetric distributions with exponential tails are observed for intermittency and crisis-induced intermittency, while for typical chaos, the distribution has a Gaussian shape. Further, the shape of the distribution distinguishes intermittent strange nonchaotic attractors from those appearing through fractalization and tori collision mechanisms. Furthermore, statistics performed on the peaks in the frequency distribution of recurrence times unveil scaling behavior in agreement with that obtained from the spectral distribution function defined as the number of peaks in the Fourier spectrum greater than a predefined value. The results of the present recurrence statistics are of relevance in classifying different dynamics and providing important insights into the dynamics of a system when only one realization of this system is available. The practical use of this approach for experimental data is shown on experimental electrochemical time series.
T. Nocke, S. Buschmann, J. F. Donges, N. Marwan, H.-J. Schulz, C. Tominski:
Review: visual analytics of climate networks, Nonlinear Processes in Geophysics, 22, 545–570 (2015). DOI:10.5194/npg-22-545-2015 » Abstract
Network analysis has become an important approach in studying complex spatiotemporal behaviour within geophysical observation and simulation data. This new field produces increasing numbers of large geo-referenced networks to be analysed. Particular focus lies currently on the network analysis of the complex statistical interrelationship structure within climatological fields. The standard procedure for such network analyses is the extraction of network measures in combination with static standard visualisation methods. Existing interactive visualisation methods and tools for geo-referenced network exploration are often either not known to the analyst or their potential is not fully exploited. To fill this gap, we illustrate how interactive visual analytics methods in combination with geovisualisation can be tailored for visual climate network investigation. Therefore, the paper provides a problem analysis relating the multiple visualisation challenges to a survey undertaken with network analysts from the research fields of climate and complex systems science. Then, as an overview for the interested practitioner, we review the state-of-the-art in climate network visualisation and provide an overview of existing tools. As a further contribution, we introduce the visual network analytics tools CGV and GTX, providing tailored solutions for climate network analysis, including alternative geographic projections, edge bundling, and 3-D network support. Using these tools, the paper illustrates the application potentials of visual analytics for climate networks based on several use cases including examples from global, regional, and multi-layered climate networks.
I. Ozken, D. Eroglu, T. Stemler, N. Marwan, G. B. Bagci, J. Kurths:
Transformation-cost time-series method for analyzing irregularly sampled data, Physical Review E, 91, 062911 (2015). DOI:10.1103/PhysRevE.91.062911 » Abstract
Irregular sampling of data sets is one of the challenges often encountered in time-series analysis, since traditional methods cannot be applied and the frequently used interpolation approach can corrupt the data and bias the subsequence analysis. Here we present the TrAnsformation-Cost Time-Series (TACTS) method, which allows us to analyze irregularly sampled data sets without degenerating the quality of the data set. Instead of using interpolation we consider time-series segments and determine how close they are to each other by determining the cost needed to transform one segment into the following one. Using a limited set of operations – with associated costs – to transform the time series segments, we determine a new time series, that is our transformation-cost time series. This cost time series is regularly sampled and can be analyzed using standard methods. While our main interest is the analysis of paleoclimate data, we develop our method using numerical examples like the logistic map and the R?ssler oscillator. The numerical data allows us to test the stability of our method against noise and for different irregular samplings. In addition we provide guidance on how to choose the associated costs based on the time series at hand. The usefulness of the TACTS method is demonstrated using speleothem data from the Secret Cave in Borneo that is a good proxy for paleoclimatic variability in the monsoon activity around the maritime continent.
I. Ozken, D. Eroglu, S. F. M. Breitenbach, N. Marwan, L. Tan, U. Tirnakli, J. Kurths:
Recurrence plot analysis of irregularly sampled data, Physical Review E, 98, 052215 (2018). DOI:10.1103/PhysRevE.98.052215 » Abstract
Irregularly sampled time series usually require data preprocessing before a desired time-series analysis can be applied. We propose an approach for distance measuring of pairs of data points which is directly applicable to irregularly sampled time series. In order to apply recurrence plot analysis to irregularly sampled time series, we use this approach and detect regime transitions in prototypical models and for an application from palaeoclimatatology. This approach might be useful for any method that is based on distance measuring, e.g., correlation sum or Lyapunov exponent estimation.
R. Pánis, K. Adámek, N. Marwan:
Averaged recurrence quantification analysis – Method omitting the recurrence threshold choice, European Physical Journal – Special Topics, 232, 47–56 (2023). DOI:10.1140/epjs/s11734-022-00686-4 » Abstract
Recurrence quantification analysis (RQA) is a well established method of nonlinear data analysis. In this work, we present a new strategy for an almost parameter-free RQA. The approach finally omits the choice of the threshold parameter by calculating the RQA measures for a range of thresholds (in fact recurrence rates). Specifically, we test the ability of the RQA measure determinism, to sort data with respect to their signal to noise ratios. We consider a periodic signal, simple chaotic logistic equation, and Lorenz system in the tested data set with different and even very small signal-to-noise ratios of lengths 102,103,104, and 105. To make the calculations possible, a new effective algorithm was developed for streamlining of the numerical operations on graphics processing unit (GPU).
A. M. T. Ramos, A. Builes-Jaramillo, G. Poveda, B. Goswami, E. E. N. Macau, J. Kurths, N. Marwan:
Recurrence measure of conditional dependence and applications, Physical Review E, 95, 052206 (2017). DOI:10.1103/PhysRevE.95.052206 » Abstract
Identifying causal relations from observational data sets has posed great challenges in data-driven causality inference studies. One of the successful approaches to detect direct coupling in the information theory framework is transfer entropy. However, the core of entropy-based tools lies on the probability estimation of the underlying variables. Here we propose a data-driven approach for causality inference that incorporates recurrence plot features into the framework of information theory. We define it as the recurrence measure of conditional dependence (RMCD), and we present some applications. The RMCD quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the possible driver and present of the potentially driven, excepting the contribution of the contemporaneous past of the driven variable. Finally, it can unveil the time scale of the influence of the sea-surface temperature of the Pacific Ocean on the precipitation in the Amazonia during recent major droughts.
T. Rawald, M. Sips, N. Marwan, D. Dransch:
Fast Computation of Recurrences in Long Time Series, In: Translational Recurrences – From Mathematical Theory to Real-World Applications, 103, Eds.: N. Marwan and M. A. Riley and A. Giuliani and C. L. Webber, Jr., Springer, Cham, 17–29 (2014). DOI:10.1007/978-3-319-09531-8_2 » Abstract
We present an approach to recurrence quantification analysis (RQA) that allows to process very long time series fast. To do so, it utilizes the paradigm Divide and Recombine. We divide the underlying matrix of a recurrence plot (RP) into submatrices. The processing of the sub matrices is distributed across multiple graphics processing unit (GPU) devices. GPU devices perform RQA computations very fast since they match the problem very well. The individual results of the sub matrices are recombined into a global RQA solution. To address the specific challenges of subdividing the recurrence matrix, we introduce means of synchronization as well as additional data structures. Outperforming existing implementations dramatically, our GPU implementation of RQA processes time series consisting of N ∼ 1,000,000 data points in about 5 min.
T. Rawald, M. Sips, N. Marwan, U. Leser:
Massively Parallel Analysis of Similarity Matrices on Heterogeneous Hardware, Proceedings of the EDBT/ICDT Joint Conference 2015, 56–62 (2015). http://ceur-ws.org/Vol-1330/#paper-11 » Abstract
We conduct a study that investigates the performance characteristics of a set of parallel implementations of the recurrence quantication analysis (RQA) using OpenCL. Being an important tool in climate impact and medical research, a central aspect of RQA is the construction of a binary matrix that captures the similarities of multi-dimensional vectors. Based on this matrix, quantitative measures are derived. Starting with a baseline implementation, we diversify its properties along four dimensions: the representation of input data, the materialisation of the similarity matrix, the representation of similarity values and the recycling of intermediate results. We evaluate the performance of ve implementations by varying the input parameter assignments, the hardware platform employed for execution and the default OpenCL compiler optimisations status. We come to the conclusion that the performance of conducting RQA highly depends on the selected implementation as well as the combination of these variables under investigation. Differences in runtime of up to one order of magnitude are observed, emphasising the importance of performance studies as presented here.
T. Rawald, M. Sips, N. Marwan:
PyRQA – Conducting Recurrence Quantification Analysis on Very Long Time Series Efficiently, Computers & Geosciences, 104, 101–108 (2017). DOI:10.1016/j.cageo.2016.11.016 » Abstract
PyRQA is a software package that efficiently conducts recurrence quantification analysis (RQA) on time series consisting of more than one million data points. RQA is a method from non-linear time series analysis that quantifies the recurrent behaviour of systems. Existing implementations to RQA are not capable of analysing such very long time series at all or require large amounts of time to calculate the quantitative measures. PyRQA overcomes their limitations by conducting the RQA computations in a highly parallel manner. Building on the OpenCL framework, PyRQA leverages the computing capabilities of a variety of parallel hardware architectures, such as GPUs. The underlying computing approach partitions the RQA computations and enables to employ multiple compute devices at the same time. The goal of this publication is to demonstrate the features and the runtime efficiency of PyRQA. For this purpose we employ a real-world example, comparing the dynamics of two climatological time series, and a synthetic example, reducing the runtime regarding the analysis of a series consisting of over one million data points from almost eight hours using state-of-the-art RQA software to roughly 69 seconds using PyRQA.
A. Rheinwalt, N. Marwan, J. Kurths, P. Werner, F.-W. Gerstengarbe:
Boundary effects in network measures of spatially embedded networks, Europhysics Letters, 100(2), 28002 (2012). DOI:10.1209/0295-5075/100/28002 » Abstract
In studies of spatially confined networks, network measures can lead to false conclusions since most measures are boundary affected. This is especially the case if boundaries are artificial and not inherent in the underlying system of interest (e.g., borders of countries). An analytical estimation of boundary effects is not trivial due to the complexity of measures. The straightforward approach we propose here is to use surrogate networks that provide estimates of boundary effects in graph statistics. This is achieved by using spatially embedded random networks as surrogates that have approximately the same link probability as a function of spatial link lengths. The potential of our approach is demonstrated for an analysis of spatial patterns in characteristics of regional climate networks. As an example networks derived from daily rainfall data and restricted to the region of Germany are considered.
M. Riedl, N. Marwan, J. Kurths:
Multiscale recurrence analysis of spatio-temporal data, Chaos, 25, 123111 (2015). DOI:10.1063/1.4937164 » Abstract
The description and analysis of spatio-temporal dynamics is a crucial task in many scientific disciplines. In this work, we propose a method which uses the mapogram as a similarity measure between spatially distributed data instances at different time points. The resulting similarity values of the pairwise comparison are used to construct a recurrence plot in order to benefit from established tools of recurrence quantification analysis and recurrence network analysis. In contrast to other recurrence tools for this purpose, the mapogram approach allows the specific focus on different spatial scales that can be used in a multi-scale analysis of spatio-temporal dynamics. We illustrate this approach by application on mixed dynamics, such as traveling parallel wave fronts with additive noise, as well as more complicate examples, pseudo-random numbers and coupled map lattices with a semi-logistic mapping rule. Especially the complicate examples show the usefulness of the multi-scale consideration in order to take spatial pattern of different scales and with different rhythms into account. So, this mapogram approach promises new insights in problems of climatology, ecology, or medicine.
M. Riedl, N. Marwan, J. Kurths:
Visualizing driving forces of spatially extended systems using the recurrence plot framework, European Physical Journal – Special Topics, 226(15), 3273–3285 (2017). DOI:10.1140/epjst/e2016-60376-9 » Abstract
The increasing availability of highly resolved spatio-temporal data leads to new opportunities as well as challenges in many scientific disciplines such as climatology, ecology or epidemiology. This allows more detailed insights into the investigated spatially extended systems. However, this development needs advanced techniques of data analysis which go beyond standard linear tools since the more precise consideration often reveals nonlinear phenomena, for example threshold effects. One of these tools is the recurrence plot approach which has been successfully applied to the description of complex systems. Using this technique's power of visualization, we propose the analysis of the local minima of the underlying distance matrix in order to display driving forces of spatially extended systems. The potential of this novel idea is demonstrated by the analysis of the chlorophyll concentration and the sea surface temperature in the Southern California Bight. We are able not only to confirm the influence of El Niño events on the phytoplankton growth in this region but also to confirm two discussed regime shifts in the California current system. This new finding underlines the power of the proposed approach and promises new insights into other complex systems.
M. Riedl, N. Marwan, J. Kurths:
Extended generalized recurrence plot quantification of complex circular patterns, European Physical Journal B, 90(58), 1–9 (2017). DOI:10.1140/epjb/e2017-70560-7 » Abstract
The generalized recurrence plot is a modern tool for quantification of complex spatial patterns. Its application spans the analysis of trabecular bone structures, Turing patterns, turbulent spatial plankton patterns, and fractals. Determinism is a central measure in this framework quantifying the level of regularity of spatial structures. We show by basic examples of fully regular patterns of different symmetries that this measure underestimates the orderliness of circular patterns resulting from rotational symmetries. We overcome this crucial problem by checking additional structural elements of the generalized recurrence plot which is demonstrated with the examples. Furthermore, we show the potential of the extended quantity of determinism applying it to more irregular circular patterns which are generated by the complex Ginzburg-Landau-equation and which can be often observed in real spatially extended dynamical systems. So, we are able to reconstruct the main separations of the system's parameter space analyzing single snapshots of the real part only, in contrast to the use of the original quantity. This ability of the proposed method promises also an improved description of other systems with complicated spatio-temporal dynamics typically occurring in fluid dynamics, climatology, biology, ecology, social sciences, etc.
J. Runge, J. Heitzig, N. Marwan, J. Kurths:
Quantifying causal coupling strength: A lag-specific measure for multivariate time series related to transfer entropy, Physical Review E, 86, 061121 (2012). DOI:10.1103/PhysRevE.86.061121 » Abstract
While it is an important problem to identify the existence of causal associations between two components of a multivariate time series, a topic addressed in Runge, Heitzig, Petoukhov, and Kurths [ Phys. Rev. Lett. 108 258701 (2012)], it is even more important to assess the strength of their association in a meaningful way. In the present article we focus on the problem of defining a meaningful coupling strength using information-theoretic measures and demonstrate the shortcomings of the well-known mutual information and transfer entropy. Instead, we propose a certain time-delayed conditional mutual information, the momentary information transfer (MIT), as a lag-specific measure of association that is general, causal, reflects a well interpretable notion of coupling strength, and is practically computable. Rooted in information theory, MIT is general in that it does not assume a certain model class underlying the process that generates the time series. As discussed in a previous paper [ Phys. Rev. Lett. 108 258701 (2012)], the general framework of graphical models makes MIT causal in that it gives a nonzero value only to lagged components that are not independent conditional on the remaining process. Further, graphical models admit a low-dimensional formulation of conditions, which is important for a reliable estimation of conditional mutual information and, thus, makes MIT practically computable. MIT is based on the fundamental concept of source entropy, which we utilize to yield a notion of coupling strength that is, compared to mutual information and transfer entropy, well interpretable in that, for many cases, it solely depends on the interaction of the two components at a certain lag. In particular, MIT is, thus, in many cases able to exclude the misleading influence of autodependency within a process in an information-theoretic way. We formalize and prove this idea analytically and numerically for a general class of nonlinear stochastic processes and illustrate the potential of MIT on climatological data.
J. Runge, V. Petoukhov, J. F. Donges, J. Hlinka, N. Jajcay, M. Vejmelka, D. Hartman, N. Marwan, M. Paluš, J. Kurths:
Identifying causal gateways and mediators in complex spatio-temporal systems, Nature Communications, 6, 8502 (2015). DOI:10.1038/ncomms9502 » Abstract
Identifying regions important for spreading and mediating perturbations is crucial to assess the susceptibilities of spatio-temporal complex systems such as the Earth's climate to volcanic eruptions, extreme events or geoengineering. Here a data-driven approach is introduced based on a dimension reduction, causal reconstruction, and novel network measures based on causal effect theory that go beyond standard complex network tools by distinguishing direct from indirect pathways. Applied to a data set of atmospheric dynamics, the method identifies several strongly uplifting regions acting as major gateways of perturbations spreading in the atmosphere. Additionally, the method provides a stricter statistical approach to pathways of atmospheric teleconnections, yielding insights into the Pacific-Indian Ocean interaction relevant for monsoonal dynamics. Also for neuroscience or power grids, the novel causal interaction perspective provides a complementary approach to simulations or experiments for understanding the functioning of complex spatio-temporal systems with potential applications in increasing their resilience to shocks or extreme events.
S. Schinkel, O. Dimigen, N. Marwan:
Selection of recurrence threshold for signal detection, European Physical Journal – Special Topics, 164(1), 45–53 (2008). DOI:10.1140/epjst/e2008-00833-5 » Abstract
Over the last years recurrence plots (RPs) and recurrence quantification analysis (RQA) have become quite popular in various branches of science. One key problem in applying RPs and RQA is the selection of suitable parameters for the data under investigation. Whereas various well-established methods for the selection of embedding parameters exists, the question of choosing an appropriate threshold has not yet been answered satisfactorily. The recommendations found in the literature are rather rules of thumb than actual guidelines. In this paper we address the issue of threshold selection in RP/RQA. The core criterion for choosing a threshold is the power in signal detection that threshold yields. We will validate our approach by applying it to model as well as real-life data.
S. Schinkel, N. Marwan, O. Dimigen, J. Kurths:
Confidence bounds of recurrence-based complexity measures, Physics Letters A, 373(26), 2245–2250 (2009). DOI:10.1016/j.physleta.2009.04.045 » Abstract
In the recent past, recurrence quantification analysis (RQA) has gained an increasing interest in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. It is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data. In the present Letter we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We study the applicability of the suggested method with model and real-life data.
T. Schmah, N. Marwan, J. S. Thomsen, P. Saparin:
Long range node-strut analysis of trabecular bone microarchitecture, Medical Physics, 38(9), 5003–5011 (2011). DOI:10.1118/1.3622600 » Abstract
Purpose: We present a new morphometric measure of trabecular bone microarchitecture, called mean node strength (NdStr), which is part of a newly developed approach called long range node-strut analysis. Our general aim is to describe and quantify the apparent "latticelike" microarchitecture of the trabecular bone network.
Methods: Similar in some ways to the topological node-strut analysis introduced by Garrahan et al. [J. Microsc. 142, 341—349 (1986)], our method is distinguished by an emphasis on long-range trabecular connectivity. Thus, while the topological classification of a pixel (after skeletonization) as a node, strut, or terminus, can be determined from the 3–×–3 neighborhood of that pixel, our method, which does not involve skeletonization, takes into account a much larger neighborhood. In addition, rather than giving a discrete classification of each pixel as a node, strut, or terminus, our method produces a continuous variable, node strength. The node strength is averaged over a region of interest to produce the mean node strength of the region.
Results: We have applied our long range node-strut analysis to a set of 26 high-resolution peripheral quantitative computed tomography (pQCT) axial images of human proximal tibiae acquired 17 mm below the tibial plateau. We found that NdStr has a strong positive correlation with trabecular volumetric bone mineral density (BMD). After an exponential transformation, we obtain a Pearson's correlation coefficient of r–=–0.97. Qualitative comparison of images with similar BMD but with very different NdStr values suggests that the latter measure has successfully quantified the prevalence of the "latticelike" microarchitecture apparent in the image. Moreover, we found a strong correlation (r–=–0.62) between NdStr and the conventional node-terminus ratio (Nd/Tm) of Garrahan et al. The Nd/Tm ratios were computed using traditional histomorphometry performed on bone biopsies obtained at the same location as the pQCT scans.
Conclusions: The newly introduced morphometric measure allows a quantitative assessment of the long-range connectivity of trabecular bone. One advantage of this method is that it is based on pQCT images that can be obtained noninvasively from patients, i.e., without having to obtain a bone biopsy from the patient.
A. Schultz, Y. Zou, N. Marwan, M. T. Turvey:
Local Minima-based Recurrence Plots for Continuous Dynamical Systems, International Journal of Bifurcation and Chaos, 21(4), 1065–1075 (2011). DOI:10.1142/S0218127411029045 » Abstract
A major issue in using recurrence plots to study dynamical systems is the choice of neighborhood size for thresholding the distance matrix that creates the plot. This is particularly important for continuous dynamical systems as temporal correlations of the trajectory might provide redundant information for recurrence analysis. We suggest an alternative procedure for creating recurrence plots (RPs) using the local minima provided by the distance profile, which more or less corresponds to the recurrence information in the orthogonal direction. The local minima-based thresholding yields a clean RP of minimized line thickness, that is compared to the plot obtained by standard radius-based method for thresholding. New definitions of line segments arising from the local minima-based method are outlined, which yield consistent results with those derived from standard methods. Our preliminary comparison suggests that the newly introduced thresholding technique is more sensitive to small changes in a system's dynamics. We demonstrate our method by the chaotic Lorenz system without the loss of generality.
D. Schultz, S. Spiegel, N. Marwan, S. Albayrak:
Approximation of diagonal line based measures in recurrence quantification analysis, Physics Letters A, 379(14–15), 997–1011 (2015). DOI:10.1016/j.physleta.2015.01.033 » Abstract
Given a trajectory of length N, recurrence quantification analysis (RQA) traditionally operates on the recurrence plot, whose calculation requires quadratic time and space (O(N2)O(N2)), leading to expensive computations and high memory usage for large N. However, if the similarity threshold ε is zero, we show that the recurrence rate (RR), the determinism (DET) and other diagonal line based RQA-measures can be obtained algorithmically taking O(Nlog(N))O(Nlog(N)) time and O(N)O(N) space. Furthermore, for the case of ε>0 we propose approximations to the RQA-measures that are computable with same complexity. Simulations with autoregressive systems, the logistic map and a Lorenz attractor suggest that the approximation error is small if the dimension of the trajectory and the minimum diagonal line length are small. When applying the approximate determinism to the problem of detecting dynamical transitions we observe that it performs as well as the exact determinism measure.
M. Sips, C. Witt, T. Rawald, N. Marwan:
Torwards Visual Analytics for the Exploration of Large Sets of Time Series, In: Recurrence Plots and Their Quantifications: Expanding Horizons, Eds.: C. L. Webber, Jr. and C. Ioana and N. Marwan, Springer, Cham, 3–17 (2016). DOI:10.1007/978-3-319-29922-8_1 » Abstract
In this chapter, we discuss the scientific question whether the clustering of time series based on RQA measures leads to an interpretable clustering structure when analyzed by human experts. We are not aware of studies answering this scientific question. Answering it is the crucial first step in the development of a Visual Analytics approach that support users to explore large sets of time series.
D. A. Smirnov, N. Marwan, S. F. M. Breitenbach, F. Lechleitner, J. Kurths:
Coping with dating errors in causality estimation, Europhysics Letters, 117(1), 10004 (2017). DOI:10.1209/0295-5075/117/10004 » Abstract
We consider the problem of estimating causal influences between observed processes from time series possibly corrupted by errors in the time variable (dating errors) which are typical in palaeoclimatology, planetary science and astrophysics. "Causality ratio" based on the Wiener-Granger causality is proposed and studied for a paradigmatic class of model systems to reveal conditions under which it correctly indicates directionality of unidirectional coupling. It is argued that in the case of a priori known directionality, the causality ratio allows a characterization of dating errors and observational noise. Finally, we apply the developed approach to palaeoclimatic data and quantify the influence of solar activity on tropical Atlantic climate dynamics over the last two millennia. A stronger solar influence in the first millennium A.D. is inferred. The results also suggest a dating error of about 20 years in the solar proxy time series over the same period.
S. Spiegel, D. Schultz, N. Marwan:
Approximate Recurrence Quantification Analysis (aRQA) in Code of Best Practice, In: Recurrence Plots and Their Quantifications: Expanding Horizons, Eds.: C. L. Webber, Jr. and C. Ioana and N. Marwan, Springer, Cham, 113–136 (2016). DOI:10.1007/978-3-319-29922-8_6 » Abstract
Recurrence quantification analysis (RQA) is a well-known tool for studying nonlinear behavior of dynamical systems, e.g. for finding transitions in climate data or classifying reading abilities. But the construction of a recurrence plot and the subsequent quantification of its small and large scale structures is computational demanding, especially for long time series or data streams with high sample rate. One way to reduce the time and space complexity of RQA are approximations, which are sufficient for many data analysis tasks, although they do not guarantee exact solutions. In earlier work, we proposed how to approximate diagonal line based RQA measures and showed how these approximations perform in finding transitions for difference equations. The present work aims at extending these approximations to vertical line based RQA measures and investigating the runtime/accuracy of our approximate RQA measures on real-life climate data. Our empirical evaluation shows that the proposed approximate RQA measures achieve tremendous speedups without losing much of the accuracy.
C. L. Webber, Jr., N. Marwan, A. Facchini, A. Giuliani:
Simpler methods do it better: Success of Recurrence Quantification Analysis as a general purpose data analysis tool, Physics Letters A, 373, 3753–3756 (2009). DOI:10.1016/j.physleta.2009.08.052 » Abstract
Over the last decade, Recurrence Quantification Analysis (RQA) has become a new standard tool in the toolbox of nonlinear methodologies. In this Letter we trace the history and utility of this powerful tool and cite some common applications. RQA continues to wend its way into numerous and diverse fields of study.
C. L. Webber, Jr., N. Marwan:
Recurrence Quantification Analysis – Theory and Best Practices, Springer, Cham, ISBN: 978-3-319-07154-1, 421 (2015). DOI:10.1007/978-3-319-07155-8 » Abstract
The analysis of recurrences in dynamical systems by using recurrence plots and their quantification is still an emerging field. Over the past decades recurrence plots have proven to be valuable data visualization and analysis tools in the theoretical study of complex, time-varying dynamical systems as well as in various applications in biology, neuroscience, kinesiology, psychology, physiology, engineering, physics, geosciences, linguistics, finance, economics, and other disciplines.
This multi-authored book intends to comprehensively introduce and showcase recent advances as well as established best practices concerning both theoretical and practical aspects of recurrence plot based analysis. Edited and authored by leading researcher in the field, the various chapters address an interdisciplinary readership, ranging from theoretical physicists to application-oriented scientists in all data-providing disciplines.
C. L. Webber, Jr., C. Ioana, N. Marwan:
Recurrence Plots and Their Quantifications: Expanding Horizons, Springer, Cham, ISBN: 978-3-319-29921-1, 381 (2016). DOI:10.1007/978-3-319-29922-8 » Abstract
The chapters in this book originate from the research work and contributions presented at the Sixth International Symposium on Recurrence Plots held in Grenoble, France in June 2015. Scientists from numerous disciplines gathered to exchange knowledge on recent applications and developments in recurrence plots and recurrence quantification analysis. This meeting was remarkable because of the obvious expansion of recurrence strategies (theory) and applications (practice) into ever-broadening fields of science.
It discusses real-world systems from various fields, including mathematics, strange attractors, applied physics, physiology, medicine, environmental and earth sciences, as well as psychology and linguistics. Even readers not actively researching any of these particular systems will benefit from discovering how other scientists are finding practical non-linear solutions to specific problems.The book is of interest to an interdisciplinary audience of recurrence plot users and researchers interested in time series analysis in particular, and in complex systems in general.
D. Wendi, N. Marwan:
Extended recurrence plot and quantification for noisy continuous dynamical systems, Chaos, 28(8), 085722 (2018). DOI:10.1063/1.5025485 » Abstract
One main challenge in constructing a reliable recurrence plot (RP) and, hence, its quantification [recurrence quantification analysis (RQA)] of a continuous dynamical system is the induced noise that is commonly found in observation time series. This induced noise is known to cause disrupted and deviated diagonal lines despite the known deterministic features and, hence, biases the diagonal line based RQA measures and can lead to misleading conclusions. Although discontinuous lines can be further connected by increasing the recurrence threshold, such an approach triggers thick lines in the plot. However, thick lines also influence the RQA measures by artificially increasing the number of diagonals and the length of vertical lines [e.g., Determinism (DET) and Laminarity (LAM) become artificially higher]. To take on this challenge, an extended RQA approach for accounting disrupted and deviated diagonal lines is proposed. The approach uses the concept of a sliding diagonal window with minimal window size that tolerates the mentioned deviated lines and also considers a specified minimal lag between points as connected. This is meant to derive a similar determinism indicator for noisy signal where conventional RQA fails to capture. Additionally, an extended local minima approach to construct RP is also proposed to further reduce artificial block structures and vertical lines that potentially increase the associated RQA like LAM. The methodology and applicability of the extended local minima approach and DET equivalent measure are presented and discussed, respectively.
D. Wendi, N. Marwan, B. Merz:
In search of determinism-sensitive region to avoid artefacts in recurrence plots, International Journal of Bifurcation and Chaos, 28(1), 1850007 (2018). DOI:10.1142/S0218127418500074 » Abstract
As an effort to reduce parameter uncertainties in constructing recurrence plots, and in particular to avoid potential artefacts, this paper presents a technique to derive artefact-safe region of parameter sets. This technique exploits both deterministic (incl. chaos) and stochastic signal characteristics of recurrence quantification (i.e. diagonal structures). It is useful when the evaluated signal is known to be deterministic. This study focuses on the recurrence plot generated from the reconstructed phase space in order to represent many real application scenarios when not all variables to describe a system are available (data scarcity). The technique involves random shuffling of the original signal to destroy its original deterministic characteristics. Its purpose is to evaluate whether the determinism values of the original and the shuffled signal remain closely together, and therefore suggesting that the recurrence plot might comprise artefacts. The use of such determinism-sensitive region shall be accompanied by standard embedding optimization approaches, e.g. using indices like false nearest neighbor and mutual information, to result in a more reliable recurrence plot parameterization.
J. P. Zbilut, N. Marwan:
The Wiener-Khinchin theorem and recurrence quantification, Physics Letters A, 372(44), 6622–6626 (2008). DOI:10.1016/j.physleta.2008.09.027 » Abstract
The Wiener-Khinchin theorem states that the power spectrum is the Fourier transform of the autocovariance function. One form of the autocovariance function can be obtained through recurrence quantification. We show that the advantage of defining the autocorrelation function with recurrences can demonstrate higher dimensional dynamics.
Y. Zou, R. V. Donner, J. F. Donges, N. Marwan, J. Kurths:
Identifying complex periodic windows in continuous-time dynamical systems using recurrence-based methods, Chaos, 20(4), 043130 (2010). DOI:10.1063/1.3523304 » Abstract
The identification of complex periodic windows in the two-dimensional parameter space of certain dynamical systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic windows can be easily made based on the maximum Lyapunov exponent of the system, this remains a challenging task for continuous systems, especially if only short time series are available (e.g., in case of experimental data). In this work, we demonstrate that nonlinear measures based on recurrence plots obtained from such trajectories provide a practicable alternative for numerically detecting shrimps. Traditional diagonal line-based measures of recurrence quantification analysis as well as measures from complex network theory are shown to allow an excellent classification of periodic and chaotic behavior in parameter space. Using the well-studied Rössler system as a benchmark example, we find that the average path length and the clustering coefficient of the resulting recurrence networks are particularly powerful discriminatory statistics for the identification of complex periodic windows.
Y. Zou, M. C. Romano, M. Thiel, N. Marwan, J. Kurths:
Inferring Indirect Coupling by Means of Recurrences, International Journal of Bifurcation and Chaos, 21(4), 1099–1111 (2011). DOI:10.1142/S0218127411029033 » Abstract
The identification of the coupling direction from measured time series taking place in a group of interacting components is an important challenge for many experimental studies. We propose here a method to uncover the coupling configuration by means of recurrence properties. The approach hinges on a generalization of conditional probability of recurrence, which was originally introduced to detect and quantify even weak coupling directions between two interacting systems, to the case of multivariate time series where indirect interactions might be present. We test our method by an example of three coupled Lorenz systems. Our results confirm that the proposed method has much potential to identify indirect coupling, which is very relevant for experimental time series analysis.
Y. Zou, J. Heitzig, R. V. Donner, J. F. Donges, J. D. Farmer, R. Meucci, S. Euzzor, N. Marwan, J. Kurths:
Power-laws in recurrence networks from dynamical systems, Europhysics Letters, 98, 48001 (2012). DOI:10.1209/0295-5075/98/48001 » Abstract
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in classical mechanics. In this letter, we demonstrate that recurrence networks obtained from various deterministic model systems as well as experimental data naturally display power-law degree distributions with scaling exponents γ that can be derived exclusively from the systems' invariant densities. For one-dimensional maps, we show analytically that γ is not related to the fractal dimension. For continuous systems, we find two distinct types of behaviour: power-laws with an exponent γ depending on a suitable notion of local dimension, and such with fixed γ=1.
Y. Zou, R. V. Donner, N. Marwan, J. F. Donges, J. Kurths:
Complex network approaches to nonlinear time series analysis, Physics Reports, 787, 1–97 (2019). DOI:10.1016/j.physrep.2018.10.005 » Abstract
In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series. While both nonlinear time series analysis and complex network theory are widely considered to be established fields of complex systems sciences with strong links to nonlinear dynamics and statistical physics, the thorough combination of both approaches has become an active field of nonlinear time series analysis, which has allowed addressing fundamental questions regarding the structural organization of nonlinear dynamics as well as the successful treatment of a variety of applications from a broad range of disciplines. In this report, we provide an in-depth review of existing approaches of time series networks, covering their methodological foundations, interpretation and practical considerations with an emphasis on recent developments. After a brief outline of the state-of-the-art of nonlinear time series analysis and the theory of complex networks, we focus on three main network approaches, namely, phase space based recurrence networks, visibility graphs and Markov chain based transition networks, all of which have made their way from abstract concepts to widely used methodologies. These three concepts, as well as several variants thereof will be discussed in great detail regarding their specific properties, potentials and limitations. More importantly, we emphasize which fundamental new insights complex network approaches bring into the field of nonlinear time series analysis. In addition, we summarize examples from the wide range of recent applications of these methods, covering rather diverse fields like climatology, fluid dynamics, neurophysiology, engineering and economics, and demonstrating the great potentials of time series networks for tackling real-world contemporary scientific problems. The overall aim of this report is to provide the readers with the knowledge how the complex network approaches can be applied to their own field of real-world time series analysis.
Y. Zou, R. V. Donner, N. Marwan, J. F. Donges, J. Kurths:
Nonlinear time series analysis by means of complex networks, Scientia Sinica: Physica, Mechanica & Astronomica, 50(1), 010509 (2020). DOI:10.1360/SSPMA-2019-0136 » Abstract
In the last decade, there has been a growing body of literature addressing the utilization of complex network methods for the characterization of dynamical systems based on time series, which has allowed addressing fundamental questions regarding the structural organization of nonlinear dynamics as well as the successful treatment of a variety of applications from a broad range of disciplines. In this report, we provide an in-depth review of three existing approaches of recurrence networks, visibility graphs and transition networks, covering their methodological foundations, interpretation and the recent developments. The overall aim of this report is to provide the Chinese readers with the future directions of time series network approaches and how the complex network approaches can be applied to their own field of real-world time series analysis.
Speleo
S. Breitenbach, N. Marwan:
Das Weißnasensyndrom (White-Nose Syndrome) bei Fledermäusen – ein Problem nicht nur für reisende Höhlenforscher, Mitteilungen des Verbandes der deutschen Höhlen- und Karstforscher, 56(2), 36–38 (2010). » Abstract
White-Nose Syndrome rapidly spreads amongst US bat populations since 2006. Up to now, more than 1 million bats died caused by the fungus species Geomyces destructans. Cavers and naturalists must help to prevent the dissemination of pathogens as intensively as technically possible. Because of the potential hazards, all cavers with international and/or transcontinental action radius working in bat caves should clean, better even disinfect their clothing and equipment very intensively before and after caving. They also should document and report bat findings with White-Nose symptoms to experts without taking samples by themselves.
S. F. M. Breitenbach, N. Marwan:
Acquisition and analysis of greyscale data from stalagmites using ImageJ software, Cave and Karst Science, 50(2), 69–78 (2023). https://bcra.org.uk/pub/candks/index.html?j=149 » Abstract
To reconstruct past climate conditions from speleothems, palaeoclimate researchers utilize a variety of advanced but expensive methods, including various stable isotope ratios and trace element analyses. Greyscale changes can be related to growth and matrix density variations in stalagmites, which in turn are probably dependent on drip rate and dripwater Ca-supersaturation, among other factors. Greyscale analysis is particularly helpful where annual layers are found in stalagmites as the greyscale data can be used to build layer-counting chronologies, similar to varve counting in lacustrine and marine sediments. Greyscale information can further be used as a valuable palaeoclimate proxy. Depending on stalagmite growth rate a spatial resolution of less than five micrometres can be obtained, which might translate to seasonal temporal resolution. Here, we present a low-cost and high-resolution method for acquisition and analysis of greyscale data from speleothems by means of the free ImageJ software. We show how greyscale data can be acquired and visualized and describe how proxy time series can be constructed and proxy record uncertainties estimated using numerical methods. Finally, we provide an example for the application of ImageJ for greyscale analysis on stalagmites. The methodology outlined might be of use to geoscientists working on laminated sediments, and speleothems in particular.
N. Marwan:
Das Karstgebiet um den Boljšoj Thač, , Verein Umwelt & Bildung e. V. Gosen (1997). » Abstract
The limestone massif of Boljsoj Thac is an alpine to tempered karst landscape with its typical karst phenomena. In this report these phenomena are documented and discussed. Most of them are old and the explorated caves are usually not active. The enormous importance of karst drainage have to be considered to all decisions about a use. Absence of vegetation leads to a irreversible full erosion of the soil and to a quick destruction of limestone. Furthermore it will lead to a higher surface drainage of the karst area and for that reason floods in far away areas are possible. Caves are complex living areals and cultural heritage which are very worth to protect. Therefore an expansion of Kavkazskij Zapovednik (national park) to save the area around Boljsoj Thac is very recommendable.
N. Marwan:
Besucherströme in der Räuberhöhle (Hrensko, Böhmische Schweiz, CZ), Mitteilungen des Verbandes der deutschen Höhlen- und Karstforscher(4), 128–129 (1997).
N. Marwan:
Kalzit-Sinter in Sandsteinhöhlen des Elbsandsteingebirges, Die Höhle, 51(1), 19-20 (2000). » Abstract
Das Elbsandsteingebirge (Böhmische und Sächsische Schweiz, Tschechische Republik und Deutschland) ist weithin bekannt durch seine imposanten Felsformationen aus Sandstein und als Kletter-Eldorado für Jung und Alt. Weniger bekannt sind dessen Höhlen. Sie haben sich im Sandstein durch Kristallisationsverwitterung (der Elbsandstein ist u. a. gekennzeichnet von einer allmählichen Verwitterung durch Alaunsalzausblühungen), Kluftöffnungen oder Felsstürze gebildet und sind relativ kleine Höhlen. Die tiefsten sind Klufthöhlen und erreichen über 40 Meter Tiefe …
N. Marwan:
Cave Blisters in der Oberländerhöhle (M3)/ Découverte de blisters dans la Oberländerhöhle (M3), Stalactite, 50(2), 103–105 (2000). » Abstract
In der Oberländerhöhle im Sägistal (Berner Oberland, Schweiz) wurden blasenartige Gebilde gefunden, sogenannte Cave Blisters. Eine Analyse mittels Röntgendiffraktometrie ergab eine Zusammensetzung der Kruste der Blasen aus Gips und Calcit. In den Blasen wurde eine lockere Mischung aus Calcit und Gips festgestellt. Der Gips entsteht durch die Verwitterung des Pyrits im Kalkstein. Die Auskristallisation des Gipses zerstört die den Kalkstein bedeckende Sinterschicht und verursacht Krusten aus einem Gemisch von Gips und Verwitterungsresten aus Kalzit. Die Blasen könnten durch die ringförmigen Ausblühungen des Gipses entstehen.
N. Marwan:
Das Karstgebiet um den Bol'shoj Tkha'c, Mitteilungen des Verbandes der deutschen Höhlen- und Karstforscher, 47(3), 61–71 (2001). » Abstract
In preparation of declaration of nature reserve, an extensive biological and geological examination of the limestone massif of Bol'shoj Tkha'c (Kaukasus, Russia) was carried out by the association Umwelt und Bildung e. V. (Gosen, Germany) in summer 1997. The limestone massif is an alpine to tempered karst landscape with typical karst phenomena. Most of these phenomena are ancient and the explored caves are usually not active.
N. Marwan:
Das Karstgebiet des Bol'šoj Thač, Abhandlungen und Berichte des Naturkundemuseums Görlitz, 79(1), 55-84 (2007). » Abstract
The limestone massif of Bolsoj Thac is an alpine to tempered karst landscape with its typical karst phenomena. These phenomena reveal a distinct fossil character. The most caves are fossil, small and decorated with dripstone. They are relicts of large extended cave systems which were eroded. Caves are complex living areals and may contain archaeological finds of cultural importance. The enormous sensibility of karst areas and their importance for the nature and archaeology have to be considered to all decisions about any use.
N. Marwan, O. Y. Krickaya, A. A. Ostapenko:
The Karst of the Bol'shoj Tkhach (NW Caucasus, Russia), In: Berliner Höhlenkundliche Berichte, 25, SCB, Berlin, 60 pages (2008). » Abstract
The Bol'shoj Tkhach massif in the NW Caucasus is a small but beautiful karst area of sub-alpine/ alpine characteristic. It comprises several, rather different caves. Visitable caves are mostly fossil, with large calcite crystals (decimetres range) or thick layers of moonmilk. Moreover, some vertical caves and siphons await future exploration and promise much unexplored continuation. Cave exploration in this area was done mainly by local speleologists. Additional research was done by various external speleologists and international expeditions. This report summarises the current knowledge about the karst area of the Bol'shoj Tkhach based on the work done so far by the several data sources available.
N. Marwan:
Das Höhlengebiet Sägistal – 20 Jahre ISAAK-Forschung, Stalactite, 60(1), 12–17 (2010). » Abstract
Die Internationale Speläologische Arbeitsgruppe Alpiner Karst (ISAAK) hat ihre Ursprünge in der Erforschung des Sägistales. 1988 trafen sich Vertreter des Vereins Höhlenforschung im Berner Oberland (VHBO) und der Höhlenforschergruppen Lethmate und Karlsruhe erstmals, um das gerade erst wiederentdeckte Sägistal zu bearbeiten.
Das Sägistal ist ein abgelegenes Hochtal der Berner Voralpen mit typischen Karsterscheinungen. Die Erforschung der Höhlen begann in den 1970er Jahren durch die SGH Interlaken und wird seit 1988 durch die Internationale Speläologische Arbeitsgruppe Alpiner Karst (ISAAK) unter Beteiligung zahlreicher Höhlenforschergruppen aus verschiedenen Ländern organisiert. Mittlerweile wurden über 400 Höhlen gefunden mit dem "Oberländer-Chessiloch"-System als größtem Objekt (2346 m Länge, −488 m Tiefe).
N. Marwan:
Der digitale Sägistal-Kataster, Stalactite, 73(1), 24–33 (2023). » Abstract
Der Höhlenkataster zum Gebiet Sägistal (Berner Oberland, Schweiz) beinhaltet fast 460 Höhlen. Er entpricht einer einfachen, skriptbasierten Lösung, die dynamisch aus den einzelnen Katasterblättern (die in Form von HTML-Seiten vorliegen) erzeugt wird. Dies erlaubt schnelle Änderungen am Inhalt mit einem beliebigen Texteditor und somit einen langjährigen und nachhaltigen Betrieb.
T. Wagner, N. Marwan, G. Pfalzer:
Wasserstandsmessung im Tiefen Stollen/ Nothweiler, Mitteilungen der Höhlenforschergruppe Karlsruhe, 29, 1–58 (2020). » Abstract
U.S. Patent No. 10895382, System and method for optimizing passive control of oscillatory instabilities in turbulent flows, January 19, 2021, Patent (PDF)
EU Patent No. 3 759 393, Verfahren zur Minimierung thermoakustischer Instabilitäten einer Gasturbine, March 30, 2022, Patent (PDF)
Indian Patent No. 484841, System and method for optimizing passive control of oscillatory instabilities in turbulent flows, December 18, 2023, Patent Certificate (PDF)
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><2024
N. Marwan:
Recurrence analysis for studying environmental dynamics,
CEIGRAM Seminario de Investigación, Universidad Politécnica de Madrid,
Madrid (Spain),
Feb 26, 2024,
Talk.
» Abstract
Recurrence is a ubiquitous and fundamental feature of many real-world processes, manifesting itself at all temporal and spatial scales. Examples include repeating patterns in a landscape, cycles of glaciation, epochs of geomagnetic polarity, alternating sedimentary layers, seasonal vegetation changes, and predator-prey cycles. The study of recurrence properties (such as frequency analysis) can provide profound insights into environmental processes. A rather novel approach to the study of recurrence is the so-called recurrence plot and its quantification, which is rooted in the theory of dynamical systems. In this talk I will present the basic concept and the main extensions applicable to different research questions, covering the identification of regime shifts in environmental dynamics, spatio-temporal recurrences for classification of land-use dynamics, and bivariate extensions for synchronisation/coupling analysis of palaeoclimate observations. I will also cover innovative extensions for handling event-like data and address methodological and numerical challenges.
N. Marwan, T. Braun, K. H. Kraemer, A. Banerjee, D. Eroglu:
New Concepts for Quantifying Extreme Events Data,
(Virtual) Workshop on Complex Networks and Application to Fluid Mechanics, IIT Madras,
Chennai (India)/ Online,
Feb 19, 2024,
Talk.
» Abstract
Many processes manifest as observable extreme events in a variety of contexts, such as sudden changes in fluid flow in pipes, abrupt pressure gradients in combustion, extreme wind events, or large-scale natural hazards (earthquakes, floods, etc). Many prominent research questions, such as correlation and synchronisation analysis, or power spectrum estimation of discrete data, pose considerable challenges to linear tools. In my talk I present approaches that utilise a specific similarity measure for discrete data and the method of recurrence plots for different applications in the field of highly discrete and extreme events data. I illustrate their potential for detecting synchronisation between signals of discrete extreme events and continuous signals and for estimating power spectra of spiky signals.
Using complex network analysis, we present a novel classification of the tropics based on the distinct spatio-temporal characteristics of the intertropical convergence zone (ITCZ). The ITCZ is a narrow tropical belt of high convection driven by the differential solar heating and convergence of moisture-laden trade winds from the Northern and Southern hemispheres. The ITCZ is popularly referred to as the ascending branch of the Hadley cell. As the moisture-laden winds convect to higher altitudes, condensation leads to the formation of deep clouds, resulting in high cloudiness and precipitation. In a seasonal cycle, the ITCZ migrates in the meridional direction towards the warming hemisphere. The ITCZ is a critical feature in tropical meteorology since it contributes towards maintaining the Earth-Atmosphere energy balance, and its position and structure are closely linked to the equatorial energy balance. The ITCZ has a significant impact on the society since several monsoon systems are dependent on the precipitation in the ITCZ. However, cloudiness and precipitation exhibit high variability across the ITCZ because they are sensitive to the local geophysical and meteorological phenomena. Furthermore, the extent of migration of the ITCZ and its structure are not uniform across the tropics. Therefore, classifying tropics based on the spatio-temporal dynamics of the ITCZ is a challenging yet necessary task as it will not only further our understanding of the underlying physics but also provide a basis for improving the performance of reduced-order and weather forecast models. The ITCZ dynamics is sensitive to phenomena occurring in decadal temporal scales, which enhances the complexity of the problem at hand. Complex networks are an appropriate and efficient approach to address the problem of classifying such complex systems and analysing their behavior across multiple temporal scales.
We construct functional complex networks where geographical locations are nodes that are connected if the dynamics of ITCZ at these locations are correlated. We use outgoing longwave radiation (OLR), which is a good proxy for cloudiness, to quantify the ITCZ dynamics. We consider the spatio-temporal OLR data from fifth-generation ECMWF atmospheric reanalysis dataset. The spatial resolution of the data is 1o×1o, and the temporal resolution is three hours. The correlation is estimated using Pearson’s correlation coefficient, and links are established when the correlation is higher than a predefined threshold and is statistically significant. To classify the tropics we perform community detection on the network, where communities refer to a group of nodes that are densely connected. While connections between nodes of different communities are sparse.
Community detection on the network reveals seven dominant communities corresponding to distinct annual ITCZ dynamics primarily driven by local topography, air-land interactions, and air-sea interactions. We perform community detection using Louvain’s method, which is a modularity-optimizing algorithm. The two largest communities in the network represent regions affected by the ITCZ during the northern and southern hemisphere summer seasons. These communities have dense connections, which is indicative of coherent ITCZ dynamics. The central and eastern equatorial Pacific and equatorial Atlantic oceans emerge as a separate community since these regions are affected by equatorial upwelling that suppresses convection along the equator and pushes the ITCZ northward. The Indian ocean community is found to have relatively sparse connectivity revealing that the ITCZ dynamics is incoherent and inhomogeneous over this region.
Through our analysis, we provide a simple and concise representation of the complex spatio-temporal dynamics of the ITCZ. The community structure and long-range teleconnections resulting from the spatio-temporal dynamics of the ITCZ indicate that it plays a crucial role in stabilizing the climate system. Long-range connections and localized community structure imply that perturbations from local geophysical processes are not localized but rather dispersed swiftly and uniformly across the globe. These characteristics enable suppressing prolonged hazardous weather conditions and ensure stability in the climate system.
We construct the proposed network using thirty years of data from 1991-2021. Therefore, the network is a robust benchmark to study the effects of phenomena occurring in global scales such as El-Niño Southern oscillations and also in decadal time-scales such as anthropogenic climate change. We explore the evolution of the network structure in decadal time scales and observe that connectivity in the network improves with time especially in the past two decades. We observe that certain regions in tropics where connectivity has improved corresponds to those where the ITCZ has strengthened and spatially enlarged because of increase in the surface temperature possibly due to anthropogenic factors.
A wide range of geoprocesses manifest as observable events in a variety of contexts, including shifts in palaeoclimate regimes, evolutionary milestones, tectonic activities, and more. Many prominent research questions, such as synchronisation analysis or power spectrum estimation of discrete data, pose considerable challenges to linear tools. We present recent advances using a specific similarity measure for discrete data and the method of recurrence plots for different applications in the field of highly discrete event data. We illustrate their potential for palaeoclimate studies, particularly in detecting synchronisation between signals of discrete extreme events and continuous signals, estimating power spectra of spiky signals, and analysing data with irregular sampling.
Challenges addressed: power spectra of highly discrete data, synchronisation analysis between different types of data (e.g., extreme events and continuous data)
Open challenges: sparsity of events, parameter selection, application for synchronisation analysis
><2023
C. E. Nava-Fernandez, T. Braun, C. Pederson, B. R. S. Fox, A. Hartland, O. Kwiecien, S. N. Höpker, S. M. Bernasconi, M. Jaggi, J. C. Hellstrom, F. Gázquez, A. French, N. Marwan, A. Immenhauser, S. F. M. Breitenbach:
Seasonally resolved stalagmite reveals ENSO variability during the Mid-Holocene,
AGU 2023 Fall Neeting,
San Francisco (USA),
Dec 12, 2023,
Poster.
» Abstract
Given the urgent need to develop action plans to mitigate the impacts of global climate change, robust and accurate climate forecast models are crucial. These models rely on time series of past climate variability, especially from key regions like the tropical Pacific, where El Niño-Southern Oscillation (ENSO) events originate. ENSO dynamics significantly impact global weather pattern and more detailed empirical information can improve understanding involved processes and teleconnections. Here we present a new seasonally to sub-decadally resolved multiproxy record of past ENSO dynamics covering the Mid-Holocene (6.4-5.4 ka BP). We interpret geochemical signals of a stalagmite from Niue Island in the tropical South Pacific where local infiltration is strongly modulated by seasonal shifts of the South Pacific Convergence Zone (SPCZ) and ENSO variations.
Stalagmite C-132 is predominantly calcitic and shows laminae couplets of ca. 400 µm thickness. Annual layer couplets are formed as dark dense and pale porous calcite layers during the dry and wet season respectively. The age model of the stalagmite is constrained with 8 U/Th dates and layer counting. The record covers 1019 years between 6.4 ka and 5.4 ka. Stable oxygen and carbon isotopes, LA-ICP-MS multi-element profiles and greyscale data reveal local infiltration and regional hydrological changes that are linked to seasonal SPCZ shifts and multi-annual ENSO dynamics. Principal component analyses supports the seasonal nature of the growth layers. Wavelet spectrum analyses shows significant periodicities between 2-8 years, indicating an active ENSO system during the Mid-Holocene. A seasonality record based on the greyscale data allows us to investigate the interactions of seasonal cycle and ENSO dynamics during the Mid-Holocene, and associated changes in dry and wet season intensity and storminess.
N. Marwan:
Recurrence Quantification Analysis for Understanding Complex Systems,
CTCS Seminar series, IIT Madras,
Chennai (India)/ Online,
Sep 25, 2023,
Talk invited.
» Abstract
Recurrence is a ubiquitous and fundamental feature in many real world processes. It is present at many scales in time and space, such as in celestial mechanics, alternating sediment layers, thermoacoustic oscillation, cardiac variability, and numerous other contexts. The study of recurrence properties (such as frequency analysis) can provide deeper insights into the underlying dynamical processes in general. A rather novel approach for the study of recurrences is the recurrence plot and its quantification, rooted in the theory of dynamical systems. In this lecture, the basic concepts and the major extensions applicable to various research questions are introduced and demonstrated. Discussed examples include the temporal change of recurrence properties for identification of regime shifts, for classification, and bivariate extensions for synchronization/coupling analysis.
N. Marwan:
Palaeoclimate research in RD4,
PIK cross-RD Paleoclimate and Long-term Climate Evolution Seminar,
Potsdam (Germany),
Sep 18, 2023,
Talk.
J. Wassmer, B. Merz, N. Marwan:
Resilience of transportation networks to road failures,
Dynamics Days Europe 2023,
Naples (Italy),
Sep 6, 2023,
Talk.
» Abstract
Damages to road infrastructure can cause disruptions in transportation and obstruct access to emergency services. With anthropogenic climate change increasing the probability of extreme weather events, such as floods or storms, the necessity for a resilient road infrastructure gets even more important.
In our research, we identify roads that play a crucial role in maintaining the stability of the transportation network. To this end we develop a framework that is built on a traffic-based centrality measure that can be interpreted as individual vehicles traversing the network. We then apply methods from the field of energy system analysis to derive the significance of each road segment in the network. The benefit of this framework is that it exclusively depends on openly accessible data sources such as OpenStreetMap, hence making it straightforward to apply and extend to different geographic locations of varying scales. As a case study, we analyse the impacts of the Ahr valley flood in Germany in 2021.
Our findings indicate that the road damages caused by the flood event led to an increase in the severity and frequency of congestion, result- ing in a deterioration of the accessibility to emergency services for a substantial portion of the population. We are further able to identify roads that are especially important for the resilience of the network. A broader application of our methodology can help decision makers to reduce costs by prioritising mitigation and reconstruction measures on important road sections.
Swarms of robots can be thought of as networks, using the tools from telecommunications and network theory. A recent study designed sets of aquatic swarms of robots to clean the canals of Venice, interacting with computers on gondolas. The interaction between gondolas is one level higher in the hierarchy of communication. In other studies, pairwise communications between the robots in robotic swarms have been modeled via quantum computing. Here, we first apply quantum computing to the telecommunication-based model of an aquatic robotic swarm. Then, we use multilayer networks to model interactions within the overall system. Finally, we apply quantum entanglement to formalize the interaction and synchronization between "heads" of the swarms, that is, between gondolas.
Our study can foster new strategies for search-and-rescue robotic-swarm missions, strengthening the connection between different areas of research in physics and engineering.
A. Syta, J. Czarnigowski, P. Jaklinski, N. Marwan:
Recurrence quantificators in misfire detection in a small aircraft engine,
10th International Symposium on Recurrence Plots,
Tsukuba (Japan),
Aug 28, 2023,
Talk.
» Abstract
Misfires in internal combustion engines are a frequent issue where one or more cylinders fail to ignite properly, leading to decreased engine performance, increased fuel consumption, and potential damage. A piston failure can be perceived as a disturbance in the repeatability of the engine operation, leading to changes in non-linearity. To study the dynamic behavior of the system over time, Recurrence Quantification Analysis (RQA) is employed in nonlinear time series analysis. The technique involves creating a recurrence plot (RP) from the time series data, which illustrates the temporal evolution of the system's states. RQA is capable of detecting changes in the system's behavior, such as transitions from regular to chaotic or from stable to unstable states. In the context of detecting piston failure, RQA can be used to identify patterns in the engine's vibration signals that are indicative of such failure. By placing sensors at different locations in the engine, vibrations can be recorded corresponding to separate engine states, including all cylinders working correctly and one of the cylinders being switched off, at various engine speeds. The RQA indices can then be used as non-linear features to classify the engine condition utilizing a linear model. Determining the RQA statistics on component signals with frequencies centered around the dominant ones increases the dimension of features and leads to higher accuracy in damage detection and identification of a cylinder with a misfire.
M. R. Sales, M. Mugnaine, J. D. Szezech Jr., R. L. Viana, I. L. Caldas, N. Marwan, J. Kurths:
Characterization of stickiness in quasi-integrable Hamiltonian systems by an entropy-based measure of the recurrence plots,
10th International Symposium on Recurrence Plots,
Tsukuba (Japan),
Aug 28, 2023,
Talk.
» Abstract
The stickiness effect is a fundamental feature of quasi-integrable Hamiltonian systems, characterized by the long time spend by a chaotic orbit when near enough a periodic island. We propose the use of an entropy-based measure of the recurrence plots (RPs), namely, the entropy of the distribution of the recurrence times (estimated from the RP), to characterize the dynamics of a typical quasi-integrable Hamiltonian system with coexisting regular and chaotic regions, the Chirikov-Taylor standard map. We show that the recurrence time entropy (RTE) is positively correlated to the largest Lyapunov exponent with a high correlation coefficient. We obtain a multi-modal distribution of the finite-time RTE and find that each mode corresponds to the motion around islands of different hierarchical levels.
B. G. Straiotto, N. Marwan, P. J. Seeley:
Exploring synchronisation in lower limb coordination in a rhythmic body movement: A quantitative analysis,
10th International Symposium on Recurrence Plots,
Tsukuba (Japan),
Aug 28, 2023,
Talk.
» Abstract
Studies of human movement often concern movement quality and that quality may be represented by the everyday term coordination. Research reports alternatively use terms such as correlation and synchronisation. We have developed a previous study of a martial arts movement pattern through study of synchronisation within and between the lower limbs. We explored synchronisation in taekwondo players who utilise repetitive backwards-forwards movements to mount attacks on their opponents and operate speedy retreats, movements that are developed in both training and competition. Eighteen players (nine elite and nine non-elite) performed backwards-forwards movements in a simulated training environment whilst their actions were recorded in detail via motion capture using multiple cameras. Recurrence analysis involved re-representing the time-dependent signals in multidimensional space and then characterising the revisits of a movement trajectory to different sub-regions of that space. The joint probability of recurrence index ($p_j$) was then calculated for centres of mass of limb segments (foot, shank, thigh) in relation to orthogonal movement coordinates (medio-lateral, anterior-posterior, vertical directions). Application of surrogation to the recurrence data indicated that derived $p_j$ values for elite and non-elite groups were deterministic in origin and not the result of data noise ($p < 0.01$). Interlimb pairwise segment relations yielded $p_j$ values in the range 0.23 to 0.29; intralimb relations in the range 0.24 to 0.40. Nonparametric statistical analysis combining Mann-Whitney and Kruskal-Wallis tests along with Bonferroni corrections directly indicated statistically significant differences between elite and non-elite groups for interlimb $p_j$ values and analogous differences for some comparisons for intralimb segment use ($0.05 > p > 0.01$). The potential of recurrence analysis for studies of limb segment synchronisation is revealed by this study. The method may be fruitfully extended in application not only to athletic movement but to transitions in coordination for general members of the public caused by ageing and pathology.
R. Pánis, K. Adámek, N. Marwan:
Averaged recurrence quantification analysis – Method omitting the recurrence threshold choice,
10th International Symposium on Recurrence Plots,
Tsukuba (Japan),
Aug 28, 2023,
Talk.
» Abstract
Recurrence quantification analysis (RQA) is a well established method of nonlinear data analysis. In this work we present a new strategy for an almost parameter-free RQA. The approach finally omits the choice of the threshold parameter by calculating the RQA measures for a range of thresholds (in fact recurrence rates). Specifically, we test the ability of the RQA measure determinism, to sort data with respect to their signal to noise ratios. We consider a periodic signal, simple chaotic logistic equation, and Lorenz system in thetested data set with different and even very small signal to noise ratios of lengths 102, 103, 104, and 105. To make the calculations possible a new effective algorithm was developed for streamlining of the numerical operations on Graphics Processing Unit (GPU).
N. Marwan, T. Braun, K. H. Kraemer, A. Banerjee, D. Eroglu:
Recurrence plots for analysing extreme events data,
10th International Symposium on Recurrence Plots,
Tsukuba (Japan),
Aug 28, 2023,
Talk.
» Abstract
The analysis of time series of extreme events is a challenging task. Many research questions, such as synchronisation analysis or power spectrum estimation, are challenging for linear tools. We demonstrate some recent extensions of the recurrence plot approach for various applications in the field of extreme events data. We demonstrate their potential for synchronisation analysis between signals of extreme events and signals with continuous and slower variations, for estimation of power spectra of spiky signals, and for analysing data with irregular sampling.
The estimation of power spectral density (PSD) of time series is an important task in many quantitative scientific disciplines. However, the estimation of PSD from discrete data, such as extreme event series is challenging. We present a novel approach for the estimation of a PSD of discrete data. Combining the edit distance metric with the Wiener-Khinchin theorem provides a simple yet powerful PSD analysis for discrete time series (e.g., extreme events). This method works directly with the event time series without interpolation or transformation to continuous data. We demonstrate the method's potential on some prototypical examples and on event sequences of atmospheric rivers (AR), narrow filaments of extensive water vapor transport in the lower troposphere. Considering the spatial-temporal event series of ARs over Europe, we investigate the presence of a seasonal cycle as well as periodicities in the multi-annual range for specific regions, likely related to the North-Atlantic Oscillation (NAO).
M. L. Fischer, V. Foerster, F. Schaebitz, N. Marwan, S. Kaboth-Bahr, W. Schwanghart, M. H. Trauth:
A pan-African spatiotemporal framework of the past one million years using advanced multi-record time-series analysis,
XXI INQUA Conference,
Rome (Italy),
Jul 19, 2023,
Poster.
» Abstract
For several decades, eastern Africa was considered the origin ofH. sapiens, documented by the oldest fossil finds from Omo Kibish (233±22 ka BP) and Herto (160–154 ka BP), from where the species was thought to have spread across the rest of the continent and beyond. Recent finds of human fossils and related stone tools in several parts of Africa between roughly 315–75 ka ago, i.e. Jebel Irhoud, southern Africa, Arabia, and eastern Africa initiated a lively discussion of a multiregional model of the origin and development of H. sapiens. The chronology and diversity of human fossils and archaeological remains, associated with a pan-African cultural patchwork, are underpinned by the availability of suitable and connected environments offering enough resources for our species to survive and reproduce. As new paleoanthropological research expands into poorly understood regions of Africa, the key to understanding emerging patterns of mobility and dispersal within and out of Africa is strongly linked to accurately reconstructed climate and environmental conditions in time and space. Here, we aim to create a spatiotemporal paleoclimatic framework for testing current hypotheses about a multiregional origin of our species. To do so, we collect and review suitable climate archives that cover the time since the Mid-Pleistocene Transition, the Mid-Bruhnes Event, and the late Pleistocene. Prerequisites for site selection are: (1) an age model without major gaps, (2) proxy data with a sufficient temporal resolution, precision, and accuracy, (3) a good understanding of the mechanisms that are represented by the proxy data, and (4) together they offer good geographical coverage of Africa's most important climates. We compare records using correlation analysis, such as windowed Spearman correlation, principal component analysis, fast Fourier transformation, and wavelet-based cross-spectral analysis. Furthermore, we analyze long-term trends, shifts, and transition types, that may have provided a catalyst for evolutionary changes, cultural innovation, and expansion/ migration, using e.g. breakfit regression, running Mann-Whitney and Ansari-Bradley test, and recurrence-based transition tests, such as recurrence quantification and recurrence networks. Here, we show the first results of our experiments.
J. Klose, D. Scholz, M. Weber, H. Vonhof, B. Plessen, S. Breitenbach, N. Marwan:
Timing and progression of Dansgaard-Oeschger events in Central Europe based on three precisely dated speleothems from Bleßberg Cave, Germany,
XXI INQUA Conference,
Rome (Italy),
Jul 19, 2023,
Poster.
» Abstract
Speleothems can be dated with unprecedented precision using U-series disequilibrium methods and provide numerous climate proxies, such as stable oxygen (δ18O) and carbon isotopes (δ13C) or trace elements, resulting in long, sometimes continuous climate proxy records. Therefore, speleothems have great potential for reconstruction of past climate variability during Marine Isotope Stage (MIS) 3 and precise determination of the timing and duration of Dansgaard-Oeschger (D/O) events. While first discovered in Greenland ice cores, various speleothem records around the globe provided clear evidence for the supra-regional character of the D/O events. However, MIS 3 speleothem records from Central Europe are very limited. Here we present three spleothem (flowstone) MIS 3 records from Bleßberg Cave, Germany.
All flowstones show episodic growth with distinctive, partially very thin (<2 mm) growth phases, interrupted by visible hiatuses consisting of detrital material. Precise and accurate 230Th/U dating of the individual growth phases is challenging due to potential detrital contamination from these layers. Combining different sampling and analytical techniques, we were able to date even the thinnest growth layers with very high precision, i.e., 2σ-age uncertainties of at most a few hundred years.
The timing of the growth phases aligns with several D/O events, which have not been recorded in other Central European speleothems yet. The δ18O and δ13C records of all three flowstones are highly correlated which suggests a dominant process influencing both isotope systems. Comparison with the Sr and Mg records provides evidence for a strong influence of Prior Calcite Precipitation (PCP) in the aquifer above and inside the cave on the stable isotope and trace element signals. In addition, all proxy records are interpreted as evidence for past changes in precipitation and vegetation density and document a clear trend from more humid climate during early MIS 3 (ca. 57 – 50 ka) to less humid conditions during mid and late MIS 3 (ca. 45 – 30 ka).
Our multi-proxy approach thus allows us not only to precisely determine the timing, duration, and progression of several D/O events, but also to deepen our general understanding of climate variability during MIS 3 in Central Europe.
V. Skiba, C. Spötl, M. Trüssel, A. Schröder-Ritzrau, B. Plessen, N. Frank, R. Eichstädter, R. Tjallingii, N. Marwan, X. Zhang, J. Fohlmeister:
High-elevation speleothems suggest close coupling between North Atlantic millennial-scale variability and Alpine glacier dynamics during Marine Isotope Stage 8,
XXI INQUA Conference,
Rome (Italy),
Jul 18, 2023,
Poster.
» Abstract
Processes triggering abrupt climate transitions during glacial periods are still not fully understood. Most research has focused on the last glacial cycle, limiting our test bed for studying the occurrence and absence of millennial-scale variability and, thus, our understanding of these large-scale reorganisations of the climate system under different background conditions.
Here, we present new stalagmite oxygen and carbon data from high-elevation caves in central Switzerland covering the period from 300 to 200 ka. We demonstrate that millennial-scale variability recorded by these speleothems is representative of Northern Hemisphere interstadial-stadial variability. We use isotope-enabled fully-coupled ocean-atmosphere model simulations to show that the δ18O value of meteoric precipitation was higher by 1 ‰ during interstadials compared to stadials. This agrees with interstadial-stadial amplitudes of the last glacial cycle recorded by stalagmites from other caves in the Alps and is likely the result of North Atlantic seawater δ18O millennial-scale variability.
We find that the effect of prior carbonate precipitation (PCP) is superimposed on the meteoric δ18O signal, amplifying the isotope signal captured by Alpine speleothems on interstadial-stadial timescales. We propose that PCP variability provides a new proxy for milllennial-scale dynamics of warm-based paleoglaciers above these caves.
B. Keenan, J. Collins, B. Aichner, F. Schenk, S. Engels, C. Lane, W. Hoek, I. Neugebauer, T. Grunwald, F. Ott, M. Slowinski, S. Wulf, B. Goswami, N. Marwan, A. Brauer, D. Sachse:
Atmospheric blocking as a stabiliser during abrupt climate change in eastern Europe during the Last Deglaciation,
XXI INQUA Conference,
Rome (Italy),
Jul 14, 2023,
Talk.
» Abstract
Abrupt climate change has occurred frequently in Earth history, most notably during the termination of major glaciations in the Quaternary. Changes occurred over decadal timescales and destabilised or transformed landscapes and ecosystems. We use the Younger Dryas as a natural experiment to better understand the regional propagation of abrupt change. We applied hydrogen isotope analyses (δD) of plant wax lipid biomarkers as indicators of hydrological change and moisture origin from five lake records across Central Europe, namely lakes Meerfelder Maar, Steisslingen, Hämelsee, and Rehwiese palaeolake in Germany, and Lake Czechowskie (Trzechowskie palaeolake) in Poland. Using recurrence analysis, a method to detect and classify time-series and characterise dynamical regime shifts (tipping points), we identify the transition from warm to cold states, or from the relatively warm Allerød to the cold Younger Dryas, and return to the Holocene warm state. Further, isotopic gradients from the Allerød, Younger Dryas and early Holocene are compared with modern gradients, revealing spatial differences in the timing of the onset of the Younger Dryas event, in the magnitude and variability of change as well as the structure of the Younger Dryas event. We show that the pattern of δD responses during the YD were not consistent geographically, and that variation at different locations suggests greater climatic stability and smaller degree of change in the east. These spatiotemporal patterns are compared with modelling results and infer that atmospheric blocking over the Fennoscandian Ice Sheet (FIS) was likely the main driver of spatiotemporal patterns, creating a sustained high-pressure system over Fennoscandia deflecting the flow of westerly winds. This blocking effect only happens during summer as there are strong westerlies from September to April or May. Despite the abrupt climate change at the end of the Deglaciation, this resulted in a more stable climate during the YD event in eastern Europe, while western Europe was affected by major climate fluctuations during the second half of the YD because of weaker summer atmospheric blocking at the end of the YD meant more Atlantic inflow reaching MFM in the west but not in the east.
S. M. Vallejo-Bernal1, L. Luna, F. Wolf, N. Marwan, N. Boers, J. Kurths:
Atmospheric rivers are the drivers of precipitation-triggered landslides in western North America,
28th IUGG General Assembly,
Berlin (Germany),
Jul 14, 2023,
Talk.
» Abstract
Characterized by their specific geometry, atmospheric rivers (ARs) are narrow, long, and transient channels of intensive water vapor transport in the lower troposphere. They play an essential role in the water supply for precipitation in the mid-latitudes but can also trigger natural hazards such as floods and landslides by facilitating heavy precipitation events. In this study, we link the occurrence of landslides in western North America (NA) during the past decades to the precipitation triggered by land-falling ARs hitting the western coastline of the region. For this, we use a landslide inventory, rainfall estimates with a daily temporal resolution, and a catalog of land-falling ARs characterized in terms of strength and persistence based on the AR scale by Ralph et al., 2019. We employ two attribution models to relate rainfall to ARs and then landslides to AR-induced rainfall. Our results show that ARs precede between 60% and 100% of the landslides reported along the western coast of North America. Intense and persistent ARs are the most common precursors. As a further analysis, we study the synchronization pattern of landslides and ARs to determine if their association is unique and significant. In the coastal regions, the precedence relation of ARs leading to landslides is statistically significant. Further inland, landslides are less likely, but those that do occur are significantly correlated with very intense and persistent ARs. Understanding and revealing the impacts of ARs on landslides in western North America will lead to better forecasts and risk assessments of these natural hazards.
Recurrence is a ubiquitous and fundamental feature in many real-world processes. The study of recurrence properties (such as frequency analysis) can provide deeper insights into the dynamical processes in general. A rather novel approach for the study of recurrences is the framework based on recurrence plots and their quantification, rooted in the theory of dynamical systems. This talk will introduce the basic concepts and major extensions applicable to various research questions. Discussed examples include the temporal change of recurrence properties for identification of regime shifts; spatio-temporal recurrences for classification tasks; and bivariate extensions for synchronization/coupling analysis. Methodological and numerical challenges and pitfalls will also be discussed.
Their amenability to radiometric dating (U-series) makes speleothems (secondary cave carbonate deposits) a key archive of past climatic and environmental changes. However, incorporation of non-radiogenic thorium can hamper U-series dating, and samples older than ca. 600 ka remain out-of-reach for U-Th dating. Our aim is to develop isothermal thermoluminescence (ITL) dating as alternative approach for otherwise ‘undatable’ samples.
The calcite thermoluminescence (TL) signal (280 °C peak) saturates at much higher doses (saturation dose up to 5000 Gy) compared to quartz and feldspar, which shows great potential to extend the dating limit. However, spurious TL signal occurred at the high temperature range hindered its application. The conventional multiple-aliquot additive-dose (MAAD) protocol used for TL dating applies extrapolation for equivalent dose (De) estimation, which also has large error. Isothermal TL (ITL) dating with the single-aliquot regenerative-dose (SAR) protocol might be a promising way as it reduces the influence of the spurious TL signal, and it applies interpolation to obtain the De. However, this protocol has not been tested on samples with independent age control.
This study tests the ITL SAR dating protocol on a speleothem sample from Bleßberg cave, which has been accurately dated with 230Th/U (ca. 320–425 ka). ITL measurement at 235 °C for 200 °C can remove the 280 °C TL peak completely without TL contribution from higher temperature range. ITL De shows a plateau when the ITL temperature varies between 230 °C and 240 °C. Peak shifting and isothermal annealing tests indicate the 280 °C TL peak has a lifetime of tens of millions years at 10 °C, which is stable enough for the age range of this speleothem sample. The accurate alpha efficiency (α-value) and the U, Th distribution within the sample are measured to estimate the dose rate. The dose rate variation with time due to U-series disequilibrium is corrected for. The ITL ages are compared with the 230Th/U ages to evaluate the performance of the ITL dating protocol.
S. M. Vallejo-Bernal, T. Braun, N. Marwan, J. Kurths:
AR-tracks: A new comprehensive global catalog of atmospheric rivers,
EGU General Assembly,
Vienna (Austria),
Apr 25, 2023,
DOI:10.5194/egusphere-egu23-9251,
Talk.
» Abstract
Atmospheric rivers (ARs) are filaments of extensive water vapor transport in the lower troposphere. They play a crucial role in the global water cycle and are a main source of fresh water for the mid-latitudes. However, very intense and persistent ARs are important triggers of heavy rainfall events and have been associated with natural and economical damage. Further motivated by their high impacts, in the last decade occurrences of ARs have been intensively studied, detection algorithms have been developed, and multiple AR catalogs have been produced. As a common approach, the detection of ARs is based on localizing anomalous atmospheric transport of moisture, usually by setting an absolute threshold on vertically integrated vapor transport (IVT) and/or vertically integrated water vapor (IWV) fields. Behind this methodology, there is the implicit assumption of stationary atmospheric moisture levels, which is not necessarily true for long periods under the context of a warming atmosphere. Also, these thresholds have proven to vary regionally which results in often excluded low-level ARs.
Here, we introduce AR-tracks, a global, high-resolution catalog of atmospheric rivers that we have developed based on the Image-Processing-based Atmospheric River Tracking (IPART) algorithm, using IVT estimates of the ERA5 reanalysis data set. As opposed to conventional detection methods, IPART calculates anomalies of the IVT field at the synoptical spatiotemporal scale of ARs and is, therefore, free from magnitude thresholds and stationarity assumptions. The resulting catalog displays a list of AR events, with a spatial resolution of 0.75° x 0.75° and a temporal resolution of 6 hours, covering the period between 1979 and 2019. For each AR, we provide common parameters such as the time and location of the landfall, the respective IVT value, the area, the width, and the length of the AR. Moreover, we also track the contour and the axis of each AR, the position of the centroid, and the proportion of the AR that is located over ocean and land, and over the different continents.
To show the potential of this new catalog, we study the spatiotemporal variability of European ARs between 1979-2019, analyzing the robustness of our results for distinct parameter choices in the definition of AR-tracks. We also use a novel power spectral measure to identify periodic cycles in the occurrence of European ARs, revealing spatially heterogeneous seasonal and multi-annual periodicities. Finally, we discuss the role of land-falling ARs as a trigger of heavy precipitation events in the regional domain.
With the extensive data we provide in this new catalog, we aim at contributing to the further understanding of the role of ARs in global climate dynamics, as long-lived ARs having cross-continent tracks can be reliably traced through their tropical/subtropical origins to high-latitude landfall, and novel topics such as inland penetration of ARs can be studied.
M. H. Trauth, A. Asrat, M. L. Fischer, P. O. Hopcroft, V. Foerster, S. Kaboth-Bahr, H. F. Lamb, N. Marwan, M. A. Maslin, F. Schäbitz, P. J. Valdes:
Early Warning Signals for the Termination of the African Humid Period(s),
EGU General Assembly,
Vienna (Austria),
Apr 24, 2023,
DOI:10.5194/egusphere-egu23-5277,
Talk.
» Abstract
The study of the mid-Holocene climate tipping point in tropical and subtropical Africa is the subject of current research, not only because there is a comparatively simple but nonlinear relationship between the change in cause (orbital forcing) and the accelerated response of the monsoon system, but also because the African monsoon is an example of a potentially positive evolution of living conditions for humans: modeling results suggest that the Sahel is expanding northward in the wake of human-induced recent global warming, with green belts spreading northward. New literature distinguishes tipping elements such as the African monsoon according to the nature of the cause and the response of the climate system. Research here focuses primarily on tipping points of the type, which is characterized by a critical slowing down and a decreasing recovery from perturbations. The African monsoon, on the other hand, is an example of the tipping point of the type, which is characterized by flickering before the transition. The two types also differ in the nature of their early warning signals (EWS). These EWS are increasingly becoming the focus of research, as they are particularly important for predicting possible tipping of climate in the future of our planet. For the African monsoon system, flickering between two stable states near the transition has been predicted by modeling, but has not yet been demonstrated on paleoclimate time series.
The paleoenvironmental record from the Chew Bahir Basin in the southern Ethiopian Rift, which documents the climate history of eastern Africa of the past 620 ka with decadal resolution in some parts provides the possibility to examine the termination of the African Humid Period (AHP, 15–5 kyr BP) with regard to the possible occurrence of EWS. Thanks to six well-dated short sediment cores (<17 m, <47 kyr BP) and two long cores ( 290 m, <620 ka BP) we can not only study the last climate transition at 5.5 kyr BP in detail, but also similar transitions including possible EWS long before the first occurrence of Homo sapiens at 318 ka BP on the African continent. The analysis of the Chew Bahir record reveals a rapid ( 880 yr) change of climate at 5.5 kyr BP in response to a relatively modest change in orbital forcing that appears to be typical of climate tipping points. If this is the case then 14 dry events at the end of the AHP and 7 wet events after the transition, each of them 20–80 yrs long and recurring every 160±40 yrs, could indeed indicate a pronounced flickering between wet and dry conditions at the end of the AHP, providing significant EWS of an imminent tipping point. Compared to the low-frequency cyclicity of climate variability before and after the termination of the AHP, the flickering occurs on time scales equivalent to a few human generations and it is very likely (albeit speculative) that people were conscious of these changes and adapted their lifestyles to the rapid changes in water and food availability.
J. Wassmer, B. Merz, N. Marwan:
Resilience of emergency infrastructure networks after flooding events,
EGU General Assembly,
Vienna (Austria),
Apr 26, 2023,
DOI:10.5194/egusphere-egu23-1383,
Talk.
» Abstract
Extreme weather events can drastically influence the dynamics and stability of networked infrastructure systems like transportation networks or power grids. Climate change is increasing the frequency of such events, making their impact on human society and ecosystems increasingly relevant. Prominent examples include damage of critical infrastructure caused by heavy rainfalls and landslides. The devastating floods that struck Germany’s Ahr valley in 2021 are yet another reminder of the threat posed by such extreme events. Due to washed-out roads and further severe infrastructure damages, critical bottlenecks effectively cut off a substantial share of the population from assistance, hampering or even impeding their rescue.
In this study, we investigate the impact of flood events on transportation networks where stability is particularly important in order to ensure the accessibility of emergency services. Local changes in the underlying network dynamics can affect the whole road network and, in the worst case, cause a total collapse of the system through cascading failures. Because of the severe consequences of cascading events, we aim to recognise such spreading processes at an early stage and, in a further step, be able to prevent them. To this end, we set up a gravity model of travel to simulate the changes of the traffic load after flooding events to identify vulnerabilities in the system. We further analyse how the accessibility of emergency services is affected and if the population can be effectively reached in time.
The estimation of power spectral density (PSD) of time series is an important task in many quantitative scientific disciplines. However, the estimation of PSD from discrete data, such as extreme event series is challenging. We present a novel approach for the estimation of a PSD of discrete data. Combining the edit distance metric with the Wiener-Khinchin theorem provides a simple yet powerful PSD analysis for discrete time series (e.g., extreme events). This method works directly with the event time series without interpolation. We demonstrate the method's potential on some prototypical examples and on event sequences of atmospheric rivers (AR), narrow filaments of extensive water vapor transport in the lower troposphere. Considering the spatial-temporal event series of ARs over Europe, we investigate the presence of a seasonal cycle as well as periodicities in the multi-annual range for specific regions, likely related to the North-Atlantic Oscillation (NAO).
N. Marwan, T. Braun:
Power Spectrum Estimation for (Extreme) Events Data,
PIK cross-RD Climate and weather extremes seminar,
Potsdam (Germany),
Apr 20, 2023,
Talk.
» Abstract
The estimation of power spectral density (PSD) of time series is an important task in many quantitative scientific disciplines. However, the estimation of PSD from discrete data, such as extreme event series is challenging. We present a novel approach for the estimation of a PSD of discrete data. Combining the edit distance metric with the Wiener-Khinchin theorem provides a simple yet powerful PSD analysis for discrete time series (e.g., extreme events). This method works directly with the event time series without interpolation or transformation to continuous data. We demonstrate the method's potential on some prototypical examples and on event sequences of atmospheric rivers (AR), narrow filaments of extensive water vapor transport in the lower troposphere. Considering the spatial-temporal event series of ARs over Europe, we investigate the presence of a seasonal cycle as well as periodicities in the multi-annual range for specific regions, likely related to the North-Atlantic Oscillation (NAO).
A deeper knowledge about the spatially coherent patterns of extreme rainfall events in the South and East Asian regions is of utmost importance for substantially improving the forecasts of extreme rainfall as their agro-based economies predominantly rely on the monsoon. In our work, we use a combination of a nonlinear synchronization measure and complex networks to investigate the spatial characteristics of extreme rainfall synchronicity in the Asian Summer Monsoon (ASM) region and gain a comprehensive understanding of the intricate relationship between its Indian and East Asian counterparts. We identify two modes of synchronization between the Indian Summer Monsoon (ISM) and the East Asian Summer Monsoon (EASM) – a southern mode between the Arabian Sea and south-eastern China in June which relates the onset of monsoon in the two locations, and a northern mode between the core ISM zone and northern China which occurs in July. Thereafter, we determine the specific times of high extreme rainfall synchronization, and identify the distinctively different large-scale atmospheric circulation, convection and moisture transport patterns associated with each mode. Furthermore, we discover that the intraseasonal variability of the ISM-EASM interconnection may be influenced by the different modes of the tropical intraseasonal oscillation (ISO). Our findings show that certain phases of the Madden-Julian oscillation and the boreal summer ISO favour the synchronization of extreme rainfall events in the June-July-August season between ISM and EASM. The impact of El Nino-Southern Oscillation on the convective sources of the two monsoon subsystems, and thus their interannual variability is investigated.
TreeEmbedding is a novel method for an optimal time delay state space reconstruction from uni- and multivariate time series. The embedding process is considered as a decision tree, in which each leaf corresponds to an embedding cycle and is subject to an evaluation through an objective function. By using a Monte Carlo ansatz, the proposed algorithm populates the tree with many leafs by computing different possible embedding paths and the final embedding is chosen as that particular path that minimises the objective function. The Monte Carlo approach aims to prevent getting stuck in a local minimum of the objective function and can be used in a modular way: Practitioners can choose suitable statistics for delay-preselection and the objective function themselves. The proposed method guarantees the optimization of the chosen objective function over the parameter space of the delay embedding as long as the tree is sampled sufficiently. To showcase the method, we demonstrate its improvements over the classical time delay embedding methods on various application examples. We compare recurrence plot-based statistics inferred from reconstructions of a Lorenz-96 system and highlight an improved forecast accuracy for map-like model data as well as for palaeoclimate isotope time series. The method is ready to use in the form of an accompanying Julia package TreeEmbedding.jl.
Atmospheric rivers (ARs) are channels of enhanced water vapor transport in the lower troposphere. They play a crucial role in the fresh water supply of Europe, contributing to up to 30% of the rainfall budget in some regions along the western coast. However, very intense and persistent ARs are important triggers of heavy rainfall events and have been associated with natural and economical damage. Here, we investigate the large-scale spatio-temporal synchronization patterns between heavy rainfall events and landfalling ARs over Europe, during the period from 1979 to 2019. For that, we employ ARtracks, a novel global catalog of ARs, and select the AR events whose footprint intercept Europe. Then, we use an AR-intensity scale to rank the ARs in terms of strength and persistence. Based on ERA5 daily precipitation estimates, we obtain binary time series indicating the absence or presence of heavy rainfall by thresholding the daily precipitation intensity at the 95th percentile. Subsequently, we utilize event synchronization incorporating varying delays to reveal the temporal evolution of spatial patterns of heavy rainfall events in the aftermath of land-falling ARs. Finally, using composites of integrated water vapor transport, geopotential height, upper-level meridional wind, and rainfall, we attribute the formation of the synchronization patterns to well-known atmospheric circulation configurations, depending on the intensity level of the ARs. Our results reveal the role of ARs in the distribution of heavy rainfall events over Europe and advance the understanding of inland heavy precipitation by revealing the characteristic circulation patterns and the main climatic drivers associated to the synchronization patterns.
Atmospheric rivers (ARs) are narrow, transient corridors of extensive water vapor transport in the lower troposphere. The role ARs play in the global water cycle can be regarded as a double-edged sword: while low-intensity ARs provide vital supply of freshwater and are rarely associated with heavy precipitation events (HPEs), high-level ARs can cause detrimental impacts when they land-fall. Detection of ARs is based on localizing anomalous atmospheric transport of moisture. Many approaches define a threshold to identify local anomalies in integrated vapor transport (IVT) in order to obtain catalogues of ARs, effectively assuming stationary atmospheric moisture levels and often excluding low-level ARs.
Here, we employ an AR-detection framework (`ARtracks') based on global ERA5 reanalysis data that utilizes image processing techniques (using the IPART algorithm). Our approach allows us to study the spatio-temporal variability of globally distributed AR tracks and potential changes due to increasing atmospheric moisture levels on a warming planet. We implement a scale that characterizes ARs based on their strength and persistence, distinguishing between ARs with potentially beneficial and detrimental impacts. A recent study has demonstrated the scope of this categorized AR catalogue for the analysis of synchronization of ARs and HPEs in North America. We analyse the robustness of our results for distinct parameter choices in the definition of AR tracks. A novel power spectral measure for the analysis of event-like time series enables us to identify significant cycles in AR occurrence. Finally, we discuss the role of land-falling ARs as a trigger of HPEs on a global scale.
The urban acoustic environment (AE) plays an underestimated role in the daily life of residents inhabiting metropolitan regions. The urban AE contains valuable information on complex sub-systems of urban areas, such as traffic, infrastructure and biodiversity. Associations between noise exposure and the mental or physical health of urban residents are an important subject of ongoing research. Despite the extensive information that is recorded by modern acoustic sensors, few approaches are designed to capture the rich complexity embedded in the time-frequency domain of the urban AE. The decreasing costs of acoustic sensors and rapid growth of storage space and computational power have led to an increase of acoustical data to be processed. Quantitative methods need to account for this complexity, while effectively reducing the high dimensionality of terabytes of audio data.
We take this as an opportunity to introduce complex networks to the field of urban acoustics. We use one of the world's most extensive longitudinal audio datasets from the SALVE study to systematically characterize the urban AE. SALVE is an ongoing study since 2019, in which 3-min acoustic recordings are made twice per hour at 23 locations in Bochum, Germany. The recorded acoustic samples exhibit a clear diel cycle and reveal site-dependent communities of interlinked frequencies. We demonstrate the utility of frequency-correlation matrices (FCMs) to effectively capture these communities. Based on these results, we construct (functional) networks of day time-specific 3-min audio recordings from 05.2019 to 03.2020 (n = 319,385 = 665 days). We show that the average shortest path length of an acoustic frequency network informs on site- and time-specific distinctiveness of frequency dynamics in the urban AE. To validate our findings, we use the land use mix around each site as a proxy for the AE, as the acoustic environment is heavily impacted by the built environment. The proposed method enables us to clearly identify 4-5 clusters of distinct urban AEs based on hourly variations in the distinctiveness of frequency dynamics. Our results indicate that complex networks represent a promising approach to analyse large-scale audio data and help to understand the time-frequency domain of the urban acoustic environment.
Extreme weather events can drastically influence the dynamics and stability of networked infrastructure systems like transportation networks or power grids. Climate change is increasing the frequency of such events, making their impact on human society and ecosystems increasingly relevant. Prominent examples include damage of critical infrastructure caused by heavy rainfalls and landslides. The devastating floods that struck Germany’s Ahr valley in 2021 are yet another reminder of the threat posed by such extreme events. Due to washed-out roads and further severe infrastructure damages, critical bottlenecks effectively cut off a substantial share of the population from assistance, hampering or even impeding their rescue.
In this study, we investigate the impact of flood events on transportation networks where stability is particularly important in order to ensure the accessibility of emergency services. Local changes in the underlying network dynamics can affect the whole road network and, in the worst case, cause a total collapse of the system through cascading failures. Because of the severe consequences of cascading events, we aim to recognise such spreading processes at an early stage and, in a further step, be able to prevent them. To this end, we set up a gravity model of travel to simulate the changes of the traffic load after flooding events to identify vulnerabilities in the system. We further analyse how the accessibility of emergency services is affected and if the population can be effectively reached in time.
The recurrence plot and recurrence quantification analysis (RQA) are well established methods for the analysis of data from complex systems. They provide import insides about the nature of the dynamics, periodicity, regime changes, and many more. This method is used in different fields of research like finance, engineering, life and earth science. In order to use this method the data has usually to be uniformly sampled. This poses a difficulty for data, which is taken from palaeoclimate archives like sediment cores or stalagmite. One frequently used solution is interpolation to generate uniform time series. However, this prepossessing changes the RQA measures like DET, LAM, or the average line length. Using auto-regression processes, we systematically analyse how these measures increase when interpolating the data. For other systems which show a smoother behavior there is only an effect if the interpolation takes place on a time scale close to the characteristic timescale of the system, like the period lengths. For the Roessler system, the RQA measures decrease when approaching this timescale and show a very irregular behavior below. For real data, we show that the course of the DET measure strongly depends on the choice of interpolation.
The stickiness effect is a fundamental characteristic of quasi-integrable Hamiltonian systems. We propose the use of an entropy-based measure of recurrence plots (RP), namely, the entropy of the distribution of the recurrence times (estimated from the RP), to characterize the dynamics of a typical quasi-integrable Hamiltonian system with coexisting regular and chaotic regions. We show that the recurrence time entropy (RTE) is positively correlated to the largest Lyapunov exponent, with a high correlation coefficient. We obtain a multi-modal distribution of the finite-time RTE and show that each mode corresponds to the motion around islands of different hierarchical levels.
To improve our understanding of climate dynamics, we first need to deeply understand the climate’s past if we hope to mitigate and adapt to oncoming critical climate change. Understanding the past climate dynamics depends on the interpretation of paleo proxies. Blending dynamical systems theory, recurrence theorem, multi-stability, and synchronization with complex networks theory and machine learning techniques have become instrumental for a more profound understanding of climate dynamics in the last few decades. However, these techniques are not directly applicable to paleoclimate research since the proxy data is subject to different distortions. The paleoclimate proxy measurements carry uncertainty in nominal and temporal dimensions, and also the choice of proxy and varying effects of local and global interactions matter.
Paleoclimate proxies typically represent the climate dynamics of large spatial regions and long periods. Furthermore, the proxies contain many switching transitions between droughts and wet seasons, showing that paleoclimate dynamics have multi-stability. To mimic paleoclimate dynamics, we introduce a multi-layer network model of coupled chaotic maps where multiple chimera configurations of synchronized subsystems co-exist as stable states. This multi-stable system goes through a series of critical transitions into another stable state through noise induction. We collect only the mean field of the state variables from each layer to imitate the spatial sparsity of paleoclimate measurements. Using this limited information, we developed a methodology to reconstruct paleoclimate networks and identify the critical switching of dynamical patterns.
Our paleoclimate network approach pivots around the recurrent property of climate system states. After suitable transformations, recurrence quantification analyses (RQA) of proxy series are shown to be robust indicators of the dynamical properties of represented dynamics in the form of time series. We construct a functional network from these series with nodes representing proxy sources using the time evolution of individual series. This allows us to classify the system state with respect to the visible relational dynamics between nodes. We also extended our studies to real paleoclimate datasets around Northern Africa and found the dominant dynamical patterns associated with known periods.
The analysis of time series of extreme events is a challenging task. Many research questions, such as synchronisation analysis or power spectrum estimation, are challenging for linear tools. We demonstrate some recent extensions of the recurrence plot approach for various applications in the field of extreme events data. We demonstrate their potential for synchronisation analysis between signals of extreme events and signals with continuous and slower variations, for estimation of power spectra of spiky signals, and for analysing data with irregular sampling.
><2022
S. De, S. Gupta, V. R. Unni, R. Ravindran, P. Kasthuri, N. Marwan, J. Kurths, R. I. Sujith:
Implications of a Complex Network-Based Approach to the Analysis of Cyclone Merger,
Conference on Nonlinear Systems & Dynamics, IISER Pune,
Pune (India),
Dec 17, 2022,
Talk.
» Abstract
When cyclones are formed in close proximity, they can interact. Such an interaction is termed as “Fujiwhara effect” [1]. Due to this effect, the mutual distance between the cyclones decreases, which triggers a variety of interactions such as elastic interaction, partial merger, and complete merger. However, the interaction between the cyclones leading to a completer merger is a rare event in nature. The complete merger between cyclones can result in a more intense, long-lived cyclone. However, understanding the dynamics of cyclonic interactions is presently challenging for weather forecasters, making the prediction of a cyclone merger more difficult. The main reason attributed to the prediction inaccuracy is that, to date, cyclone forecasting models have not completely incorporated the Fujiwhara effect due to a lack of knowledge [2,3]. As a consequence, inaccurate cyclone merger predictions may result in substantial economic losses and fatalities. Hence, we require a method that can enable us to obtain profound insights into the dynamics of cyclone interaction that leads to a complete cyclone merger.
S. Kulkarni, U. Öztürk, N. Marwan, J. Kurths, B. Merz, A. Agarwal:
Complex networks in hydrologic sciences,
AGU 2022 Fall Meeting,
New Orleans (USA),
December 12–16, 2022,
Talk.
» Abstract
Complex network science is a stemming interdisciplinary field of research spreading to diverse branches of sciences such as physics, engineering, social science, and Earth Sciences. The complex systems can be represented as graphs with individual components called nodes and the links representing the interaction between nodes. Regardless of their physical nature, complex networks of different systems exhibit common structural properties that distinguish them from purely random graphs. The application of complex networks in hydrology and water resources management is in its infancy but overgrowing. However, this innovative approach has already led to important insights in hydrology. In this review, we first provide a comprehensive overview of the multiple aspects of complex networks and their measures; further, we summarize applications of complex networks in water science to offer a current picture of state-of-the-art; and lastly, we highlight arising open problems and new directions. Our work, with the help of examples, advocates that complex network science can be a generic theory to understand different hydrologic systems.
A. Manapat, J. L. Oster, F. Lechleitner, H. Cheng, J. F. Adkins, S. M. Bernasconi, W. D. Sharp, N. Marwan, B. Plessen, S. F. M. Breitenbach:
Stalagmite record of Indian Summer Monsoon variability during Marine Isotope Stage 3,
AGU 2022 Fall Meeting,
New Orleans (USA),
December 12–16, 2022,
Poster.
» Abstract
Variation in the strength of the Indian Summer Monsoon (ISM) affects the food security and livelihood of around one-third of the world’s population. However, many of the causes of variation in ISM strength remain poorly understood. Variation in the stable oxygen and carbon isotope ratios (d18O and d13C) in speleothems have been used as proxies to understand pre-instrumental variation in ISM intensity- with δ18O variation linked to changes in precipitation dynamics and δ13C reflecting changes in the local rainfall amounts.
We present a stable isotope record from MAW-3, a stalagmite from Mawmluh cave, northeast India. This site receives between 70-80% of its annual rainfall between June and September. Precipitation, cave drip monitoring, and studies of modern stalagmites from this site indicate that stalagmite d18O reflects changes in ISM strength linked to large-scale atmospheric dynamics. We discuss the interval of growth for stalagmite MAW-3 that occurred between 44 ka BP and 28 ka BP, corresponding to Marine Isotope Stage 3 (MIS3). The resultant δ18O record displays significant millennial-scale oscillations of between 1.5-3.0 ‰, possibly corresponding to Dansgaard-Oeschger (D-O) events 5-8. Continuous Wavelet Transform (CWT) indicates a 1350-year cycle in δ18O. Stalagmite δ13C also decreases by 2.0-4.0 ‰ during D-O interstadials, likely due to reduced prior carbonate precipitation (PCP) during periods of higher rainfall. The MAW3 δ18O shifts to more negative values during the D-O warmings (interstadials) noted in the North Greenland Ice Core Project (NGRIP) oxygen isotope record. However, the δ18O variation in MAW-3 is much more gradual than that of NGRIP, indicating differences in how these D-O events affect climate variation outside of the North Atlantic region. Variations in δ18O in MAW3 are also in phase with δ18O variations in the Hulu Cave record over this interval indicating synchronous variability between the ISM and East Asian Monsoon over D-O events 5-8. The MAW3 record further strengthens evidence for climate teleconnections between the North Atlantic and the Indian and East Asian monsoon systems. Reconstructing such variation is important in understanding how the monsoons may change in a warming planet.
N. Marwan:
Methods for Extreme Events Time Series,
PIK cross-RD Climate and weather extremes seminar,
Potsdam (Germany),
Dec 8, 2022,
Talk.
N. Marwan:
Investigating palaeoclimate conditions with nonlinear time series analysis,
MARUM research seminar, University of Bremen,
Bremen (Germany),
Dec 5, 2022,
Talk invited.
» Abstract
The study of palaeoclimate data is related with specific challenges, such as nonstationarities, nonlinear feedbacks, irregular sampling, or different kinds of uncertainties. Recurrence analysis and complex networks are concepts based on nonlinear dynamics and complex systems science that can help to identify regime transitions and couplings in palaeoclimate data. I demonstrate their potential for studying variations and couplings for selected palaeoclimate research questions.
Recurrence is a ubiquitous and fundamental feature in many real world processes. Recurrence plots are versatile tools for studying such phenomena. The lecture introduces the basic concepts and major extensions of quantifying recurrence plots. Discussed examples include the temporal change of recurrence properties for identification of regime shifts, methodological and numerical challenges, as well as potential pitfalls.
V. Skiba, M. Trüssel, B. Plessen, C. Spötl, R. Eichstädter, A. Schröder-Ritzrau, T. Braun, T. Mitsui, N. Frank, N. Boers, N. Marwan, J. Fohlmeister, R. Tjallingii, X. Zhang:
On the forcing of glacial abrupt climate transitions of the last 300,000 years,
DEUQUA-Tagung 2022,
Potsdam (Germany),
Sep 26, 2022,
Talk.
» Abstract
Abrupt stadial-interstadial transitions, are a prominent feature of the last glacial as recorded in Greenland ice core records (Dansgaard-Oeschger events). Event abruptness and presence of statistical early warning signals before these transitions indicate that they involve crossing of a tipping point of the climate system. However, only little information is available for periods before the last glacial period as Greenland ice cores and many other high-resolution records do not extent beyond the last glacial cycle. Given the lack of understanding of the triggering mechanisms responsible for glacial abrupt climate transitions with palaeoclimate data from the last glacial, it is essential to investigate this phenomenon during earlier glacial periods.
Here, we present a new highly resolved, precisely U-Th-dated speleothem oxygen isotope record from the Northern European Alps for the penultimate glacial (MIS7-MIS8), a region which has been shown to record similar climate variability as Greenland ice core records. Together with previously obtained speleothem data from this cave site for MIS5-MIS7 and Greenland ice core data (NGRIP, MIS1-4), we investigate background climate conditions which favour occurrence of abrupt climate transitions using regression analysis. Besides intermediate background conditions (sea level, CO2 and CH4) and low precession, we find either relatively low or high obliquity to favour glacial abrupt climate transitions, perhaps depending on the initial mode of the Atlantic Meridional Overturning Circulation before these occurrences.
T. Braun, N. Marwan:
A recurrence flow based approach to state space reconstruction,
Dynamics Days Europe 2022,
University of Aberdeen (UK),
Aug 23, 2022,
Talk.
» Abstract
In the study of nonlinear observational time series, reconstructing the system’s state space via time-delay embedding represents the basis for many widely-used analyses. Recurrence plots indicate the appropriateness of the underlying embedding parameters by the presence of well-formed diagonal lines that represent the predictability of the system's evolution. However, an approach that systematically exploits this information for optimal state space reconstruction is so far missing. In this talk, we propose a recurrence based framework for state space reconstruction. The concept is based on a novel recurrence quantification measure that captures how well a fictive fluid can permeate an RP diagonally, the recurrence flow. The recurrence flow can be regarded as a nonlinear dependence measure that quantifies the relationship between multiple time series based on the predictability of their joint evolution. We demonstrate the effectiveness of the proposed method in detecting nonlinear multiscale relations and informing on the choice of optimal embedding parameters for complex real-world time series.
N. Marwan, K. H. Kraemer:
Recent Exciting Developments in Recurrence Plot Analysis,
Dynamics Days Europe 2022,
University of Aberdeen (UK),
Aug 23, 2022,
Talk.
» Abstract
The last decade has witnessed a number of important and exciting developments that had been achieved for improving recurrence plot based data analysis and to widen its application potential. I will give a brief overview about important and innovative developments, such as computational improvements, alternative recurrence definitions (event-like, multiscale, heterogeneous, and spatio-temporal recurrences) and ideas for parameter selection, theoretical considerations of recurrence quantification measures, new recurrence quantifiers (e.g., for transition detection and causality detection), and correction schemes. Moreover, new perspectives have recently been opened by combining recurrence plots with machine learning.
N. Marwan:
Reconstructing Complex Networks from Data,
(Virtual) Workshop on the Application of Complex Networks to Fluid Mechanics, IIT Madras,
Chennai (India)/ Online,
Aug 15, 2022,
Talk.
» Abstract
Complex networks provide an interesting tool to investigate spatio-temporal data. The first step is to reconstruct a (functional) network from data. I will show different reconstruction approaches depending on the research question and the nature of the data. The procedure is illustrated with applications on climate data.
S. Gupta, Z. Su, N. Boers, J. Kurths, N. Marwan, F. Pappenberger:
Spatial Synchronization Patterns of Extreme Rainfall Events in the Asian Summer Monsoon Region,
AOGS2022 Virtual 19th Annual Meeting,
(online meeting),
Aug 1, 2022,
Talk.
» Abstract
A deeper knowledge about the spatially coherent patterns of extreme rainfall events in the South and East Asian regions is of utmost importance for substantially improving the forecasts of extreme rainfall as their agro-based economies predominantly rely on the monsoon. In our work, we use a combination of a nonlinear synchronization measure and complex networks to investigate the spatial characteristics of extreme rainfall synchronicity in the Asian Summer Monsoon (ASM) region and gain a comprehensive understanding of the intricate relationship between its Indian and East Asian counterparts. We identify two modes of synchronization between the Indian Summer Monsoon (ISM) and the East Asian Summer Monsoon (EASM) – a southern mode between the Arabian Sea and south-eastern China in June which relates the onset of monsoon in the two locations, and a northern mode between the core ISM zone and northern China which occurs in July. Thereafter, we determine the specific times of high extreme rainfall synchronization, and identify the distinctively different large-scale atmospheric circulation, convection and moisture transport patterns associated with each mode. Furthermore, we discover that the intraseasonal variability of the ISM-EASM interconnection may be influenced by the different modes of the tropical intraseasonal oscillation (ISO). Our findings show that certain phases of the Madden-Julian oscillation and the boreal summer ISO favour the synchronization of extreme rainfall events in the June-July-August season between ISM and EASM. This work is funded by the CAFE project which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 813844.
J. Klose, M. Weber, H. Vonhof, B. Plessen, S. F. M. Breitenbach, N. Marwan, D. Scholz:
Timing of Dansgaard-Oeschger events in Central Europe based on three precisely dated speleothems from Bleßberg Cave, Germany,
Climate Change, The Karst Record IX (KR9),
Innsbruck (Austria),
July 18, 2022,
Talk.
» Abstract
The last glacial period and especially Marine Isotope stage 3 (MIS 3, ca. 57 - 27 ka) was characterized by various climate oscillations (i.e., rapid increases in temperature, followed by a gradual cooling, the Dansgaard-Oeschger (D/O) events), which were first discovered in Greenland ice cores. Although their causes are still not fully understood, clear evidence for their supra-regional character was found in various climate records around the globe. However, European speleothem samples, which grew during MIS 3, are limited and mainly restricted to alpine regions, where glacier meltwater enabled speleothem growth, and to south/south-western parts of Europe characterised by a generally warmer climate. This led to the opinion that it was too cold and/or too dry in central Europe for speleothem growth. Here we present three speleothem (flowstone) records from Bleßberg Cave, Germany, which grew during MIS 3.
All flowstones show episodical growth patterns with distinctive, thin growth phases. Potential contamination deriving form detrital material deposited during hiatuses between individual growth phases, open-system behaviour around the hiatuses and the limited thickness of the growth layers are the biggest challenges during sampling for 230Th/U dating. By combination of different sampling techniques (i.e., laser ablation and micro-milling) in addition to the common approach of handheld drilling and due to the relatively high 238U concentration of the samples (approx. 0.4 - 1 μg/g), we were able to date even the thinnest growth layers (< 2 mm) of the Bleßberg flowstones with a very high precision (i.e., with 2σ-age uncertainties of a few hundred years or even lower).
The timing of the growth phases of the Bleßberg flowstones correlates with several D/O events recorded in the Greenland ice cores. This proves that at least some phases of MIS 3 had favourable climate conditions for speleothem growth in Central Europe. In addition, the analysis of the stable oxygen and carbon isotopes (δ18O and δ13C) for all three flowstones revealed several D/O events, which have not been recorded in any other speleothem from central Europe so far. This will enhance our understanding of climate variability during MIS 3 and specific D/O events in central Europe.
The study of palaeoclimate data is related with specific challenges, such as irregular sampling or different kinds of uncertainties. Recurrence analysis and complex networks are concepts based on nonlinear dynamics and complex systems science that can help to identify regime transitions and couplings. I demonstrate their potential for studying variations and couplings in the palaeoclimate Monsoon system.
N. Marwan:
Das Sägistal - Alpines Karstgebiet im Berner Oberland,
60. Jahrestagung des VdHK,
Truckenthal (Germany),
Jun 17, 2022,
Talk.
Based on a set of various marine palaeoclimate proxy records, we investigate African climate variations during the past 5 million years. We use a collection of modern approaches from non-linear time series analysis to identify and characterise dynamical regime shifts as changes in signal predictability, regularity, complexity, and higher-order stochastic properties such as multi-stability. We observe notable nonlinear transitions and important climate events in the African palaeoclimate, which can be attributed to phases of intensified Walker circulation, marine isotope stage M2, the onset of northern hemisphere glaciation, and the mid-Pleistocene transition, and relate them to variations of the Earth's orbital parameters.
A. Giesche, D. A. Hodell, C. A. Petrie, G. H. Haug, J. F. Adkins, B. Plessen, N. Marwan, H. J. Bradbury, A. Hartland, A. D. French, S. F. M. Breitenbach:
Northwest Indian stalagmite shows evidence for recurring summer and winter droughts after 4.2 ka BP,
EGU General Assembly,
Vienna (Austria),
May 24, 2022,
DOI:10.5194/egusphere-egu22-396,
Talk.
» Abstract
We reconstructed changes in summer and winter precipitation using a well-dated (±18 years 2σ error) speleothem spanning 4.2-3.1 ka BP from Dharamjali Cave in the central Himalaya. The record was sampled at a sub-annual resolution for a suite of trace elements, as well oxygen and carbon stable isotopes. Calcium isotopes at decadal resolution provide additional hydroclimatic evidence. This DHAR-1 stalagmite records a 230-year period of increased drought frequency in both the summer and winter seasons after 4.2 ka BP, with aridity events centered on 4.19, 4.11 and 4.02 ka BP each lasting between 25 and 90 years. The data after 3.97 ka BP support a recovery in summer monsoon rainfall, peaking around 3.7 ka BP. The significance of this new record includes remarkable coherence between the moisture proxies over 4.2-3.97 ka BP in a well-dated record, which provides confidence in the duration of droughts and timing of monsoon recovery. It also places seasonal climate variability on a timescale relevant to human decision-making, which is particularly significant for this region nearby the Indus River Basin. The Indus Civilization reached its urban apex by 4.2 ka BP, and archaeologists have documented a shift in settlement locations, population, health, and agricultural strategies thereafter for a period of several centuries. This stalagmite record provides valuable insights into seasonal precipitation availability during a critical climatic and cultural transition phase.
J. Wassmer, N. Marwan, B. Merz:
Impact of extreme events on topological robustness of infrastructure networks,
EGU General Assembly,
Vienna (Austria),
May 26, 2022,
DOI:10.5194/egusphere-egu22-2705,
Talk.
» Abstract
Climate change is increasing the frequency of extreme weather events such as floods, making their impact on human society and ecosystems increasingly relevant. Extreme weather events can drastically influence the dynamics and stability of networked infrastructure systems like transportation networks or power grids. Local changes in the dynamics can affect the whole network and, in the worst case, cause a total collapse of the system through cascading failures. Hence, methods are needed to understand and prevent such collapses.
In this project, we analyse the influences of flooding events on transportation networks using the Ahr valley flood of July 2021 in Germany as a case study. To this end, we set up a gravity model for road networks to compute the traffic loads. We use satellite data provided by EU Copernicus programme to access information about the state of the road network right after the flooding event. By removing flooded roads from the model, we can estimate the effect on the traffic load and identify secondarily affected roads. This approach enables us to identify and optimise critical links to ensure that affected areas are not isolated after extreme weather events and can receive disaster assistance from surrounding areas.
F. Wolf, S. M. Vallejo-Bernal, N. Boers, N. Marwan, D. Traxl, J. Kurths:
Spatio-temporal synchronization of heavy rainfall events triggered by atmospheric rivers in North America,
EGU General Assembly,
Vienna (Austria),
May 24, 2022,
DOI:10.5194/egusphere-egu22-2993,
» Talk (PDF, 758.19K).
» Abstract
Atmospheric rivers (ARs) are filaments of extensive water vapor transport in the lower troposphere. They are important triggers of heavy rainfall events, contributing to more than 50% of the rainfall sums in some regions along the western coast of North America. ARs play a crucial role in the distribution of water, but can also cause natural and economical damage by facilitating heavy rainfall. Here, we investigate the large-scale spatio-temporal synchronization patterns of heavy rainfall triggered by ARs over the western coast and the continental regions of North America.
For our work, we employ daily ERA5 rainfall estimates at a spatial resolution of 0.25°x0.25° latitude and longitude which we threshold at the 95th percentile to obtain binary time series indicating the absence or presence of heavy rainfall. Subsequently, we separate periods with ARs and periods without ARs and investigate the differing spatial synchronization pattern of heavy rainfall. To establish that our results are not dependent on the chosen AR catalog, this is conducted in two different ways: first based on a recently published catalog by Gershunov et al. (2017) , and second based on a catalog constructed using the IPART algorithm (Xu et al, 2020). For both approaches, we subsequently utilize event synchronization and a complex network framework to reveal distinct spatial patterns of heavy rainfall events for periods with and without active ARs. Using composites of upper-level meridional wind, we attribute the formation of the rainfall synchronization patterns to well-known atmospheric circulation configurations, whose intensity scales with the strength of the ARs. Furthermore, we demonstrate that enhanced AR activity is going in hand with a suppressed seasonal shift of the characteristic meridional wind pattern. To verify and illustrate how small changes of the high-level meridional wind affect the distribution of heavy rainfall, we, additionally, perform a case study focusing on the boreal winter.
Our results indicate the strong sensitivity of the intensity, location, frequency, and pattern of synchronized heavy rainfall events related to ARs to small changes in the large-scale circulation.
S. M. Vallejo-Bernal, F. Wolf, L. Luna, N. Boers, N. Marwan, J. Kurths:
Relationship between atmospheric rivers and landslides in western North America,
EGU General Assembly,
Vienna (Austria),
May 25, 2022,
DOI:10.5194/egusphere-egu22-8096,
» Talk (PDF, 1.79M).
» Abstract
In this study, we investigate the relationship between land-falling atmospheric rivers (ARs) and landslides in western North America. ARs are channels of enhanced water vapor flux in the atmosphere and play an essential role in the water supply for precipitation in the midlatitudes. However, they can also trigger natural hazards such as floods and landslides. Our objective is to determine if the occurrence of landslides in western North America can be attributed to ARs hitting the western coastline and causing rainfall at the locations of the landslides and to characterize the strength and persistence of the ARs that lead to landslides. To that aim, we use landslide records with daily temporal resolution along with daily rainfall estimates from the ERA5 reanalysis, for the period between 1996 and 2018. We propose and run two attribution models to relate landslides to rainfall and rainfall to ARs and subsequently verify statistically if there is a unique and significant association between the landslides and the ARs. Our results show that the majority of the landslides reported along the western coast of North America are preceded by an AR. In the coastal regions, ARs and landslides are significantly correlated. Further inland, landslides are less likely, but those that do occur are significantly correlated with very intense ARs. Understanding and revealing the impacts of ARs on landslides in western North America will lead to better forecasts and risk assessments of these natural hazards.
S. Gupta, Z. Su, N. Boers, J. Kurths, N. Marwan, F. Pappenberger:
Interrelation between the Indian and East Asian Summer Monsoon: A complex network-based approach,
EGU General Assembly,
Vienna (Austria),
May 23, 2022,
DOI:10.5194/egusphere-egu22-8626,
» Talk (PDF, 1.96M).
» Abstract
The Indian Summer Monsoon (ISM) and the East Asian Summer monsoon (EASM) are two integral components of the Asian Summer Monsoon system, largely influencing the agro-based economy of the densely populated southern and eastern parts of Asia. In our study, we use a complex network based approach to investigate the spatial coherence of extreme precipitation in the Asian Summer Monsoon region and gain a deep insight into the complex nature of the interaction between the ISM and the EASM. We identify two dominant modes of ISM-EASM interaction – (a) a southern mode connecting onset of the ISM over the Arabian Sea and southern India in June to the onset of Meiyu over south-eastern China, i.e., lower and middle reaches of the Yangtze river valley, and (b) a northern mode relating the occurrence and intensity of rainfall over the northern and central parts of India to that in northern China during July. Through determination of specific times of high synchronization of extreme precipitation, we distinctly identify the particular large-scale atmospheric circulation and moisture transport patterns associated with each mode. Thereafter, we investigate the role of the different components of the tropical intraseasonal oscillations, such as the Madden-Julian Oscillation and the boreal summer intraseasonal oscillation, in the intraseasonal variability of the relationship between the ISM and the EASM.
This work is funded by the CAFE project which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 813844.
T. Braun, K. H. Kraemer, N. Marwan:
A Recurrence Flow based Approach to Attractor Reconstruction,
EGU General Assembly,
Vienna (Austria),
May 25, 2022,
DOI:10.5194/egusphere-egu22-9626,
Talk.
» Abstract
In the study of nonlinear observational time series, reconstructing the system’s state space represents the basis for many widely-used analyses. From the perspective of dynamical system’s theory, Taken’s theorem states that under benign conditions, the reconstructed state space preserves the most fundamental properties of the real, unknown system’s attractor. Through many applications, time delay embedding (TDE) has established itself as the most popular approach for state space reconstruction. However, standard TDE cannot account for multiscale properties of the system and many of the more sophisticated approaches either require heuristic choice for a high number of parameters, fail when the signals are corrupted by noise or obstruct analysis due to their very high complexity.
We present a novel semi-automated, recurrence based method for the problem of attractor reconstruction. The proposed method is based on recurrence plots (RPs), a computationally simple yet effective 2D-representation of a univariate time series. In a recent study, the quantification of RPs has been extended by transferring the well-known box-counting algorithm to recurrence analysis. We build on this novel formalism by introducing another box-counting measure that was originally put forward by B. Mandelbrot, namely succolarity. Succolarity quantifies how well a fluid can permeate a binary texture. We employ this measure by flooding a RP with a (fictional) fluid along its diagonals and computing succolarity as a measure of diagonal flow through the RP. Since a non-optimal choice of embedding parameters impedes the formation of diagonal lines in the RP and generally results in spurious patterns that block the fluid, the attractor reconstruction problem can be formulated as a maximization of diagonal recurrence flow.
The proposed state space reconstruction algorithm allows for non-uniform embedding delays to account for multiscale dynamics. It is conceptually and computationally simple and (nearly) parameter-free. Even in presence of moderate to high noise intensity, reliable results are obtained. We compare the method’s performance to existing techniques and showcase its effectiveness in applications to paradigmatic examples and nonlinear geoscientific time series.
V. Skiba, M. Trüssel, B. Plessen, C. Spötl, R. Eichstädter, A. Schröder-Ritzrau, T. Braun, T. Mitsui, N. Frank, N. Boers, N. Marwan, J. Fohlmeister:
Abrupt climate events recorded in speleothems from the ante penultimate glacial,
EGU General Assembly,
Vienna (Austria),
May 23, 2022,
DOI:10.5194/egusphere-egu22-11671,
» Talk (PDF, 1.04M).
» Abstract
Millennial-scale climate variability, especially abrupt stadial-interstadial transitions, are a prominent feature of the last glacial as recorded in Greenland ice core records (Dansgaard-Oeschger events). Event abruptness and presence of statistical early warning signals before these transitions indicate that they involve repeated crossing of a tipping point of the climate system. However, only little information is available for periods before the last glacial period as Greenland ice cores and many other high-resolution records do not extent beyond the last glacial cycle. Given the lack of understanding of the triggering mechanism responsible for glacial millennial-scale variability with palaeoclimate data from the last glacial, it is essential to investigate this phenomenon during earlier glacial periods.
Here, we present a new highly resolved, precisely U-Th-dated speleothem oxygen isotope record from the Northern European Alps, a region which has been previously shown to resemble the glacial millennial-scale climate variability obtained from Greenland ice core records very well. Our new data covers the time interval from the ante-penultimate glacial to the penultimate glacial (MIS8-MIS6) with a high degree of replication. For both glacial periods, we find phases of pronounced millennial-scale variability but also several, 10 ka long phases with the climate system being exclusively in stadial conditions. We compare our data with conceptual model results and investigate the occurrence and absence of abrupt climate transitions of the last 300,000 a.
T. Braun, C. N. Fernandez, D. Eroglu, A. Hartland, S. F. M. Breitenbach, N. Marwan:
Sampling rate-corrected time series analysis of irregularly sampled palaeoclimate proxy records,
6th PAGES Open Science Meeting,
(online meeting),
May 18, 2022,
Talk.
» Abstract
Irregular sampling remains a challenge in the analysis of time series from different palaeoclimate archives. Aside from rendering most standard time series analysis methods inapplicable, changes in the sampling rate of a record entail significant biases that can not be corrected by basic pre-processing procedures such as linear interpolation. Yet, sampling rates frequently show non-stationary characteristics, e.g. for speleothems, as they are coupled to environmental parameters via their growth rate.
Consequently, methods that account for continuous and abrupt changes of sampling resolution without introducing additional biases are required. In several applications, the edit–distance has proven to be an effective metric to quantitatively compare time series segments of unequal length by computing the cost of transforming one segment into the other. We demonstrate that transformation costs generally exhibit a non-trivial relationship with local sampling rate. If the sampling rate undergoes significant variations, this dependence rules out an unbiased comparison between different time episodes. We study the impact of this effect on recurrence quantification analysis, a framework that is well-suited for identifying regime shifts in nonlinear time series. A constrained randomization procedure is proposed as a bias correction for recurrence quantification analysis.
We demonstrate the effectiveness of the proposed approach in the analysis of an irregularly sampled speleothem proxy record with seasonal laminae from Niue island in the central tropical Pacific. Application of the proposed correction scheme identifies a spurious transition that is solely imposed by an abrupt shift in sampling rate and uncovers periods of reduced seasonal rainfall predictability associated with enhanced ENSO and tropical cyclone activity.
M. H. Trauth, A. Asrat, A. S. Cohen, W. Duesing, V. Foerster, S. Kaboth-Bahr, K. H. Kraemer, H. F. Lamb, N. Marwan, M. A. Maslin, F. Schäbitz:
Tipping points in the 620 kyr proxy record from Chew Bahir, S Ethiopia,
6th PAGES Open Science Meeting,
(online meeting),
May 18, 2022,
Talk.
» Abstract
We have used a change point analysis (CPA) and a recurrence plot/recurrence quantification analysis (RP/RQA) on a 300 m / 620 kyr lake-sediment record from the Chew Bahir basin in the southern Ethiopian Rift to determine the amplitude and duration of past climate transitions. In this record, there are numerous transitions from wet to dry conditions, as well as from dry to wet, which show the typical characteristics of a tipping point, where the change is always faster than the forcing and the actual transition is preceded by possible precursor events. One of the most interesting transition examined with the CPA and RP/RQA was the termination of the African Humid period (15–5 kyr BP). The rapid ( 880 yr) change of climate in response to a relatively modest change in orbital forcing appears to be typical of tipping points in complex systems such as the Chew Bahir basin. If this is the case then 14 dry events at the end of the AHP at 5.5 kyr BP, each of them 20–80 yrs long and recurring every 160±40 yrs as documented in the Chew Bahir cores could represent precursors of an imminent tipping point which, if properly interpreted, would allow predictions to be made of future climate change in the Chew Bahir basin. Compared to the low-frequency cyclicity of climate variability before and after the termination of the AHP, this type of cyclicity occurs on time scales equivalent to a few human generations. In other words, it is very likely (albeit speculative) that people were conscious of these changes and adapted their lifestyles to the consequent changes in water and food availability. A deeper analysis of our data is however required to understand whether the wet-dry climate transition in the area was due to a saddle-node bifurcation in the structural stability of the climate, or whether it was induced by a stochastic fluctuation.
N. Marwan:
Palaeoclimate variability in Central America in the last 2 millenia,
Thematic Einstein Semester "The Mathematics of Complex Social Systems: Past, Present, and Future",
Berlin (Germany),
April 25, 2022,
Talk.
» Abstract
Description: (i) Stable isotope (d18O) climate record derived from stalagmite YOK-I from Yok Balum Cave in Belize, representing regional palaeoclimate variation between 40 BC and 2006 AD. (ii) Reconstruction of tropical Atlantic sea surface temperatures (SSTs) spanning the last 2000 years using seasonally representative foraminifera from the Cariaco Basin.
Background: The stalagmite based stable isotope climate record from Belize represents variability in tropical rainfall over the last 2000 years. This variability is related to a displacement of the Intertropical Convergence Zone (ITCZ) which seems to be controlled by the North Atlantic Oscillation (NAO) or changes in the tropical Atlantic sea surface temperatures (SSTs)
Original Purpose: The stable isotope record of stalagmite YOK-I is a reference record of regional past rainfall variability, used to investigate, e.g., droughts and their impact on politics, war, and population fluctuations of the Mayans. Related studies: 10.1126/science.1226299, 10.1038/srep45809, 10.1002/2013GL058458.
Questions: Is there a relationship between the SST variability of the tropical Atlantic and the rainfall variability in Belize (including leads and lags)? Does this relationship change over time? Consider uncertainties in the dating procedure and include them in the analysis.
N. Marwan:
Nonlinear Data Analysis Concepts,
Graduate School NatRiskChange, University of Potsdam,
Potsdam (Germany),
March 28-29, 2022,
Lecture.
» Abstract
The lecture introduces the basic concepts of nonlinear dynamics and chaos and how they can be applied for the study of complex systems, spatiotemporal data, and nonlinear interrelationships in geosciences. The specific topics contain
Basic terminology, dynamical systems, and simple prototypical models
Dimensions, fractals
Concept of symbolic dynamics
Concept of phase space, phase space reconstruction, Lyapunov exponent and correlation sum
Concept of recurrence in phase space, recurrence plots, recurrence quantification analysis
Detection of regime transitions, statistical tests
Concept of synchronization, coupling analysis
Spatial and spatio-temporal data analysis using recurrence features
Functional networks, reconstruction of networks, climate networks
Complex networks based time series analysis
R. Krishnan, M. Singh, T. P. Sabin, B. Goswami, A. D. Choudhury, P. Swapna, R. Vellore, A. G. Prajeesh, N. Sandeep, C. Venkataraman, R. V. Donner, N. Marwan, J. Kurths:
Implications of volcanic aerosols for seasonal forecasting of the Indian monsoon in a changing climate,
Seventh WMO International Workshop on Monsoons (IWM-7),
New Delhi (India),
March 22-26, 2022,
Talk invited.
» Abstract
There is unequivocal evidence that human-induced climate change, in particular greenhouse gas (GHG) emissions, has been the main driver of the observed intensification of heavy precipitation over the land regions across the globe, and has also contributed to increases in agricultural droughts in some regions, which are further projected to enhance with additional warming during the 21st century (IPCC AR6 WG1, 2021). In addition to GHG forcing, anthropogenic aerosol emissions from the Northern Hemisphere (NH) are recognized to have influenced monsoon precipitation changes over the West African, South Asian and East Asian monsoon regions, since the second half of the 20th century (IPCC AR6 WG1, 2021). In particular, the expected enhancement of the South Asian monsoon precipitation by GHG forcing since 1950s has been offset by precipitation reduction caused by the NH anthropogenic aerosols (IPCC AR6 WG1, 2021).
Near-term climate projections for the period 2021-2040 indicate that the South Asian monsoon will be dominated by the effects of internal variability, but will increase in the long-term (IPCC AR6 WG1, 2021). In this context, it must be highlighted that uncertainties due to unpredictable natural forcings such as large volcanic eruptions can lower the degree of confidence in projecting near-term monsoonal changes. This talk is aimed to provide some insights into the role of large volcanic eruptions on the tropical atmosphere-ocean coupled system and the Indian monsoon, with implications for monsoon seasonal forecasting.
N. Marwan:
Transparent and efficient data storage,
Graduate School NatRiskChange University of Potsdam,
Potsdam (Germany),
March 14-15, 2022,
Lecture.
» Abstract
The lecture provides an overview of the need for sustainable storage of scientific data, various concepts of data storage and archiving, their planning and practical implementation, both at the personal, institutional, and public levels in publicly accessible data archives. Specific topics discussed include reproducibility and transparency, important data formats, data integrity, standards, encryption, backup, coding conventions, documentation/meta-data, and version control.
><2021
M. Gadhawe, R. Guntu, A. Banerjee, N. Marwan, A. Agarwal:
A complex network approach to study the extreme precipitation patterns in a river basin,
AGU 2021 Fall Meeting,
New Orleans (USA),
December 13–17, 2021,
DOI:10.1002/essoar.10509273.1,
Poster.
» Abstract
The spatiotemporal patterns of precipitation are critical for understanding the underlying mechanism of many hydrological and climate phenomena. Over the last decade, applications of the complex network theory as a data-driven technique has contributed significantly to study the intricate relationship between many variable in a compact way. In our work, we conduct a study to compare an extreme precipitation pattern in Ganga River Basin, by constructing the networks using two nonlinear methods - event synchronization (ES) and edit distance (ED). Event synchronization has been frequently used to measure the synchronicity between the climate extremes like extreme precipitation by calculating the number of synchronized events between two events like time series. Edit distance measures the similarity/dissimilarity between the events by reducing the number of operations required to convert one segment to another, that consider the events’ occurrence and amplitude. Here, we compare the extreme precipitation patterns obtained from both network construction methods based on different network’s characteristics. We used degree to understand network topology and identify important nodes in the networks. We also attempted to quantify the impact of precipitation seasonality and topography on extreme events. The study outcomes suggested that the degree is decreased in the southwest to the northwest direction and the timing of peak precipitation influences it. We also found an inverse relationship between elevation and timing of peak precipitation exists and the lower elevation greatly influences the connectivity of the stations. The study highlights that Edit distance better captures the network’s topology without getting affected by artificial boundaries.
T. Braun, S. Breitenbach, E. Ray, J. U. L. Baldini, L. M. Baldini, F. Lechleitner, Y. Asmerom, K. M. Prufer, N. Marwan:
Two millennia of seasonal rainfall predictability in the neotropics with repercussions for agricultural societies,
AGU 2021 Fall Meeting,
New Orleans (USA),
December 13–21, 2021,
Talk.
» Abstract
The reconstruction and analysis of palaeoseasonality from speleothem records remains a notoriously challenging task. Although the seasonal cycle is obscured by noise, dating uncertainties and irregular sampling, its extraction can identify regime transitions and enhance the understanding of long-term climate variability. Shifts in seasonal predictability of hydroclimatic conditions have immediate and serious repercussions for agricultural societies. We present a highly resolved speleothem record (ca. 0.22 years temporal resolution with episodes twice as high) of palaeoseasonality from Yok Balum cave in Belize covering the Common Era (400-2006 CE) and demonstrate how seasonal-scale hydrological variability can be extracted from δ13C and δ18O isotope records. We employ a Monte-Carlo based framework in which dating uncertainties are transferred into magnitude uncertainty and propagated. Regional historical proxy data enable us to relate climate variability to agricultural disasters throughout the Little Ice Age and population size variability during the Terminal Classic Maya collapse.
Spectral analysis reveals the seasonal cycle as well as nonstationary ENSO- and multi-decadal-scale variability. The degree to which farmers can reliably predict crop yield is both affected by long-term hydroclimate conditions and short-term variations in the subannual distribution of rainfall. A recurrence analysis reveals transitions in seasonal-scale predictability and links them to the mean hydroclimate. Predictability of seasonal rainfall variations was rendered progressively less predictable during the classic Maya collapse. These results are discussed in the context of their implications for rainfall dependent agricultural societies.
N. Marwan:
Nonlinear Time Series Analysis in Geosciences,
Kolloquium of Institute of Geoscience, University of Potsdam,
Potsdam (Germany),
December 13, 2021,
Lecture.
N. Marwan, H. Kraemer:
Hands-on workshop on complex systems,
GFZ Potsdam,
Potsdam (Germany),
November 4–5, 2021,
Lecture and workshop.
M. Kemter, N. Marwan, G. Villarini, B. Merz:
United States Flood Trends and Their Drivers,
Second International Conference on Natural Hazards and Risks in a Changing World,
Potsdam (Germany),
October 5-6, 2021,
Poster.
» Abstract
Climate change has already altered the magnitude and frequency of river floods around the world and if these trends persist in the future, our flood risk management will have to adapt to the changing conditions. However, to predict future changes, we must first understand how floods have changed in the past. Here we present a study of more than 4000 river gauges across the USA with time series of annual maximum streamflow between 1960–2010. We use a novel clustering approach to find 12 hydro-meteorologically and spatially distinct clusters of catchments with similar flood behavior. Based on re-analysis data we calculate more than 30 hydro-climatological and land-use variables to use them as predictors for 12 separate Random Forest models, one for each cluster. With these we search for the drivers of past trends in flood magnitudes, differences between common and rare floods as well as in the synchrony of floods in different catchments. We use Accumulated Local Effect plots to understand how each of the predictors affected the different trends. We find that in many regions changes in precipitation (e.g. annual precipitation sum, flood generating precipitation) translated to similar changes in flood magnitudes. Furthermore, we show that static land use conditions were of unexpected importance for flood trends, especially in the form of canopy cover, reservoirs, and impervious surfaces. We show that forests and reservoirs have mitigated some of the effects of a changing climate on floods, while urbanization has amplified them. We find varying importance and occasionally opposing effects of the same predictors in different clusters, showing that flood trends are highly dependent on the hydro-climatological circumstances of the catchments. Our results highlight the importance of a holistic approach to the analysis of flood trends and their drivers, considering a wide and consistent range of variables while taking into account the regional variability in flood generation.
A. Banerjee, B. Goswami, N. Marwan, B. Merz, B., J. Kurths:
Complex network approach to study the impacts of ENSO over the United States,
Second International Conference on Natural Hazards and Risks in a Changing World,
Potsdam (Germany),
October 5-6, 2021,
Poster.
» Abstract
Complex network analysis is a powerful tool that encodes the intricate relationship between the many components of a complex system. Functional climate network analysis is particularly designed to study the complex interactions between the different components of the Earth’s climate system. As the weather changes, the dynamical interaction between the grid points or the nodes should also change. We have used an evolving climate network approach to study this evolution of interaction between the nodes over time. In our work, we study temperature and precipitation patterns in the United States using this framework. El Niño–Southern Oscillation (ENSO) is one of the most important sources of annual global climate variability, associated with characteristic patterns of rainfall and temperature, includinng extreme events such as floods and droughts. The United States is one of the most susceptible regions to severe weather outbreaks due to the ENSO. We use Pearson correlation and edit-distance methods as similarity measures to construct temperature and extreme precipitation networks respectively.
We study the course of evolution of the link patterns using network measures such as robust links, link density, and transitivity during the different phases of the ENSO. Through our analysis, we are able to distinguish between the different phases of the ENSO, and hence, identify the different large-scale atmospheric circulation patterns associated with them.
S. M. Vallejo-Bernal, F. Wolf, N. Boers, N. Marwan, J. Kurths:
Synchronicity of heavy rainfall induced by atmospheric rivers over North America,
Second International Conference on Natural Hazards and Risks in a Changing World,
Potsdam (Germany),
October 5-6, 2021,
Poster.
» Abstract
Atmospheric rivers (ARs) are dynamical features of the low atmosphere, responsible for much of the moisture transport in the midlatitudes, that can produce copious amounts of precipitation as long as an external uplifting mechanism is available. In particular, land-falling ARs are strongly linked to heavy precipitation over the orographically complex western coast of the United States. Recently, complex network approaches have proven to effectively extract spatiotemporal variability patterns from climate data and have contributed to significant advances in the understanding and prediction of extreme weather events. In this study, we investigate the synchrony and interdependency of heavy rainfall occurrences related to ARs along the west coast of North America and the underlying physical mechanisms. We use the SIO R1 catalog of land-falling ARs and the daily rainfall estimates of the ERA5 reanalysis project during the period 1980–2018 to construct complex climate networks by applying the nonlinear Event Synchronization measure to the rainfall events above the 95th percentile. Our results reveal substantially different spatiotemporal rainfall patterns depending on the presence (or absence) of ARs. On the one hand, we find that ARs are linked with highly interconnected regions of synchronous heavy rainfall along the coastline and the adjacent Pacific Ocean. On the other hand, weaker but significant connections are observed over the continental North America in the absence of land-falling ARs. Also, the underlying atmospheric conditions differ visibly and exhibit a robust decadal pattern that is, however, highly variable for seasonal means. Resolving the typical synchrony structures of heavy rainfall related to the land-falling ARs, should lead to improved understanding of hydroclimate variability, likely leading to improved seasonal predictability of extreme precipitation.
N. Marwan:
Recent exciting developments in recurrence plot analysis,
9th International Symposium on Recurrence Plots,
Lublin (Poland),
September 22–24, 2021,
Talk.
» Abstract
I reported on recent achievements in recurrence plot research ten years ago. It is time to look back at the last ten years of exciting developments that had been achieved for improving recurrence plot analysis and to widen its application potential. I will give a brief overview about important and innovative developments, such as conceptual recurrence plots, ideas for parameter selection, recurrence grammars, event-like, multiscale, and heterogeneous recurrences, and correction schemes. New perspectives have recently been opened by combining recurrence plots with machine learning.
A. Das, A. P. Nandan, N. Marwan, A. Koseska:
Identifying transient metastable states from live-cell imaging data,
9th International Symposium on Recurrence Plots,
Lublin (Poland),
September 22–24, 2021,
Talk.
» Abstract
The current models of cellular information processing are formulated with the assumption that the relevant dynamics occur near or at the steady-state. One of the advantages when focusing on the asymptotic behavior at or near a steady-state is that it simplifies the analysis of the system. Recently, however, we proposed theoretical and practical reasons that steady-state analysis misses essential behavior of living systems, especially when describing how single cells process non-stationary signals. Using fluorescence measurements of real-time protein activities in single cells, we demonstrate that protein networks utilize transient dynamics away from steady-state to maintain a memory of previously encountered signals and thereby navigate in complex environments. To identify such out-of-equilibrium transients from experimental data in general, we develop a recurrence-based method that can be applied to a broad class of systems, without prior knowledge of the underlying dynamics of the system.
I. Pavithran, V. R. Unni, R. I. Sujith, J. Kurths, N. Marwan:
Recurrence condensation during critical transitions in complex systems,
9th International Symposium on Recurrence Plots,
Lublin (Poland),
September 22–24, 2021,
Talk.
» Abstract
Many dynamical systems exhibit critical transitions, which can result in catastrophic changes to the state of the system. Spontaneous emergence of an ordered dynamics from disorder is common among several systems. Even inherently turbulent systems can undergo such transition to ordered periodic dynamics. A recent discovery shows that the emergence of self-sustained periodic oscillations from an initially disordered state in various systems is accompanied by the phenomenon of spectral condensation. It is the sharpening of the peak in the amplitude spectrum accompanied by the growth of amplitude of the dominant oscillatory mode.
In the present work, we identify an analogous phenomenon known as recurrence condensation in recurrence plots (RPs) of the system variables during the transition to self-sustained periodic oscillations. We construct RPs from the time series of state variables by fixing the recurrence rate to be constant. During the transition from a chaotic state to periodic oscillations via intermittency, the RP changes from a disordered arrangement of short, broken diagonal lines to patches of ordered short diagonal lines and then to a pattern with long diagonal lines. Here, the scattered RP changes to diagonal lines, and their spacing corresponds to the dominant time scale in the system.
We aim to quantify recurrence condensation using recurrence quantification measures, an appropriate method for analyzing nonlinear, high-dimensional complex systems. Here, we use these measures to study the emergence of periodicity, which is reflected as long diagonal lines in RPs. The recurrence measures such as determinism, entropy, laminarity, and trapping time exhibit a gradual variation during recurrence condensation. Further, these recurrence measures follow a power-law scaling with the control parameter on approaching the transition. These scaling relations hold only till a critical point during the transition.
The best power-law fit with minimum scatter is observed when considering the measures only up to a particular control parameter. The fitting error increases afterwards, indicating a deviation from the scaling. Utilizing this property, we find a critical value of the control parameter up to which the recurrence measures follow scalings. Further, we construct RPs of synthetic data from a noisy Hopf bifurcation model and uncover that the value of the critical point detected is the same as the Hopf point. Our analysis indicates that the finding of the optimal power law can be used to define critical points in noisy systems with gradual transitions, where the transition point is not easily identifiable.
T. Braun, V. R. Unni, R. I. Sujith, J. Kurths, N. Marwan:
Multiscale recurrence quantification with recurrence lacunarity,
9th International Symposium on Recurrence Plots,
Lublin (Poland),
September 22–24, 2021,
Talk.
» Abstract
We propose Recurrence Lacunarity (RL) as a novel recurrence quantification measure. Lacunarity, as originally introduced by B.Mandelbrot (1983), is usually interpreted as a measure of heterogeneity or translational invariance of some spatial pattern. Compared to traditional recurrence quantifiers, RL offers the advantage that it is sensitive to more general geometric features beyond line structures of a recurrence plot. It is demonstrated how RL can be used to characterize the recurrence between dynamical states at all relevant time scales of a complex system. An application to time series of acoustic pressure fluctuations from a turbulent combustor showcases the great potential of RL in detecting abrupt regime shifts of different origin in nonlinear dynamical systems. Finally, potential future applications and conceptual extensions of RL are discussed.
K. H. Kraemer, F. Hellmann, J. Kurths, N. Marwan:
Recurrence powerspectra,
9th International Symposium on Recurrence Plots,
Lublin (Poland),
September 22–24, 2021,
Talk.
» Abstract
A novel kind of powerspectrum is constructed, the textitspike powerspectrum, which transforms spike-train-like signals into their frequency domain. This method clearly shows the apparent cycles in the data and overcomes the problems when using the obvious idea of Fourier-transforming it. We invent this instructive approach with the idea of transforming the $\tau$-recurrence rate of a recurrence plot (RP), which often has a spiky appearance. The $\tau$-recurrence rate is the density of recurrence points along diagonals of the RP, which are parallel to the main diagonal with a distance of $\tau$. In this context the spike powerspectrum can be interpreted as a nonlinear power spectrum of a potentially high dimensional system which constitutes the RP. The proposed measure is simple to compute, robust to noise and is able to detect bifurcations inducing regular-regular, regular-chaos as well as chaos-chaos transitions.
C. Ozdes, S. Breitenbach, D. Eroglu, N. Marwan, N:
Revealing past climate networks from data,
9th International Symposium on Recurrence Plots,
Lublin (Poland),
September 22–24, 2021,
Talk.
» Abstract
Real-world complex systems such as the climate system of interacting spatially-diverse weather patterns or ecological communities are essential parts of our everyday lives. Such systems are composed of a large number of units represented by the nodes of a network enacting an intricate interaction structure. These structures are the topic of network science, a very active research field significantly improving the quality of living standards by forecasting the dynamical behavior of complex systems. These interaction structures are also very hard to detect in climate networks, where a reconstruction procedure requires dealing with sparse and noisy data coming from multi-scale spatiotemporal dynamics. Paleoclimate data sets are also not regularly sampled, and the measurements are not precise. To model this error process, we fit a trained transformation-cost time series to paleoclimate data using the metric of segment similarity, which maximizes prior normality. This transformation-cost series can act as a regularly sampled proxy to be used in detecting the dynamical properties of data sets using recurrence quantification methods. This procedure reveals interactions that are often not detectable in the original data. We then use sliding windows analyses of these recurrence measures to obtain the temporal correlation networks that define interaction between our data sources. We use this method to reconstruct the evolution of the climate interaction network for Asia to reveal its transient and stable interaction patterns in the past.
B. G. Straiotto, N. Marwan, D. C. James, P. J. Seeley:
A combination of principal component and recurrence analyses discriminates between closely similar movement patterns,
9th International Symposium on Recurrence Plots,
Lublin (Poland),
September 22–24, 2021,
Talk.
» Abstract
Investigation of the movement of body segments and their coordination can provide insight into underpinning motor control strategies. We aimed to determine whether combined application of principal component and recurrence quantification analyses might discriminate between spatial and temporal aspects of apparently similar movement patterns. Backwards-forwards movements of elite (n = 9) and non-elite (n = 9) taekwondo players employed in both defensive and attacking actions were recorded using motion capture techniques, and features of whole-body movement defined at segment level were investigated by principal component analysis. For both groups of players, four movement components explained > 90% of the variability in the data.
The time series derived from scores for each of the principal components were subsequently subjected to recurrence quantification analysis, player by player. For the first component, statistically significant differences between groups were detected for the recurrence measurement determinism (p < 0.05). For the third component, statistically significant differences were detected for the recurrence measurements laminarity and maxline (p < 0.01). Application of surrogation to recurrence data indicated that differences between elite and non-elite groups were deterministic in origin and not the result of data noise ( p < 0.01).
Contrasting operation of taekwondo movements within and between our player groups were revealed qualitatively in the coefficients derived from principal component analysis and quantitatively through combined principal component and recurrence techniques. Variations in TKD player execution of this apparently simple movement pattern may represent more skilled motor control in elite players that is related to the functional importance of backwards-forwards movements in sparring and competition.
N. Marwan:
Co-authorship network of the recurrence plot domain,
9th International Symposium on Recurrence Plots,
Lublin (Poland),
September 22–24, 2021,
» Poster (PDF, 58.87M).
N. Marwan, T. Braun:
Module 5 – Complex Systems, Recurrence and Networks in Climate,
Summer school on Trends, rhythms and events in the Earth's climate system,
Online/ Potsdam (Germany),
August 30 – September 3, 2021,
Lecture.
» Abstract
Many processes in the Earth's climate system are complex, behave in an unpredictable way, and are nonlinearly coupled, which is why linear methods of time series analysis fail to characterize them or to uncover their complex interrelationships. This module will teach fundamental properties of complex systems and the basics of dynamical systems theory. Examples from atmospheric science and paleoclimate variability will be used to demonstrate the challenges in investigating such systems. Modern methods from nonlinear dynamics will be introduced, such as recurrence-based methods and complex networks. The students will learn in which applications these methods will provide complimentary information, how to reliably apply these methods, and how to develop corresponding statistical tests. Moreover, concepts to address common challenges in (paleo-)climate data analysis (such as heavy-tailed and event-like data, dating uncertainties, and irregular sampling) will be introduced. A focus will be on detecting subtle regime changes and complex interrelationships, where linear methods fail.
M. Kemter, N. Marwan, G. Villarini, B. Merz:
Drivers of Flood Trends in the United States,
Tag der Hydrologie,
Potsdam (Germany),
August 30 – September 1, 2021,
Poster.
I. Pavithran, V. R. Unni, A. Saha, A. J. Varghese, R. I. Sujith, J. Kurths, N. Marwan:
Predicting the Amplitude of Thermoacoustic Instability Using Universal Scaling Behaviour,
ASME Turbo Expo 2022,
Rotterdam (The Netherlands),
June 9, 2021,
Talk.
» Abstract
The complex interaction between the turbulent flow, combustion and the acoustic field in gas turbine engines often results in thermoacoustic instability that produces ruinously high-amplitude pressure oscillations. These self-sustained periodic oscillations may result in a sudden failure of engine components and associated electronics, and increased thermal and vibrational loads. Estimating the amplitude of the limit cycle oscillations that are expected during thermoacoustic instability helps in devising strategies to mitigate and to limit the possible damages due to thermoacoustic instability. We propose two methodologies to estimate the amplitude using only the pressure measurements acquired during stable operation. First, we use the universal scaling relation of the amplitude of the dominant mode of oscillations with the Hurst exponent to predict the amplitude of the limit cycle oscillations. We also present a methodology to estimate the amplitudes of different modes of oscillations separately using “spectral measures,” which quantify the sharpening of peaks in the amplitude spectrum. The scaling relation enables us to predict the peak amplitude at thermoacoustic instability, given the data during the safe operating condition. The accuracy of prediction is tested for both methods, using the data acquired from a laboratory-scale turbulent combustor. The estimates are in good agreement with the actual amplitudes.
A. Banerjee, B. Goswami, N. Marwan, B. Merz, J. Kurths:
Recurrence based coupling analysis between event-like data and continuous data,
(Virtual) EGU General Assembly,
Vienna (Austria),
April 19–30, 2021,
DOI:10.5194/egusphere-egu21-14831,
Talk.
» Abstract
Extreme events such as earthquakes, tsunamis, heat weaves, droughts, floods, heavy precipitation, or tornados – affect the human communities and cause tremendous loss of property and wealth, but can be related to multiple and complex sources. For example, a flood is a natural event caused by many drivers such as extreme precipitation, soil moisture, or temperature. We are interested in understanding the direct and indirect coupling between flood events with different climatological and hydrological drivers such as soil moisture and temperature.
We use multivariate recurrence plot and recurrence quantification analysis as a powerful framework to study the couplings between the different systems, especially the direction of coupling. The standard delay-embedding method is not a suitable for the recurrence analysis of event-like data. Therefore, we apply the novel edit-distance method to compute recurrence plots of time series of flood events and use the standard recurrence plot method for the continuous varying time series such as soil moisture and temperature. The coupling analysis is performed using the mean conditional probabilities of recurrence derived from the different recurrence plots. We demonstrate this approach on a prototype system and apply it on the hydrological data. Using this approach we are able to indicate the coupling direction and lag between the different coupled systems.
T. Braun, S. Breitenbach, E. Ray, J. U. L. Baldini, L. M. Baldini, F. Lechleitner, Y. Asmerom, K. M. Prufer, N. Marwan:
Two millennia of seasonal rainfall predictability in the neotropics with repercussions for agricultural societies,
(Virtual) EGU General Assembly,
Vienna (Austria),
April 19–30, 2021,
DOI:10.5194/egusphere-egu21-11012,
Talk.
» Abstract
The reconstruction and analysis of palaeoseasonality from speleothem records remains a notoriously challenging task. Although the seasonal cycle is obscured by noise, dating uncertainties and irregular sampling, its extraction can identify regime transitions and enhance the understanding of long-term climate variability. Shifts in seasonal predictability of hydroclimatic conditions have immediate and serious repercussions for agricultural societies.
We present a highly resolved speleothem record (ca. 0.22 years temporal resolution with episodes twice as high) of palaeoseasonality from Yok Balum cave in Belize covering the Common Era (400-2006 CE) and demonstrate how seasonal-scale hydrological variability can be extracted from δ13C and δ18O isotope records. We employ a Monte-Carlo based framework in which dating uncertainties are transferred into magnitude uncertainty and propagated. Regional historical proxy data enable us to relate climate variability to agricultural disasters throughout the Little Ice Age and population size variability during the Terminal Classic Maya collapse.
Spectral analysis reveals the seasonal cycle as well as nonstationary ENSO- and multi-decadal-scale variability. Variations in both the subannual distribution of rainfall and mean average hydroclimate pose limitations on how reliably farmers can predict crop yield. A characterization of year-to-year predictability as well as the complexity of seasonal patterns unconver shifts in the seasonal-scale variability. These are discussed in the context of their implications for rainfall dependent agricultural societies.
Z. Su, S. Gupta, N. Marwan, N. Boers, J. Kurths:
A comparative study of extreme precipitation patterns using complex networks,
(Virtual) EGU General Assembly,
Vienna (Austria),
April 19–30, 2021,
DOI:10.5194/egusphere-egu21-8740,
Talk.
» Abstract
The spatio-temporal patterns of precipitation are of considerable relevance in the context of understanding the underlying mechanism of climate phenomena. The application of the complex network paradigm as a data-driven technique for the investigation of the climate system has contributed significantly to identifying the key regions influencing the climate variability of a target region of interest and, in particular, to improving the predictability of extreme events. In our work, we conduct a comparative study of precipitation patterns by constructing functional climate networks using two nonlinear event similarity measures – event synchronization (ES) and edit-distance (ED). Event synchronization has been widely applied to identify interactions between occurrences of different climate phenomena by counting the number of synchronized events between two event series. Edit-distance measures the similarity between sequences by minimizing the number of operations required to transform one sequence to another. We suggest edit-distance as an alternative approach for network reconstruction that can measure similarity between two event series by incorporating not only event occurrences but also event amplitudes. Here, we compare the global extreme precipitation patterns obtained from both reconstruction methods based on the topological characteristics of the resulting networks. As a case study, we compare selected features of network representations of East Asian heavy precipitation events obtained using both ES and ED. Our results reveal the complex nature of the interaction between the Indian Summer Monsoon (ISM) and the East Asian Summer Monsoon (EASM) systems. Through a systematic comparison, we explore the limitations of both measures and show the robustness of the network structures.
H. Kraemer, G. Datseris, J. Kurths, I. Kiss, J. L. Ocampo-Espindola, N. Marwan:
A unified and automated approach to attractor reconstruction,
(Virtual) EGU General Assembly,
Vienna (Austria),
April 19–30, 2021,
DOI:10.5194/egusphere-egu21-1495,
Talk.
» Abstract
Since acquisition costs for sensors and data collection decrease rapidly especially in the geo-scientific fields, researchers often have to deal with a large amount of multivariable data, which they would need to automatically analyze in an appropriate way. In nonlinear time series analysis, phase space reconstruction often makes the very first step of any sophisticated analysis, but the established methods are either unable to reliably automate the process or they can not handle multivariate time series input. Here we present a fully automated method for the optimal state space reconstruction from univariate and multivariate time series. The proposed methodology generalizes the time delay embedding procedure by unifying two promising ideas in a symbiotic fashion. Using non-uniform delays allows the successful reconstruction of systems inheriting different time scales. In contrast to the established methods, the minimization of an appropriate cost function determines the embedding dimension without using a threshold parameter. Moreover, the method is capable of detecting stochastic time series and, thus, can handle noise contaminated input without adjusting parameters. The superiority of the proposed method is shown on some paradigmatic models and experimental data.
J. Fohlmeister, N. Sekhon, A. Columbu, K. Rehfeld, L. Sime, C. Veige-Pires, N. Marwan, N. Boers:
Global reorganization of atmospheric circulation during Dansgaard-Oschger cycles,
(Virtual) EGU General Assembly,
Vienna (Austria),
April 19–30, 2021,
DOI:10.5194/egusphere-egu21-9433,
Talk.
» Abstract
Ice core records from Greenland provide evidence for multiple abrupt warming events recurring at millennial time scales during the last glacial interval. Although climate transitions strongly resembling these Dansgaard-Oeschger (DO) transitions have been identified in several speleothem records, our understanding of the climate and ecosystem impacts of the Greenland warming events in lower latitudes remains incomplete.
Here, we investigate the influence of DO transitions on the global atmospheric circulation pattern. We comprehensively analyse d18O changes during DO transitions in a globally distributed dataset of speleothems (SISALv2; Comas-Bru et al., 2020). Speleothem d18O signals mostly reflect changes in precipitation amount and moisture source. Thereby this proxy allows us to infer spatially resolved changes in global atmospheric dynamics that are characteristically linked to DO transitions. We confirm the previously proposed shift of the Intertropical Convergence Zone towards more northerly positions. In addition, we find evidence for a similar northward shift of the westerly winds of the Northern Hemisphere. Furthermore, we identify a decreasing trend in the transition amplitudes with increasing distances from the North Atlantic region. This confirms previous suggestions of this region being the core and origin of these past abrupt climate changes.
M. Singh, R. Krishnan, B. Goswami, A. Dey Choudhury, S. Panickal, R. Vellore, P. A. Gopinathan, S. Narayanasetti, C. Venkataraman, R. Donner, N. Marwan, J. Kurths:
Fingerprint of volcanic forcing on the ENSO–Indian monsoon coupling,
(Virtual) EGU General Assembly,
Vienna (Austria),
April 19–30, 2021,
DOI:10.5194/egusphere-egu21-9059,
Talk.
» Abstract
The coupling between the El Niño–Southern Oscillation (ENSO) and Indian Monsoon (IM) plays a significant role in the summer rainfall over the Indian subcontinent. In this study, we provide insights into the IM variability with regard to the degree of ENSO variability and radiative forcing from large volcanic eruptions (LVEs). Volcanic dust and gas injected into the stratosphere during major eruptions influence the ENSO from seasonal to interannual timescales. However, the effects of LVEs on the ENSO-IM coupling remain unclear. The relationship between ENSO and IM systems in the context of LVEs is examined using a panoply of datasets and advanced statistical analysis techniques in this study. We find that there is a significant enhancement of the phase-synchronization between ENSO and IM oscillations due to increase in angular frequency of ENSO in the last millennium. Twin surrogates-based statistical significance testing is also used to affirm this result and similar evidence is found in the combinations of 14 ENSO and 11 IM paleoclimate proxy records in the last millennium. Bayesian probabilities conditioned with and without LVEs show LVEs lead to a strong ENSO-IM phase-coupling, with the probabilities remaining higher till the fourth year from the eruption. A large-ensemble climate model experiment with and without the 1883 Krakatoa eruption is conducted using the IITM-ESM, and also with varied volcanic radiative forcing (VRF) depending on the evolved state of ENSO. The simulations show that LVEs force the ENSO-IM systems into a coupled state, and increase (decrease) in the VRF leads to an enhanced (decreased) probability of the phase synchronisation of ENSO-IM systems with a high chance of El Niño-IM drought in the year following the LVE. Our results promisingly pave a way not only for improving the seasonal monsoon prediction improvements but also for the regional impact assessment from the proposed geo-engineering activities over the South Asian region.
Complex networks provide an interesting tool to investigate spatio-temporal data. The first step is to reconstruct a (functional) network from data. I will show different reconstruction approaches depending on the research question and the nature of the data. The procedure is illustrated with applications on climate data.
><2020
M. Kemter, B. Merz, N. Marwan:
Trends in flood magnitudes, flood extents and their drivers,
AGU Fall Meeting,
online,
December 1–17, 2020,
Talk.
» Abstract
When rivers flood, they often do so simultaneously with surrounding rivers. We call the area across which this happens the flood extent. We study trends in flood extents in Europe and the US, and analyze how they are linked to trends in flood magnitude. For the time period 1960-2010 we analyze the annual maximum floods of 5000 US- and 4000 European hydrometric stations and investigate generating processes of all floods based on climate re-analysis data. We use event synchronization and complex networks to find groups of stations that have similar flood behavior. For both regions, we find a positive correlation between extents and magnitudes for 93% of the stations. While the trends of both variables are well aligned in Europe (increasing in the west, decreasing in the south), the same is not true for the US. The station groups help us to understand these differences. We show that the changing influence of snowmelt on flood generation is crucial for the relationship of magnitude and extent trends.
A. Agarwal, N. Marwan, R. Maheswaran, U. Ozturk, J. Kurths, B. Merz:
Optimal design of hydrometric station networks based on complex network analysis,
AGU Fall Meeting,
online,
December 1–17, 2020,
Talk.
» Abstract
Hydrometric networks play a vital role in providing information for decision-making in water resources management. They should be set up optimally to provide as much and as accurate information as possible, and at the same time, be cost-effective. Although the design of hydrometric networks is a well-identified problem in hydrometeorology and has received considerable attention, yet there is scope for further advancement. In this study, we use complex network analysis, defined as a collection of nodes interconnected by links, to propose a new measure that identifies critical nodes of station networks. The approach can support the design and redesign of hydrometric station networks. The science of complex networks is a relatively young field and has gained significant momentum in the last years in different areas such as brain networks, social networks, technological networks, or climate networks. The identification of influential nodes in complex networks is an important field of research. We propose a new node ranking measure, the weighted degree-betweenness (WDB), to evaluate the importance of nodes in a network. It is compared to previously proposed measures on synthetic sample networks and then applied to a real-world rain gauge network comprising 1229 stations across Germany to demonstrate its applicability. The proposed measure is evaluated using the decline rate of network efficiency and the kriging error. The results suggest that WDB effectively quantifies the importance of rain gauges, although the benefit of the method needs to be investigated in more detail.
T. Westerhold, N. Marwan, A. Joy Drury, D. Liebrand, C. Agnini, E. Anagnostou, J. Barnet, S. M. Bohaty, D. De Vleeschouwer, F. Florindo, T. Frederichs, D. A. Hodell, A. Holbourn, D. Kroon, V. Lauretano, K. Littler, L. J. Lourens, M. W. Lyle, H. Paelike, U. Roehl, J. Tian, R. Wilkens, Paul. A. Wilson, J. C. Zachos:
Changing state of Earth’s climate for the last 66 million years,
AGU Fall Meeting,
online,
December 1–17, 2020,
Talk.
» Abstract
We combined the best available high-resolution ocean drilling records with newly generated data to produce a continuous, astronomically tuned 66-million-year record of global climate that can serve as a new Cenozoic global reference benthic foraminiferal carbon and oxygen isotope dataset (CENOGRID). The CENOGRID represents the first community effort to systematically assemble a high-fidelity deep-sea isotope record that captures the high and low frequency variations of the climate system on a global scale, providing the framework required for understanding the nature of the major climate states, transitions and events. Within the constraints imposed by temporal resolution in older segments and potential artefacts related to differences in the regional response to orbital forcing, (e.g., obliquity), this singly unique record reveals how long-term gradual shifts in boundary conditions, principally paleogeography, ice-volume, and the mean level of greenhouse gases create state dependent shifts in the sensitivity of the climate system to periodic oscillations in solar forcing. We believe that this phenomenon is related to feedbacks associated with the carbon cycle supporting the critical role of GHG in enhancing climate sensitivity to solar radiative forcing.
N. Marwan:
Measuring complexity of recurrence plots,
GMT Morning Workshop on Nonlinear Dynamics and Statistics,
virtual,
December 3, 2020,
Talk.
N. Marwan:
Investigation of Recurrence Phenomena in the Earth System,
Seminar "Big Data Platform" at DLR Institute of Data Science,
Jena (Germany),
August 6, 2020,
Lecture.
» Abstract
Recurrence is a ubiquitous and fundamental feature in many real world processes. Here, I will focus on recurrence in the system Earth, where it is present at many scales in time and space, such as the rock cycle, activity of an active geyser, celestial mechanics, repeating patterns in a landscape, cycles of glaciation, epochs of geomagnetic polarity, or alternating sediment layers. The study of recurrence properties (such as frequency analysis) can provide deeper insights into the dynamical processes in general. A rather novel approach for the study of recurrences is the so-called recurrence plot and its quantification, rooted in the theory of dynamical systems. In this talk, I will present the basic concept and the major extensions applicable to various research questions. Discussed examples include the temporal change of recurrence properties for identification of regime shifts in climate; spatio-temporal recurrences for classification of landuse dynamics; and bivariate extensions for synchronization/coupling analysis for time scale alignment of palaeoclimate observations. Methodological and numerical Challenges and pitfalls will also be discussed.
N. Marwan:
Investigation of Recurrence Phenomena in the Earth System,
HEIBRIDS Lecture Series,
Berlin (Germany),
July 1, 2020,
Lecture.
» Abstract
Recurrence is a ubiquitous and fundamental feature in many real world processes. Here, I will focus on recurrence in the system Earth, where it is present at many scales in time and space, such as the rock cycle, activity of an active geyser, celestial mechanics, repeating patterns in a landscape, cycles of glaciation, epochs of geomagnetic polarity, or alternating sediment layers. The study of recurrence properties (such as frequency analysis) can provide deeper insights into the dynamical processes in general. A rather novel approach for the study of recurrences is the so-called recurrence plot and its quantification, rooted in the theory of dynamical systems. In this talk, I will present the basic concept and the major extensions applicable to various research questions. Discussed examples include the temporal change of recurrence properties for identification of regime shifts in climate; spatio-temporal recurrences for classification of landuse dynamics; and bivariate extensions for synchronization/coupling analysis for time scale alignment of palaeoclimate observations. Methodological and numerical Challenges and pitfalls will also be discussed.
B. Goswami, A. Hartland, C. Hu, S. Hoepker, B. R. S Fox, N. Marwan, S. F. M. Breitenbach:
Paleo-drip rates from trace metal concentrations in stalagmites: An inverse modeling problem with data uncertainties,
(Virtual) EGU General Assembly,
Vienna (Austria),
May 4-8, 2020,
DOI:10.5194/egusphere-egu2020-19959,
Talk.
» Abstract
The concentration of trace elements such as Ni, Co, and Cu in a stalagmite is determined by (i) the amount of these elements present in so-called organic-metal complexes (OMCs) that trap the ionic forms of such elements in the dripwater, and (ii) the amount that is able to decay from the OMCs into the aqueous phase, from where the elements can adsorb to the growing stalagmite surface (and remain captured within the stalagmite crystal structure). A statistical treatment of the decay of a population of trace element ions from OMCs allow us to model the rates at which the dripwater dropped from the roof of the cave on to the stalagmite's surface. The problem is however made challenging due to: (i) the lack of reliable monitoring data that quantifies the relationship between OMC trace metal ion concentration and stalagmite trace metal ion concentration, and (ii) the presence of chronological uncertainties in our estimates of trace element concentrations at past time points from the depth-based measurements along the stalagmite. We present here a semi-heuristic, semi-theoretical approach that estimates dripwater rates using a theoretical model based on the population-level chemical kinetics of trace element decay from OMCs, and a heuristic choice of calibration data sets based on precipitation and temperature from nearby weather station data. Our approach is applied to trace metal data from the Heshang Cave in southeastern China, and we are able to reconstruct a driprate proxy time series – a first quantitative hydrological proxy record presented along with well-defined estimates of uncertainty.
T. Braun, N. Marwan, V. R. Unni, R. I. Sujith, J. Kurths:
Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure,
(Virtual) EGU General Assembly,
Vienna (Austria),
May 4-8, 2020,
DOI:10.5194/egusphere-egu2020-3475,
Talk.
» Abstract
We propose Lacunarity as a novel recurrence quantification measure and apply it in the context of dynamical regime transitions. Many complex real-world systems exhibit abrupt regime shifts. We carry out a recurrence plot based analysis for different paradigmatic systems and thermoacoustic combustion time series in order to demonstrate the ability of our method to detect dynamical transitions on variable temporal scales. Lacunarity is usually interpreted as a measure of "gappiness" of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogenity in the temporal recurrent patterns. Our method succeeds to distinguish states of varying dynamical complexity in presence of noise and short time series length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and features beyond the scope of line structures can be accounted for. Applied to acoustic pressure fluctuation time series, it captures both the rich variability in dynamical complexity and detects shifts of characteristic time scales.
K. Prufer, S. F. M. Breitenbach, J. Baldini, T. Braun, E. Ray, L. Baldini, V. Polyak, F. Lechleitner, N. Marwan, D. Kennett, Y. Asmerom:
A 1,600 year record of paleoseasonality from the neotropics of Central America and its implications for rainfall predictability in agricultural societies,
(Virtual) EGU General Assembly,
Vienna (Austria),
May 4-8, 2020,
DOI:10.5194/egusphere-egu2020-18100,
Talk.
» Abstract
For millions of people living in the humid neotropics seasonally predictable rainfall is crucial for agricultural success and food security. Understanding long-term stability and volatility of seasonal rainfall distributions should be of concern to researchers and policy makers. However, reconstructions of paleorainfall seasonality in the neotropics have been constrained by a lack of precisely dated and sub-annually resolved records. We present a 1,600-year rainfall paleoseasonality reconstruction from speleothem sample Yok G, from Yok Balum Cave located in southern Belize, Central America. Yok G grew continuously from 400 C.E. to 2,006 C.E. and its age is constrained by 52 U-series dates with a mean error of 7 years. The isotope record consists of 7,151 δ18O and δ13C measurements at 0.22-year resolution allowing us to detect the presence and amplitude of annual wet-dry cycles. In Belize rainfall distribution and seasonality controls are currently dominated by the annual migration of the intertropical convergence zone (ITCZ) with marked meridional contrast. The Yok G record suggest distinct changes in seasonality at multi-centennial intervals. The earliest portion of the record (400- 850 C.E.) shows little intra-annual seasonal variation, the period from 850-1400 C.E. has highly variable annual oscillations and periods of low seasonality, while the period from 1,400-2,006 C.E. shows well developed seasonal signals. Element ratios (Mg/Ca, Sr/Ca, and U/Ca) are used to assess Prior Carbonate Precipitation in the epikarst system. We review these changes and the isotopic record from Yok G and discuss tools for interpreting the stability and volatility in seasonal rainfall distributions and possible implications for past and modern agricultural societies.
A. Giesche, S. F. M. Breitenbach, N. Marwan, A. Hartland, B. Plessen, J. F. Adkins, H. H. Haug, A. French, C. A. Petrie, D. A. Hodell:
Rainfall seasonality changes in northern India across the 4.2 ka event,
(Virtual) EGU General Assembly,
Vienna (Austria),
May 4-8, 2020,
DOI:10.5194/egusphere-egu2020-16898,
Talk.
» Abstract
For millions of people living in the humid neotropics seasonally predictable rainfall is crucial for agricultural success and food security. Understanding long-term stability and volatility of seasonal rainfall distributions should be of concern to researchers and policy makers. However, reconstructions of paleorainfall seasonality in the neotropics have been constrained by a lack of precisely dated and sub-annually resolved records. We present a 1,600-year rainfall paleoseasonality reconstruction from speleothem sample Yok G, from Yok Balum Cave located in southern Belize, Central America. Yok G grew continuously from 400 C.E. to 2,006 C.E. and its age is constrained by 52 U-series dates with a mean error of 7 years. The isotope record consists of 7,151 δ18O and δ13C measurements at 0.22-year resolution allowing us to detect the presence and amplitude of annual wet-dry cycles. In Belize rainfall distribution and seasonality controls are currently dominated by the annual migration of the intertropical convergence zone (ITCZ) with marked meridional contrast. The Yok G record suggest distinct changes in seasonality at multi-centennial intervals. The earliest portion of the record (400- 850 C.E.) shows little intra-annual seasonal variation, the period from 850-1400 C.E. has highly variable annual oscillations and periods of low seasonality, while the period from 1,400-2,006 C.E. shows well developed seasonal signals. Element ratios (Mg/Ca, Sr/Ca, and U/Ca) are used to assess Prior Carbonate Precipitation in the epikarst system. We review these changes and the isotopic record from Yok G and discuss tools for interpreting the stability and volatility in seasonal rainfall distributions and possible implications for past and modern agricultural societies.
K. Riechers, N. Boers, J. Fohlmeister, N. Marwan:
Hypothesis testing and uncertainty propagation in paleo climate proxy data evidencing abrupt climate shifts,
(Virtual) EGU General Assembly,
Vienna (Austria),
May 4-8, 2020,
DOI:10.5194/egusphere-egu2020-15148,
Talk.
» Abstract
Reconstruction of ancient climate variability relies on inference from paleoclimate proxy data. However, such data often suffers from large uncertainties in particular concerning the age assigned to measured proxy values, which makes the derivation of clear conclusions challenging. Especially in the study of abrupt climatic shifts, dating uncertainties in the proxy archives merit increased attention, since they frequently happen to be of the same order of magnitude as the dynamics of interest. Yet, analyses of paleoclimate proxy reconstructions tend to focus on mean values and thereby conceal the full range of uncertainty. In addition, the statistical significance of the reported results is sometimes not or at least not accurately tested. Here we discuss both, methods for rigorous propagation of uncertainties and for hypothesis testing with applications to the Dansgaard-Oeschger (DO) events of the last glacial interval and their varying timings in different proxy variables and archives. We scrutinized the mathematical analysis of different paleoclimate records evidencing the DO events and provide results that take into account the full range of uncertainties. We discuss several possibilities of testing the significance of apparent leads and lags between transitions found in proxy data evidencing DO events within and across different ice core archives from Greenland and Antarctica.
D.-D. Rousseau, S. Barbosa, W. Bagniewski, N. Boers, E. Cook, J. Fohlmeister, B. Goswami, N. Marwan, S. O. Rasmussen, L. Sime, A. Svensson:
Data quality in different paleo archives and covering different time scales: A key issue in studying tipping elements,
(Virtual) EGU General Assembly,
Vienna (Austria),
May 4-8, 2020,
DOI:10.5194/egusphere-egu2020-14267,
Talk.
» Abstract
Although the Earth system is described to react relatively abruptly to present anthropogenic forcings, the notion of abruptness remains questionable as it refers to a time scale that is difficult to constrain properly. Recognizing this issue, the tipping elements as listed in Lenton et al. (2008) rely on long-term observations under controlled conditions, which enabled the associated tipping points to be identified. For example, there is evidence nowadays that if the rate of deforestation from forest fires and the climate change does not decrease, the Amazonian forest will reach a tipping point towards savanna (Nobre, 2019), which would impact the regional and global climate systems as well as various other ecosystems, directly or indirectly. However, if the present tipping elements, which are now evidenced, are mostly related to the present climate change and thus directly or indirectly related to anthropogenic forcing, their interpretation must still rely on former cases detected in the past, and especially from studies of abrupt climatic transitions evidenced in paleoclimate proxy records. Moreover, recent studies of past changes have shown that addressing abrupt transitions in the past raises the issue of data quality of individual records, including the precision of the time scale and the quantification of associated uncertainties. Investigating past abrupt transitions and the mechanisms involved requires the best data quality possible. This can be a serious limitation when considering the sparse spatial coverage of high resolution paleo-records where dating is critical and corresponding errors often challenging to control. In theory, this would therefore almost limit our investigations to ice-core records of the last climate cycle, because they offer the best possible time resolution. However, evidence shows that abrupt transitions can also be identified in deeper time with lower resolution records, but still revealing changes or transitions that have impacted the dynamics of the Earth system globally. TiPES Work Package 1 will address these issues and collect paleorecords permitting to evidence the temporal behavior of tipping elements in past climates, including several examples.
Many dynamical processes in Earth Sciences are the product of many interacting components and have often limited predictability, not least because they can exhibit regime transitions (e.g. tipping points).To quantify complexity, entropy measures such as the Shannon entropy of the value distribution are widely used. Amongst other more sophisticated ideas, a number of entropy measures based on recurrence plots have been suggested. Because different structures, e.g. diagonal lines, of the recurrence plot are used for the estimation of probabilities, these entropy measures represent different aspects of the analyzed system and, thus, behave differently. In the past, this fact has led to difficulties in interpreting and understanding those measures. We review the definitions, the motivation and interpretation of these entropy measures, compare their differences and discuss some of the pitfalls when using them.
Finally, we illustrate their potential in an application on paleoclimate time series. Using the presented entropy measures, changes and transitions in the climate dynamics in the past can be identified and interpreted.
J. Fohlmeister, N. Bores, N. Marwan, A. Columbu, K. Rehfeld, N. Sekhon, L. Sime, C. Veiga-Pires:
Composite data set of last glacial Dansgaard/Oeschger events obtained from stable oxygen isotopes in speleothems,
(Virtual) EGU General Assembly,
Vienna (Austria),
May 4-8, 2020,
DOI:10.5194/egusphere-egu2020-6894,
Talk.
» Abstract
Millennial scale climate variations called Dansgaard-Oeschger cycles occurred frequently during the last glacial, with their central impact on climate in the North Atlantic region. These events are, for example, well captured by the stable oxygen isotope composition in continental ice from Greenland, but also in records from other regions. Recently, it has been shown that a water isotope enabled general circulation model is able to reproduce those millennial-scale oxygen isotope changes from Greenland (Sime et al., 2019). On a global scale, this isotope-enabled model has not been tested in its performance, as stable oxygen isotope records covering those millennial scale variability were so far missing or not systematically compiled.
In the continental realm, speleothems provide an excellent archive to store the oxygen isotope composition in precipitation during those rapid events. Here, we use a newly established speleothem data base (SISAL, Atsawawaranunt et al., 2018) from which we extracted 126 speleothems, growing in some interval during the last glacial period. We established an automated method for identification of the rapid onsets of interstadials. While the applied method seems to be not sensitive enough to capture all warming events due to the diverse characteristics of speleothem data (temporal resolution, growth stops and dating uncertainties) and low signal-to-noise-ratio, we are confident that our method is not detecting variations in stable oxygen isotopes that do not reflect stadial-interstadial transitions. Finally, all found transitions were stacked for individual speleothem records in order to provide a mean stadial-interstadial transition for various continental locations. This data set could be useful for future comparison of isotope enabled model simulations and corresponding observations, and to test their ability in modelling millennial scale variability.
R. van Dongen, D. Scherler, D. Wendi, E. Deal, C. Meier, N. Marwan, L. Mao:
El Niño-Southern Oscillation (ENSO) controls on mean streamflow and streamflow variability in Central Chile,
(Virtual) EGU General Assembly,
Vienna (Austria),
May 4-8, 2020,
DOI:10.5194/egusphere-egu2020-14011,
Talk.
» Abstract
Understanding hydrological extremes is becoming increasingly important for future adaptation strategies to global warming. Hydrologic extremes affect food security, water resources, natural hazards, and play an important role in the context of erosional processes and landscape evolution. The Pacific region is strongly affected by large-scale climatic anomalies induced by the El Niño-Southern Oscillation (ENSO). How these climatic anomalies translate into hydrological extremes is complex, because both temperature and precipitation deviate from normal conditions and the effect of this simultaneous change on hydrological processes in river catchments (e.g., snowmelt, evapotranspiration) is challenging to understand.
In this study, we investigate the effect of ENSO on mean precipitation, mean temperature, mean stream flow, and streamflow variability in Chile. We have applied extensive quality control on a large hydrological dataset from the Dirección General de Aguas in Chile, resulting in 200 good quality streamflow stations. The dataset envelopes the extent from semi-arid climate in the north ( 28°S) to humid climate in the south ( 42°S). Additionally, the dataset includes low elevation catchments located in the Coastal Cordillera and high elevation catchments in the Andes. We used the monthly Multivariate ENSO Index (MEI) to classify the 5 strongest El Niño and La Niña years, and 5 non-ENSO years after 1975. Changes in mean streamflow and streamflow variability were calculated based on the monitored data from the streamflow stations. For each river catchment, we calculated mean seasonal precipitation using the 0.25°-resolution gridded dataset from the Global Precipitation Climatology Centre (GPCC) and mean seasonal temperature using the 0.5°-resolution global temperature dataset from the Climatology Prediction Centre (CPC).
The precipitation, temperature, and discharge patterns show seasonal variation, varying in strength over the north-south gradient and between low and high elevation catchments. Mean annual precipitation generally increases significantly during El Niño events, and slightly decreases during La Niña events. For both El Niño and La Niña events the mean temperature predominantly changes between 28°S and 35°S and shows increasing temperatures in the Andes and decreasing temperatures in the low elevation Coastal Cordillera. The mean annual streamflow increases during El Niño events, and shows similarities to the pattern of increased mean annual precipitation. However, at the seasonal level, there is a time-lag between precipitation and streamflow, which is regulated by slower snowmelt processes. During La Niña events, the mean annual streamflow increases in the north (28°S-34°S) and decreases in the south (34°S-42°S). Interestingly, the mean annual precipitation and mean annual streamflow patterns behave inversely in the northern Andes. Mean streamflow increases, whereas mean precipitation decreases. This possibly results from enhanced snowmelt because of increased temperatures, but this needs to be further investigated. Finally, the magnitude and frequency of extreme floods predominantly increases in the northern Andean catchments and decreases towards the south for both El Niño and La Niña events. This study shows that large-scale climatic phenomena like ENSO affect catchment hydrology through both anomalies in precipitation and temperature.
W. Duesing, A. Asrat, A. S. Cohen, V. S. Foerster, S. Kaboth-Bahr, K. H. Kraemer, H. F. Lamb, N. Marwan, H. M. Roberts, F. Schaebitz:
Climate beats from Africa: a statistical analysis of the 620 kyr Chew Bahir climate record, eastern Africa,
(Virtual) EGU General Assembly,
Vienna (Austria),
May 4-8, 2020,
DOI:10.5194/egusphere-egu2020-13026,
Talk.
» Abstract
The sediment cores of the Chew Bahir drilling project, part of the Hominin Sites and Paleolakes Drilling Project (HSPDP), from southern Ethiopia, were used to reconstruct climatic changes by analyzing the sediment geochemistry with high-resolution XRF scanning. To interpret the multidimensional XRF dataset we computed a principal component analysis. We used the first principal component (PC1) to detect changes in variability by running a windowed standard deviation analysis and additionally a change point analysis to detect the exact timing of variability changes.
Additionally we used the established Chew Bahir log(K/Zr) aridity proxy, representing clay mineral chemistry-detrital input ratio and compared it to a new Chew Bahir climate indicator, the log(Ca/Ti) proxy, an evaporation signal that is probably inversely related to lake level stands. We find that the log(Ca/Ti) record is also an exceptionally good climate indicator because, compared to the established log(K/Zr) proxy, it reacts with greater amplitude to insolation-controlled signals such as orbital precession. This is confirmed by the log (Ca/Ti) record showing a very clear signal during the African Humid Period, which is however less pronounced in the log(K/Zr) record.
To gain a deeper understanding of the climate cycles and their temporal evolution, we computed a continuous wavelet transformation (CWT) for each of the climate proxies, and studied temporal changes in their cyclicity. Our results indicate that in addition to the precession cycle ( 20 kyr), the Chew Bahir climate record contains earth eccentricity cycles ( 100 kyr), as well as half-precession cycles during high eccentricity. During low eccentricity (450-350 kyr ago), we find reduced variability, three of five changes in standard deviation, damped precession and half precession cycles, and an abrupt transition from dry to wet climate, possibly due to climatic change in high latitudes which may be related to the Mid-Bruhnes event (MBE).
The results confirm that during high eccentricity the tropics are insolation controlled, largely independent of the high latitudes, whereas during low eccentricity the climate of tropical eastern Africa is sensitive to climatic drivers other than precession, possibly originating from high latitudes. Such a period occurring 450 to 350 kyr ago could have led to large regional differences in moisture availability and may have affected early humans by habitat separation, which by isolating populations, resulted in technological diversification. This possible scenario may help to explain the technological transition from Middle Stone Age (MSA) to Acheulean technology that was documented in the Olorgesailie basin during the same time period.
M. H. Trauth, A. Asrat, A. S. Cohen, W. Duesing, V. Foerster, S. Kaboth-Bahr, K. H. Kraemer, H. Lamb, N. Marwan, M. A. Maslin, F. Schaebitz:
Recurrence quantification analysis of the \sim 620 kyr record of climate change from the Chew Bahir basin, southern Ethiopia,
(Virtual) EGU General Assembly,
Vienna (Austria),
May 4-8, 2020,
DOI:10.5194/egusphere-egu2020-4660,
Talk.
» Abstract
The Chew Bahir Drilling Project (CBDP) aims to test possible linkages between climate and evolution in Africa through the analysis of sediment cores that record Quaternary environmental changes in the Chew Bahir basin. In this statistical project we used recurrence plots (PRs) together with a recurrence quantification analysis (RQA) to distinguish two types of variability and transitions in Chew Bahir and compare them with the ODP 967 wetness index from the eastern Mediterranean. The first type of variability are slow variations with cycles of 20 kyr and subharmonics of this cycle. In addition to the these cyclical wet-dry fluctuations in the area, extreme events often occur, i.e. short wet or dry episodes, lasting for several centuries or even millennia, with rapid transitions between wet and dry episodes. The second type of variability is characterized by relatively low variation on orbital time scales, but significant century-to-millennium-scale variations with increasing frequency in the course of an episode of type 2 variability. Within this type of variability there are extremely fast transitions between dry and wet, and vice versa, within a few decades or years, in contrast to those within type 1 which have transitions lasting several hundred years. Type 1 variability probably reflects the influence of precessional forcing in the lower latitudes at times of increased eccentricity, with the tendency towards extreme events, whereas type 2 variability seems to be linked with minimum values of the long (400 kyr) eccentricity cycle, and there does not seem to be a link with atmospheric CO2 levels. The different types of variability and transitions certainly had a completely different influence on the availability of water, food and shelter, and hence eastern Africa's biotic environment, including the habitat of H. sapiens.
M. Kemter, B. Merz, N. Marwan, S. Vorogushyn, G. Blöschl:
Mutual increases in flood extents and magnitudes intensify flood hazard in Central and Western Europe,
(Virtual) EGU General Assembly,
Vienna (Austria),
May 4-8, 2020,
DOI:10.5194/egusphere-egu2020-4731,
Talk.
» Abstract
Climate change has led to changing flood synchrony scales (extents) and flood magnitudes across Europe. We discovered a tight alignment between extents and magnitudes and found the drivers of their joint trends. We analyzed the annual maximum floods of 3872 hydrometric stations across Europe from 1960-2010 and classified all floods in terms of their generating processes based on antecedent weather conditions. There is a positive correlation between flood extents and magnitudes for 95% of the stations. While both parameters increased in Central and Western Europe, they jointly decreased in the East. This widespread magnitude extent correlation is caused by similar correlations for precipitation, soil moisture and snowmelt. We found trends in the relevance of the different flood generation processes, which explain the regional flood trends. The aligned increases of flood extents and magnitudes emphasize the growing importance of transnational flood risk management.
A. Krishnan, R. Manikandan, P. R. Midhun, K. V. Reeja, V. R. Unni, R. I. Sujith, N. Marwan, J. Kurths:
Suppression of oscillatory instability in turbulent reactive flows using network theory,
Complex Dynamical Systems and Applications 2020 (CDSA 2020), Central University of Rajasthan,
Ajmer (India),
February 22, 2020,
Talk.
><2019
A. Hartland, B. Goswami, C. Hu, B. Fox, N. Marwan, S. F. M. Breitenbach:
Stalactite flow rates in a central Chinese cave over the last 9000 years,
AGU Fall Meeting,
San Francisco (USA),
December 9–13, 2019,
Talk.
» Abstract
Chinese stalagmites represent unparalleled archives of past East Asian monsoon dynamics. However, the so-called 'amount effect' which links stalagmite oxygen isotope (δ18O) values to monsoon intensity is increasingly questioned. This study introduces a new method to quantitatively reconstruct stalactite discharge (drip rates) to stalagmites, representing a direct hydrological proxy that measures karst aquifer recharge, and by extension effective rainfall. Heshang Cave stalagmite HS4, from central China, grew under a perennial drip point which fluctuates in direct response to annual effective rainfall. The cave system is among the best studied and monitored in the world, providing a strong foundation for calibrating and testing this new proxy. Our analysis shows that drip discharge is highly correlated with stalagmite δ18O, broadly following insolation throughout the Holocene, with centennial-scale variability mainly in phase with δ18O. Flow rates had peak values between 8000-6000 years BP, subsequently declining to minimum flow around 300 years BP. Drip discharge decoupled from δ18O at important intervals in the early, mid and late Holocene. While fluctuations in monsoon rains are clearly coupled to previously identified forcings, we suggest that paleoclimatic drip rates have the potential to redefine our understanding of 'monsoon failure' and to test the drivers embedded in traditional but ambiguous proxies.
N. Marwan:
Datenmanagement in den Geowissenschaften,
Institute of Geoscience, University of Potsdam,
Potsdam (Germany),
November 27, 2019,
Lecture.
» Abstract
Die Vorlesung gibt einen Überblick über die Notwendigkeit nachhaltiger Aufbewahrung wissenschaftlicher Daten, über verschiedene Konzepte zur Datenaufbewahrung, deren Planung und praktischen Umsetzung, sowohl auf persönlicher, institutioneller, als auch auf öffentlicher Ebene in öffentlich zugänglichen Datenarchiven. Konkret werden u. a. Reproduzierbarkeit und Transparenz, wichtige Datenformate, Datenintegrität, Standards, Verschlüsselung, Backup, Coding-Konventionen, Dokumentation/ Meta-Daten und Versionskontrolle besprochen
N. Marwan:
Recurrence Plot Techniques for the Investigation of Recurring Phenomena in the System Earth,
GFZ Earth Surface Seminar Series "Nonlinear Dynamics Workshop",
Potsdam (Germany),
November 11, 2019,
Talk.
N. Marwan:
Recurrence Plot Techniques for the Investigation of Recurring Phenomena in the System Earth,
Habilitation Kolloquium Institute of Geoscience, University of Potsdam,
Potsdam (Germany),
October 16, 2019,
Talk.
» Abstract
Das immer wiederkehrende Auftreten von ähnlichen Zuständen ist eine grundlegende Eigenschaft von Prozessen, die unsere belebte und unbelebte Welt formen und beeinflussen. So gibt es auch zahlreiche Beispiele geologischer und klimatischer Vorgänge sowohl auf kurzen als auch langen Zeit- und Raumskalen, wie dem El Niño-Klimaphänomen, das alle drei bis fünf Jahre auftritt, den Milanković-Zyklen, die in regelmäßigen Abständen zu Eiszeiten führen, die regelmäßige Aktivität von Geysiren, oder das mehr unregelmäßige aber trotzdem wiederkehrende Auftreten von Erdbeben. Die Wiederkehr von Zuständen solch eines dynamischen Prozesses erzeugt ein typisches Wiederkehrmuster, das mit einem Verfahren aus der nichtlinearen Zeitreihenanalyse untersucht werden kann, den sogenannten recurrence plots. In der Habilitation werden fortgeschrittene Aspekte dieser Methodik besprochen. Diese beinhalten
die Bedeutung der Strukturen und Informationen in recurrence plots,
die Erweiterung zur Beschreibung räumlich und raumzeitlich wiederkehrender Muster, deren Anwendung zur Identifizierung von
abrupten Änderungen in der Dynamik und
äußeren Einflüssen auf die Dynamik eines Systems als auch
Kopplungen zwischen verschiedenen Systemen,
eine Kombination mit der Methodik der komplexen Netzwerke,
Modifikationen zur Behandlung typischer Probleme mit geowissenschaftlichen Daten, wie unregelmäßiges Datensampling und Unsicherheiten in den Daten,
die Entwicklung eines Signifikanztests und schließlich
einen Überblick typischer Fehler, die im Zusammenhang mit dieser Methode auftreten können und wie man diese vermeidet.
Neben den methodischen Aspekten werden Anwendungsmöglichkeiten vor allem für geowissenschaftliche Fragestellungen vorgestellt, wie die Analyse von Klimaänderungen, von externen Einflußfaktoren auf ökologische oder klimatische Systeme, oder der Landnutzungsdynamik anhand von Fernerkundungsdaten.
H. Kraemer, N. Marwan:
Border effect corrections for diagonal line based Recurrence Quantification Analysis measures,
16th International Workshop on Complex Systems and Networks,
Berlin (Germany),
September 16, 2019,
Talk.
» Abstract
Recurrence quantification analysis (RQA) is a powerful tool for the identification of characteristic dynamics and of regime changes. This approach is successfully applied in many scientific disciplines. Several measures of complexity are defined on features (such as diagonal and vertical lines) in the recurrence plot (RP) and the corresponding recurrence network (RN). These line structures represent typical dynamical behavior and can be related to certain properties of the dynamical system, e.g., chaotic or periodic dynamics. Therefore, their quantitative study by the RQA measures within sliding windows is a frequently used task for the detection of regime changes. However, as some RQA measures rely on the probability distribution of the lengths of the diagonal lines in an RP, the artificial alteration of these lines due to border effects, insufficient embedding, or a certain sampling setting can have a significant impact on these measures. A few ideas have been suggested to overcome problems. Here we review these ideas, propose novel correction schemes, and systematically compare them. Specifically, we investigate the proper estimation of the diagonal line length entropy for exemplary systems (discrete and continuous). We propose corrections schemes, which yield less biased estimates, especially under noise.
N. Marwan, H. Kraemer, B. Goswami, D. Eroglu, S. Breitenbach, J. Leonhardt:
Quantifiers from Recurrence Plots,
Quantitative paleoenvironments from speleothems workshop, Waikato University,
Cambridge (New Zealand),
September 10, 2019,
Talk.
N. Marwan:
Entropies from Recurrence Plots,
Seminar, Fudan University,
Shanghai (China),
August 26, 2019,
Talk.
N. Marwan, H. Kraemer, K. Wiesner, S. Breitenbach, J. Leonhardt:
Recurrence based entropies,
8th International Symposium on Recurrence Plots,
Zhenjiang (China),
August 21-23, 2019,
Talk.
» Abstract
Dynamical processes in Earth Sciences are generally considered to be of complex nature. The term complexity is frequently used for processes that are either unpredictable (e.g. nonlinear dynamics), consist of many different components, or exhibit regime transitions (e.g. tipping points). To measure complexity, the Shannon entropy is mainly used.
Here we present various entropy measures that have been defined on the base of the recurrence plot. Because of the different features used, these entropy measures represent different aspects of the analysed system and, thus, behave differently. In the past, this fact has lead to difficulties in interpreting and understanding those measures. We summarize the definitions, the motivation and interpretation of these entropy measures, compare their differences and discuss some of the pitfalls when using them.
Finally, we illustrate their potential by applying them on a speleotheme-based palaeoclimate record from Blessberg Cave (Germany). Using entropy measures, the alternating influence of continental versus maritime climate in past central Europe can be identified.
H. Kraemer, N. Marwan:
Border effect corrections for diagonal line based recurrence quantification analysis measures,
8th International Symposium on Recurrence Plots,
Zhenjiang (China),
August 21-23, 2019,
Talk.
» Abstract
Recurrence quantification analysis (RQA) is a powerful tool for the identification of characteristic dynamics and of regime changes. This approach is successfully applied in many scientific disciplines. Several measures of complexity are defined on features (such as diagonal and vertical lines) in the recurrence plot (RP), which represents time points $j$ when a state $\vec{x}_i$ at time $i$ recurs. These line structures represent typical dynamical behavior and can be related to certain properties of the dynamical system, e.g., chaotic or periodic dynamics. Therefore, their quantitative study by the RQA measures within sliding windows is a frequently used task for the detection of regime changes. However, as some RQA measures rely on the probability distribution of the lengths of the diagonal lines in an RP, the artificial alteration of these lines due to border effects, insufficient embedding, or a certain sampling setting can have a significant impact on these measures. A few ideas have been suggested to overcome the mentioned problems. Here we review these ideas, propose novel correction schemes, and systematically compare them.
Specifically, we investigate the proper estimation of the diagonal line length entropy for exemplary systems (discrete and continuous). We propose corrections schemes, which yield less biased estimates, especially under noise.
I. Pavithran, P. Kasthuri, A. Krishnan, S. A. Pawar, R. I. Sujith, R. Gejji, W. E. Anderson, N. Marwan, J. Kurths:
Recurrence networks of spiky signals,
8th International Symposium on Recurrence Plots,
Zhenjiang (China),
August 21-23, 2019,
Talk.
» Abstract
Thermoacoustic instability is a challenging problem faced in gas turbines and rockets. It is a state of self-sustained large amplitude periodic oscillations arising due to the positive feedback between the unsteady heat release rate oscillations and the acoustic field in a confinement. The large amplitude oscillations occurring during thermoacoustic instability are detrimental and their presence can lead to increased heat transfer, violent vibrations causing fatigue failure of the components and even mission failure in rockets. Thermoacoustic system involves interaction between processes at different timescales and length scales leading to complex spatio-temporal dynamics.
In order to study the transitions to such oscillatory instabilities in a complex system, we use a complex networks approach. Complex network is an efficient tool to study systems composed of different interacting entities. Various types of networks have been used in literature such as correlation networks, visibility graphs, recurrence networks, cycle networks, etc. Among these networks, recurrence-based complex networks (RNs) provide information about the topology of the attractor in high dimensional phase space. We can interpret the characteristics of the networks in terms of geometric properties of the phase space.
In the present work, we construct recurrence networks from the time series of acoustic pressure fluctuations obtained during different dynamical regimes from a liquid rocket combustor. We notice that the dynamics of acoustic pressure during thermoacoustic instability is akin to a spiky periodic signal. Such behaviour of the pressure signal is in contrary to the sinusoidal variation observed during thermoacoustic instability in gas turbine combustors. Previous studies have shown that the RN during thermoacoustic instability in gas turbines display a ring-like structure. We unravel a different pattern in RN for a rocket combustor which shows protrusions at different locations on the ring-like structure. These extra patterns are found to be exhibited due to the spiky nature of the time series. We create synthetic time series similar to the experimental data to explain this particular topology. The reconstructed phase space of such largely unexplored signals allows us to get deeper insights about the underlying dynamics of the system. Further, complex networks based on recurrences are an appropriate method for analysing highly nonlinear, high dimensional complex systems.
A. Banerjee, B. Goswami, N. Marwan, B. Merz, J. Kurths:
Recurrence analysis of flood events,
8th International Symposium on Recurrence Plots,
Zhenjiang (China),
August 21-23, 2019,
Poster.
» Abstract
Extreme hydrological events such as floods severely affect the communities living in the corresponding river basins and result in tremendous loss of property and wealth.
The aim of this work is to investigate flood behavior with respect to local effects, e.g. implementation of flood retention basins, and external controls by using recurrence analysis. Flood events occur at irregular time intervals and have a heavy tailed distribution, hence, such data often require data preprocessing and special methods able to analyze data with heavy tailed distribution. In this study, we use the edit distance approach in combination with recurrence plots and recurrence quantification analysis to investigate flood events.
The edit distance approach allows us to use the recurrence-based characteristics to quantify how the dynamics of the flood occurrence has changed over time. We apply our approach to the river discharge data from the river Elbe and study the dynamical interactions of different variables such as precipitation, temperature and catchment wetness.
H. Kraemer, R. Donner, J. Heitzig, N. Marwan:
Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions,
8th International Symposium on Recurrence Plots,
Zhenjiang (China),
August 21-23, 2019,
Poster.
» Abstract
The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors in the studied system's state space reconstructed by means of time-delay embedding as the key characteristic that should guide the corresponding choice for obtaining an adequate resolution of a recurrence plot. Specifically, we present an empirical description of the distance distribution, focusing on characteristic changes of its shape with increasing embedding dimension. Our results suggest that selecting the recurrence threshold according to a fixed percentile of this distribution reduces the dependence of recurrence characteristics on the embedding dimension in comparison with other commonly used threshold selection methods. Numerical investigations on some paradigmatic model systems with time-dependent parameters support these empirical findings.
A presentation of the co-authorship network of publications on recurrence plots, recurrence networks and recurrence quantification analysis.
N. Marwan:
Karstgebiet Sägistal,
14. Nationaler Höhlenforscher-Kongress Sinterlaken19,
Interlaken (Switzerland),
August 9-11, 2019,
Talk.
» Abstract
Das Sägistal ist ein abgelegenes Hochtal der Berner Voralpen mit typischen Karsterscheinungen. Die Erforschung der Höhlen begann in den 1970er Jahren durch die SGH Interlaken und wird seit 1988 durch die Internationale Speläologische Arbeitsgruppe Alpiner Karst (ISAAK) unter Beteiligung zahlreicher Höhlenforschergruppen aus verschiedenen Ländern organisiert. Mittlerweile wurden über 400 Höhlen gefunden mit dem "Oberländer-Chessiloch"-System als größtem Objekt (2346 m Länge, -488 m Tiefe).
D. Wendi, B. Merz, N. Marwan:
Novel quantification method for hydrograph similarity,
SimHydro 2019,
Sophia Antipolis (France),
June 12, 2019,
Talk.
» Abstract
We propose an additional elaborate hydrological signature index to quantify similarity (and dissimilarity) between recurring flood dynamics and between observation and model simulation as implied by their phase space trajectories. These phase space trajectories are reconstructed from their corresponding hydrographs (i.e., event time series) using Taken's time delay embedding method. This reconstructed phase space allows multi-dimensional relationship between observation points (i.e., at different time of the event) to be analyzed. Such approach considers the relationships of set of magnitude points in their unique time sequence that are relevant to the complex temporal cascading processes in flood. In a simpler terms, the new index considers the characteristics shape dynamics of a hydrograph and optionally the antecedent discharge conditions that may implicitly cascade to the subsequent rainfall-runoff event and cause an extreme or unusual hydrograph shape. This new similarity index can be used to comprehensively assess the recurrence of extreme event characteristics, change of flood dynamics, shift of seasonality, and as additional metric or objective function to evaluate and calibrate hydrological and hydraulics models.
N. Marwan:
Recurrence Plots for Time Series Analysis,
Geological Remote Sensing Seminar, University of Potsdam,
Potsdam (Germany),
June 4, 2019,
Lecture.
U. Ozturk, N. Malik, K. Cheung, N. Marwan, J. Kurths:
Tracking tropical and frontal storms driven extreme rainfalls over Japan using complex networks,
SIAM Workshop on Network Science 2019,
Snowbird (USA),
May 22-23, 2019,
Talk.
» Abstract
Predicting extreme rainfall is a challenging but a necessary task due to the concomitant natural hazards, such as flash floods or landslides. Theory of network science offers alternative tools to explore the spatiotemporal properties of extreme rainfall, which might reveal the predictive behavior of those extremes. In this case study, we use complex network metrics in conjunction with a nonlinear correlation measures of event synchronization to study extreme rainfall generated by the tropical and frontal (Baiu) storms over Japan. These two weather systems trigger extreme events in two discrete seasons; the Baiu front dominates the rainfall events from June to July, whereas tropical storms activity peak at August, and are active until November. We found that the spatial scales involved in the Baiu driven rainfall extremes are consistently more extensive than the extremes due to tropical storms. We further delineate an east-west extending horizontal region of coherent rainfall during Baiu season based on network communities, whereas nearly all Japan fall in one single coherent rainfall community during tropical storm season.
N. Marwan, H. Kraemer, K. Wiesner, S. Breitenbach, J. Leonhardt:
Recurrence based entropies,
Fourth International Conference on Recent Advances in Nonlinear Mechanics,
Łódz (Poland),
May 7-10, 2019,
Talk.
N. Marwan, H. Kraemer, K. Wiesner, S. Breitenbach, J. Leonhardt:
Recurrence based entropies,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2019,
» Poster (PDF, 6.42M).
» Abstract
Dynamical processes in Earth sciences are often considered to be of complex nature. The term complexity is often used for processes that are either unpredictable (e.g. nonlinear dynamics), consist of many different components, or exhibit regime transitions (e.g. tipping points). To measure complexity, the Shannon entropy is often used. Here we present various entropy measures that have been defined on the base of the recurrence plot. Because of the different features that are used, these entropy measures represent different aspects of the analysed system and, thus, behave differently. In the past, this fact has lead to difficulties in interpreting and understanding those measures. We summarize the definitions, the motivation and interpretation of these entropy measures, compare their differences and discuss some of the pitfalls when using them.
Finally, we illustrate their potential in an application on palaeoclimate time series. Using entropy measures, changes and transitions in the climate dynamics in the past can be identified and interpreted.
W. Düsing, H. Kraemer, A. Asrat, M. Chapot, A. Cohen, A. Deino, V. Foerster, H. Lamb, N. Marwan, C. Lane, M. Maslin, C. Ramsey, H. Roberts, F. Schaebitz, M. Trauth, C. Vidal:
Differentiating local from regional climate signals using the 600 ka Chew Bahir paleoclimate record from South Ethiopia,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2019,
Talk.
» Abstract
Cores from terrestrial archives, such as the lacustrine sediments from the Chew Bahir basin in southern Ethiopia, which cover the last 600 ka, often reflect both local, regional and global climate influences. In our analysis we were able to identify several time windows in which the Chew Bahir climate is in resonance with regional and global climate change.
As a contribution to understanding and differentiating these connections recorded in the Chew Bahir sediments, we have correlated the 2nd principal component of the MSCL based color reflectance values representing wet conditions in the Chew Bahir basin, with the wetness index from ocean core ODP 967 from the eastern Mediterranean Sea. The correlation between these two time series was calculated using the Spearman correlation coefficient in a sliding window. Episodes with high correlation between the two records of wetness could indicate a strong link between both regions, possibly through an increased outflow of the river Nile into the eastern Mediterranean Sea due to higher precipitation values on the Ethiopian plateau.
Our preliminary results show that when correlating the two records, two distinct temporal units can be distinguished. Between 570 ka and 350 ka the correlation is dominated by cycles that correspond with orbital precession whereas the second unit (after 350 ka) reveals a strong influence of atmospheric CO2. This observation suggests that both orbital precession and atmospheric CO2. may cause a synchronization of different regions in the African climate system, possibly depending on boundary conditions which are still to be identified.
As a next step we'll investigate the nonlinear relationships between the two records by focusing on the transition between the two main observed phases. The transition around 350 kyrs however, is not only highly interesting from a climatic perspective, but it is also a noteworthy period for human cultural evolution as a transition from Acheulean to Middle Stone Age (MSA) technologies takes place at this time. So far our results outline that during this climatically and evolutionary relevant episode a relatively stable, long-lasting, pan-African wet phase may have existed, with possible green corridors connecting the habitats of hominins, and ample resources supporting large population sizes.
A. Banerjee, B. Goswami, N. Marwan, B. Merz, J. Kurths:
Recurrence Analysis of Flood Events,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2019,
Poster.
» Abstract
Extreme hydrological events such as floods severely affect the communities living in the corresponding river basins and result in tremendous loss of property and wealth.
The aim of this work is to investigate flood behavior with respect to local effects, e.g. implementation of flood retention basins, and external controls by using recurrence analysis. Flood events occur at irregular time intervals and hence such data often requires data preprocessing. In this study, we use the TACTS approach in combination with recurrence plot and recurrence quantification analysis to investigate flood events, which occur on irregular time scales.
The TACTS approach allows us to construct a recurrence plot from the irregularly spaced flood event series, and the recurrence-based characteristics help to quantify how the dynamics of the flood occurrence have changed over time. We apply our approach to the 150-year river discharge data from the river Elbe and study the dynamic interactions of different variables such as precipitation, temperature and catchment wetness.
A. Agarwal, L. Caesar, N. Marwan, R. Maheswaran, B. Merz, J. Kurths:
Detection of short- and long-range teleconnections in SST patterns on different time scales,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2019,
Poster.
» Abstract
Sea surface temperature (SST) anomaly patterns can - as surface climate forcing -affect the weather at large distances. This is why following an El Niño event major global climate anomalies occur. This paper characterizes the links between the cells of a global SST grid data set at different temporal and spatial scales with the help of climate networks. These networks are constructed using wavelet multi-scale correlation. This way we identify and visualise the SST patterns that develop very similarly over time and distinguish them from those that have long-range teleconnections to other ocean regions. Our findings re-confirm accepted knowledge about known highly linked SST patterns like El Niño Southern Oscillation and the Pacific Decadal Oscillation, but also suggest new insights into the characteristics and origins of long-range teleconnections.
M. Kemter, B. Merz, N. Marwan:
Using multi-layer complex networks to understand interrelationships and changes in extreme flood generation,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2019,
Poster.
» Abstract
The generation of extreme flood events is influenced by a multitude of parameters that interact in complex ways. To understand their temporal and spatial relationships as well as changes in this system we need adequate tools. We therefore use multilayer complex networks and extreme event statistics to discover and interpret relationships between flood influencing parameters (e.g. precipitation, catchment wetness, discharge). Complex networks have formerly been successfully used for climatic and hydrological representations. A multilayer approach enables us to find inter-relationships between the different influences. We use non-linear similarity measures to generate the network connections. By analysis of variations of the network appearance and metrics with time, we can reconstruct temporal changes in the underlying processes.We are investigating several hundred river gauges across Europe over a timeframe of 70 years.
M. Trauth, A. Asrat, C. Bronk Ramsey, M. Chapot, A. Cohen, A. Deino, W. Duesing, V. Foerster, H. Kraemer, H. Lamb, C. Lane, N. Marwan, M. Maslin, H. Roberts, F. Schaebitz, C. Vidal:
Recurring types of variability and transitions in the \~280 m long (\~600 kyr) sediment core from the Chew Bahir basin, southern Ethiopia,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2019,
Poster.
» Abstract
The Chew Bahir Drilling Project (CBDP) aims to test hypothesized linkages between climate and human evolution, dispersal and technological innovation by the acquisition and analysis of long (280 m) sediment cores that have recorded environmental change in the Chew Bahir basin, southern Ethiopia. In this time-series analysis project, we consider the Chew Bahir palaeolake to be a dynamical system consisting of interactions between its different components, such as the waterbody, the sediment beneath lake, and the organisms living within and around the lake, and humans within the lake catchment. Recurrence is a common feature of such dynamical systems, with recurring patterns in the state of the system reflecting typical influences. Identifying and defining these influences contributes significantly to our understanding of the dynamics of the system.
We use methods of linear and nonlinear time series analysis, such as change point detection, semblance analysis and recurrence plots, to identify and classify recurring types of variability and transitions on the time scales of human life spans. For example, we investigate the rapidness of transitions, possible precursor events, and tipping points in our palaeoenvironmental data and discuss their possible impact on the living conditions of humans in the region. First results of the analysis show that we indeed find, as an example, recurring threshold-type transitions, when the Chew Bahir system switched from one stable mode to another, such as from stable wet to dry conditions. Such a rapid change of climate in response to a relatively modest change in forcing appears to be typical of tipping points in complex systems such as the Chew Bahir. If this is the case then the 14 dry events idenfified at the end of the African Humid Period (15-5 kyr BP) could represent precursors of an imminent tipping point that, if properly interpreted, would allow predictions to be made of future climate change in the Chew Bahir basin.
N. Marwan:
Recurrence Plots for Time Series Analysis,
Seminar at MPI Molecular Physiology,
Dortmund (Germany),
March 18, 2019,
Talk.
N. Marwan:
Transparent and efficient data storage,
Graduate School NatRiskChange University of Potsdam,
Potsdam (Germany),
March 13-14, 2019,
Lecture.
» Abstract
The lecture provides an overview of the need for sustainable storage of scientific data, various concepts of data storage and archiving, their planning and practical implementation, both at the personal, institutional, and public levels in publicly accessible data archives. Specific topics discussed include reproducibility and transparency, important data formats, data integrity, standards, encryption, backup, coding conventions, documentation/meta-data, and version control.
><2018
W. Duesing, J. Thom, A. Deino, A. Asrat, V. Foerster, H. Kraemer, N. Marwan, H. Lamb, F. Schaebitz, M. H. Trauth:
Human evolution and climate change: What can we learn from the 0-630 kyrs BP paleoclimate record from the Chew Bahir basin in eastern Africa?,
AGU Fall Meeting,
Washington DC (USA),
December 10-14, 2018,
Talk.
» Abstract
Numerous authors have developed hypotheses linking climate, the environment and human evolution, expansion and technological innovation in eastern Africa (e.g., Potts, 2013, Potts et al. 2018; Maslin et al., 2015). The Chew Bahir Drilling Project (CBDP) as part of the Hominin Sites Paleolakes Drilling Project (HSPDP) aims to test some of these hypotheses by providing a long, continuous and high-resolution paleoclimate records of climatic and environmental change through critical intervals of human evolution.
Testing such hypothesis requires a very accurate age model both for the paleoclimate record, but also for the archeological/anthropological evidence. We therefore developed a MATLAB-based Multiband Wavelet Based Age Modeling Technique (mubawa), which generates an orbital tuned age model that comprises uncertainties. Next, we use a piecewise correlation using a set of different sliding windows to compare the Chew Bahir paleo records on different time scales with Indian Ocean SSTs, Terrestrial Dust and Nile-Outflow records. To classify variability and transitions we use recurrence plots/recurrence quantification analysis. Application of this method detects nonlinear features such as tipping points, which are often coherent with changes in variability and strong precursor events. The recurrences of such precursor events often lie within the life span of hominins. For individuals living during that time these drastic climate shift were perceptive and probably provoked new survival strategies that may have preserved in the archeological record.
In a last step we evaluate if these detected climate and environmental shifts can be related to archeological sights, human evolution, technological innovation, migration and dispersal events.
E. Macau, A. M. Ramos, J. Kurths, N. Marwan:
Detecting causal relations from real data experiments by using recurrence,
Dynamics Days Latin America and the Caribbean 2018,
Punta del Este (Uruguay),
November 26-30, 2018,
Talk.
» Abstract
In this work, we present the Recurrence Measure of Conditional Dependence (RMCD), a recent data-driven causality inference method using the framework of recurrence plots. The RMCD incorporates the recurrence behavior into the transfer entropy theory. We apply this methodology to some paradigmatic models and to investigate the possible influence of the Pacific Ocean temperatures on the South West Amazon for the 2010 and 2005 droughts. The results reveal that for the 2005 drought there is not a significant signal of dependence from the Pacific Ocean and that for 2010 there is a signal of dependence of around 200 days. These outcomes are confirmed by the traditional climatological analysis of these episodes available in the literature and show the accuracy of RMCD inferring causal relations in climate systems.
T. Vantuch, I. Zelinka, A. Adamatzky, N. Marwan:
Detecting causal relations from real data experiments by using recurrence,
17th International Conference on Unconventional Computation and Natural Computation,
Fontainebleau (France),
June 26, 2018,
Talk.
» Abstract
Natural systems often exhibit chaotic behavior in their space-time evolution. Systems transiting between chaos and order manifest a potential to compute, as shown with cellular automata and artificial neural networks. We demonstrate that swarms optimisation algorithms also exhibit transitions from chaos, analogous to motion of gas molecules, when particles explore solution space disorderly, to order, when particles follow a leader, similar to molecules propagating along diffusion gradients in liquid solutions of reagents. We analyse these ‘phase-like’ transitions in swarm optimization algorithms using recurrence quantification analysis and Lempel-Ziv complexity estimation. We demonstrate that converging and non-converging iterations of the optimization algorithms are statistically different in a view of applied chaos, complexity and predictability estimating indicators.
W. Duesing, A. Asrat, V. E. Foerster, H. Kraemer, H. F. Lamb, N. Marwan, F. Schaebitz, M. H. Trauth:
Trends, rhythms and transitions during the Late Quaternary in southern Ethiopia,
EGU General Assembly,
Vienna (Austria),
April 8-13, 2018,
Poster.
» Abstract
This project aims at statistically analyzing the long ( 278 m) sediment record of the Chew Bahir basin, as part of the ICDP-funded Hominin Sites and Paleolakes Drilling Project (HSPDP). The aim of the project is (1) to establish a robust age-depth model for the sediment cores, (2) to correlate the Chew Bahir record with other records within and outside HSPDP, (3) to detect trends, rhythms and events in the environmental record of the basin, and (4) identify recurrent, characteristic types of climate transitions in the time series, as compared with the ones of the other HSPDP sites and climate records outside HSPDP. The work presented here will provide first results of age-depth modelling, including cyclostratigraphy, of the long Chew Bahir cores. Second, it gives an overview of the first results from evolutionary spectral analysis to detect changes in the response of the Chew Bahir to orbital forcing during the last 550 kyr. Third, the results of a change point analysis will be presented to define the amplitude and duration of past climate transitions and their possible influence on the development of early modern human cultures.
M. H. Trauth, A. Asrat, W. Duesing, V. Foerster, H. Kraemer, H. Lamb, N. Marwan, M. A. Maslin, F. Schaebitz::
Classifying past climate variation in the Chew Bahir basin, southern Ethiopia, using recurrence quantification analysis,
EGU General Assembly,
Vienna (Austria),
April 8-13, 2018,
Poster.
» Abstract
The Chew Bahir Drilling Project (CBDP) aims to test hypothesized linkages between climate and mammalian (including hominin) evolution in tropical-subtropical eastern Africa by the acquisition and analysis of long ( 280 m) sediment cores that have recorded environmental change in the Chew Bahir basin. In our statistical project, we describe the Chew Bahir paleolake as a dynamical system composed of interacting components, such as the water body, the sediment below the bottom of the (paleo-)lake, and the organisms living in the lake and its surroundings. A common feature of dynamical systems is the property of recurrence, where patterns of recurring states reflect typical system characteristics whose description contribute significantly to understanding its dynamics. In our example it could be a recurrence of changes in the state variables precipitation, evaporation and wind speed, which lead to similar (but not identical) conditions in the lake (e.g., depth and size of the lake, alkalinity and salinity of the lake water, species assemblage in the water body, diagenesis in the sediment). A recurrence plot (RP), first introduced by J.P. Eckmann in 1987, is a graphical display of such recurring states of the system, calculated from the distance (e.g. Euclidean) between all pairs of observations x(t), within a cutoff limit. To complement the visual inspection of recurrence plots, measures of complexity were introduced for their quantitative description to perform the recurrence quantification analysis (RQA). Here we present and discuss preliminary results of a RQA of the 550 kyr long environmental record from the Chew Bahir basin.
A. Agarwal, N. Marwan, M. Rathinasamy, U. Ozturk, B. Merz, J. Kurths:
Complex network-based approach for identification of influential and expandable station across rainfall network,
EGU General Assembly,
Vienna (Austria),
April 8-13, 2018,
Poster.
» Abstract
The complex network has gained significant momentum in last decades and has found application wide areas ranging from biological networks to climate networks. In analysing physical complex networks, identification of key influential nodes is l an important field of research. In this study, we propose a new effective node ranking method based on network measure degree and betweenness values. The proposed method is tested and compared to previously proposed node ranking methods on synthetic sample networks and then applied to a real-world raingauge network of 1229 stations from Germany to check its replicability and applicability. Raingauge networks play a vital role in providing information for making crucial decisions in water resources management and resources estimation. The network of operating raingauges should be set up optimally to provide as much and as accurate information as possible and at the same time cost-effective. The proposed method is evaluated using decline rate efficiency and kriging error. The results of the study show that the proposed method based on complex network theory for ranking the raingauges is robust and can be used for design and redesign the raingauge network. The method is very useful in identifying the highly influential station which needs high attention and expendable stations which either can be relocated, uninstalled or removed without much effect on the overall accuracy of the observations provided by the raingauge network.
D. Wendi, N. Marwan, B. Merz:
The recurrence of unseasonable and rare flood dynamics,
EGU General Assembly,
Vienna (Austria),
April 8-13, 2018,
» Poster (PDF, 2.26M).
» Abstract
The question whether a certain flood is rare/ unusual or not is often evaluated from the frequency curve analysis (also called growth curve) of flood discharge peaks and their corresponding recurrence interval (return period). Flood discharge peak and maximum depth are some of the hydrological signatures (i.e. an element of hydrograph) and are popular choice for flood risk assessment due to their close relationship with socio-economic impact of flood and often used for damage modeling. However what if our question now is whether the flood process dynamics is rare (influenced by unusual or more driving mechanism, e.g. ice jam, dam break, clogged drain, etc) and especially if hydrological boundary condition is no longer the same as before.
The confinement of flood peaks reduces the information about the flood dynamics inferred by the shape of hydrograph, especially should one be interested to evaluate a rarity/ extremity of a flood process dynamics since flood peak is just one element of a flood hydrograph. Although other indices derived from hydrological signature (e.g. volume, slopes, base flow index, etc) are useful descriptors of a process dynamics, most of them are still either just a part of hydrograph, or derived as an aggregate (e.g. slopes and volume) and therefore unable to provide bigger picture of the flood dynamics and suffer from statistical uncertainty. Furthermore, with singular descriptor from the mentioned, different flood dynamics (i.e. resulted from different processes/ boundary conditions) could be mistaken as the same and might lead to misinterpretation (e.g. snow melt and rainfall triggered runoff may easily share similar flood peak and volume). Moreover, stationarity in season is often assumed in flood frequency analysis, that different flood processes are classified to follow strict calendar month seasons. Such practice could fail to analyze the occurrence of unusual climatic event such as early or late snow melt and unseasonably heavy rainfall in winter.
In this study, we focus on the utilization of hydrological signature to characterize temporal flood event dynamics with the objective to analyze their recurrences and to be able to evaluate if a process dynamic of a certain flood is rare or perhaps unprecedented. We propose using the analysis of phase space trajectories reconstructed through time delay embedding of a time series to characterize different flood events. To allow the visualization and analysis of high embedding dimension (i.e. above 3), we suggest the use of recurrence plot (RP) and quantification (RQA) as similarity measures between the flood dynamics of one event to another and allow non-stationarity occurrence of their typology.
B. Goswami, S. Breitenbach, F. Lechleitner, J. Baldini, H. Cheng, N. Marwan:
Is this an event? – Detecting abrupt changes in palaeoclimate records,
EGU General Assembly,
Vienna (Austria),
April 8-13, 2018,
» Poster (PDF, 772.16K).
» Abstract
Abrupt shifts in a certain climate state is a pertinent question in palaeoclimate studies and is crucial for determining leads or lags between spatially disperse observations. Such events have also a direct bearing on the vulnerability of society to drastic – and possibly difficult to mitigate – changes. Determining whether or not, and when exactly, abrupt changes in climate occurred is made challenging by temporal resolution and uncertainties associated with determining the age of climate proxy measurements.
In this study, we present a robust, ‘uncertainty-aware’ approach to determine periods of abrupt change from palaeoclimate proxy records. Our method is based on a new representation of time series and it utilises the recurrence properties of the proxy record to distinguish time points of abrupt climate change. We first validate our approach with a synthetic example, and thereafter, we apply our approach to speleothem records from China and India. Our results reveal a highly non-trivial spatio-temporal pattern of the detected events in the Asian monsoon domain.
U. Öztürk, N. Malik, N. Marwan, J. Kurths:
Comparison of tropical and frontal storms using complex networks,
EGU General Assembly,
Vienna (Austria),
April 8-13, 2018,
Poster.
» Abstract
Complex network analysis supports exploring spatiotemporal dynamics of significant climate phenomena, such as heavy precipitation. Complex networks are able to capture the spreading and concentration of extreme rainfall by using event-synchronization, such as rainfall propagation patterns of the Indian Summer Monsoon by parameterizing the delay from precipitation time-series. Despite much advancement in monitoring extreme rainfall, capturing spatiotemporal dynamics of the fast-evolving atmospheric events (e.g., tropical storms) is still a challenge. Quantifying spatial scales of extreme rainfall will aid mitigating concomitant flood and landslide hazards.
We use network analysis to compare spatial features of extreme rainfall over Japan using satellite-derived rainfall data (TRMM-3B42V7). We first divide the time series into two subsets: June to July (JJ) and August to November (ASON) to concentrate on the Baiu front season (JJ) and the tropical storms season (ASON). We assess the spatial scales involved in the two distinct mechanisms and define regions of coherent rainfall during the two seasons. We additionally propose using radial statistics to trace the network flux over long distances, which allows us to observe the general pattern of extreme rainfall tracks. Extreme rainfall associated with tropical storms show smaller spatial scales (in the range of 100 km) compared to Baiu linked extremes. We also discovered a consistent deviation of the extreme rainfall from the eye of the tropical storm tracks.
H. Kraemer, R. V. Donner, N. Marwan, M. H. Trauth:
Detecting abrupt transitions during the Late Quaternary in southern Ethiopia using Recurrence Quantification Analyses,
EGU General Assembly,
Vienna (Austria),
April 8-13, 2018,
Poster.
» Abstract
In many data driven fields of research, categorizing abrupt transitions / regime changes is of high interest. The different aspects of temporal recurrence patterns of previous states can help to identify and characterize subtle changes in systems dynamics. Besides the identification of transitions, recurrence methods can provide a better understanding of the process underlying these transitions by statistically describing the dynamical characteristics, e.g. the predictability, determinism and complexity of the dynamical system. For example, the characteristic block structures in the recurrence plot can be used to identify different types of intermittency. In general, changes between different dynamical regimes are visually well expressed in recurrence plots. The introduction of selected recurrence quantifiers (such as recurrence rate, determinism, or laminarity) together with a running window approach has paved the way for a quantitative recurrence analysis of transitions and therefore should be able to provide a classification of different transition types.
In order to achieve such a classification there is necessity for developing a method which is capable to statistically analyze the behavior of recurrence quantifiers at transitions. In this work, we show how to make statements about the significance of estimated values of recurrence quantifiers using a bootstrap approach. We also highlight the specific technical problems related to that task. The presented method also allows gaining information about the duration of a transition. Here we demonstrate potentials of the proposed approach to detect abrupt transitions in (1) prototypical models of transitions as well as in (2) real data of past climate variations in the Chew Bahir basin (South Ethiopia), investigated within the Hominin Sites and Paleolakes Drilling Project (HSPDP).
B. Goswami, N. Boers, A. Rheinwalt, N. Marwan, J. Heitzig, S. Breitenbach, J. Kurths:
Identifying sudden dynamical shifts in time series with uncertainties,
EGU General Assembly,
Vienna (Austria),
April 8-13, 2018,
Poster.
S. Breitenbach, B. Plessen, S. Waltgenbach, R. Tjallingii, J. Leonhardt, K.-P. Jochum, H. Meyer, N. Marwan, D. Scholz:
Tracing past shifts of the boundary between maritime and continental climate over Central Europe,
EGU General Assembly,
Vienna (Austria),
April 8-13, 2018,
Poster.
» Abstract
European climate is characterized by heterogeneous climate conditions, with distinct boundaries between zones that can be classified according to the Köppen classification (Peel et al. 2007), and detected using climate network techniques (Rheinwalt et al. 2016). These boundaries are not stationary, but shift geographically, depending on large scale atmospheric conditions.
Central European climate is strongly influenced by intricately linked North Atlantic Oscillation and Siberian High (SH), which govern precipitation and temperature over Europe. Shifts of these climatic boundaries in response to global warming and circulation changes might lead to more frequent extreme weather patterns like heat waves, with significant repercussions for society (Cohen et al. 2014).
Speleothem-based palaeoclimate reconstructions enable us to understand underlying forcing mechanisms and speed of climatic reorganizations. Here we present a first reconstruction of multi-centennial shifts of the boundary between western European maritime Cfb climate and continental Dfb climate through the last ca. 5,000 years using speleothems from Bleßberg Cave, Thuringia, Central Europe.
Thanks to its location near the Cfb-Dfb climatic boundary, Bleßberg Cave is ideally suited to reconstruct past W-E shifts of this divide longitudinally crossing Central Europe. We compare a decadally resolved stalagmite δ18O record with data from Bunker Cave (Mischel et al. 2017), western Germany, and an NAO reconstruction from Greenland (Olsen et al. 2012).
Over the last 5,000 years, the boundary between Cfb and Dfb climate shifted repeatedly. When the Cfb-Dfb border was east (west) of Bleßberg (Bunker) Cave maritime (continental) climate prevailed at both sites. Discrepancies between investigated proxy records are found when the boundary is located between the two caves. Comparison with the Greenland NAO record shows that a westerly shifted boundary is often associated with a strong SH and a negative NAO. An easterly shift, in contrast, is found to be linked with weak a SH and a positive NAO.
><2017
D. Wendi, N. Marwan, B. Merz:
The importance of hydrological signature and its recurring dynamics,
AGU Fall Meeting,
New Orleans (USA),
December 1–17, 2017,
Poster.
» Abstract
Temporal changes in hydrology are known to be challenging to detect and attribute due to multiple drivers that include complex processes that are non-stationary and highly variable. These drivers, such as human-induced climate change, natural climate variability, implementation of flood defense, river training, and land use change, could impact variably on space-time scales and influence or mask each other. Besides, data depicting these drivers are often not available.
One conventional approach of analyzing the change is based on discrete points of magnitude (e.g. the frequency of recurring extreme discharge) and often linearly quantified and hence do not reveal the potential change in the hydrological process. Moreover, discharge series are often subject to measurement errors, such as rating curve error especially in the case of flood peaks where observation are derived through extrapolation.
In this study, the system dynamics inferred from the hydrological signature (i.e. the shape of hydrograph) is being emphasized. One example is to see if certain flood dynamics (instead of flood peak) in the recent years, had also occurred in the past (or rather extraordinary), and if so what is its recurring rate and if there had been a shift in its occurrence in time or seasonality (e.g. earlier snow melt dominant flood). The utilization of hydrological signature here is extended beyond those of classical hydrology such as base flow index, recession and rising limb slope, and time to peak. It is in fact all these characteristics combined i.e. from the start until the end of the hydrograph. Recurrence plot is used as a method to quantify and visualize the recurring hydrological signature through its phase space trajectories, and usually in the order of dimension above 2. Such phase space trajectories are constructed by embedding the time series into a series of variables (i.e. number of dimension) corresponding to the time delay. Since the method is rather novel in hydrological community, the study presents an overview and a guideline to the method with an application example on analyzing the change of hydrological signature and discussion of its benefits and flaws.
N. Marwan:
Recurrence Plots for Data Analysis,
QUEST Workshop on palaeoclimate time series analysis and statistics,
Potsdam (Germany),
November 3, 2017,
Lecture and workshop.
N. Marwan:
Transparent and efficient data storage,
QUEST Workshop on palaeoclimate time series analysis and statistics,
Potsdam (Germany),
November 3, 2017,
Lecture.
N. Marwan:
Höhlen als wissenschaftliche Archive,
20th Anniversary of Speleo Club Berlin,
Kienitz (Germany),
September 23, 2017,
Talk.
Recurrence plots exhibit features and patterns which are characteristic for typical dynamics. How difficult does it be to visually recognize the dynamics from the recurrence plot? Does everybody see the same or judges the different patterns with similar importance? In this (interactive) talk we will figure out the subjective nature of visual inspection and discuss the difficulties. It finally underlines the importance of applying objective quantifiers such as recurrence quantification analysis.
The complex nature of a variety of phenomena in physical, biological, or earth sciences is driven by a large number of degrees of freedom which are strongly interconnected. Although the evolution of such systems is described by multivariate time series (MTS), so far research mostly focuses on analyzing these components one by one.
Recurrence based analyses are powerful methods to understand the underlying dynamics of a dynamical system and have been used for many successful applications including examples from earth science, economics, or chemical reactions. The backbone of these techniques is creating the phase space of the system. However, increasing the dimension of a system requires increasing the length of the time series in order get significant and reliable results. This requirement is one of the challenges in many disciplines, in particular in palaeoclimate, thus, it is not easy to create a phase space from measured MTS due to the limited number of available obervations (samples). To overcome this problem, we suggest to create recurrence networks from each component of the system and combine them into a multiplex network structure, the it multiplex recurrence network (MRN). We test the MRN by using prototypical mathematical models and demonstrate its use by studying high-dimensional palaeoclimate dynamics derived from pollen data from the Bear Lake (Utah, US). By using the MRN, we can distinguish typical climate transition events, e.g., such between Marine Isotope Stages.
H. Kraemer, N. Marwan, M. H. Trauth:
Classifying abrupt transitions in IPCC climate models and paleoclimate proxy data using recurrence quantification analysis,
7th International Symposium on Recurrence Plots,
São Paulo (Brazil),
August 23-25, 2017,
Talk.
» Abstract
In many data driven disciplines, categorising abrupt transitions / regime changes are of high interest. The different aspects of recurrence can help to identify and characterize subtle changes in systems dynamics. Besides the identification of transitions, recurrence methods can help to provide a better understanding of the underlying process of these transitions by statistically describing the dynamical characteristics, e.g. the predictability, determinism and complexity of the dynamical system. For example, the characteristic block structures in the recurrence plot can be used to identify different types of intermittency. In general, changes between different dynamics are visually well expressed in recurrence plots. The introduction of selected recurrence quantifiers (such as recurrence rate, determinism, or laminarity) together with a running window approach has paved the way for a quantitative recurrence analysis of transitions and therefore allow a classification of different transition types.
In this work first results of such recurrence based classification is shown. We demonstrate it by analysing prototypical models of transitions as well as on real world data related to palaeoclimate. The prototypical models are selected from a catalogue of transition types which have been used and discussed in models presented in the reports of the Intergovernmental Panel on Climate Change (IPCC)[1]. In the palaeoclimate example we consider two Potassium time series of two drilling cores from the Chew Bahir Bassin, which is part of the Hominin Sites and Paleolakes Drilling Project (HSPDP).
D. Wendi, N. Marwan, B. Merz, J. Kurths:
Change in flood hazard dynamics from recurrence perspective,
7th International Symposium on Recurrence Plots,
São Paulo (Brazil),
August 23-25, 2017,
Talk.
» Abstract
Temporal changes in flood hazard systems are known to be difficult to detect and attribute due to multiple drivers that include processes that are non-stationary and highly variable. Often such analysis of change is quantified from single points perspective (i.e. extreme values) that may subject to high errors and uncertainties. In contrast, the hydrological signature derived from the time series could provide a better picture of a process characteristic resulting from the drivers and hence a step closer to understanding the change of process and is less prone to artifacts caused by single point analysis.
This study focuses on the application of recurrence based data analysis techniques (recurrence plot) for understanding and quantifying spatio-temporal changes in flood hazards in Germany through its hydrological signature. The recurrence plot is known as an effective tool to visualize the dynamics of phase space trajectories i.e. constructed from a time series by using an embedding dimension and a time delay, and it is known to be effective in analyzing non-stationary and non-linear time series. The emphasis will be on the identification of characteristic recurrence properties that could associate typical dynamic behavior to certain flood situations.
A. M. T. Ramos, A. Builes-Jaramillo, G. Poveda, B. Goswami, E. E. N. Macau, J. Kurths, N. Marwan:
Causality detection based on recurrence plot,
7th International Symposium on Recurrence Plots,
São Paulo (Brazil),
August 23-25, 2017,
Talk.
» Abstract
We will present the Recurrence Measure of Conditional Dependence (RMCD), a recent data-driven causality inference method using the framework of recurrence plots. The RMCD incorporates the recurrence behavior into the transfer entropy theory. We will discuss how this methodology can reveal the lagged coupling of some paradigmatic models and how it reveals causal relations of climate systems. For instance, RMCD detects the influence of the Pacific Ocean temperatures on the South West Amazon rainfall during the 2010 droughts, as well as its influence absence during 2005.
The complex nature of a variety of phenomena in physical, biological, or earth sciences is driven by a large number of degrees of freedom which are strongly interconnected. Although the evolution of such systems is described by multivariate time series (MTS), so far research mostly focuses on analyzing these components one by one.
Recurrence based analyses are powerful methods to understand the underlying dynamics of a dynamical system and have been used for many successful applications including examples from earth science, economics, or chemical reactions. The backbone of these techniques is creating the phase space of the system. However, increasing the dimension of a system requires increasing the length of the time series in order get significant and reliable results. This requirement is one of the challenges in many disciplines, in particular in palaeoclimate, thus, it is not easy to create a phase space from measured MTS due to the limited number of available obervations (samples). To overcome this problem, we suggest to create recurrence networks from each component of the system and combine them into a multiplex network structure, the multiplex recurrence network (MRN). We test the MRN by using prototypical mathematical models and demonstrate its use by studying high-dimensional palaeoclimate dynamics derived from pollen data from the Bear Lake (Utah, US). By using the MRN, we can distinguish typical climate transition events, e.g., such between Marine Isotope Stages.
F. Brenner, N. Marwan, P. Hoffmann:
Modelling fast spreading patterns of airborne infectious diseases using complex networks,
EGU General Assembly,
Vienna (Austria),
April 23-28, 2017,
Talk.
» Abstract
The pandemics of SARS (2002/2003) and H1N1 (2009) have impressively shown the potential of epidemic outbreaks of infectious diseases in a world that is strongly connected. Global air travelling established an easy and fast opportunity for pathogens to migrate globally in only a few days. This made epidemiological prediction harder. By understanding this complex development and its link to climate change we can suggest actions to control a part of global human health affairs.
In this study we combine the following data components to simulate the outbreak of an airborne infectious disease that is directly transmitted from human to human:
GlobalAirTrafficNetwork(fromopenflights.org) with information on airports, airportlocation, directflight connection, airplane type
Global population dataset (from SEDAC, NASA)
Susceptible-Infected-Recovered (SIR) compartmental model to simulate disease spreading in the vicinity of airports. A modified Susceptible-Exposed-Infected-Recovered (SEIR) model to analyze the impact of the incubation period.
WATCH-Forcing-Data-ERA-Interim(WFDEI) climatedata: temperature, specific humidity, surface air pressure, and water vapor pressure
These elements are implemented into a complex network. Nodes inside the network represent airports. Each single node is equipped with its own SIR/SEIR compartmental model with node specific attributes. Edges between those nodes represent direct flight connections that allow infected individuals to move between linked nodes. Therefore the interaction of the set of unique SIR models creates the model dynamics we will analyze.
To better figure out the influence on climate change on disease spreading patterns, we focus on Influenza-like-Illnesses (ILI). The transmission rate of ILI has a dependency on climate parameters like humidity and temperature. Even small changes of environmental variables can trigger significant differences in the global outbreak behavior. Apart from the direct effect of climate change on the transmission of airborne diseases, there are indirect ramifications that alter spreading patterns. An example is seasonal human mobility behavior which will change with varied climate conditions. The direct and indirect effects of climate change on disease spreading patterns will be discussed in this study.
A. Agarwal, N. Marwan, M. Rathinasamy, U. Oeztuerk, B. Merz, J. Kurths:
Multiscale complex network analysis: An approach to study spatiotemporal rainfall pattern in south Germany,
EGU General Assembly,
Vienna (Austria),
April 23-28, 2017,
Poster.
» Abstract
Understanding of the climate sytems has been of tremendous importance to different branches such as agriculture, flood, drought and water resources management etc. In this regard, complex networks analysis and time series analysis attracted considerable attention, owing to their potential role in understanding the climate system through characteristic properties. One of the basic requirements in studying climate network dynamics is to identify connections in space or time or space-time, depending upon the purpose. Although a wide variety of approaches have been developed and applied to identify and analyse spatio-temporal relationships by climate networks, there is still further need for improvements in particular when considering precipitation time series or interactions on different scales. In this regard, recent developments in the area of network theory, especially complex networks, offer new avenues, both for their generality about systems and for their holistic perspective about spatio-temporal relationships.
The present study has made an attempt to apply the ideas developed in the field of complex networks to examine connections in regional climate networks with particular focus on multiscale spatiotemporal connections. This paper proposes a novel multiscale understanding of regional climate networks using wavelets. The proposed approach is applied to daily precipitation records observed at 543 selected stations from south Germany for a period of 110 years (1901-2010). Further, multiscale community mining is performed on the same study region to shed more light on the underlying processes at different time scales.
Various network measure and tools so far employed provide micro-level (individual station) and macro-level (community structure) information of the network. It is interesting to investigate how the result of this study can be useful for future climate predictions and for evaluating climate models on their implementation regarding heavy precipitation.
U. Ozturk, N. Marwan, J. Kurths:
Identifying typhoon tracks based on event synchronization derived spatially embedded climate networks,
EGU General Assembly,
Vienna (Austria),
April 23-28, 2017,
Poster.
» Abstract
Complex networks are commonly used for investigating spatiotemporal dynamics of complex systems, e.g. extreme rainfall. Especially directed networks are very effective tools in identifying climatic patterns on spatially embedded networks. They can capture the network flux, so as the principal dynamics of spreading significant phenomena. Network measures, such as network divergence, bare the source-receptor relation of the directed networks. However, it is still a challenge how to catch fast evolving atmospheric events, i.e. typhoons.
In this study, we propose a new technique, namely Radial Ranks, to detect the general pattern of typhoons forward direction based on the strength parameter of the event synchronization over Japan. We suggest to subset a circular zone of high correlation around the selected grid based on the strength parameter. Radial sums of the strength parameter along vectors within this zone, radial ranks are measured for potential directions, which allows us to trace the network flux over long distances. We employed also the delay parameter of event synchronization to identify and separate the frontal storms’ and typhoons’ individual behaviors.
U. Ozturk, N. Marwan, O. Korup, J. Jensen:
Completing the record of 20th century sea level rise in the Eastern Mediterranean,
EGU General Assembly,
Vienna (Austria),
April 23-28, 2017,
Poster.
» Abstract
Quantitative studies of sea-level rise in the Mediterranean are becoming more and more accurate thanks to detailed satellite monitoring campaigns. However, these studies cover several years to a couple of decades at best, while longer-term sea-level records for the area are rare. Long-term sea-level measurements are essential in order to derive accurate trends free of conspicuous oscillations in shorter records. We use an approach from data archaeology to meet this shortcoming, and to offer a more complete record of sea-level rise cross-checked among several tide gauges. Specifically, we investigate monthly mean sea-level data of the Antalya-I (1935-1977) tide gauge provided by the Turkish National Mapping Agency. We checked how accurately and reliably these monthly records were digitized, quality-controlled, and tied to a common datum. We then merged these data with the more recent records of the nearby Antalya-II (1985-2010) tide gauge, obtaining a composite time series of monthly and annual mean sea levels spanning approximately 75 years. We thus offer the hitherto longest record in the Eastern Mediterranean Basin as an essential tool for studying the region’s sea-level trends. We estimate a relative mean sea-level rise of 2.46 ± 1.65 mm/yr between 1935 and 2010, with a sub-decadal variability (σresiduals = 49.47 mm) that is higher than at nearby tide gauges (e.g. Thessaloniki, Greece, σresiduals = 28.71 mm). Our study highlights the value of data archaeology for recovering and integrating early tide-gauge data for long-term sea-level and climate studies.
A. M. D. T. Ramos, L. A. Builes-Jaramillo, G. Poveda, B. Goswami, E. E. N. Macau, J. Kurths, N. Marwan:
Non-linear interactions between Niño region 3 and the Southern Amazon,
AGU Fall Meeting,
San Francisco (USA),
December 12-16, 2016,
» Talk (PDF, 2.17M).
» Abstract
Identifying causal relations from the observational dataset has posed great challenges in data-driven inference study. However, complex system framework offers promising approaches to tackle such problems. Here we propose a new data-driven causality inference method using the framework of recurrence plots. We present the Recurrence Measure of Conditional Dependence (RMCD) and its applications. The RMCD incorporates the recurrence behavior into the transfer entropy theory. Therefore, it quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the potential driver and present on the potential driven, except for any contribution that has already been in the past of the driven. We apply this methodology to some paradigmatic models and to investigate the possible influence of the Pacific Ocean temperatures on the South West Amazon for the 2010 and 2005 droughts. The results reveal that for the 2005 drought there is not a significant signal of dependence from the Pacific Ocean and that for 2010 there is a signal of dependence of around 200 days. These outcomes are confirmed by the traditional climatological analysis of these episodes available in the literature and show the accuracy of RMCD inferring causal relations in climate systems.
A. Agarwal, N. Marwan, R. Maheswaran, U. Ozturk, B. Merz, J. Kurths:
Multiscale event synchronization analysis for unraveling climate processes: A wavelet-based approach,
AGU Fall Meeting,
San Francisco (USA),
December 12-16, 2016,
» Poster (PDF, 2.43M).
» Abstract
The temporal dynamics of natural processes (climatic/hydrological) are spread across different time scales and, as such, the study of these processes only at a given scale would not reveal all the underlying governing processes spanning over different scales. As needs be, it is vital to investigate such processes at various time-scales. Wavelets have been used extensively to comprehend the multiscale process and have been appeared to be exceptionally reliable and useful in understanding dynamics of the process across various time scales as these evolve in time. Recently, event synchronization has picked up an interest in capturing the nonlinear interactions between different climatic signals based on synchronization and time delays of events (characterized as local maxima) in the timeseries. At present, the event synchronization analyses the relationship at a single scale. However, visualization of the time evolution of delay and synchronization at multiscale would be of great interest to comprehend the dynamics of the signal.
In this paper, a wavelet based multi-scale event synchronization (MSES) methodology has been proposed and tested. The main advantage of this method is that it provide a quantitative measure of process across different scales. The applicability of the proposed method has explored using various case studies –both real as well as synthetic. The study also shows that proposed methodology works well also for model evaluation.
D. Wendi, N. Marwan, B. Merz:
Identifying changes of complex flood dynamics with recurrence analysis,
AGU Fall Meeting,
San Francisco (USA),
December 12-16, 2016,
Talk invited.
» Abstract
Temporal changes in flood hazard system are known to be difficult to detect and attribute due to multiple drivers that include complex processes that are non-stationary and highly variable. These drivers, such as human-induced climate change, natural climate variability, implementation of flood defense, river training, or land use change, could impact variably on space-time scales and influence or mask each other. Flood time series may show complex behavior that vary at a range of time scales and may cluster in time. Moreover hydrological time series (i.e. discharge) are often subject to measurement errors, such as rating curve error especially in the case of extremes where observation are actually derived through extrapolation.
This study focuses on the application of recurrence based data analysis techniques (recurrence plot) for understanding and quantifying spatio-temporal changes in flood hazard in Germany. The recurrence plot is known as an effective tool to visualize the dynamics of phase space trajectories i.e. constructed from a time series by using an embedding dimension and a time delay, and it is known to be effective in analyzing non-stationary and non-linear time series. Sensitivity of the common measurement errors and noise on recurrence analysis will also be analyzed and evaluated against conventional methods. The emphasis will be on the identification of characteristic recurrence properties that could associate typical dynamic to certain flood events.
F. Brenner, P. Hoffmann, N. Marwan:
Combining a complex network approach and a SEIR compartmental model to link fast spreading of infectious diseases with climate change,
AGU Fall Meeting,
San Francisco (USA),
December 12-16, 2016,
Talk.
» Abstract
Infectious diseases are a major threat to human health. The spreading of airborne diseases has become fast and hard to predict. Global air travelling created a network which allows a pathogen to migrate worldwide in only a few days. Pandemics of SARS (2002/03) and H1N1 (2009) have impressively shown the epidemiological danger in a strongly connected world.
In this study we simulate the outbreak of an airborne infectious disease that is directly transmitted from human to human. We use a regular Susceptible-Infected-Recovered (SIR) model and a modified Susceptible-Exposed-Infected-Recovered (SEIR) compartmental approach with the basis of a complex network built by global air traffic data (from openflights.org). Local Disease propagation is modeled with a global population dataset (from SEDAC and MaxMind) and parameterizations of human behavior regarding mobility, contacts and awareness. As a final component we combine the worldwide outbreak simulation with daily averaged climate data from WATCH-Forcing-Data-ERA-Interim (WFDEI) and Coupled Model Intercomparison Project Phase 5 (CMIP5).
Here we focus on Influenza-like illnesses (ILI), whose transmission rate has a dependency on relative humidity and temperature. Even small changes in relative humidity are sufficient to trigger significant differences in the global outbreak behavior. Apart from the direct effect of climate change on the transmission of airborne diseases, there are indirect ramifications that alter spreading patterns. For example seasonal changing human mobility is influenced by climate settings.
N. Marwan:
Hot Topics in Recurrence Plot Analysis,
Humboldt-Kolleg,
Yaoundé (Cameroon),
November 22-24, 2016,
Lecture.
N. Marwan:
Recurrence Analysis,
Graduate School NatRiskChange, University of Potsdam,
Potsdam (Germany),
November 8, 2016,
Lecture.
Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. We show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply this method on spatially extended chaos, such as derived from the Lorenz96 model and show that the recurrence plot based measures can qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analyzing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world.
N. Marwan:
Modern approaches for nonlinear time series analysis,
Course Global Change Management Studies, University of Applied Science Eberswalde,
Eberswalde (Germany),
June 7, 2016,
Lecture.
N. Marwan, S. Foerster, J. Kurths:
Analysing spatially extended high-dimensional dynamics by recurrence plots,
EGU General Assembly,
Vienna (Austria),
April 17-22, 2016,
» Poster (PDF, 2.92M).
» Abstract
Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. We show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply this method on spatially extended chaos, such as derived from the Lorenz96 model and show that the recurrence plot based measures can qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analyzing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world.
N. Marwan, N. Malik, N. Boers, A. Rheinwalt, V. Stolbova, B. Bookhagen, J. Kurths:
Potentials of complex network analysis of regional rainfall co-variability,
EGU General Assembly,
Vienna (Austria),
April 17-22, 2016,
Poster.
» Abstract
Regional variability of extreme precipitation is characterised by distinctive patterns of statistical interrelations. The propagation, structure, and complexity of such patterns can be studied by means of complex network theory. We demonstrate the potential of this analytical framework for identification of teleconnections, propagation patterns, or finding prediction schemes for extreme rainfall.
T. Nocke, S. Buschmann, J. Donges, N. Marwan:
Visualization techniques and tools for large geo-physical networks,
EGU General Assembly,
Vienna (Austria),
April 17-22, 2016,
Talk.
» Abstract
Network analysis is an important approach in studying complex phenomena within geophysical observation and simulation data. This field produces increasing numbers of large geo-referenced networks to be analyzed. Particular focus lies on the network analysis of the complex statistical interrelationship structure within climatological fields. The typical procedure for such network analyzes is the extraction of network measures in combination with static standard visualization methods.
To analyze the visualization challenges within this field, we performed a questionnaire with climate and complex system scientists, and identified a strong requirement for solutions visualizing large and very large geo-referenced networks by providing alternative mappings for static plots and allowing for interactive visualization for networks with 100.000 or even millions of edges. In addition, the questionnaire revealed, that existing interactive visualization methods and tools for geo-referenced network exploration are often either not known to the analyst or their potential is not fully exploited.
Within this presentation, we illustrate how interactive visual analytics methods in combination with geo-visualisation can be tailored for visual large climate network investigation (see as well Nocke et al. 2015). Therefore, we present a survey of requirements of network analysts and the related challenges and, as an overview for the interested practitioner, we review the state-of-the-art in climate network visualization techniques and tools, underpinned with concrete examples from climate network research and innovative solutions (e.g. alternative projections, 3D layered networks) implemented within the network visualization system GTX.
J. Runge, V. Petoukhov, J. Donges, J. Hlinka, N. Jajcay, M. Vejmelka, D. Hartman, N. Marwan, M. Palus, J. Kurths:
Identifying causal gateways and mediators in complex spatio-temporal systems,
EGU General Assembly,
Vienna (Austria),
April 17-22, 2016,
Talk.
» Abstract
Identifying regions important for spreading and mediating perturbations is crucial to assess the susceptibilities of spatio-temporal complex systems such as the Earth’s climate to volcanic eruptions, extreme events or geoengineering. Here a data-driven approach is introduced based on a dimension reduction, causal reconstruction, and novel network measures based on causal effect theory that go beyond standard complex network tools by distinguishing direct from indirect pathways. Applied to a data set of atmospheric dynamics, the method identifies several strongly uplifting regions acting as major gateways of perturbations spreading in the atmosphere. Additionally, the method provides a stricter statistical approach to pathways of atmospheric teleconnections, yielding insights into the Pacific–Indian Ocean interaction relevant for monsoonal dynamics. The novel causal interaction perspective provides a complementary approach to simulations or experiments for understanding the functioning of complex spatio-temporal systems with potential applications in increasing their resilience to shocks or extreme events.
T. Nocke, S. Buschmann, J. Donges, N. Marwan:
New solutions for climate network visualization,
EGU General Assembly,
Vienna (Austria),
April 17-22, 2016,
Talk.
» Abstract
An increasing amount of climate and climate impact research methods deals with geo-referenced networks, including energy, trade, supply-chain, disease dissemination and climatic tele-connection networks. At the same time, the size and complexity of these networks increases, resulting in networks of more than hundred thousand or even millions of edges, which are often temporally evolving, have additional data at nodes and edges, and can consist of multiple layers even in real 3D. This gives challenges to both the static representation and the interactive exploration of these networks, first of all avoiding edge clutter (“edge spagetti”) and allowing interactivity even for unfiltered networks.
Within this presentation, we illustrate potential solutions to these challenges. Therefore, we give a glimpse on a questionnaire performed with climate and complex system scientists with respect to their network visualization requirements, and on a review of available state-of-the-art visualization techniques and tools for this purpose (see as well Nocke et al., 2015). In the main part, we present alternative visualization solutions for several use cases (global, regional, and multi-layered climate networks) including alternative geographic projections, edge bundling, and 3-D network support (based on CGV and GTX tools), and implementation details to reach interactive frame rates.
S. F. M. Breitenbach, B. Plessen, S. Wenz, J. Leonhardt, R. Tjallingii, D. Scholz, K. P. Jochum, N. Marwan:
A multi-proxy reconstruction of Holocene climate change from Blessberg Cave,
EGU General Assembly,
Vienna (Austria),
April 17-22, 2016,
» Poster (PDF, 2.85M).
» Abstract
Although Holocene climate dynamics were relatively stable compared to glacial conditions, climatic changes had significant impact on ecosystems and human society on various timescales (Mayewski et al. 2004, Donges et al. 2015, Tan et al. 2015). Precious few high-resolution records on Holocene temperature and precipitation conditions in Central Europe are available (e.g., von Grafenstein et al. 1999, Fohlmeister et al. 2012).
Here we present a speleothem-based reconstruction of past climate dynamics from Blessberg Cave, Thuringia, central Germany. Three calcitic stalagmites were recovered when the cave was discovered during tunneling operations in 2008. Samples BB-1, -2 and -3 were precisely dated by the 230Th/U-method, with errors between 10 and 160 years (2σ). The combined record covers large parts of the Holocene (10 – 0.4 ka BP). δ13C and δ18O were analysed at 100 μm resolution. To gain additional insights in infiltration conditions, Sr/Ca and S/Ca were measured on BB-1 and BB-3 using an Röntgenanalytik Eagle XXL μXRF scanner.
Differences to other central European records (e.g., von Grafenstein et al. 1999, Fohlmeister et al. 2012) suggest complex interaction between multiple factors influencing speleothem δ18O in Blessberg Cave. Furthermore, no clear influence of the North Atlantic Oscillation on our proxies is found. However, a link across the N Atlantic realm is indicated by a centennial-scale correlation between Blessberg δ18O values and minerogenic input into lake SS1220 in Greenland over the last 5 ka (Olsen et al. 2012). In addition, recurrence analysis indicates an imprint of Atlantic Bond events on Blessberg δ18O values (Marwan et al. 2014), corroborating the suggested link with high northern latitudes. Larger runoff into the Greenland lake seems to be associated with lower δ18O, higher δ13C and S/Ca ratios, as well as lower Sr/Ca ratios in Blessberg Cave speleothems. This might be linked to lower local temperature and/or changes in precipitation seasonality. Opposing millennial scale trends with lowering S/Ca ratios and δ13C values but increasing Sr/Ca ratios calls for more than one controlling factor. Most likely, δ13C decreased through the Holocene due to afforestation, which in turn might have increased sulphate retention in the thickening soil cover (Frisia et al. 2005) and limited sulphur flux into the cave. Alternatively, marine sulfur flux could have diminished with winter wind intensities. However, additional data is required to clarify this hypothesis. A positive Sr/Ca trend through the Holocene might result from increasing prior calcite precipitation induced by a negative moisture balance in summer.
D. Wendi, B. Merz, N. Marwan:
Novel flood detection and analysis method using recurrence property,
EGU General Assembly,
Vienna (Austria),
April 17-22, 2016,
Poster.
» Abstract
Temporal changes in flood hazard are known to be difficult to detect and attribute due to multiple drivers that include processes that are non-stationary and highly variable. These drivers, such as human-induced climate change, natural climate variability, implementation of flood defence, river training, or land use change, could impact variably on space-time scales and influence or mask each other. Flood time series may show complex behavior that vary at a range of time scales and may cluster in time.
This study focuses on the application of recurrence based data analysis techniques (recurrence plot) for understanding and quantifying spatio-temporal changes in flood hazard in Germany. The recurrence plot is known as an effective tool to visualize the dynamics of phase space trajectories i.e. constructed from a time series by using an embedding dimension and a time delay, and it is known to be effective in analyzing non-stationary and non-linear time series. The emphasis will be on the identification of characteristic recurrence properties that could associate typical dynamic behavior to certain flood situations.
J. Donges, J. Heitzig, B. Beronov, M. Wiedermann, J. Runge, Q. Y. Feng, L. Tupikina, V. Stolbova, R. Donner, N. Marwan, H. Dijkstra, J. Kurths:
Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package,
EGU General Assembly,
Vienna (Austria),
April 17-22, 2016,
Poster.
» Abstract
We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology. pyunicorn is available online at https://github.com/pik-copan/pyunicorn.
D. Eroglu, N. Marwan, I. Ozken, T. Stemler, J. Kurths:
How to overcome data based difficulties in geoscience?,
EGU General Assembly,
Vienna (Austria),
April 17-22, 2016,
Poster.
» Abstract
There are many challenges in the field of time series analysis such as cumulative trends or sampling irregularities. Geophysical time series, particularly paleo-climate ones, have such problems almost in all proxies. The novel TrAnsformation-Cost Time-Series (TACTS) method is a suitable approach to overcome these challenges of cumulative trends and irregular sampling without degenerating the quality of the data set by, e.g., interpolation.
The standard method to regularize time sampling of time series is interpolation, but it collapses the quality of the proxies. Moreover, there are many different approaches to de-trend time series such as Gaussian high-pass filter, the de-trended fluctuation analysis. At the same time, the TACTS is able to de-trend and regularize the time series at the same time with keeping the quality of time series rather high. After applying the TACTS method the resulting cost time series shows regular sampling and can be further analyzed using standard methods.
The TACTS method has been developed and tested by using prototypical mathematical models. We have demonstrated its use by studying paleoclimate dynamics derived from speleothem data from the Secret Cave in Borneo, the KNI-51 cave in North Australia, and Dongge Cave, East China. By using the TACTS, we could distinguish all extreme transition events and found interesting alternating monsoon dynamics between North Australia and East China.
M. Riedl, N. Marwan, J. Kurths:
Extended quantification of the generalized recurrence plot,
EGU General Assembly,
Vienna (Austria),
April 17-22, 2016,
Poster.
» Abstract
The generalized recurrence plot is a modern tool for quantification of complex spatial patterns. Its application spans the analysis of trabecular bone structures, Turing structures, turbulent spatial plankton patterns, and fractals. But, it is also successfully applied to the description of spatio-temporal dynamics and the detection of regime shifts, such as in the complex Ginzburg-Landau-equation. The recurrence plot based determinism is a central measure in this framework quantifying the level of regularities in temporal and spatial structures. We extend this measure for the generalized recurrence plot considering additional operations of symmetry than the simple translation. It is tested not only on two-dimensional regular patterns and noise but also on complex spatial patterns reconstructing the parameter space of the complex Ginzburg-Landau-equation. The extended version of the determinism resulted in values which are consistent to the original recurrence plot approach. Furthermore, the proposed method allows a split of the determinism into parts which based on laminar and non-laminar regions of the two-dimensional pattern of the complex Ginzburg-Landau-equation. A comparison of these parts with a standard method of image classification, the co-occurrence matrix approach, shows differences especially in the description of patterns associated with turbulence. In that case, it seems that the extended version of the determinism allows a distinction of phase turbulence and defect turbulence by means of their spatial patterns. This ability of the proposed method promise new insights in other systems with turbulent dynamics coming from climatology, biology, ecology, and social sciences, for example.
O. Kwiecien, N. Marwan:
What drives the δ18O signal in European carbonates during LGM and Termination II – multi-archive approach revised,
EGU General Assembly,
Vienna (Austria),
April 17-22, 2016,
Poster.
» Abstract
Due to their natural occurrence in a wide spectrum of environmental settings (marine, lacustrine, terrestrial) carbonates constitute one of the most widely used archives of (paleo)environmental information Although the thermodynamic laws controlling isotopic fractionation are universal, each of the different environments leaves its characteristic imprint on the carbonate chemistry. Consequently, individual carbonate-based records are a combination of regional-scale and archive- or site-specific factors. Environmental heterogeneity, even within a confined geographical area, remains a challenge in teasing out the regional or local nature of the recorded climatic signal. Similarly, interpretation of new data often pays tribute to outdated assumptions.
Here we compare and contrast published oxygen isotope records from different archives (lake sediments and stalagmites) from central Europe and the Black Sea region covering the time span between 26 and 8 ka BP. This exercise aims at (1) identification of the regional-scale mechanisms responsible for common trends and (2) better understanding of archive- and site-specific factors accounting for differences in the records. Additionally, this approach allows for testing ‘closed vs outflowing’ scenarios for the glacial Black Sea basin.
It appears that changes in isotopic composition of atmospheric precipitation are a common denominator for the analyzed records. Site-specific factors include moisture source (stalagmites) and volume of the basin (lakes). Both, comparison of available geochemical records and data-based theoretical calculations suggest that since the LGM and until reconnection with Mediterranean at ca. 8 ka BP the Black Sea was an open system.
D. Eroglu, I. Ozken, F. McRobie, T. Stemler, N. Marwan, K.-H. Wyrwoll, J. Kurths:
A solar variability driven monsoon see-saw: switching relationships of the Holocene East Asian-Australian summer monsoons,
EGU General Assembly,
Vienna (Austria),
April 17-22, 2016,
» Poster (PDF, 842.68K).
» Abstract
The East Asian-Indonesian-Australian monsoon is the predominant low latitude monsoon system, providing a major global scale heat source. Here we apply newly developed non-linear time series techniques on speleothem climate proxies, from eastern China and northwestern Australia and establish relationships between the two summer monsoon regimes over the last ∼9000 years. We identify significant variations in monsoonal activity, both dry and wet phases, at millennial to multi-centennial time scales and demonstrate for the first time the existence of a see-saw antiphase relationship between the two regional monsoon systems. Our analysis attributes this inter-hemispheric linkage to the solar variability that is effecting both monsoon systems.
N. Marwan, Y. Zou, M. Riedl, N. Wessel, J. Kurths:
Bestimmung der Kopplungsrichtungen im kardiorespiratorischen System anhand wiederkehrbasierter Methoden,
Workshop Biosignalverarbeitung 2016,
Berlin (Germany),
April 7, 2016,
Talk.
» Abstract
The asymmetry of coupling between complex systems can be studied by conditional probabilities of recurrence, which can be estimated by joint recurrence plots. This approach is applied for the first time on experimental data: time series of the human cardiorespiratory system in order to investigate the couplings between heart rate, mean arterial blood pressure and respiration. We find that the respiratory system couples towards the heart rate, and the heart rate towards the mean arterial blood pressure. However, our analysis could not detect a clear coupling direction between the mean arterial blood pressure and respiration.
N. Marwan:
Recurrence Plots for the Analysis of Complex Systems,
Seminar Department of Knowledge Engineering, University of Maastricht,
Maastricht (The Netherlands),
February 17, 2016,
Talk.
><2015
N. Boers, A. Rheinwalt, B. Bokkhagen, N. Marwan, J. Kurths, H. M. J. Barbosa, J. Marengo:
Complex network analysis of extreme rainfall in South America: Climatic analysis – model evaluation – prediction,
International Workshop "Analysis of dynamic networks and data driven modelling of the climate",
Potsdam (Germany),
October 12–14, 2015,
Talk.
» Abstract
We construct networks from synchronization of extreme rainfall events over South America for the monsoon season from December to February, using 6 different datasets. This methodology is designed to complement PCA-based techniques in the case of extreme events. A climatological interpretation of various network measures (1) reveals the most important features of the South American Monsoon System (SAMS), (II) allows to compare the representation of the spatiotemporal co-variability of extreme rainfall in different datasets and models, and (III) leads to a statistical forecasting framework of extreme events.
B. Goswami, A. Rheinwalt, N. Boers, N. Marwan, J. Heitzig, S. F. M. Breitenbach, J. Kurths:
Using complex networks to detect abrupt climate change in paleoclimate datasets,
International Workshop "Analysis of dynamic networks and data driven modelling of the climate",
Potsdam (Germany),
October 12–14, 2015,
Talk.
» Abstract
A fundamental obstacle in the analysis of paleoclimate datasets is the uncertainty involved in determining the liming of past climatic events. Principled approaches to such data necessarily represents them as a probability distribution at eacli time point of the past rather than a point estimate. Here, we provide an approach that helps infer dynamical shifts from paleoclimate proxy records, considering them as a sequence of possibly correlated time-ordered marginal probability distributions instead of a point-estimate time series. Using bounds on the difference distriburions we define a probability of recurrence matrix with which we estimate the recurrence network for the data. We propose that the identification of communities in the recurrence network corresponds to the detection of sudden dynamical shifts. We demonstrate our approach with a synthetic paleomonsoon dataset and use it thereafter to infer periods of sudden climatic change in Asian monsoon records that span the past 9000 years.
M. Sips, T. Rawald, C. Witt, N. Marwan:
Towards multi-scale RQA using Visual Analytics,
6th International Symposium on Recurrence Plots,
Grenoble (France),
June 17-19, 2015,
Talk.
» Abstract
Time series often capture a variety of sub processes on different temporal scales. Applying the recurrence quantification analysis (RQA) to time series describes the behavior of all processes simultaneously. In many application scenarios, users want to restrict the RQA only on relevant processes. Therefore, there is increasing interest to extract relevant processes from time series.
Previous work has shown that multi-scale methods, such as wavelet transformation, are capable of isolating relevant processes. Our research goal is to extent the traditional RQA into a multi-scale RQA method. Our current research efforts show that multi-scale RQA involves two major challenges. First, the decomposition of a time series produces a huge set of time series; each time series is associated with a particular temporal scale. Second, users need to locate the temporal scales at which relevant processes operate. To address these two challenges, we currently work on a Visual Analytics approach that combines multi-scale decomposition, the fast computation of RQA for all temporal scales, and the clustering of these RQA results.
In our presentation, we will discuss the three main components of our Visual Analytics approach. First, our approach supports a broad range of multi-scale methods. Second, our fast RQA computation is based on subdividing the RQA computation and distributing the computational work across multiple graphics processing units. Third, the clustering of RQA measures allow users to focus on characteristic RQA results. We will present our latest research efforts and discuss the challenges involved to extent traditional RQA into a multi-scale method.
D. Eroglu, T. K. D. Peron, N. Marwan, F. A. Rodrigues, L. da F. Costa, M. Sebek, I. Z. Kiss, J. Kurths:
Entropy of weighted recurrence plots,
6th International Symposium on Recurrence Plots,
Grenoble (France),
June 17-19, 2015,
Talk.
» Abstract
Phase-space binning and using information in the bins is the standard method to establish complexity of a dynamical system. Methods such as the Shannon entropy, the Hausdorff dimension, the Kolmogorov complexity etc., can be used to quantify transitions between different dynamical regimes. In order to create a recurrence plot, we divide the phase space into equi-distant but overlapping bins. The information in the bins shows us similar features as in the mentioned measures before. Here we suggest a method based on weighted recurrence plots and show that the associated Shannon entropy is positively correlated with the largest Lyapunov exponent. We demonstrate the potential on a prototypical example as well as on experimental data of a chemical experiment.
D. Schultz, S. Spiegel, N. Marwan, S. Albayrak:
Approximation of diagonal line based measures in recurrence quantification analysis,
6th International Symposium on Recurrence Plots,
Grenoble (France),
June 17-19, 2015,
Talk.
» Abstract
Given a trajectory of length N, recurrence quantification analysis (RQA) traditionally operates on the recurrence plot, whose calculation requires quadratic time and space (O(N2)), leading to expensive computations and high memory usage for large N. However, if the similarity threshold ε is zero, we show that the recurrence rate (RR), the determinism (DET) and other diagonal line based RQA-measures can be obtained algorithmically taking O(N log(N)) time and O(N) space. Furthermore, for the case of ε > 0 we propose approximations to the RQA-measures that are computable with same complexity. Simulations with autoregressive systems, the logistic map and a Lorenz attractor suggest that the approximation error is small if the dimension of the trajectory and the minimum diagonal line length are small. When applying the approximate determinism to the problem of detecting dynamical transitions we observe that it performs as well as the exact determinism measure.
Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. We show the potential of selected recurrence plot measures for the investigation of spatially extended high-dimensional dynamics by applying them to data from the Lorenz96 model. The recurrence plot based measures are able to qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analyzing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world.
M. Riedl, J. Kurths, N. Marwan:
Spatial-temporal recurrence analysis based on a global measure of spatial similarity,
6th International Symposium on Recurrence Plots,
Grenoble (France),
June 17-19, 2015,
Talk.
» Abstract
The analysis of spatial-temporal data is still a methodological question of current research, e.g. in earth science. In this work an extension of the recurrence plot is suggested in order to track regime shifts in spatial patterns. For this purpose, the global state, i.e. all data in one time step, is compared to each other by means of a similarity measure that is known from tracking algorithms. This routine consists of a digitalization, blurring and bin wise comparison of the single global states. In its roughest version, the algorithm is equivalent to the kappa-statistic which is widely used to assess similarities of spatial pattern in ecosystems. The use of this similarity measure in the framework of recurrence plots enables a visualization and quantification of the temporal evolution of the spatial extended system. In the end, the extended recurrence plot and its quantification allows a detection of changes in the spatial-temporal dynamic of the observed system.
O. Afsar, N. Marwan, J. Kurths:
Scaling relations from recurrence quantification analysis for the Logistic map at the edge of chaos: Connection with universal Huberman-Rudnick scaling law,
6th International Symposium on Recurrence Plots,
Grenoble (France),
June 17-19, 2015,
Poster.
» Abstract
Huberman-Rudnick universal Lyapunov scaling law is a kind of predictive capability if a system become chaotic through a sequence of period doublings, then one could be predict how it will be as a function of the control parameter [R.C. Hilborn, Chaos and Nonlinear Dynamics (Oxford University Press, NewYork, 1994)]. As chaos threshold is approached within this scaling law, it is fact that the Lyapunov exponent exhibits a power law behaviour depending to distance of the chaos threshold (a-a_c) possessing the a universal critical exponent with ν=ln2/ln δ ∼ 0.45 (δ is the Feigenbaum constant) [B. A. Huberman and J. Rudnick, PRL 45 (1980) 154]. We numerically introduce the new relationships and scaling laws related to the recurrence rate (RR), the average length of the diagonal lines (L), the determinism (DET) and exponantial divergence of phase space trajectory (DIV) as the measures from Recurrence Quantification Analysis (RQA) as we approach the chaos threshold of the logistic map with Huberman-Rudnick scaling procedure. After we determine the critical values (RRc, Lc, DETc and DIVc) of these measures on the chaos threshold of the logistic map, firstly, we verify that a scaling law of type RR-RRc ∝ (a-ac)α is evident with the critical exponent α=0.47 ±0.01. Secondly, we show that the quantity L scales as | L - Lc| ∝ (a-ac)β, where the exponent is β=0.46±0.02. Thirdly, we numerically verify that DET exhibits a scaling law of type | DET-DETc | ∝ (a-ac)γ, where the exponent is γ=0.27±0.01. Finally, we numerically show relation between the Huberman-Rudnick universal Lyapunov scaling law and Divergence scaling which behaves as λ ∝ (a-ac)ν and DIV ∝ (a-ac)κ, where the exponents are ν=0.449±0.001 and κ=0.50±0.03.
B. Goswami, A. Rheinwalt, N. Boers, N. Marwan, J. Heitzig, S. Breitenbach, J. Kurths:
Detecting paleoclimate transitions of the East Asian Summer Monsoon with recurrence networks,
NetSci2015,
Zaragoza (Spain),
June 1-5, 2015,
Talk.
N. Boers, B. Bookhagen, H. Barbosa, N. Marwan, J. Kurths, J. Marengo:
Prediction of the most extreme rainfall events in the South American Andes: A statistical forecast based on complex networks,
EGU General Assembly,
Vienna (Austria),
April 12-17, 2015,
Talk.
» Abstract
During the monsoon season, the subtropical Andes in South America are exposed to spatially extensive extreme rainfall events that frequently lead to flashfloods and landslides with severe socio-economic impacts. Since dynamical weather forecast has substantial problems with predicting the most extreme events (above the 99th percentile), alternative forecast methods are called for. Based on complex network theory, we developed a general mathematical framework for statistical prediction of extreme events in significantly interrelated time series. The key idea of our approach is to make the internal synchronization structure of extreme events mathematically accessible in terms of the topology of a network which is constructed from measuring the synchronization of extreme events at different locations. The application of our method to high-spatiotemporal resolution rainfall data (TRMM 3B42) reveals a migration pattern of large convective systems from southeastern South America towards the Argentinean and Bolivian Andes, against the direction of the northwesterly low-level moisture flow from the Amazon Basin. Once these systems reach the Andes, they lead to spatially extensive extreme events up to elevations above 4000m, leading to substantial risks of associated natural hazards. Based on atmospheric composites, we could identify an intricate interplay of frontal systems approaching from the South, low-level moisture flow from the Amazon Basin to the North, and the Andean orography as responsible climatic mechanism. These insights allow to formulate a simple forecast rule predicting 60% (90% during El Niño conditions) of extreme rainfall events at the eastern slopes of the subtropical Andes. The rule can be computed from readily available rainfall and pressure data and is already being tested by local institutions for disaster preparation.
N. Boers, N. Marwan, H. Barbosa, J. Kurths:
How Amazonian deforestation can alter the South American circulation regime: Insights from a non-linear moisture transport model,
EGU General Assembly,
Vienna (Austria),
April 12-17, 2015,
Talk.
» Abstract
A key driver of South American climate are the low-level trade winds from the tropical Atlantic Ocean towards the continent. After crossing the Amazon Basin, they are blocked by the Andes mountain range, and forced southward to the subtropics. These winds are crucial for the atmospheric moisture supply in most parts of South America. In particular, the hydrology of the two largest river basins of the Continent, namely the Amazon and the La Plata Basins, strongly depend on the moisture inflow provided by the trade winds. In turn, the Amazon rainforest can be assumed to have a strong influence on this low-level moisture circulation over South America by exchanging moisture with the atmosphere through precipitation and evapotranspiration. A pronounced positive feedback in this context is established through precipitation-induced release of latent heat over the Amazon Basin, which significantly enhances the moisture inflow from the tropical Atlantic Ocean toward the continent and can thus be considered to be crucial for the existence of today’s South American climate. Ongoing deforestation and resulting reduction in evapotranspiration rates in particular in the eastern Amazon carry the risk of a strongly nonlinear response in these interactions with the low-level atmosphere. We propose a simple differential transport model describing the cascading moisture transport from the eastern coast of South America across the Amazon Basin to the Andes, taking into account the nonlinearity associated with the release of latent heat. The results of the model suggest that the system is indeed very sensitive to relatively small reductions of the evapotranspiration rates in the eastern Amazon Basin. These reductions increase river runoff, but limit the moisture availability farther west. This leads to a reduction in precipitation rates and thereby diminishes the release of latent heat which, in turn, reduces the overall moisture inflow. We show that, according to our model, there exist critical thresholds on the spatial extents and intensities of deforestation. Beyond these thresholds, the positive feedback between the Amazon rainforest and the low-level circulation would collapse, resulting in substantial reductions in moisture available for precipitation in the western part of the Amazon Basin and further downstream of the low-level flow, including most of subtropical South America.
D. Eroglu, I. Ozken, T. Stemler, N. Marwan, K. -H. Wyrwoll, J. Kurths:
How to analyse irregularly sampled geophysical time series?,
EGU General Assembly,
Vienna (Austria),
April 12-17, 2015,
Talk.
» Abstract
One of the challenges of time series analysis is to detect dynamical changes in the dynamics of the underlying system.There are numerous methods that can be used to detect such regime changes in regular sampled times series. Here we present a new approach, that can be applied, when the time series is irregular sampled. Such data sets occur frequently in real world applications as in paleo climate proxy records.
The basic idea follows Victor and Purpura [1] and considers segments of the time series. For each segment we compute the cost of transforming the segment into the following one. If the time series is from one dynamical regime the cost of transformation should be similar for each segment of the data. Dramatic changes in the cost time series indicate a change in the underlying dynamics. Any kind of analysis can be applicable to the cost time series since it is a regularly sampled time series. While recurrence plots are not the best choice for irregular sampled data with some measurement noise component, we show that a recurrence plot analysis based on the cost time series can successfully identify the changes in the dynamics of the system.
We tested this method using synthetically created time series and will use these results to highlight the performance of our method. Furthermore we present our analysis of a suite of calcite and aragonite stalagmites located in the eastern Kimberley region of tropical Western Australia. This oxygen isotopic data is a proxy for the monsoon activity over the last 8,000 years. In this time series our method picks up several so far undetected changes from wet to dry in the monsoon system and therefore enables us to get a better understanding of the monsoon dynamics in the North-East of Australia over the last couple of thousand years.
N. Marwan, P. Koethur, C. Witt, S. F. M. Breitenbach, M. Sips:
Analysing the degree of replication of palaeoclimate records,
EGU General Assembly,
Vienna (Austria),
April 12-17, 2015,
» Poster (PDF, 2.97M).
» Abstract
Palaeoclimate proxy records (such as time series derived from ice cores or stalagmites) from the same or nearby location would be expected to represent similar climate variation. This is called replication of proxy records but is often difficult to achieve, because either the proxies are not reflecting the paleoclimate variation, external factors overprint the climate signal in the proxy record, or chronological uncertainties cause a serious mismatch between the individual records. In order to minimize the later issue and take the chronological uncertainties into account, we combine a Monte Carlo based approach (COPRA) with an ensemble based windowed cross-correlation analysis. This allows the investigation of potential replication of proxy records from a statistical perspective. We demonstrate this approach by comparing two stalagmite δ18O records from Heshang cave and Sanbao cave, both strongly influenced by the East Asian Summer Monsoon and covering the period between 9000 yr BP and 500 yrBP. We find that both proxy records reproduce well, although not perfectly. Main issues are differences between the records caused by unresolved geochemical processes influencing the U-series system and possibly kinetic fractionation in the oxygen isotope system. Overall, the proposed approach can provide a means to extract a correction function which reduces the uncertainties in the dating procedure. This method is a precursory step towards composite reconstructions that are based on multiple, replicating, time series.
N. Marwan, S. Foerster, J. Kurths:
Recurrence plot analysis of spatially extended high-dimensional dynamics,
EGU General Assembly,
Vienna (Austria),
April 12-17, 2015,
» Poster (PDF, 1.96M).
» Abstract
Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. We show the potential of selected recurrence plot measures for the investigation of spatially extended high-dimensional dynamics by applying them to data from the Lorenz96 model. The recurrence plot based measures are able to qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analyzing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world.
J. Runge, J. Donges, J. Hlinka, N. Jajcay, N. Marwan, M. Palus, J. Kurths:
Quantifying causal pathways of interactions in the complex tropical climate system,
EGU General Assembly,
Vienna (Austria),
April 12-17, 2015,
Talk.
» Abstract
The focus of this work is to better understand the complex interplay between different subprocesses in the climate system, especially how tropical processes such as El Nino-Southern Oscillation (ENSO), the Indian Ocean Dipole, Tropical Atlantic Variability, and the tropical monsoons affect global climate.
Here a novel data-driven method is proposed based on: (1) a dimension reduction of the global surface pressure field yielding components that represent various known subprocesses such as ENSO or the North Atlantic Oscillation, (2) a causal reconstruction algorithm to detect which subprocesses are only indirectly interacting or are only spuriously correlated due to common drivers, and (3) measures to identify causal pathways in the reconstructed interaction network.
Two main results will be presented: (1) an hypothesis of a mechanism by which ENSO influences the Indian Monsoon within the surface pressure field. (2) In an explorative analysis it is shown that the method correctly identifies the major regions of upwelling convergence in the tropical oceans and also regions of strong downwelling. The approach provides a novel causal interaction perspective on complex spatio-temporal systems.
L. Tupikina, N. Molkentin, C. Lopez, E. Hernandez-Garcia, N. Marwan, J. Kurths:
Time-dependent flow-networks,
EGU General Assembly,
Vienna (Austria),
April 12-17, 2015,
Poster.
» Abstract
Complex networks have been successfully applied to various systems such as society, technology, and recently climate. Links in a climate network are defined between two geographical locations if the correlation between the time series of some climate variable is higher than a threshold. Therefore, network links are considered to imply information or heat exchange. However, the relationship between the oceanic and atmospheric flows and the climate network's structure is still unclear. Recently, a theoretical approach verifying the correlation between ocean currents and surface air temperature networks has been introduced, where the Pearson correlation networks were constructed from advection-diffusion dynamics on an underlying flow. Since the continuous approach has its limitations, i.e. high computational complexity and fixed variety of the flows in the underlying system, we introduce a new, method of flow-networks for changing in time velocity fields including external forcing in the system, noise and temperature-decay. Method of the flow-network construction can be divided into several steps: first we obtain the linear recursive equation for the temperature time-series. Then we compute the correlation matrix for time-series averaging the tensor product over all realizations of the noise, which we interpret as a weighted adjacency matrix of the flow-network and analyze using network measures. We apply the method to different types of moving flows with geographical relevance such as meandering flow. Analyzing the flow-networks using network measures we find that our approach can highlight zones of high velocity by degree and transition zones by betweenness, while the combination of these network measures can uncover how the flow propagates within time. Flow-networks can be powerful tool to understand the connection between system's dynamics and network's topology analyzed using network measures in order to shed light on different climatic phenomena.
B. Goswami, A. Rheinwalt, N. Boers, N. Marwan, J. Heitzig, S. F. M. Breitenbach, J. Kurths:
Different stages of the East Asian Summer Monsoon in the Holocene,
EGU General Assembly,
Vienna (Austria),
April 12-17, 2015,
Poster.
» Abstract
Paleoclimate proxy reconstructions (e.g. from lake sediments, ice cores, or stalagmites) have inherent age uncertainties resulting in a time-ordered series of correlated probability distributions rather than a precisely measured time series. Correlated errors make it challenging to analyze and extract valuable climate information from such records.
We show how (a) dynamical recurrences can be estimated in the presence of correlated noise, and (b) the modularity of recurrence networks can be used to infer dynamical transitions. We demonstrate our approach with a simple model and apply it to two isotope records from China to identify dynamical transitions of the East Asian Summer Monsoon (EASM) in the last 9000 years. Our results suggest that the Holocene EASM proceeded in four consecutive stages, becoming abruptly weaker at around 6400, 4400 and 3000 years ago. These transitions are known from earlier studies as abrupt, dry periods of weak monsoon superimposed on a long-term trend of gradual monsoon weakening. However, our results indicate that these events are critical shifts between four basins of stability of the Holocene EASM. We propose that these shifts could be triggered by small changes in the rate of solar insolation, which are then amplified by regional feedbacks.
J. Donges, I. Petrova, A. Löw, N. Marwan, J. Kurths:
How complex climate networks complement eigen techniques for the statistical analysis of climatological data,
EGU General Assembly,
Vienna (Austria),
April 12-17, 2015,
Poster.
» Abstract
Eigen techniques such as empirical orthogonal function (EOF) or coupled pattern (CP) / maximum covariance analysis have been frequently used for detecting patterns in multivariate climatological data sets. Recently, statistical methods originating from the theory of complex networks have been employed for the very same purpose of spatio-temporal analysis. This climate network (CN) analysis is usually based on the same set of similarity matrices as is used in classical EOF or CP analysis, e.g., the correlation matrix of a single climatological field or the cross-correlation matrix between two distinct climatological fields. In this study, formal relationships as well as conceptual differences between both eigen and network approaches are derived and illustrated using global precipitation, evaporation and surface air temperature data sets. These results allow us to pinpoint that CN analysis can complement classical eigen techniques and provides additional information on the higher-order structure of statistical interrelationships in climatological data. Hence, CNs are a valuable supplement to the statistical toolbox of the climatologist, particularly for making sense out of very large data sets such as those generated by satellite observations and climate model intercomparison exercises.
S. F. M. Breitenbach, H. E. Ridley, F. A. Lechleitner, Y. Asmerom, K. Rehfeld, K. M. Prufer, D. J. Kennett, V. V. Aquino, V. Polyak, B. Goswami, N. Marwan, G. H. Haug, and J. U. L. Baldini:
Volcanic forcing of the North Atlantic Oscillation over the last 2,000 years,
EGU General Assembly,
Vienna (Austria),
April 12-17, 2015,
Poster.
» Abstract
The North Atlantic Oscillation (NAO) is a principal mode of atmospheric circulation in the North Atlantic realm (Hurrell et al. 2003) and influences rainfall distribution over Europe, North Africa and North America. Although observational data inform us on multi-annual variability of the NAO, long and detailed paleoclimate datasets are required to understand the mechanisms and full range of its variability and the spatial extent of its influence. Chronologies of available proxy-based NAO reconstructions are often interdependent and cover only the last 1,100 years, while longer records are characterized by low sampling resolution and chronological constraints. This complicates the reconstruction of regional responses to NAO changes.
We present data from a 2,000 year long sub-annual carbon isotope record from speleothem YOK-I from Yok Balum Cave, Belize, Central America. YOK-I has been extensively dated using U-series (Kennett et al. 2012). Monitoring shows that stalagmite δ13C in Yok Balum cave is governed by infiltration changes associated with tropical wet season rainfall. Higher (lower) δ13C values reflect drier (wetter) conditions related to Intertropical Convergence Zone position and trade winds intensity.
Comparison with NAO reconstructions (Proctor et al. 2000, Trouet et al. 2009, Wassenburg et al. 2013) reveals that YOK-I δ13C sensitively records NAO-related rainfall dynamics over Belize. The Median Absolute Deviation (MAD) of δ13C extends NAO reconstructions to the last 2,000 years and indicates that high latitude volcanic aerosols force negative NAO phases.
We infer that volcanic aerosols modify inter-hemispheric temperature contrasts at multi-annual scale, resulting in meridional relocation of the ITCZ and the Bermuda-Azores High, altering NAO and tropical rainfall patterns. Decade-long dry periods in the 11th and the late 18th century relate to major high northern latitude eruptions and exemplify the climatic response to volcanic forcing by reorganization of atmospheric circulation over the North Atlantic.
P. Martin, V. Stolbova, B. Bookhagen, N. Marwan, J. Kurths:
Topology and seasonal evolution of the network of extreme precipitation over the Indian subcontinent and Sri Lanka,
EGU General Assembly,
Vienna (Austria),
April 12-17, 2015,
Poster.
» Abstract
The Indian Summer Monsoon (ISM) is one of the active components of the global climate system, and its behavior and variability is of great interest to climate researchers around the world. Here, we examine the topology and evolution of extreme rainfall across the Indian subcontinent by constructing a complex network of extreme rainfall events in the region for three periods - pre-monsoon (March - May), ISM (June - August), and post-monsoon (October - December). Networks are constructed using a synchronization measure between grid cells for a satellite-derived data set (TRMM) and a rain-gauge interpolated data set (APHRODITE). Through the analysis of various complex network metrics, such as degree, betweenness, and average link length, we describe typical repetitive patterns in North Pakistan, the Eastern Ghats, and the Tibetan Plateau. These patterns appear during the premonsoon season, evolve during the ISM, and disappear during the post-monsoon season. Our findings suggest that these are important meteorological features that deserve further attention and may be useful for the prediction of the strength and timing of the ISM.
><2014
K. Guhathakurta, N. Marwan:
Investigating chaos in emerging and developed stock markets using recurrence network analysis,
4th India Finance Conference 2014,
Bangalore (India),
December 17-19, 2014,
Talk.
P. Martin, V. Stolbova, B. Bookhagen, N. Marwan, J. Kurths:
Topology and Seasonal Evolution of the Network of Extreme Precipitation over the Indian Subcontinent and Sri Lanka,
AGU Fall Meeting,
San Francisco (USA),
December 15-19, 2014,
Talk.
» Abstract
The Indian Summer Monsoon (ISM) is one of the active components of the global climate system, and its behavior and variability is of great interest to climate researchers around the world. Here, we examine the topology and evolution of extreme rainfall across the Indian subcontinent by constructing a complex network of extreme rainfall events in the region for three periods - pre-monsoon (March - May), ISM (June - September), and post-monsoon (October - December). Networks are constructed using a synchronization measure between grid cells for a satellite-derived data set (TRMM) and a rain-gauge interpolated data set (APHRODITE). Through the analysis of various complex network metrics, such as degree, betweenness, and average link length, we describe typical repetitive patterns in North Pakistan, the Eastern Ghats, and the Tibetan Plateau. These patterns appear during the pre-monsoon season, evolve during the ISM, and disappear during the post-monsoon season. Our findings suggest that these are important meteorological features that deserve further attention and may be useful for the prediction of the strength and timing of the ISM.
N. Marwan:
Modern Approaches for Nonlinear Time Series Analysis,
Seminar at the Institute for Geology, Mineralogy and Geophysics, Ruhr University Bochum,
Bochum (Germany),
December 3, 2014,
Lecture.
N. Marwan:
Recurrence plots for time series analysis,
Workshop on Network Analysis and Data Driven Modelling of the Climate,
Potsdam (Germany),
October 27-29, 2014,
Talk.
N. Marwan:
Caves as Scientific Archives,
PIK Science & Pretzels,
Potsdam (Germany),
October 8, 2014,
Lecture.
A. Rheinwalt, B. Goswami, N. Boers, J. Heitzig, N. Marwan, R. Krishnan, J. Kurths:
A network of networks approach to investigate the influence of sea surface temperature variability on monsoon systems,
International Symposium Topical Problems of Nonlinear Wave Physics,
Nizhny Novgorod/Saratov (Russia),
July 17-23, 2014,
Talk.
» Abstract
In this study we analyze large-scale inter-dependences between Sea Surface Temperature (SST) and rainfall variability using climate networks. On account of this analysis, we coarse-grain gridded SST and rainfall datasets by merging grid points that are dynamically similar to each other. We consider the SST and rainfall systems as two distinct climate networks and use established cross-network measures to understand their interrelations. As a first step, the spatial distributions of these cross-network measures illustrate regions which are of particular importance in the interaction between SST and rainfall. Secondly, we go into further detail by investigating the cross-network topology explicitly for these regions. Here, strong influences from regions in the SST system in relation to other regions in the rainfall system are detected. These influences structured in a spatially embedded directed network describe important mechanisms behind monsoon systems. For example, behind the Indian Summer Monsoon, which is known to be controlled by SST variability over the adjacent Indian Ocean.
N. Boers, B. Bookhagen, H. M. J. Barbosa, N. Marwan, J. A. Marengo, J. Kurths:
A Complex Network approach to investigate the spatiotemporal co-variability of extreme rainfall,
4th International Workshop on Climate Informatics,
Boulder (USA),
September 25-26, 2014,
» Poster (PDF, 15.60M).
» Abstract
The analysis of spatial patterns of covariability of extreme rainfall is challenging because traditional, PCA-based techniques only involve the first two statistical moments of the data distribution, and are thus not able to capture the behavior in the right tails of the distributions. Here, we propose an alternative to these techniques which is based on the combination of a non-linear synchronization measure and complex network theory. This approach allows to derive spatial patterns encoding the co-variability of extreme rainfall at different locations. By introducing suitable network measures, the methodology can be used to perform climatological analysis, dataset and model intercomparisons, as well as prediction of extreme rainfall events. We introduce the methodological framework as well as applications to highspatiotemporal resolution rainfall data (TRMM 3B42) over South America.
R. Donner, J. Feldhoff, J. Donges, N. Marwan, J. Kurths:
Multivariate Extensions of Recurrence Networks Reveal Geometric Signatures of Coupling Between Nonlinear Systems,
NOLTA Conference,
Luzern (Switzerland),
September 14-18, 2014,
Talk.
» Abstract
Recurrence networks have recently proven their great potential for characterizing important properties of dynamical systems. However, in the real-world such systems typically do not evolve completely isolated from each other, but exhibit mutual interactions with their neighborhood. Here, we extend the recent view on isolated systems towards an coupled network approach to interacting systems. Specifically, we illustrate how to modify the concept of recurrence networks for studying dynamical interrelationships between two or more coupled nonlinear dynamical systems exclusively based on their attractors' geometric structures in phase space.
T. Rawald, M. Sips, N. Marwan, D. Dransch:
Fast Recurrence Quantification Analysis on GPUs,
NOLTA Conference,
Luzern (Switzerland),
September 14-18, 2014,
Talk.
» Abstract
We present a novel computing approach for recurrence quantification analysis (RQA). We refer to the concepts of "Divide and Recombine" subdividing a recurrence matrix into multiple sub matrices, computing basic RQA measures for each sub matrix in a massively parallel manner, and recombining the individual results into a valid global RQA result. Providing an implementation running on multiple graphics card processors at the same time, we are able to reduce the runtime for analyzing a temperature profile consisting of more than one million data points from over six hours to roughly five minutes.
Recurrence plots and derived techniques are powerful and modern time series analysis tools with a wide applicability. Recent developments have linked recurrence plots with complex networks analysis, thus, providing new and complementary measures of complexity for time series analysis. The complex network measures are related to geometrical and topological properties of the phase space representation of the dynamics. Recent applications have demonstrated the potential for data classification (e.g., for medical diagnosis), transition analysis (e.g., for detecting paleoclimatic regime transitions), or coupling analysis (e.g., for identifying coupling directions or indirect couplings).
N. Boers, B Bookhagen, H. Barbosa, N. Marwan, J. Kurths, J. Marengo:
Prediction of extreme floods in the Central Andes by means of Complex Networks,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Talk.
» Abstract
Based on a non-linear synchronisation measure and complex network theory, we present a novel framework for the prediction of extreme events of spatially embedded, interrelated time series. This method is general in the sense that it can be applied to any type of spatially sampled time series with significant interrelations, ranging from climate observables to biological or stock market data.
In this presentation, we apply our method to extreme rainfall in South America and show how this leads to the prediction of more than 60% (90% during El Niño conditions) of extreme rainfall events in the eastern Central Andes of Bolivia and northern Argentina, with only 1% false alarms. From paleoclimatic to decadal time scales, the Central Andes continue to be subject to pronounced changes in climatic conditions. In particular, our and past work shows that frequency as well as magnitudes of extreme rainfall events have increased significantly during past decades, calling for a better understanding of the involved climatic mechanisms. Due to their large spatial extend and occurrence at high elevations, these extreme events often lead to severe floods and landslides with disastrous socioeconomic impacts. They regularly affect tens of thousands of people and produce estimated costs of the order of several hundred million USD.
Alongside with the societal value of predicting natural hazards, our study provides insights into the responsible climatic features and suggests interactions between Rossby waves in polar regions and large scale (sub-)tropical moisture transport as a driver of subseasonal variability of the South American monsoon system. Predictable extreme events result from the propagation of extreme rainfall from the region of Buenos Aires towards the Central Andes given characteristic atmospheric conditions. Our results indicate that the role of frontal systems originating from Rossby waves in polar latitudes is much more dominant for controlling extreme rainfall in subtropical South America than has been assumed so far: These cold fronts cause abundant rainfall in southeastern South America, but they also dictate the direction of low-level flow from the Amazon to the subtropics. The low-level flow provides moisture for extreme rainfall which subsequently propagates from the La Plata Basin towards the eastern slopes of the Central Andes. These events become particularly interesting in view of the important role of tropical to extra-tropical couplings for assessing impacts of global warming to regional climate systems.
J. Donges, R. Donner, N. Marwan, S. Breitenbach, K. Rehfeld, J. Kurths:
A multi-archive method for robustly detecting nonlinear regime shifts in palaeoclimate dynamics under consideration of dating uncertainties,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Talk.
» Abstract
The number of available high-resolution palaeoclimate records, e.g., such as those from speleothems, is currently growing quickly. This wealth of data calls for robust methods of time series analysis that can detect common signals in a set of several records and at the same time cope with dating uncertainties and irregular sampling. In this contribution, a multi-archive method is proposed for identifying nonlinear regime shifts that are common to several palaeoclimate records. In a first step, the COPRA framework (Breitenbach et al., Clim. Past 8, 1765-1779, 2012) is applied to convert each individual irregularly sampled record into an ensemble of regularly sampled time series that are all consistent with the given dating uncertainties. Next, recurrence network analysis (RNA, Donges et al., PNAS 108, 20422-20427, 2011) is used to detect epochs with significant nonlinear deviations from the dominant dynamical regime for all records and ensemble members. Finally, we employ a Monte Carlo approach to identify the relevant time periods during which a significant fraction of all available records shows a regime shift according to RNA. We apply the proposed methodology for revealing continental-scale nonlinear transitions in the Asian monsoon system during the Holocene based on oxygen isotope records from speleothems.
J. Donges, R. Donner, N. Marwan, S. Breitenbach, K. Rehfeld, J. Kurths:
Regime shifts in Holocene Asian monsoon dynamics inferred from speleothems: Potential impacts on cultural change and migratory patterns,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Talk.
» Abstract
The Asian monsoon system has been recognized as an important potential tipping element in Earth’s climate. A global warming-driven change in monsoonal circulation, potentially towards a drier and more irregular regime, would profoundly affect up to 60% of the global human population. Hence, to improve our understanding of this major climate system, it is mandatory to investigate evidence for nonlinear transitions in past monsoonal dynamics and the underlying mechanisms that are contained in the available palaeoclimatic record. For this purpose, speleothems are among the best available high-resolution archives of Asian palaeomonsoonal variability during the Holocene and well beyond.
In this work, we apply recurrence networks, a recently developed technique for nonlinear time series analysis of palaeoclimate data (Donges et al., PNAS 108, 20422-20427, 2011), for detecting episodes with pronounced changes in Asian monsoon dynamics during the last 10 ka in oxygen isotope records from spatially distributed cave deposits covering the different branches of the Asian monsoon system. Our methodology includes multiple archives, explicit consideration of dating uncertainties with the COPRA approach and rigorous significance testing to ensure the robust detection of continental-scale changes in monsoonal dynamics.
We identify several periods characterised by nonlinear changes in Asian monsoon dynamics (e.g., ∼0.5, 2.2-2.8, 3.6-4.1, 5.4-5.7, and 8.0-8.5 ka before present [BP]), the timing of which suggests a connection to extra-tropical Bond events and rapid climate change (RCC) episodes during the Holocene. Interestingly, we furthermore detect an epoch of significantly increased regularity of monsoonal variations around 7.3 ka BP, a timing that is consistent with the typical 1.0-1.5 ka periodicity of Bond events but has been rarely reported in the literature so far. Furthermore, we find that the detected epochs of nonlinear regime shifts in Asian monsoon dynamics partly coincide with known major periods of migration, pronounced cultural changes, and the collapse of ancient human societies from the archaeological record. These findings point to a possible causal mechanism, which indicates that also future changes in monsoonal dynamics could significantly contribute to potentially severe socio-economic impacts of climate change in the Asian monsoon domain.
J. Hlinka, D. Hartman, N. Jajcay, M. Vejmelka, R. Donner, N. Marwan, J. Kurths, M. Palus:
Regional and inter-regional effects in evolving climate network,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Talk.
» Abstract
Real-world systems composed of many interacting subsystems are frequently studied as complex networks. Studied systems are thus represented by graphs composed of nodes standing for the subsystems and edges denoting interactions present among the nodes; the characteristic properties of the graph are subsequently studied and related to the system’s behavior. Potential time-dependency of edges is conveniently captured in so-called evolving networks. There is a growing interest in the application of complex network analysis approach to climate data. Use of evolving networks is a promising technique in this research area due to non-stationarity of the climate dynamics. Recently, it has been shown that an evolving climate network can be used to disentangle different types of El-Nino episodes described in the literature. In particular, an evolving network was constructed as thresholded correlation matrix of a year-long daily surface air temperature data from the NCEP/NCAR reanalysis dataset remapped onto a 10242-point equidistant geodesic grid. The time evolution of several graph characteristics, including density, clustering coefficient or average path length, has been compared with the intervals of El Niño and La Niña episodes. In the current study we identify the sources of the evolving network characteristics by considering a reduceddimensionality description of the climate system. First, we have used low density geodesic grid remapping as well as rotated principal component analysis to define the network nodes. In a more detailed analysis, the uncovered components were used to segment the whole globe surface into 68 regions. The time evolution of temperature correlation structures in local intra-component networks was studied and compared to evolving inter-component connectivity. This detailed analysis showed that the evolution of graph properties of the global network can be mostly attributed to the evolution of the intra-regional connectivity of the ENSO area and adjacent tropical regions and of the inter-regional connectivity between those.
N. Marwan, S. Breitenbach, B. Plessen, D. Scholz, J. Leonhardt:
Recurrence properties as signatures for abrupt climate change,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Talk.
» Abstract
The study of recurrence properties of dynamical systems has been shown to be very successful in characterising typical dynamical behaviour, finding regime transitions, or detecting couplings and synchronisations, even for short, noisy, and nonstationary data, as typical in Earth Sciences. Recurrence plots and their quantifications are powerful techniques for the investigation of recurrence and increasingly attract attention in recent years.
We demonstrate the potential of the newly introduced extension of recurrence plot analysis by complex network measures for the detection of abrupt dynamical changes. This method is applied on a Holocene palaeoclimate data set from Central Europe derived from a stalagmite from Blessberg Cave, Thuringia, Germany. The stalagmite δ18O proxy record covers the middle to late Holocene (6000–400 years BP). Dating uncertainties are considered by an ensemble approach derived from the COPRA framework. Characteristic changes in the recurrence properties reflecting regular dynamics coincide well with the occurrence of the Bond events 1, 2, and 3. During Bond events the Central European climate variability appears more regular. The analysis presented here examplifies the potency of quantitative recurrence methods in detecting climatic events, which otherwise remain hidden in the raw proxy time series.
D. Eroglu, N. Marwan, S. Prasad, J. Kurths:
How to use recurrence networks for geophysical time series analysis?,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Poster.
» Abstract
Recurrence plot based recurrence networks are an approach to analyze time series using complex networks theory. In both approaches, recurrence plot and the recurrence networks, we define a threshold to identify recurrent states. The selection of the threshold is very important for analysing the time series correctly via recurrence networks approach. In this talk we contribute a novel method to choose a threshold adaptively for time series. We show comparison between constant threshold and adaptive threshold cases to study transitions in the dynamics due to a change in the control parameters. This novel methods enables us to identify climate transitions from a lake sediment record.
T. Rawald, M. Sips, N. Marwan, D. Dransch:
Fast computation of recurrences in long time series,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Poster.
» Abstract
The quadratic time complexity of calculating basic RQA measures, doubling the size of the input time series leads to a quadrupling in operations, impairs the fast computation of RQA in many application scenarios. As an example, we analyze the Potsdamer Reihe, an ongoing non-interrupted hourly temperature profile since 1893, consisting of 1,043,112 data points. Using an optimized single-threaded CPU implementation this analysis requires about six hours. Our approach conducts RQA for the Potsdamer Reihe in five minutes.
We automatically split a long time series into smaller chunks (Divide) and distribute the computation of RQA measures across multiple GPU devices. To guarantee valid RQA results, we employ carryover buffers that allow sharing information between pairs of chunks (Recombine). We demonstrate the capabilities of our Divide and Recombine approach to process long time series by comparing the runtime of our implementation to existing RQA tools.
We support a variety of platforms by employing the computing framework OpenCL. Our current implementation supports the computation of standard RQA measures (recurrence rate, determinism, laminarity, ratio, average diagonal line length, trapping time, longest diagonal line, longest vertical line, divergence, entropy, trend) and also calculates recurrence times. To utilize the potential of our approach for a number of applications, we plan to release our implementation under an Open Source software license. It will be available at http://www.gfz-potsdam.de/fast-rqa/.
Since our approach allows to compute RQA measures for a long time series fast, we plan to extend our implementation to support multi-scale RQA.
L. Tupikina, N. Molkenthin, N. Marwan, J. Kurths:
Flow networks for ocean currents,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Poster.
» Abstract
Complex networks have been successfully applied to various systems such as society, technology, and recently climate. Links in a climate network are defined between two geographical locations if the correlation between the time series of some climate variable is higher than a threshold. Therefore, network links are considered to imply heat exchange. However, the relationship between the oceanic and atmospheric flows and the climate network’s structure is still unclear. Recently, a theoretical approach verifying the correlation between ocean currents and surface air temperature networks has been introduced, where the Pearson correlation networks were constructed from advection-diffusion dynamics on an underlying flow. Since the continuous approach has its limitations, i.e. by its high computational complexity, we here introduce a new, discrete construction of flow-networks, which is then applied to static and dynamic velocity fields. Analyzing the flow-networks of prototypical flows we find that our approach can highlight the zones of high velocity by degree and transition zones by betweenness, while the combination of these network measures can uncover how the flow propagates within time. We also apply the method to time series data of the Equatorial Pacific Ocean Current and the Gulf Stream ocean current for the changing velocity fields, which could not been done before, and analyse the properties of the dynamical system. Flow-networks can be powerful tools to theoretically understand the step from system’s dynamics to network’s topology that can be analyzed using network measures and is used for shading light on different climatic phenomena.
A. Rheinwalt, B. Goswami, N. Boers, J. Heitzig, N. Marwan, J. Kurths:
A network of networks approach to investigate the influence of sea surface temperature variability on monsoon systems,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Poster.
B. Goswami, J. Heitzig, N. Marwan, J. Kurths:
Recurrence networks, age uncertainties, and joint distributions: An analysis motivated by problems in paleoclimate studies,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Poster.
» Abstract
Chronological uncertainties are a typical feature of paleoclimate datasets, making their analysis non-trivial. Recent advances in age modeling and paleoclimate proxy reconstruction methodologies have enabled the representation of age uncertainties as uncertainties in the proxy value, resulting in an error-free time axis of measurement. This results in an ensemble of proxy measurements which are effectively described by a marginal probability density of the proxy value at each time instant of consideration.
However, most complex systems methods that characterize time series are not easily applicable to analyze such probability densities, primarily because the covariance between the densities at any two given points is typically unavailable. The knowledge of the covariance (or equivalently the joint probability) of the proxy values, at pairs of time points of interest, is crucial for estimating system characteristics such as the auto-correlation, power spectrum, and recurrence properties.
We present here some ideas on how to analyze such a given sequence of time-ordered probability densities in the absence of the covariance information between the densities at two distinct times. We focus mainly on the recurrence properties of the system and estimate relevant recurrence network measures along with their uncertainties of estimation. We also present a test case where the joint distribution of such probability densities could be made available and how one can analyze the recurrences in such a case.
Y. Zou, R. Donner, N. Marwan, M. Small, J. Kurths:
Long-term changes in the North-South asymmetry of solar activity: a nonlinear dynamics characterization using visibility graphs,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Poster.
» Abstract
Solar activity is characterized by complex dynamics superimposed to an almost periodic, about 11-years cycle. One of its main features is the presence of a marked, time-varying hemispheric asymmetry, the deeper reasons of which have not yet been completely uncovered. Traditionally, this asymmetry has been studied by considering amplitude and phase differences. Here, we use visibility graphs, a novel tool of nonlinear time series analysis, to obtain complementary information on hemispheric asymmetries in dynamical properties. Our analysis provides deep insights into the potentials and limitations of this method, revealing a complex interplay between factors relating to statistical and dynamical properties, i.e. effects due to the probability distribution and the regularity of observed fluctuations. We demonstrate that temporal changes in the hemispheric predominance of the graph properties lag those directly associated with the total hemispheric sunspot areas. Our findings open a new dynamical perspective on studying the North-South sunspot asymmetry, which is to be further explored in future work.
V. Stolbova, B. Bookhagen, N. Marwan, J. Kurths:
Geographic patterns of networks derived from extreme precipitation over the Indian subcontinent,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Poster.
» Abstract
Complex networks (CN) and event synchronization (ES) methods have been applied to study a number of climate phenomena such as Indian Summer Monsoon (ISM), South-American Monsoon, and African Monsoon. These methods proved to be powerful tools to infer interdependencies in climate dynamics between geographical sites, spatial structures, and key regions of the considered climate phenomenon. Here, we use these methods to study the spatial temporal variability of the extreme rainfall over the Indian subcontinent, in order to filter the data by coarse-graining the network, and to identify geographic patterns that are signature features (spatial signatures) of the ISM. We find four main geographic patterns of networks derived from extreme precipitation over the Indian subcontinent using up-to-date satellite-derived, and high temporal and spatial resolution rain-gauge interpolated daily rainfall datasets. In order to prove that our results are also relevant for other climatic variables like pressure and temperature, we use re-analysis data provided by the National Center for Environmental Prediction and Na- tional Center for Atmospheric Research (NCEP/NCAR). We find that two of the patterns revealed from the CN extreme rainfall analysis coincide with those obtained for the pressure and temperature fields, and all four above mentioned patterns can be explained by topography, winds, and monsoon circulation. CN and ES enable to select the most informative regions for the ISM, providing realistic description of the ISM dynamics with fewer data, and also help to infer geographic pattern that are spatial signatures of the ISM. These patterns deserve a special attention for the meteorologists and can be used as markers of the ISM variability.
N. Boers, B. Bookhagen, N. Marwan, J. Kurths, J. Marengo:
Complex networks identify spatial patterns of extreme rainfall of the South American monsoon system,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Poster.
» Abstract
In this study, we investigate the spatial characteristics of extreme rainfall synchronicity of the South American Monsoon System (SAMS) by means of Complex Networks. We first show how this approach leads to the identification of linkages between large-scale atmospheric conditions and natural hazards occurring at the earth’s surface. Thereafter, we exemplify how our methodology can be used to compare different datasets and to test the performance of climate models.
In recent years, complex networks have attracted great attention for analyzing the spatial characteristics of interrelations of various time series. Outstanding examples in this context are functional brain networks as well as so-called climate networks. In most approaches, the basic idea is to represent time series at different locations by network nodes, which will be connected by network links if the corresponding time series behave similar. Information on the spatial characteristics of these similarities can be inferred by network measures quantifying different aspects of the networks’ topology.
By combining several network measures and interpreting them in a climatic context, we investigate climatic linkages and classify the spatial characteristics of extreme rainfall synchronicity. Although our approach is based on only one variable (high spatiotemporal resolution rainfall), it reveals the most important features of the SAMS, such as the main moisture pathways, areas with frequent development of Mesoscale Convective Systems, and the major convergence zones. We will show that these features are only partially reproduced by reanalysis and (regional and global) climate model data.
V. Stolbova, B. Bookhagen, N. Marwan, J. Kurths:
Indian Monsoon: complex network analysis, spatial patterns and the prospects for prediction,
EGU General Assembly,
Vienna (Austria),
April 27-May 2, 2014,
Poster.
» Abstract
The Indian Summer Monsoon (ISM) is a global climate phenomenon that affects half of the world’s population. The prediction of the Indian Summer Monsoon rainfall and its extremes remains an important concern. In our study we aim to determine spatial distribution of patterns of extreme rainfall and their synchronization, because the understanding of the structure of the spatial heterogeneity of extreme rainfall is crucial for Indian agriculture and economy.
We use complex networks to identify dominant spatial patterns that govern the organization of extreme rainfall during the ISM season. We construct networks of extreme rainfall events during the ISM, the pre-monsoon, and the post-monsoon period from satellite-derived (TRMM, Tropical Rainfall Measurement Mission, product 3B42 V7) and rain-gauge interpolated (APHRODITE) datasets. The structure of the networks is determined by the level of synchronization of extreme rainfall events between different grid cells throughout the Indian subcontinent. Through the analysis of various complex-network metrics, we describe typical repetitive patterns that can be used as indicators of the ISM variability: North Pakistan (NP), Western Ghats (WG), Eastern Ghats (EG), and Tibetan Plateau (TP). These patterns appear during the pre-monsoon season, evolve during the ISM season, and disappear during the post-monsoon season. We compare obtained results with wind fields, temperature, and pressure networks in this region derived from re-analysis data provided by the National Center for Environmental Prediction and National Center for Atmospheric Research (NCEP/NCAR). The areas of Eastern Ghats, Western Ghats, and Tibetan Plateau were previously known as areas that influence the ISM dynamics. These patterns occur because of the intricate topography of this region. The Western Ghats pattern, specifically, the Kerala region, is commonly used by climatologists for the prediction of the onset of the ISM (Pai and Nair, 2009). However, North Pakistan has not widely been considered as an important region in the analysis of the ISM. We have identified a pattern in North Pakistan that plays an important role in the extreme rainfall organization during the ISM, because it is strongly influenced by winter westerlies during the pre-monsoon season and monsoon season, which strongly influence the ISM variability. Accordingly, this pattern may serve as a marker of winter westerlies. We suggest that our obtained spatial patterns are important meteorological features that may be useful for prediction of the Indian Summer Monsoon.
><2013
B. Bookhagen, N. Boers, N. Marwan, N. Malik, J. Kurths:
Spatiotemporal variability of rainfall extremes in monsoonal climates – examples from the South American Monsoon and the Indian Monsoon Systems,
AGU Fall Meeting,
San Francisco (USA),
December 9-13, 2013,
Talk invited.
» Abstract
Monsoonal rainfall is the crucial component for more than half of the world’s population. Runoff associated with monsoon systems provide water resources for agriculture, hydropower, drinking-water generation, recreation, and social well-being and are thus a fundamental part of human society. However, monsoon systems are highly stochastic and show large variability on various timescales. Here, we use various rainfall datasets to characterize spatiotemporal rainfall patterns using traditional as well as new approaches emphasizing nonlinear spatial correlations from a complex networks perspective. Our analyses focus on the South American (SAMS) and Indian (ISM) Monsoon Systems on the basis of Tropical Rainfall Measurement Mission (TRMM) using precipitation radar and passive-microwave products with horizontal spatial resolutions of 5x5 km^2 (products 2A25, 2B31) and 25x25 km^2 (3B42) and interpolated rainfall-gauge data for the ISM (APHRODITE, 25x25 km^2). The eastern slopes of the Andes of South America and the southern front of the Himalaya are characterized by significant orographic barriers that intersect with the moisture-bearing, monsoonal wind systems. We demonstrate that topography exerts a first-order control on peak rainfall amounts on annual timescales in both mountain belts. Flooding in the downstream regions is dominantly caused by heavy rainfall storms that propagate deep into the mountain range and reach regions that are arid and without vegetation cover promoting rapid runoff. These storms exert a significantly different spatial distribution than average-rainfall conditions and assessing their recurrence intervals and prediction is key in understanding flooding for these regions. An analysis of extreme-value distributions of our high-spatial resolution data reveal that semi-arid areas are characterized by low-frequency/high-magnitude events (i.e., are characterized by a ‘heavy tail’ distribution), whereas regions with high mean annual rainfall have a less skewed distribution. In a second step, an analysis of the spatial characteristics of extreme rainfall synchronicity by means of complex networks reveals patterns of the propagation of extreme rainfall events. These patterns differ substantially from those obtained from the mean annual rainfall distribution. In addition, we have developed a scheme to predict rainfall extreme events in the eastern Central Andes based on event synchronization and spatial patterns of complex networks. The presented methods and result will allow to critically evaluate data and models in space and time.
H. E. Ridley, Y. Asmerom, J. U. L. Baldini, V. V. Aquino, S. F. M. Breitenbach, V. Polyak, K. M. Prufer, D. J. Kennett, B. J. Culleton, N. Marwan, F. A. Lechleitner, C. G. Macpherson G. H. Haug, J. Awe, :
Variability in Central American rainfall amount and seasonality over the past four centuries: evidence from a monthly resolved Belizean stalagmite,
AGU Fall Meeting,
San Francisco (USA),
December 9-13, 2013,
Talk.
» Abstract
Climate variability in the tropical Atlantic is notoriously complex and has been poorly characterised beyond the instrumental record. Climate fluctuations in this region are linked to global temperatures, making understanding past variability critical in light of the scenario of unprecedented recent warming. High resolution palaeoclimate records provide essential information on climate fluctuations and development on annual to centennial scales, which will be fundamental in understanding the complex climate evolution of the region during the last 2000 years. We have generated a 453 year long, precisely-dated, monthly-resolved oxygen and carbon stable isotope dataset from stalagmite YOK-G from Yok Balum Cave, southern Belize. Annual δ13C cycles, which are clear through much of the record, provide sub-annual chronological control (i.e., year and season of deposition) and facilitate the reconstruction of palaeoseasonality. Stalagmite δ18O suggests a significant positive correlation with northern hemisphere temperature (NHT), most likely via interactions of ITCZ position and regional temperature. A close link also exists with cave records from China and the Caribbean region. The δ13C record is interpreted as directly reflecting effective rainfall, and indicates that during the pre-industrial period high NHT resulted in increased boreal summer rainfall. During the Modern Warm Period (post 1850), a significant decrease in wet and dry season rainfall and seasonality occurred, possibly due to a more southerly boreal summer ITCZ position and enhanced evapotranspiration in response to shifts in greenhouse gas (GHG) moderated pressure gradients. The YOK-G dataset suggests that both rainfall amount and seasonality in Central America are decreasing and that future scenarios of GHG induced global warming may lead further rainfall reductions in the region.
N. Marwan:
Recurrence Plots for the Analysis of Complex Systems,
LINC Mid-Term Review Workshop,
Potsdam (Germany),
November 17-20, 2013,
Lecture.
A. Rheinwalt, N. Marwan, J. Kurths:
Spatial effects on network measures in complex networks,
Dynamics Days Berlin-Brandenburg,
Berlin (Germany),
September 20, 2013,
Talk.
» Abstract
In studies of spatially confined networks, network measures can lead to false conclusions since most measures are boundary-affected. This is especially the case if boundaries are artificial and not inherent in the underlying system of interest (e.g. borders of countries). But also, the distribution of nodes in space has an influence on network measures. An analytical estimation of these effects is not trivial due to the complexity of measures. The straightforward approach we propose here is to use surrogate networks that provide estimates of spatial effects in graph statistics. This is achieved by using spatially embedded random networks as surrogates that have approximately the same link probability as a function of spatial link lengths. The potential of our approach is demonstrated by an analysis of spatial patterns in characteristics of link weighted and unweighted regional climate networks. As an example, networks derived from daily rainfall data that are restricted to the region of Germany are considered.
N. Molkenthin, K. Rehfeld, N. Marwan, J. Kurths:
Networks from flows – From dynamics to topology,
Dynamics Days Berlin-Brandenburg,
Berlin (Germany),
September 20, 2013,
Talk.
» Abstract
Complex network approaches have recently been applied to continuous spatial dynamical systems, like climate, successfully uncovering the system's interaction structure. Yet the relationship between the underlying atmospheric or oceanic flow's dynamics and the estimated network measures have remained largely unclear. We bridge this crucial gap in a bottom-up approach and define a continuous analytical analogue of Pearson correlation networks for advection-diffusion dynamics on a background flow. Analysing complex networks of prototypical flows and from time series data of the equatorial Pacific, we find that our analytical model reproduces the most salient features of these networks and thus provides a general foundation of climate networks. The relationships we obtain between velocity field and network measures show that line-like structures of high betweenness originate from properties of the underlying oceanic flow rather than, as it was previously thought, from tire dynamical information propagated in the flow itself.
J. Hlinka, D. Hartman, M. Vejmelka, N. Jajcay, L. Pokorná, J. Runge, N. Marwan, J. Kurths, M. Paluš:
Challenges in directed network analysis documented on climate reanalysis surface temperature data,
Dynamics Days Berlin-Brandenburg,
Berlin (Germany),
September 20, 2013,
Talk.
» Abstract
In this presentation we shall outline a range of challenges that may be encountered during construction, analysis and interpretation of directed network analysis of climate reanalysis surface air temperature data. The challenges include the high dimensionality of the data, in particular in combination of a small number of time points, nonlinearity of the underlying systems, non-stationarity, temporal and spatial autocorrelation of both the measurements and the underlying processes, sampling problems us well as physical interpretation of directed networks constructed by causality analysis methods (e.g. Granger causality analysis or conditional mutual information). For each challenge, potential solutions and their strong and weak points will be outlined. The challenges will be documented using a particular dataset: surface air temperature data from the NCEP/NCAR reanalysis dataset. Some of the challenges have been recently discussed using this particular dataset. In particular, stability was compared across several basic methods for causality networks estimated from dimension-reduced data. However, they are in general pertinent, to many other real-world complex dynamical systems. The main purpose of the contribution is to ignite discussions of alternative solutions to challenges that may in various forms appear in the network analysis of a wide range of real-world complex dynamical systems, provide candidate solutions and facilitate the exchange of expertise among the workshop participants.
B. Goswami, J. Heitzig, K. Rehfeld, N. Marwan, A. Ambili, S. Prasad, J. Kurths:
Possible pasts: How to measure, interpret and work with uncertainties in paleoclimatic datasets,
Dynamics Days Berlin-Brandenburg,
Berlin (Germany),
September 20, 2013,
Talk.
» Abstract
Investigations of the past climatic conditions of the earth are hinged on reliable records constructed from paleoclimatic ‘proxy’ archives. These archives are typically sediment cores from lakes, caves, peats, etc. that record climatic signals along their depths as measurable physical quantities called proxies, e.g. isotopes, pollen, grain size, etc. However, limitations in precisely measuring the ages of the depth layers of the core imply that the time axis of the proxy (vs. time) record is inherently uncertain. The general approach to dealing with the age uncertainties have been to develop extensive methods to minimize the errors of the age-depth relations with little or no focus paid to the propagation of these uncertainties to the proxies themselves.
We present a Bayesian framework that allows us to analytically arrive at the posterior probability densities of the proxy at individual points of time in the past. Besides enabling us to estimate the mean/median values along with their uncertainties, our method also gives insight into how the age and other sources of uncertainties impact the estimation of the proxy value. We use this approach to two proxies from Lonar lake in central India, and find that the variance of the proxy measurements along the depth were a greater contributor to the final uncertainty rather than the errors of age measurements.
Lastly, we present an ensemble interpretation of the posterior proxy distributions which leads to a picture of infinite possible pasts that could have given rise to the set of measurement data that we start with. We hope that our study brings us one step closer to understanding past climatic dynamics from measurements together with the uncertainties involved in estimating the quantities of interest.
After 25 years, recurrence plots have become a well-known and promising tool in many scientific disciplines, what is reflected by the growing number of applications and publications. Recurrence based methods have on the one hand a deep foundation in the theory of dynamical systems and are on the other hand powerful tools for the investigation of a variety of problems. The increasing interest encompasses the growing risk of misuse and uncritical application of these methods. Therefore, in my talk I would like to point out potential problems and pitfalls related to different aspects of the application of recurrence plots and recurrence quantification analysis.
J. H. Feldhoff, R. V. Donner, J. F. Donges, N. Marwan, J. Kurths:
Geometric signatures of complex synchronization scenarios – A recurrence network perspective,
5th International Symposium on Recurrence Plots,
Chicago (USA),
August 14-16, 2013,
Talk.
» Abstract
Synchronization between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the coupling strength often leads to qualitative changes in the dynamics exhibiting different types of synchronization. Here, we study the geometric signatures of coupling along with the onset of generalized synchronization (GS) between two coupled chaotic oscillators by mapping the systems' individual as well as joint recurrences in phase space to a complex network. For a paradigmatic continuous-time model system, we show that the transitivity properties of the resulting joint recurrence networks display distinct variations associated with changes in the structural similarity between different parts of the considered trajectories. They therefore provide a useful new indicator for the emergence of GS.
L. Tupikina, K. Rehfeld, S. Polanski, N. Marwan, J. Kurths:
Complex network analysis of Indian Summer Monsoon variability for the past 1000 years,
NetSci 2013,
Copenhagen (Denmark),
June 3-7, 2013,
» Poster (PDF, 1.08M).
V. Stolbova, P. Martin, N. Marwan, J. Kurths:
Complex network analysis of extreme precipitaion over the Indian subcontinent,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2013,
Poster.
» Abstract
The Indian monsoon is a large scale pattern in the climate system of the Earth. The motivation of our work was to reveal spatial structures in strong precipitation over the Indian subcontinent, and their evolution during the year, because it is crucial as for understanding of monsoon regularities as well for India’s agriculture and economy.
We present an analysis of extreme rainfall over the Indian peninsula and Sri Lanka. Using the method of event synchronization we constructed networks of extreme rainfall events(heavier than the 90-th percentile) for three time periods: during the Indian summer monsoon (ISM, June–September), the Northeast monsoon (NEM, October – December, so called winter monsoon) and period before the summer monsoon (January - May). Obtained networks show how extreme rainfall for specific areas in India is synchronized with extreme rainfall for other areas in India. Analysis of degree centrality of the networks reveals clusters of extreme rainfall events in India which are strongly connected to maximal number of other areas with extreme rainfall events, e.g., North Pakistan and the Eastern Ghats. Additionally, betweenness centrality shows areas that are important in the sense of water transport in the networks (e.g. the Himalayas, Western Ghats, Eastern Ghats etc.). By comparison of networks before the summer monsoon, during summer and winter monsoon season we determined how spatial patterns of rainfalls synchronization change during the year. These changes play a crucial role in the organization of the rainfall all over the Indian subcontinent.
K. Rehfeld, B. Goswami, N. Marwan, S. Breitenbach, F. Lechleitner, N. Molkenthin, J. Kurths:
Teleconnections and internal variability of the Asian Monsoon in the last 1000 years from paleoclimate data,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2013,
Talk.
» Abstract
The Asian monsoon is a climate phenomenon with global reach, impacting on 60% of the world’s population, and extremes in its dynamics affect both the people and the economies of Asia. Investigating past climate changes in the Asian monsoon system offers a unique key to understanding its future behavior under anthropogenic perturbation, because our global past is the only truthful realization of the "Earth System experiment" we can access. Paleoclimate data are hereby the only witnesses that testify directly about the state of the Earth system in the past. However, in order to be able to infer on the climatic processes reflected in the proxy data, three inherent challenges need to be met: the datasets are heterogeneously sampled in time (i), space (ii) and time itself is a variable that needs to be reconstructed, which (iii) introduces additional uncertainties.
Addressing these issues using adapted similarity estimators, flexible network measures and numerical simulation, we infer spatio-temporal dependencies from paleoclimate networks. We then investigate, to what extent the decadal-scale variability recorded in the paleoclimate data from trees, speleothems, sediments and ice cores is due to internal variability of the Indian and the East Asian monsoon systems, and how potential teleconnections with the El Niño southern oscillation, the North Atlantic oscillation, and solar variability have varied over the last 1000 years.
K. Rehfeld, J. Heitzig, N. Marwan, B. Goswami, N. Marwan, J. Kurths:
Comparison of linear and nonlinear similarity measures for irregularly sampled and age-uncertain time series,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2013,
Talk.
» Abstract
Paleoclimate time series are oftentimes sparse and heterogeneously sampled. Furthermore, time itself is a variable that has to be reconstructed prior to analysis, which results in additional – and substantial – uncertainties. Statistical analysis of such time series usually dictates, that they be sampled regularly, a requirement often met by means of linear interpolation. Such interpolation is, however, immediately linked with loss of information on short timescales, and over-estimation of variability on long timescales.
We adapted similarity estimators for Pearson correlation, mutual information and event synchronization that do not require the time series to be sampled regularly. We performed benchmark tests on synthetic data to infer, which estimators are most robust in the presence of irregular sampling, and how they are influenced by additional uncertainty on the time axis.
We compared results for standard estimators, using interpolated time series, and the adapted estimators. We observe that interpolation of the time series results in the largest estimation error for cross correlation estimation, while the event synchronization function and Gaussian-kernel-based correlation estimation show the overall lowest error.
N. Marwan, K. Rehfeld, B. Goswami, S. Breitenbach, J. Kurths:
COnstructing Proxy-Record Age models (COPRA),
EGU General Assembly,
Vienna (Austria),
April 7-12, 2013,
Poster.
» Abstract
Reliable age models are fundamental for any palaeoclimate reconstruction. The increasing availability of high- resolution palaeoclimate time series, e.g., based on speleothem archives, has attracted some new activity in the development of alternative and novel approaches for reconstructing chronologies. Challenges in this effort are (semi-)automatic outlier, reversal, and hiatus detection and treatment, as well as the inclusion of information on age uncertainties and independent layer counting to improve the overall precision of the chronology. However, dif- ferent dating strategies, different kinds of palaeoarchive formation, dating uncertainties, and different chronology construction methods cause a limited comparability of the different palaeoclimate records.
We present a recently developed framework which addresses these challenges and which allows the incorporation of layer counting data to improve the reconstructed chronology of a given time series. Moreover, we introduce the concept of an “absolute” time scale, a common time axis which works as an invariant reference allowing the comparison of different palaeoclimate records. This concept translates the age uncertainties into uncertainties in the proxy values.
This framework is implemented as an open source software (COPRA) for Octave and Matlab.
K. Rehfeld, B. Goswami, N. Marwan, S. Breitenbach, J. Kurths:
Paleoclimate networks: a concept meeting central challenges in the reconstruction of paleoclimate dynamics,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2013,
Poster.
» Abstract
Statistical analysis of dependencies amongst paleoclimate data helps to infer on the climatic processes they reflect. Three key challenges have to be addressed, however: the datasets are heterogeneous in time (i) and space (ii), and furthermore time itself is a variable that needs to be reconstructed, which (iii) introduces additional uncertainties. To address these issues in a flexible way we developed the paleoclimate network framework, inspired by the increasing application of complex networks in climate research. Nodes in the paleoclimate network represent a paleoclimate archive, and an associated time series. Links between these nodes are assigned, if these time series are significantly similar. Therefore, the base of the paleoclimate network is formed by linear and nonlinear estimators for Pearson correlation, mutual information and event synchronization, which quantify similarity from irregularly sampled time series. Age uncertainties are propagated into the final network analysis using time series ensembles which reflect the uncertainty. We discuss how spatial heterogeneity influences the results obtained from network measures, and demonstrate the power of the approach by inferring teleconnection variability of the Asian summer monsoon for the past 1000 years.
J. Kurths, N. Boers, B. Bookhagen, J. Donges, R. Donner, N. Malik, N. Marwan, V. Stolbova:
Network of Networks and the Climate System,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2013,
Medal lecture.
» Abstract
Network of networks is a new direction in complex systems science. One can find such networks in various fields, such as infrastructure (power grids etc.), human brain or Earth system. Basic properties and new characteristics, such as cross-degree, or cross-betweenness will be discussed. This allows us to quantify the structural role of single vertices or whole sub-networks with respect to the interaction of a pair of subnetworks on local, mesoscopic, and global topological scales.
Next, we consider an inverse problem: Is there a backbone-like structure underlying the climate system? For this we propose a method to reconstruct and analyze a complex network from data generated by a spatio-temporal dynamical system. This technique is then applied to 3-dimensional data of the climate system. We interpret different heights in the atmosphere as different networks and the whole as a network of networks. This approach enables us to uncover relations to global circulation patterns in oceans and atmosphere. The global scale view on climate networks offers promising new perspectives for detecting dynamical structures based on nonlinear physical processes in the climate system.
This concept is applied to Indian Monsoon data in order to characterize the regional occurrence of strong rain events and its impact on predictability.
B. Goswami, N. Marwan, G. Feulner, J. Kurths:
Directed network of global temperature drivers,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2013,
Talk.
» Abstract
We present a recurrence-based approach to quantify an interacting, directed network of various global climatic factors that influence global mean temperature. Extending the notion of an earlier measure based on joint recurrences, we present a new approach to capture directed influences among structurally different systems such as the El Niño Southern Oscillation, volcanic activity, and solar irradiance. We find that the various climatic phenomena interact and influence each other at multiple delays with feedbacks. All measures estimated in the analysis are tested for significance using twin surrogates. We stress the need to incorporate multiple, delayed interactions involving feedback in analyses focussed on understanding and predicting global mean temperature.
A. Rheinwalt, N. Marwan, J. Kurths, F. -W. Gerstengarbe, P. C. Werner:
Non-linear time series analysis of precipitation events using regional climate networks for the region of Germany,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2013,
Talk.
» Abstract
Knowledge about the spatiotemporal occurrence of precipitation events is of great interest. A vast number of decisions rely to a great extend on this knowledge. Ranging from agricultural decisions to ones regarding insurances. However it is often only for smaller regions feasible to study high density data sets. Here we study precipitation events using the non-linear measure event synchronization. The spatial synchronization structure is used as a climate network and analyzed as such. Using network measures that are corrected for boundary effects and irregular sampled nodes in space, we can detect interesting spatial synchronization patterns of precipitation events as well as their temporal evolution.
J. Donges, J. Heitzig, J. Runge, C. H. C. Schultz, M. Wiedermann, A. Zech, J. Feldhoff, A. Rheinwalt, H. Kutza, A. Radebach, N. Marwan, J. Kurths:
Advanced functional network analysis in the geosciences: The pyunicorn package,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2013,
Poster.
» Abstract
Functional networks are a powerful tool for analyzing large geoscientific datasets such as global fields of climate time series originating from observations or model simulations. pyunicorn (pythonic unified complex network and recurrence analysis toolbox) is an open-source, fully object-oriented and easily parallelizable package written in the language Python. It allows for constructing functional networks (aka climate networks) representing the structure of statistical interrelationships in large datasets and, subsequently, investigating this structure using advanced methods of complex network theory such as measures for networks of interacting networks, node-weighted statistics or network surrogates. Additionally, pyunicorn allows to study the complex dynamics of geoscientific systems as recorded by time series by means of recurrence networks and visibility graphs. The range of possible applications of the package is outlined drawing on several examples from climatology.
K. Olouch, N. Marwan, M. Trauth, J. Kurths:
Evolving Complex Networks Analysis of Space-Time Multi-Scale Wavelike Fields: Application to African Rainfall Dynamics,
EGU General Assembly,
Vienna (Austria),
April 7-12, 2013,
Poster.
» Abstract
Evolving complex networks analysis is a very recent and very promising attempt to describe, in the most realistic ways, complex systems or multi-system dynamics.
The Earth system is comprised of many attractors that are multi-scaled, multi-complexity non-linear sys- tems of systems. Space time propagations responsible for precipitation is one example in which the interactions between the aforementioned properties of complex systems can be applied; especially the spatio-temporal wave likeness of spatial patterning and temporal recurrences representative of the underlying dynamics.
Tobler’s first law of geography states: "Everything is related to everything else, but near things are more related than distant things" (Waldo Tobler, 1970 Economic Geography 46: 234-40). Most time-series analysis are pairwise correlations and even when faced with gridded data, the neighborhood characteristics is never used as an input variable. In our point of view, such analysis ignore vital information on the multi-scale non-linear spatial patterns of the continuities and singularities possibly resulting from underlying random processes.
This work in progress is an application, mainly inspired by wave theory and non-linear dynamics. It is a systematic method of methods, which exploits the nonlinear multi-scale wave nature of virtually everything in nature including financial data, disease dynamics et cetera and applies it to climate through complex network analysis of rainfall data. The method uses a continuous spatial wavelet transform for non-linear multi-scale decomposition. Such an output carries all vital information pertaining the singularity structures in the data. Similarity measures are obtained by considering the multi-fractal nature of the distribution of discontinuities. The more similar the point-wise generalized dimensions are in-terms of their continuity, fractal, entropy, information and correlation dimensions, the higher the chance that they characterize similar underlying dynamics. The similarities are then weighted by their recurrence rate to ensure that the similarities are not a one time noise but regular temporal occurrence. Finally, the evolving complex networks are constructed. These networks are envisioned to shade more light into the patterns of African rainfall dynamics and their possible underlying sources. Last but not least, the global measures from the network will give new time series to compare with external possible forcing in the global network and the the rainfall dynamics.
N. Marwan:
Recurrence Plots for the Analysis of Complex Systems,
Theme Workshop on Recurrence Plots, University of Tokyo,
Tokyo (Japan),
April 10, 2013,
Talk.
N. Marwan, G. Zamora-Lopez:
Juergen Kurths' world of publications,
Conference Nonlinear Data Analysis and Modeling,
Potsdam (Germany),
March 21-23, 2013,
» Poster (PDF, 4.40M).
» Abstract
We present the co-authorship network of Juergen Kurth's publications.
P. Menck, J. Heitzig, N. Marwan, J. Kurths:
How basin stability complements the linear-stability paradigm,
Conference Nonlinear Data Analysis and Modeling,
Potsdam (Germany),
March 21-23, 2013,
Poster.
» Abstract
The human brain, power grids, arrays of coupled lasers and the Amazon rainforest are all characterized by multistability. The likelihood that these systems will remain in the most desirable of their many stable states depends on their stability against significant perturbations, particularly in a state space populated by undesirable states. Here we claim that the traditional linearization-based approach to stability is too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of the basin of attraction. Basin stability is non-local, nonlinear and easily applicable, even to high-dimensional systems. It provides a long-sought-after explanation for the surprisingly regular topologies of neural networks and power grids, which have eluded theoretical description based solely on linear stability. We anticipate that basin stability will provide a powerful tool for complex systems studies, including the assessment of multistable climatic tipping elements.
R. V. Donner, J. F. Donges, Y. Zou, N. Marwan, J. Heitzig, J. Kurths:
A complex network perspective for time series analysis of dynamical systems,
Conference Nonlinear Data Analysis and Modeling,
Potsdam (Germany),
March 21-23, 2013,
Poster.
» Abstract
In the last years, several approaches have been proposed for studying properties of dynamical systems represented by time series by means of complex network methods. Recently, two main concepts have attracted particular interest: recurrence networks and visibility graphs. This contribution presents a thorough review of the state of the art of both approaches, with a special emphasis on what kind of information about a dynamical system can be inferred from its adjoint network representations. On the one hand, recurrence networks are based on the mutual proximity of sampled state vectors in the (possibly reconstructed) phase space of a dynamical system under study. Their local as well as global properties have been proven to characterize important structural aspects of the underlying attractors. Specifically, the emergence of scale-free degree distributions highlights the presence of power-law singularities of the invariant densities, whereas the transitivity properties are related to a novel notion of fractal dimension of the system. Successful and relevant real-world applications particularly include the identification of dynamical transitions in observational time series. On the other hand, visibility graphs and related concepts characterize stochastic properties of a system such as its Hurst exponent or the absence of time-reversal symmetry indicating nonlinearity of the observed process. The potentials and possible methodological problems of both approaches are highlighted and illustrated based on some real-world geoscientific time series.
A. Rheinwalt, N. Marwan, J. Kurths, P. Werner, F.-W. Gerstengarbe:
Boundary effects in network measures of spatially embedded networks,
Conference Nonlinear Data Analysis and Modeling,
Potsdam (Germany),
March 21-23, 2013,
Poster.
» Abstract
In studies of spatially confined networks, network measures can lead to false conclusions since most measures are boundary-affected. This is especially the case if boundaries are artificial and not inherent in the underlying system of interest (e.g. borders of countries). An analytical estimation of emphboundary effects is not trivial due to the complexity of measures. The straightforward approach we propose here is to use surrogate networks that provide estimates of boundary effects in graph statistics. This is achieved by using spatially embedded random networks as surrogates that have approximately the same link probability as a function of spatial link lengths. The potential of our approach is demonstrated for an analysis of spatial patterns in characteristics of regional climate networks. As an example networks derived from daily rainfall data and restricted to the region of Germany are considered.
N. Molkenthin, K. Rehfeld, N. Marwan, J. Kurths:
Networks from flows – From dynamics to topology,
Conference Nonlinear Data Analysis and Modeling,
Potsdam (Germany),
March 21-23, 2013,
Poster.
» Abstract
We define a continuous analogue of the Pearson correlation in order to compute networks in a bottom-up approach directly from simple stationary flows using the fluiddynamical advection-diffusion-equation. We solved this for the case of a homogeneous and circular flow as well as an approximation for general flows and compare the resulting networks to time series networks of the equatorial counter current.
J. Runge, J. Heitzig, V. Petoukhov, N. Marwan, J. Kurths:
Quantifying causality from time series of complex systems,
Conference Nonlinear Data Analysis and Modeling,
Potsdam (Germany),
March 21-23, 2013,
Poster.
» Abstract
While it is an important problem to identify the existence of causal associations from multivariate time series it is even more important to assess the strength of their association in a meaningful way. Mutual information (MI) and transfer entropy (TE) are commonly used, but how meaningful are they? Our alternative: Momentary Information Transfer (MIT).
J. F. Donges, R. V. Donner, M. H. Trauth, N. Marwan, H. J. Schellnhuber, J. Kurths:
Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution,
Conference Nonlinear Data Analysis and Modeling,
Potsdam (Germany),
March 21-23, 2013,
Poster.
» Abstract
Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross- disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the last 5 Ma (million years) has triggered an ongoing debate about possible candidate pro- cesses and evolutionary mechanisms. In this work, we apply a novel nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Mid-Pliocene (3.35-3.15 Ma BP (before present)), (ii) Early Pleistocene (2.25-1.6 Ma BP), and (iii) Mid-Pleistocene (1.1-0.7 Ma BP). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Mid-Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa.
K. Rehfeld, N. Marwan, B. Goswami, S. F. M. Breitenbach J. Kurths:
Paleoclimate networks: A concept meeting central challenges in the reconstruction of paleoclimate dynamics,
Conference Nonlinear Data Analysis and Modeling,
Potsdam (Germany),
March 21-23, 2013,
Poster.
» Abstract
Statistical analysis of dependencies amongst paleoclimate data helps to infer on the climatic processes they reflect. Three key challenges have to be addressed, however: the datasets are heterogeneous in time (i) and space (ii), and furthermore time itself is a variable that needs to be reconstructed, which (iii) introduces additional uncertainties.
To address these issues in a flexible way we developed the paleoclimate network framework, inspired by the increasing application of complex networks in climate research. Nodes in the paleoclimate network represent a paleoclimate archive, and an associated time series. Links between these nodes are assigned, if these time series are significantly similar. Therefore, the base of the paleoclimate network is formed by linear and nonlinear estimators for Pearson correlation, mutual information and event synchronization, which quantify similarity from irregularly sampled time series. Age uncertainties are propagated into the final network analysis using time series ensembles which reflect the uncertainty. We discuss how spatial heterogeneity influences the results obtained from network measures, and demonstrate the power of the approach by inferring teleconnection variability of the Asian summer monsoon for the past 1000 years.
A. Rheinwalt, N. Marwan, J. Kurths, F. -W. Gerstengarbe, P. C. Werner, N. Boers, B. Goswami:
Spatial effects on network measures in complex networks,
XXXIII Dynamics Days Europe,
Madrid (Spain),
June 3-7, 2013,
Talk.
N. Marwan, S. Breitenbach, J. Kurths:
Detection of climate transitions in Asia derived from speleothems,
SAGE2013 Conference,
Berlin (Germany),
March 14, 2013,
Talk.
» Abstract
Monsoonal precipitation dynamics and their possible change due to global warming have strong socio-economic impacts in most of South-East Asia. The study of past transitions and dynamical properties in the Asian monsoon system helps in understanding and modelling future Asian summer monsoon dynamics.
Speleothems offer archives of climatic variability in the past. We analyse isotope records of stalagmites from several caves at different locations in Asia, representing the rainfall variability at these locations and covering the past 16 kyr BP.
Recurrence is a fundamental property of dynamical systems. Recurrence plots and recurrence networks are modern methods of nonlinear data analysis that allow us to uncover hidden transitions in time series, which are not obvious using linear statistical methods.
Analysis of the recurrence structure of stalagmite isotope records reveals synchronous climate transitions over Asia, although the data series themselves do not correlate. This result suggests that during climate transitions the entire Asian summer monsoon system underwent changes that are recorded in the isotope time series, despite different reactions of local rainfall pattern on climate forcing factors.
D. van de Wetering, J. H"\utterman, A. Mewes, N. Marwan:
Extrem weather events and social resonance,
Symposium Extreme Events: Modeling, Analysis, and Prediction,
Hannover (Germany),
February 13-15, 2013,
» Poster (PDF, 54.22K).
><2012
S. F. M. Breitenbach, F. Lechleitner, B. Plessen, N. Marwan, H. Cheng, J. F. Adkins, G. H. Haug:
Reconstructing monsoon variations in India – Evidence from speleothems,
AGU Fall Meeting,
San Francisco (USA),
December 3–7, 2012,
Talk invited.
» Abstract
Indian summer monsoon (ISM) rainfall is of vital importance for ca. one fifth of the world’s population, yet little is known about the factors governing its variability. Changing seasonality and/or rainfall intensity have profound impacts on the well-being of Asian agriculture-based societies. Most proxy-records from the Indian realm lack temporal resolution and age control sufficient to allow detailed analysis of high-frequency ISM rainfall variations. Low spatial coverage further restricts understanding spatial differences and the interactions between subsystems of the Asian summer monsoon, limiting understanding, not to mention reliable forecasting. Here, we summarize available information on rainfall changes over India, as reflected in speleothems. Suitable stalagmites offer highly precise chronologies and multi-proxy time series. Oxygen isotope and greyscale time series can track ISM intensity. Using published and new records from NE India, we present evidence for significant rainfall changes during the Holocene. Available proxy records show that while long-term ISM rainfall pattern changed in concert with supra-regional variations of the Asian summer monsoon, sub-decadal-scale ISM variations are influenced by local and regional influences. Complex network analysis of Indian and Chinese proxy data reveals that during the Medieval Warm Period ISM and East Asian summer monsoon (EASM) were more tightly linked, with a seemingly strong ISM influence on the EASM. During the cooler Little Ice Age however, the ISM and EASM connection weakened and local effects exerted influence on both sub-systems of the Asian monsoon. In order to allow detailed insights in spatio-temporal variations of the ISM and external teleconnections, precisely dated high-resolution time series must be obtained from various places in the Indian peninsula and beyond. Only a combination of high temporal and spatial coverage will allow assessments of the likelihood of drought recurrence in a given region. Especially in light of ancient civilizations in the Indus and South Asian regions nearby palaeoclimate records must be established to reconstruct local and regional effects that are superimposed on variations of the global climate.
J. Kurths, N. Marwan, J. Donges:
Measuring topology in interacting climate networks,
NOLTA Conference,
Palma de Mallorca (Spain),
October 22-26, 2012,
Talk.
N. Marwan, Y. Zou, J. F. Donges, R. V. Donner, M. H. Trauth, N. Wessel, G. M. Ramírez Ávila, J. Kurths:
Complex network analysis of recurrence plots,
5th Shanghai International Symposium on Nonlinear Sciences And Applications, Fudan University,
Shanghai (China),
June 27-July 3, 2012,
Talk.
» Abstract
Recurrence as a fundamental property in dynamical systems has been used to characterise the dynamics, to investigate dynamical transitions, or to study synchronisation between multiple systems. A popular method for such analysis is based on the recurrence plot (RP). Several quantification approaches for recurrence plots have been developed and successfully applied in many scientific disciplines. Recently, these quantification techniques have been enriched with measures originating from complex networks theory. These new network measures complement the typical recurrence measures and offer novel insights into dynamical systems. We will introduce here into the concept of recurrence network analysis, explain some relationships with the topology of the phase space, and illustrate the usefulness of recurrence network analysis with examples from life and earth science.
A recurrence plot, i.e., a recurrence network is a representation of recurrences of the states x(i) a system experiences with time t = Δt i:
R(i,j) = Θ(ε – ∥ x(i) – x(j) ∥ – δ(i,j),
with Θ being the Heaviside function, δ(i,j) the Kronecker delta, and ε a threshold for proximity [4]. The binary matrix R contains the value one for all close pairs ∥ x(i) – x(j) ∥ < ε and is in fact the adjacency matrix of a network. In terms of such a complex network, each state vector in phase space represents one distinct node and closeness of two states (i.e., recurrence) represents a link.
Such a network of recurrences can be quantified by complex network measures. A complex network is invariant under permutation of the node order. Consequently, network measures will not directly reflect the dynamical properties of the system studied with RPs, but topological properties of the attractor. For example, the local clustering coefficient measures the presence of closed triangles in the network and, hence, characterises localised higher-order spatial correlations between observations. Specifically, since recurrence networks are spatial networks, it is possible to interpret the structures resolved by spatial variations of the local clustering coefficient in terms of the heterogeneity of the spatial filling of points. High values of the local clustering coefficient often coincide with dynamically invariant objects, such as unstable periodic orbits or, more generally, invariant manifolds. The average of the local clustering coefficient, the global clustering coefficient and the very similar transitivity coefficient, can detect qualitative changes in the system's dynamics, because different local divergence behaviour between neighbouring trajectories, e.g., in case of periodic and chaotic systems, cause different local clustering. Thus, these two measures reveal a specific kind of regularity. Further measures from complex network analysis can also be applied, e.g., average path length or betweenness centrality. In the following we focus on the clustering measures.
Pre-eclampsia in pregnancy is a serious disease with high risk of fetal and maternal morbidity. The usual positive predictive value is 20–30%. Including cardiovascular variability, it has been recently shown that this predictive power can be improved. Using the recurrence network approach, in particular the clustering coefficient, it is possible to further improve the predictive power of discrimination between healthy and pre-eclampsia women. We have analysed data of beat-to-beat values together with diastolic and systolic blood pressure measured in the 20th week of gestation (96 pregnant woman, 24 of them have finally suffered on pre-eclampsia). The data have not been pre-processed. These three measurements have been used to construct the phase space vectors, from which we have created recurrence plots, calculated clustering coefficients and further recurrence quantification measures. We have used a Mann-Whitney U test for testing whether the medians of the distributions of the calculated measures of pre-eclampsia and control group differ. Considering the original measurements alone, as well as some of the recurrence measures, like laminarity (which has been found to be a good candidate for the detection of cardiovascular disorders), the medians are not able to distinguish between the two groups. In contrast, the clustering coefficient was able to discriminate the two groups of pre-eclampsia and control with good confidence (positive predictive accuracy was 60%, negative accuracy was 80%). For pre-eclampsia, the clustering coefficient is slightly lower than for the control group, suggesting a less regular cardiovascular oscillating regime related to the disorder.
We have further illustrated the abilities of a recurrence network analysis by investigating the dynamical regime transitions in the palaeo-climate. Long-term variation in eolian dust deposits (e.g., available in marine cores from drilling projects) is linked with changes in terrestrial vegetation and is often used as a proxy for a changing climate regime. Three distinct marine records of terrigenous dust flux from the Eastern Atlantic, the Eastern Mediterranean sea, and the Arabian sea (ODP 659, ODP 967, ODP 721/722) have been investigated as proxies for environmental variability in East Africa during the past 5 Ma using the recurrence network approach. The transitivity measure has identified three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35–3.15 Ma B.P.), (ii) Early Pleistocene (2.25–1.6 Ma B.P.), and (iii) Middle Pleistocene (1.1–0.7 Ma B.P.). These transitions can be linked with sea level highstands in East Africa and, on a more global scale, unanimously correlate with important global climate transitions, such as changing ocean circulation (after 3.5 Ma B.P.), the intensification of the low-latitude Walker Circulation (ca. 1.7 Ma B.P.), and the onset of 100ka glacial-interglacial cycles during the Middle Pleistocene transition (ca. 1.25–0.7 Ma B.P.). A comparison of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa.
N. Marwan, R. Donner, J. Donges, Y. Zou, J. Kurths:
Complex network analysis of recurrences in phase space,
12th Experimental Chaos Conference, University of Michigan,
Ann Arbor (USA),
May 16-19, 2012,
» Talk invited (PDF, 21.06M).
» Abstract
During the last years, increasing efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant statistical properties of time series. We present a novel approach for analysing time series using complex network theory. Starting from the concept of recurrences in phase space, we identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network, thus linking different points in time if the considered states are closely neighboured in phase space.
We demonstrate that fundamental relationships between topological properties of recurrence networks and different nontrivial statistical properties of the phase space density of the underlying dynamical system exist. This novel interpretation of the recurrence matrix provides new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) and, thus, complementary information about structural features of dynamical systems that substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) methods.
An application from palaeo-climate illustrates the potential of the new approach.
N. Boers, B. Bookhagen, N. Marwan, J. Kurths:
Complex networks from event synchronization of rainfall events over South America,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
» Poster (PDF, 6.85M).
» Abstract
The Amazon rainforest is of distinct climatological interest due to its carbon storage capability. It has been suggested that the region may undergo dramatic shifts in global warming scenarios, thereby possibly loosing its stabilizing effect on the regional and global climate. In the last decade, several extreme droughts have been reported, causing the rainforest to release substantially more carbon dioxide than it could absorb. In combination with ongoing deforestation, this raises concerns that the Amazon rainforest may indeed experience a tipping point in the near future. It has been speculated that the rainforest ecosystem might become unstable and change towards a savanna or desert, with drastic impacts on the global climate system. The physical mechanisms at work, in particular the interplay of temperature, precipitation, and vegetation are complex and not well understood. Relying on both climatological re-analysis and satellite-derived rainfall and temperature data, we investigate temperature and precipitation patterns in the region using complex networks. This new approach has proven very useful in the analysis of spatio-temporal data in general and of global temperature dependencies in particular.We construct precipitation networks by quantifying the degree of synchronization of rainfall events and temperature networks by measuring the degree of correlation between time series at different places. In both network types, we investigate structural differences corresponding to different ENSO-stages. Furthermore, we search for patterns in both precipitation and temperature networks which might possibly explain the reported droughts.
S. F. M. Breitenbach, B. Plessen, F. Lechleitner, N. Marwan, J. F. Adkins, G. H. Haug:
The glacial Indian summer monsoon – precipitation changes during Heinrich and D-O events in NE India,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
Poster.
» Abstract
While glacial/interglacial changes in monsoonal precipitation and their link to external forcing's have been studied extensively for East Asia, little is known about the millennial scale variations of the glacial Indian Summer Monsoon (ISM).
Here, we present novel oxygen isotope data from an U-series dated stalagmite from a cave in NE India, which cover large parts of Marine Isotope Stage 3. Based on monitoring information, we interpret our stalagmite carbonate isotope profile to reflect ISM strength. Higher 18O values in precipitation and in stalagmite carbonate indicate drier intervals, while lower 18O values characterize wetter periods.
The 1.2 m long stalagmite MAW-3 has been sampled every 0.2 to 2 mm, which translates to (sub-)decadal resolution. The 18O record varies from −1 to −7 permil, which is several permil higher than Holocene 18O values (−6 to −9 permil).
Our record suggests that the ISM was significantly weaker during MIS 3, though still perceptible. Moreover, it shows the clear sawtooth pattern of Dansgaard-Oeschger (D-O) cycles. We argue that ISM precipitation was greatly reduced during the Glacial and especially during the Heinrich events, while increased during the interstadials of the D-O cycles. We argue that glacial climatic changes in the Northern Hemisphere rapidly influenced ISM precipitation via the westerlies and/or the Tibetan High. We compare our NE Indian stalagmite record with proxy records from other locations in order to identify teleconnection patterns.
J. F. Donges, R. V. Donner, M. H. Trauth, N. Marwan, H. J. Schellnhuber, J. Kurths:
Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
Talk.
» Abstract
Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of crossdisciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the last 5 Ma (million years) has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a novel nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Mid-Pliocene (3.35-3.15 Ma BP (before present)), (ii) Early Pleistocene (2.25-1.6 Ma BP), and (iii) Mid-Pleistocene (1.1-0.7 Ma BP). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Mid-Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa.
J. F. Donges, R. V. Donner, M. H. Trauth, N. Marwan, H. J. Schellnhuber, J. Kurths:
Recurrence network-based time series analysis for identifying tipping points in Plio-Pleistocene African climate,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
Talk invited.
» Abstract
The analysis of paleoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, the statistical properties of recurrence networks are promising candidates for characterizing a system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. The results of recurrence network analysis are robust under changes in the age model and are not directly affected by nonequidistant sampling of the data. Specifically, we investigate three marine records of African climate variability during the Plio-Pleistocene. We detect several statistically significant dynamical transitions or tipping points and show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. Finally, relating the identified tipping points in paleoclimate-variability to speciation and extinction events in the available fossil record of human ancestors contributes to the understanding of climatic mechanisms driving human evolution in Africa during the past 5 million years.
J. H. Feldhoff, R. V. Donner, J. F. Donges, N. Marwan, J. Kurths:
Bi- and multivariate recurrence network analysis for identifying and characterizing coupled geophysical systems,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
Poster.
» Abstract
Recently, it has been suggested to reinterpret the recurrence plot obtained from a time series of an arbitrary dynamical system as the connectivity matrix of an associated complex network. Statistical measures characterizing the topology of such recurrence networks on both local and global scale have already demonstrated their great potentials for detecting changes in the underlying dynamics as reflected in the geometry of the corresponding attractor in phase space.
Here, we introduce two possible extensions of the recurrence network approach for studying two or more potentially coupled dynamical systems. Specifically, the established concepts of cross- and joint recurrence plots, as well as the recently introduced graph-theoretic framework for describing the properties of interacting networks are utilized for deriving a corresponding complex network representation.
We discuss the interpretation of both approaches in terms of the associated phase space properties and provide some examples highlighting their performance for studying interacting complex systems with respect to identifying their coupling direction and investigating complex synchronization processes. Finally, we present an application to recent observational as well as palaeoclimate data from the Asian monsoon system which illustrates some of the potentials and practical limitations of the two proposed methods.
B. Goswami, J. Heitzig, K. Rehfeld, N. Marwan, J. Kurths:
Using Bayesian regression to construct proxy time series from palaeoclimate archives,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
Talk.
» Abstract
Age-depth observations from palaeoclimatic archives (i.e., peat cores, lake sediments, marine cores, etc.) consist of a set of dating points that comprise of the calibrated radiocarbon-dated ages and corresponding depths measured in the archive. However, the actual understanding of palaeo-climate comes from proxies (such as oxygen isotopes) that are related to various climatic parameters. Due to limitations of measurement, radiocarbon (i.e., 14C) age-depth measurements are far fewer in number than the number of proxy-depth measurements. Thus, the first step in palaeoclimatic studies becomes the construction of an age-depth relationship that transforms the proxy measurements from the depth domain to a time series.
However, it still remains to be resolved as to how the errors of radiocarbon dating be effectively captured in the final proxy time series. Recent advances in this area have shown an emerging consensus favouring the use of Monte Carlo interpolation techniques. These methods typically involve approximate probability distributions that are generated by using thousands of Monte Carlo age-depth models. Despite their relative success and applicability, these methods have one primary drawback: they assume that the calibrated ages have a Gaussian distribution. This is an untenable assumption as the process of calibration - in which the measured 14C age is related to the actual age using a standard 14C calibration curve - converts the simple Gaussian error distribution of the 14C measurement into a complicated multimodal error distribution as a result of the fundamental irregular nature of the calibration curves.
We present a regression based Bayesian approach to this issue. Our method focuses on the ultimate goal of arriving at a meaningful proxy time series and not on the in-between stage of constructing an age-depth model. We suggest to employ the conditional distributions of the measurements (of both the 14C ages as well as the proxies with depth) and thereafter construct an estimator based on regression that provides the distribution of the proxy time series. In this approach, we arrive at meaningful results - such as the mean and standard deviation of the proxy - without having to assume that the calibrated ages have Gaussian errors. The method is validated using simulated data sets where the true values of the age and proxy are known. Moreover, besides radiocarbon dating, the method is applicable to other dating methods as well.
This novel approach based on a perspective of regression can open up newer possibilities of tackling the issue of uncertainties in age-depth relationships and proxy measurements.
B. Goswami, J. Heitzig, K. Rehfeld, N. Marwan, J. Kurths:
The problem of calibration: A possible way to overcome the drawbacks of age models,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
» Poster (PDF, 1.43M).
» Abstract
Constructing a meaningful age model from a set of radiocarbon age-depth measurements made on a palaeoclimatic archive is the crucial backbone of all proxy-based research carried out thereafter. Significant progress in the development of Monte Carlo based interpolation techniques and Bayesian methods has been made recently, targeting the uncertainties of radiocarbon dating, which then reflect meaningfully as time domain errors in the proxy vs. time relationship. However, one primary limitation of these approaches is the debatable assumption of Gaussianity of the errors in calibrated ages as calibration often results in highly irregular and non-trivial probability distributions of the age for every measurement. Here, we present a method that circumvents this limitation by focussing on the construction of the proxy vs. time relationship rather than emphasising on the estimation of an age-depth relation as the intermediary step. Our method is based on a simple analysis of the involved probabilistic uncertainties and the use of (preferably non-parametric) regression methods that give an estimate of the uncertainty of regression at every point as well. With the appropriate use of Bayes' Theorem we then provide a regression-based estimator for the proxy measurements and compute the respective distribution parameters (such as mean and variance) that quantify the uncertainties of the proxy in the time domain. We verify this method with the help of an artificial data set involving the accumulation history of a simulated core and noisy radiocarbon dating and proxy measurements made on it. To our best knowledge, this is the first method that manages to overcome the fundamental problem of irregular distributions induced by calibration of radiocarbon ages. We feel that this approach shall enable us to look at the problem of dating uncertainties in a new light and open up newer possibilities for studying not only speleothem proxies but, more generally, from other palaeoclimatic archives as well.
H. Kutza, J. F. Donges, N. Marwan, R. V. Donner, U. Feudel, J. Kurths:
Pattern recognition in complex networks, based on spatially embedded time series,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
» Poster (PDF, 8.76M).
» Abstract
Already known phenomena in the global climate system resemble characteristic patterns of movement and transport processes on different scales of both, time and space. The approach of complex networks allows to reveal important features of a high dimensional dynamical system, such as advective processes in flows. Given a number of time series that are spatially embedded in the considered physical system, a complex network can be constructed, e.g, using Pearson's cross correlation. The directed and weighted network measures of betweenness centrality and node degree are applied to this complex network. Additionally, the newly developed measure of edge angle anisotropy is then able to indicate directed transport pathways of, e.g., the advected material or climate patterns. The combination of these measures is able to distinguish between static structures and advective dynamics. Moreover, these measures capture local as well as global phenomena. Teleconnections as large scale patterns in the climate system are a good example for the importance of separating directed spreading of distinctive patterns from tightly enclosed local dynamics that do not further contribute to global interactions. Investigating the patterns in the considered physical system can support a better understanding and interpretation of different quantities in climate complex networks and their mutual interrelations. Hence, valuable novel insights in the characteristics of complex systems and their dynamics at different scales are provided.
P. Martin, N. Malik, N. Marwan, J. Kurths:
Complex network analysis of high rainfall events during the northeast monsoon over south peninsular India and Sri Lanka,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
Poster.
» Abstract
The Indian Summer monsoon (ISM) accounts for a large part of the annual rainfall budget across most of the Indian peninsula; however, the coastal regions along the southeast Indian peninsula, as well as Sri Lanka, receive 50% or more of their annual rainfall budget during the northeast monsoon (NEM), or winter monsoon, during the months from October through December. In this study, we investigate the behavior of the NEM over the last 60 years using complex network theory. The network is constructed according to a method previously developed for the ISM, using event synchronization of extreme rainfall events as a correlation measure to create directed and undirected links between geographical locations, which represent potential pathways of moisture transport. Network measures, such as degree centrality and closeness centrality, are then used to illuminate the dynamics of the NEM rainfall over the relevant regions, and to examine the spatial distribution and temporal evolution of the rainfall. Understanding the circulation of the monsoon cycle as a whole, i.e. the NEM together with the ISM, is vital for the agricultural industry and thus the population of the affected areas.
N. Marwan, K. Rehfeld, B. Goswami, S. F. M. Breitenbach, J. Kurths:
Proxy records with uncertainties on an absolute (true) time scale,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
» Poster (PDF, 7.78M).
» Abstract
The usefulness of a proxy record is largely dictated by accuracy and precision of its age model, i.e., its depthage relationship. Only if age model uncertainties are minimized correlations or lead-lag relations can be reliably studied. Moreover, due to different dating strategies (14C, U-series, OSL dating, or counting of varves), dating errors or diverging age models lead to difficulties in comparing different palaeo proxy records. Uncertainties in the age model are even more important if an exact dating is necessary in order to calculate, e.g., data series of flux or rates (like dust flux records, pollen deposition rates).
Several statistical approaches exist to handle the dating uncertainties themselves and to estimate the age-depth relationship. Nevertheless, linear interpolation is still the most commonly used method for age modeling. The uncertainties of a certain event at a given time due to the dating errors are often even completely neglected.
Here we demonstrate the importance of considering dating errors and implications for the interpretation of variations in palaeo-climate proxy records from stalagmites (U-series dated). We present a simple approach for estimating age models and their confidence levels based on Monte Carlo methods and non-linear interpolation. This novel algorithm also allows for removing age reversals. Our approach delivers a time series of a proxy record with a value range for each age depth also, if desired, on an equidistant time axis. The algorithm is implemented in interactive scripts for use with MATLAB, Octave, and FreeMat.
N. Marwan, B. Goswami, K. Rehfeld, S. F. M. Breitenbach, J. Kurths:
Reconstruction of uncertain age-depth relationships,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
Poster.
» Abstract
Dating geoscientific records inevitably includes uncertainties, originating from systematic errors, such as dating errors, positioning errors during sampling, and from random errors (e.g., disturbances in the sediment). However, age models are frequently derived simply by linear interpolation, considering, if any, only the systematic dating error. Even though discrete dating points are presented with their errors, these uncertainties are often not discussed while interpreting the proxy record. Recapitulation of subjectively calculated age models is often hampered by insufficient reporting of the details of the interpolation procedure.
We present a new approach of estimating ensembles of age models by simple Monte Carlo simulation and nonlinear interpolation, its potential in removing age reversals and in translating dating uncertainties into time series with uncertainties. We demonstrate the effects of dating uncertainties and the usability of our method in an application of palaeo-climate variation derived from stalagmites from the Asian monsoon region.
K. Oluoch, N. Marwan, M. H. Trauth, A. Loew, J. Kurths:
Complex networks dynamics based on events-phase synchronization and intensity correlation applied to the anomaly patterns and extremes in the tropical African climate system,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
Poster.
» Abstract
The African continent lie almost entirely within the tropics and as such its (tropical) climate systems are predominantly governed by the heterogeneous, spatial and temporal variability of the Hadley and Walker circulations. The variabilities in these meridional and zonal circulations lead to intensification or suppression of the intensities, durations and frequencies of the Inter-tropical Convergence Zone (ICTZ) migration, trade winds and subtropical high-pressure regions and the continental monsoons. The above features play a central role in determining the African rainfall spatial and temporal variability patterns. The current understanding of these climate features and their influence on the rainfall patterns is not sufficiently understood. Like many real-world systems, atmospheric-oceanic processes exhibit non-linear properties that can be better explored using non-linear (NL) methods of time-series analysis.
Over the recent years, the complex network approach has evolved as a powerful new player in understanding spatio-temporal dynamics and evolution of complex systems. Together with NL techniques, it is continuing to find new applications in many areas of science and technology including climate research. We would like to use these two powerful methods to understand the spatial structure and dynamics of African rainfall anomaly patterns and extremes. The method of event synchronization (ES) developed by Quiroga et al., 2002 and first applied to climate networks by Malik et al., 2011 looks at correlations with a dynamic time lag and as such, it is a more intuitive way to correlate a complex and heterogeneous system like climate networks than a fixed time delay most commonly used. On the other hand, the short comings of ES is its lack of vigorous test statistics for the significance level of the correlations, and the fact that only the events' time indices are synchronized while all information about how the relative intensities propagate within network framework is lost.
The new method we present is motivated by the ES and borrows ideas from signal processing where a signal is represented by its intensity and frequency. Even though the anomaly signals are not periodic, the idea of phase synchronization is not far fetched. It brings into one umbrella, the traditionally known linear Intensity correlation methods like Pearson correlation, spearman's rank or non-linear ones like mutual information with the ES for non-linear temporal synchronization. The intensity correlation is only performed where there is a temporal synchronization. The former just measures how constant the intensity differences are. In other words, how monotonic are the two functions. The overall measure of correlation and synchronization is the product of the two coefficients. Complex networks constructed by this technique has all the advantages inherent in each of the techniques it borrows. But, it is more superior and able to uncover many known and unknown dynamical features in rainfall field or any variable of interest. The main aim of this work is to develop a method that can identify the footprints of coherent or incoherent structures within the ICTZ, the African and the Indian monsoons and the ENSO signal on the tropical African continent and their temporal evolution.
K. Rehfeld, N. Marwan, J. Heitzig, J. Kurths:
Mutual information estimation for irregularly sampled time series,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
Talk.
» Abstract
For the automated, objective and joint analysis of time series, similarity measures are crucial. Used in the analysis of climate records, they allow for a complimentary, unbiased view onto sparse datasets. The irregular sampling of many of these time series, however, makes it necessary to either perform signal reconstruction (e.g. interpolation) or to develop and use adapted measures. Standard linear interpolation comes with an inevitable loss of information and bias effects. We have recently developed a Gaussian kernel-based correlation algorithm with which the interpolation error can be substantially lowered, but this would not work should the functional relationship in a bivariate setting be non-linear.
We therefore propose an algorithm to estimate lagged auto and cross mutual information from irregularly sampled time series. We have extended the standard and adaptive binning histogram estimators and use Gaussian distributed weights in the estimation of the (joint) probabilities. To test our method we have simulated linear and nonlinear auto-regressive processes with Gamma-distributed inter-sampling intervals. We have then performed a sensitivity analysis for the estimation of actual coupling length, the lag of coupling and the decorrelation time in the synthetic time series and contrast our results to the performance of a signal reconstruction scheme.
Finally we applied our estimator to speleothem records. We compare the estimated memory (or decorrelation time) to that from a least-squares estimator based on fitting an auto-regressive process of order 1. The calculated (cross) mutual information results are compared for the different estimators (standard or adaptive binning) and contrasted with results from signal reconstruction.
We find that the kernel-based estimator has a significantly lower root mean square error and less systematic sampling bias than the interpolation-based method. It is possible that these encouraging results could be further improved by using non-histogram mutual information estimators, like k-Nearest Neighbor or Kernel- Density estimators, but for short (<1000 points) and irregularly sampled datasets the proposed algorithm is already a great improvement.
K. Rehfeld, N. Marwan, J. Heitzig, J. Kurths:
Pearson correlation estimation for irregularly sampled time series,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
Poster.
» Abstract
Many applications in the geosciences call for the joint and objective analysis of irregular time series. For automated processing, robust measures of linear and nonlinear association are needed. Up to now, the standard approach would have been to reconstruct the time series on a regular grid, using linear or spline interpolation. Interpolation, however, comes with systematic side-effects, as it increases the auto-correlation in the time series.
We have searched for the best method to estimate Pearson correlation for irregular time series, i.e. the one with the lowest estimation bias and variance. We adapted a kernel-based approach, using Gaussian weights. Pearson correlation is calculated, in principle, as a mean over products of previously centralized observations. In the regularly sampled case, observations in both time series were observed at the same time and thus the allocation of measurement values into pairs of products is straightforward. In the irregularly sampled case, however, measurements were not necessarily observed at the same time. Now, the key idea of the kernel-based method is to calculate weighted means of products, with the weight depending on the time separation between the observations. If the lagged correlation function is desired, the weights depend on the absolute difference between observation time separation and the estimation lag.
To assess the applicability of the approach we used extensive simulations to determine the extent of interpolation side-effects with increasing irregularity of time series. We compared different approaches, based on (linear) interpolation, the Lomb-Scargle Fourier Transform, the sinc kernel and the Gaussian kernel. We investigated the role of kernel bandwidth and signal-to-noise ratio in the simulations. We found that the Gaussian kernel approach offers significant advantages and low Root-Mean Square Errors for regular, slightly irregular and very irregular time series. We therefore conclude that it is a good (linear) similarity measure that is appropriate for irregular time series with skewed inter-sampling time distributions.
K. Rehfeld, N. Marwan, S. F. M. Breitenbach, J. Kurths:
Holocene monsoon variability as resolved in small complex networks from palaeodata,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
Poster.
» Abstract
To understand the impacts of Holocene precipitation and/or temperature changes in the spatially extensive and complex region of Asia, it is promising to combine the information from palaeo archives, such as e.g. stalagmites, tree rings and marine sediment records from India and China. To this end, complex networks present a powerful and increasingly popular tool for the description and analysis of interactions within complex spatially extended systems in the geosciences and therefore appear to be predestined for this task. Such a network is typically constructed by thresholding a similarity matrix which in turn is based on a set of time series representing the (Earth) system dynamics at different locations. Looking into the pre-instrumental past, information about the system's processes and thus its state is available only through the reconstructed time series which – most often – are irregularly sampled in time and space. Interpolation techniques are often used for signal reconstruction, but they introduce additional errors, especially when records have large gaps. We have recently developed and extensively tested methods to quantify linear (Pearson correlation) and non-linear (mutual information) similarity in presence of heterogeneous and irregular sampling. To illustrate our approach we derive small networks from significantly correlated, linked, time series which are supposed to capture the underlying Asian Monsoon dynamics. We assess and discuss whether and where links and directionalities in these networks from irregularly sampled time series can be soundly detected. Finally, we investigate the role of the Northern Hemispheric temperature with respect to the correlation patterns and find that those derived from warm phases (e.g. Medieval Warm Period) are significantly different from patterns found in cold phases (e.g. Little Ice Age).
A. Rheinwalt, N. Marwan, J. Kurths, P. Werner:
Boundary effects in network measures of spatially embedded networks – A case study for German rainfall data,,
EGU General Assembly,
Vienna (Austria),
April 22-27, 2012,
Talk.
» Abstract
In studies of spatially confined networks, network measures can lead to false conclusions since most measures are boundary effected. This is especially the case if boundaries are artificial and not inherent to the underlying system of interest (e.g. borders of countries). An analytical estimation of boundary effects is not trivial due to the complexity of measures. A straightforward approach we propose is to use surrogate networks that can provide estimates of boundary effects in graph statistics. This is achieved by using spatially embedded random networks as surrogates that have approximately the same distribution of spatial link lengths.
Our approach is used in an analysis of spatial patterns in characteristics of regional climate networks. As an example a network derived from daily rainfall data and restricted to the region of Germany is considered.
><2011
J. F. Adkins, S Breitenbach, B. Plessen, N. Marwan, D. C. Lund, P. Huybers, G. H. Haug:
Holocene History of $\delta$18O and Grayscale from a Stalagmite in NE India, with Implications for Monsoon and ENSO Variability,
AGU Fall Meeting,
San Francisco (USA),
December 5-9, 2011,
Talk.
» Abstract
We present the first stalagmite record documenting Indian summer monsoon (ISM) variability spanning the entire Holocene. Over 1400 stable isotope measurements and 37 U-series dates provide a δ18O record with 5-50 year resolution. These data show a broad early Holocene optimum in δ18O that is consistent with higher rainfall following peak intensities of Northern Hemisphere summer insolation. Several abrupt changes in stalagmite δ18O are present in the record with the largest variance occurring in the last 2,000 years. Similar to other tropical and monsoon records, there is a signal of the end of the "African Humid Period" at about 5.5ka. We also document the annual cycle in gray scale variability in stalagmite KRUM-3 using a high-resolution scanner. These annual bands in gray scale have been counted back 5400 years and agree within error with the U-series dates. The gray-scale seasonality record from KRUM-3 exhibits significant coherence and an in-phase relationship with other high-resolution tropical records that are indicative of ENSO variability at periods of 100 years and longer. At shorter periods coherence is lost, as expected given the relative time uncertainty between records. The variance of the gray-scale record at the 2-7 year band is low during the mid-Holocene, but high during both the early and late Holocene. When we rescale the Lake Pallcacocha red layer record so as to account for its changes in sedimentation rate, a similar pattern of high-low-high variability in the ENSO frequency band is found. Contrary to the widespread view that ENSO variability strengthened in the mid- to late Holocene, these results indicate that ENSO variance was high across the tropics during both the early and late Holocene.
J. F. Donges, R. V. Donner, M. H. Trauth, N. Marwan, H. J. Schellnhuber, J. Kurths:
Nonlinear detection of large-scale transitions in Plio-Pleistocene African climate,
AGU Fall Meeting,
San Francisco (USA),
December 5-9, 2011,
Talk.
» Abstract
Potential paleoclimatic driving mechanisms acting on human development present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the last 5 Ma (million years) has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a novel nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Mid-Pliocene (3.35-3.15 Ma BP (before present)), (ii) Early Pleistocene (2.25-1.6 Ma BP), and (iii) Mid-Pleistocene (1.1-0.7 Ma BP). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Mid-Pleistocene, respectively. A statistical reexamination of the available fossil record demonstrates a remarkable coincidence between the detected transition periods and major steps in hominin evolution. This suggests that the observed shifts between more regular and more erratic environmental variability have acted as a trigger for rapid change in the development of humankind in Africa.
In the last years some new directions in recurrence plot based research have been developed. I will give a brief overview about the recent developments, like network analysis of recurrence plots, analysing point processes, indirect couplings, or significance tests for recurrence plot structures and measures.
J. Feldhoff, R. Donner, J. Donges, N. Marwan, J. Kurths:
On bi- and multivariate extensions of recurrence network analysis,
4th International Symposium on Recurrence Plots,
Hong Kong (China),
December 5-8, 2011,
Talk.
» Abstract
Recently, it has been suggested to reinterpret a recurrence plot as the connectivity matrix of a complex network associated with the time series under study. Statistical measures characterizing the topology of such recurrence networks on both local and global scale have already demonstrated their great potential for detecting changes in the underlying dynamics as reflected in the geometry of the corresponding attractor in phase space.
Here, we introduce two possible extensions of the recurrence network approach for studying two or more potentially coupled dynamical systems. Specifically, the established concepts of cross- and joint recurrence plots, as well as the recently introduced graph-theoretic framework for describing the properties of interacting networks are utilized for deriving a corresponding complex network representation. We discuss the interpretation of both approaches in terms of the associated phase space properties and provide some examples highlighting their performance for studying interacting complex systems.
The present work shows that measures for the characterization of complex networks can be used as an efficient alternative to other existing tools of nonlinear analysis in order to unveal subtle transitions in the phase space of dynamical systems. An analogy between the recurrence matrix encoding the recurrences and closeness of phase space vectors of dynamical systems and the adjacency matrix of an undirected and unweighted complex network is exploited and some complex network measures are extracted. The potential of these recurrence network measures in unvealing different transitions in the dynamics of quasiperiodically forced systems is illustrated and attention is drawn to strange nonchaotic dynamics which is clearly depicted by those measures. Instances of (anti-) correlation of these complex network measures with the largest Lyapunov exponent are observed.
N. Marwan:
Recurrence Plot Analysis for Physiological Data,
Seminar in the LOEWE Research Center Preventive Biomechanics, Frankfurt University,
Frankfurt/M. (Germany),
November 16, 2011,
Lecture.
N. Marwan:
Einführung in die Nichtlineare Datenanalyse,
Graduate School "Visibility" at University of Potsdam,
Potsdam (Germany),
June 29, 2011,
Lecture.
N. Marwan:
Graphentheoretische Untersuchung komplexer Systeme,
Workshop Klimawandel, Parasiten und Infektionskrankheiten,
Berlin (Germany),
March 3-4, 2011,
Talk.
K. Rehfeld, N. Marwan, J. Heitzig, J. Kurths:
Kernel-based correlation estimation for irregularly sampled time series,
EGU General Assembly,
Vienna (Austria),
April 4-7, 2011,
Talk.
» Abstract
In order to understand the complex interplay of variables that result in climate, paleo records like those from stalagmites, ocean, lake or ice core records present our only opportunity to gain knowledge about the past. Due to the nature of their genesis their time resolution is heterogeneous, nevertheless their inter-comparison is of high importance to gain insights on the interactions in the earth system. Standard cross correlation evaluation requires the time series to have the same, regular, observation times, which can only be achieved by interpolation. This, however, creates artificial memory in the time series, which changes the spectra and correlation functions. In a thorough benchmark test we compare the performance of the standard approach, consisting of linear interpolation followed by a fft-based estimator, to the results from different kernel-based estimators and an estimator based on the Lomb-Scargle periodogram, which do not require the observations to be regularly sampled. In our tests we find a 40% lower RMSE for the lag-1 ACF for the gaussian kernel method vs the linear interpolation scheme, for the CCF the RMSE is lower by 60%. The application of the Lomb-Scargle technique yielded comparable results for the univariate but very poor results for the bivariate case. We find that especially the high-frequency components of the signal, where classical methods show a strong negative bias, are preserved when using the kernel methods. We apply the gaussian kernel estimator and interpolation followed by the standart FFT-routine to paleo records from the Asian Monsoon domain. We estimate cross-correlation and persistence time of two speleothem δ18O records, one from Dandak cave in Southern India and one fromWanxiang cave in North-central China. The correlation between the records in the overlapping section is significant to the 95% level for both methods which could mean that both records are influenced by an overall Asian Monsoon signal. The gaussian kernel results for the AR-1 persistence times of the individual records is close to that of the independent least-squares estimator, where interpolation results in a doubling of the persistence time.
The gaussian kernel estimator is, we find, a reliable, robust technique with significant advantages over other methods and suitable for wider application to paleo-data.
N. Malik, Y. Zou, N. Marwan, J. Kurths:
Employing nonlinear similarities to identify distinct dynamical regimes in short palaeo records,
EGU General Assembly,
Vienna (Austria),
April 4-7, 2011,
Talk.
» Abstract
We present an intriguing new technique based on nonlinear similarities to detect regimes and states of distinct dynamical complexity in a short time series. We provide detailed tests and verification of the new approach on several numerical models by uncovering their bifurcation structures. We also provide comparison of the presented technique with existing traditional measures like Lyapunov exponent. Further, we apply the method to identify abrupt dynamical changes and transitions in several different palaeo records. Most significant being the pelistocene record of Asian Monsoon, where we found that monsoonal system almost linearly responded to solar insolation. But this response can be disrupted by internal forcing on monsoonal dynamics, i.e. the glaciation cycles of the Northern Hemisphere and the onset of certain oceanic circulations. A statistical test is developed to estimate the significance of the identified transitions.
J. Donges, H. C. H. Schultz, N. Marwan, Y. Zou, J. Kurths:
Coupled climate networks for analysing the terrestrial atmosphere's vertical dynamical structure,
EGU General Assembly,
Vienna (Austria),
April 4-7, 2011,
Poster.
» Abstract
Network theory provides various tools for investigating the structural or functional topology of many complex systems found in nature, technology and society. Nevertheless, it has recently been realised that a considerable number of systems of interest should be treated, more appropriately, as interacting networks or networks of networks. Here we introduce a novel graph-theoretical framework for studying the interaction structure between subnetworks embedded within a complex network of networks. This framework allows us to quantify the structural role of single vertices or whole subnetworks with respect to the interaction of a pair of subnetworks on local, mesoscopic and global topological scales.
Climate networks have recently been shown to be a powerful tool for the analysis of climatological data. Applying the general framework for studying interacting networks, we introduce coupled climate subnetworks to represent and investigate the topology of statistical relationships between the fields of distinct climatological variables. Using coupled climate subnetworks to investigate the terrestrial atmosphere's three-dimensional geopotential height field uncovers known as well as interesting novel features of the atmosphere's vertical stratification and general circulation. Specifically, the new measure "cross-betweenness" identifies regions which are particularly important for mediating vertical wind field interactions. The promising results obtained by following the coupled climate subnetwork approach present a first step towards an improved understanding of the Earth system and its complex interacting components from a network perspective.
K. Rehfeld, N. Marwan, J. F. Donges, J. Kurths:
Linear and nonlinear similarity measures for networks from irregularly sampled data,
EGU General Assembly,
Vienna (Austria),
April 4-7, 2011,
Poster.
» Abstract
Paleo records from proxy archives present the opportunity to study past climate and its changes. Owing to different archive properties, reconstructed observation times are not spaced at regular intervals and are prone to errors. Their automated and objective joint analysis and intercomparison is still of much interest due to the large number of proxy records available.
Standard linear and nonlinear similarity measures require regular sampling times and their application makes interpolation prior to analysis necessary. Interpolation introduces additional bias, especially for the high-frequency components.
Using a kernel-based correlation approach, we circumvent the need for interpolation and use the information that the time series offer at the different time scales directly.
In a benchmark test we compare the correlative patterns and network measures obtained from standard approach and kernel-based results. We illustrate robustness and reliability of the new method using synthetic time series of known inter-sampling time distributions similar to those found in reality and show that the results we obtain from paleo records show the same characteristics.
We find that the kernel-based approach offers a reliable and safe method to estimate linear and nonlinear correlation properties and that based on this we can construct complex networks representing similarity relationships between paleo records.
R. Donner, J. F. Donges, M. H. Trauth, N. Marwan, J. Kurths:
Large-scale transitions in Plio-Pleistocene African dust flux dynamics identified by recurrence network analysis,
EGU General Assembly,
Vienna (Austria),
April 4-7, 2011,
Poster.
» Abstract
These days, long-term environmental changes are believed to have acted as a key factor in the evolutionary history of the human race. For the Plio-Pleistocene climate history of East Africa (the "cradle of mankind"), recent studies on terrestrial as well as marine paleoclimate archives suggested different possible climatic forcing mechanisms. Here, we apply recurrence network analysis, a novel nonlinear statistical technique, to three distinct marine records of terrigeneous dust flux. Our method identifies subtle transitions between qualitatively different types of dust flux dynamics at about (i) 3.45-3.05, (ii) 2.1-1.7, and (iii) 1.2-0.7 Myr BP, which reflect changes in the variability of environmental conditions in North and East Africa. The timing of the identified transition periods reveals both lowand high-latitude climatic changes as possible dynamic origins of the observed regime shifts, the sources of which are identified and critically discussed. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our analysis method, including detrending, choice of the size of the running window used for analysis, and embedding delay.
R. Donner, J. Heitzig, J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
The Geometry of Chaotic Dynamics \u2013 A Complex Network Perspective,
EGU General Assembly,
Vienna (Austria),
April 4-7, 2011,
Poster.
» Abstract
Recently, several complex network approaches to time series analysis have been developed and applied to study a wide range of model systems as well as real-world data, e.g., geophysical or financial time series. Among these techniques, recurrence-based concepts and prominently ε-recurrence networks, most faithfully represent the geometrical fine structure of the attractors underlying chaotic (and less interestingly non-chaotic) time series. In this paper we demonstrate that the well known graph theoretical properties local clustering coefficient and global (network) transitivity can meaningfully be exploited to define two new local and two new global measures of dimension in phase space: local upper and lower clustering dimension as well as global upper and lower transitivity dimension. Rigorous analytical as well as numerical results for self-similar sets and simple chaotic model systems suggest that these measures are well-behaved in most non-pathological situations and that they can be estimated reasonably well using "-recurrence networks constructed from relatively short time series. Moreover, we study the relationship between clustering and transitivity dimensions on the one hand, and traditional measures like pointwise dimension or local Lyapunov dimension on the other hand. We also provide further evidence that the local clustering coefficients, or equivalently the local clustering dimensions, are useful for identifying unstable periodic orbits and other dynamically invariant objects from time series. Our results demonstrate that "-recurrence networks exhibit an important link between dynamical systems and graph theory.
N. Marwan, J. F. Donges, R. Donner, J. Heitzig, Y. Zou, J. Kurths:
Duality of complex network analysis and recurrence based analysis of time series,
Climate Knowledge Discovery Workshop,
Hamburg (Germany),
March 30 - April 1, 2011,
» Talk (PDF, 16.55M).
N. Marwan, J. F. Donges, R. Donner, J. Heitzig, Y. Zou, J. Kurths:
Complex network approach for recurrence analysis of time series,
ECONS Spring School,
Wandlitz (Germany),
March 28 - March 31, 2011,
Talk.
><2010
N. Marwan, R. Donner, J. Kurths:
Complex networks,
ECONS Workshop,
Potsdam (Germany),
July 19, 2010,
Lecture.
N. Marwan, N. Wessel, J. Kurths:
Complex network analysis of time series for early detection of pregnant pre-eclampsia,
BioSignal 2010: Advanced Technologies in Intensive Care and Sleep Medicine,
Berlin (Germany),
July 14-16, 2010,,
Talk.
» Abstract
Pre-eclampsia in pregnancy is a serious disease with high risk of fetal and maternal morbidity. The usual positive predictive value is 20–30%. Including cardiovascular variability, it has been recently shown that this predictive power can be improved.
Here we propose a novel approach for analysing time series of systolic and diastolic blood pressure as well as heart rate variability measured in the 20th week of gestation in order to predict pre-eclampsia. For this aim, we identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. We demonstrate the potential of the complex network measures for a further improvement of the positive predictive value of pre-eclampsia.
N. Marwan:
Workshop on recurrence analysis for social therapies,
Seminar Dept. of Psychology at the LMU,
Munich (Germany),
June 25, 2010,
Lecture.
N. Marwan:
Modern nonlinear approaches for data analysis,
GRADE Graduate School of University of Frankfurt,
Frankfurt/M. (Germany),
June 24, 2010,
» Lecture (PDF, 37.28M).
N. Marwan, J Donges, R. Donner, Y. Zou, J. Kurths:
Complex network approach for recurrence analysis of time series,
458th WE-Heraeus-Seminar on Theory and Applications in Neuroscience and Climatology (SYNCLINE),
Bad Honnef (Germany),
May 26-29, 2010,
» Talk invited (PDF, 16.31M).
» Abstract
We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. We illustrate similarities and differences between the recurrence quantification analysis and the complex network analysis. By using the logistic map, we demonstrate the potential of the complex network measures for the detection of dynamical transitions. Finally, we apply the proposed approach to a marine palaeo-climate record and identify the subtle changes to the climate regime.
J. Heitzig, N. Marwan, Y. Zou, J. F. Donges, J. Kurths:
Consistently weighted measures for complex network topologies,
458th WE-Heraeus-Seminar on Theory and Applications in Neuroscience and Climatology (SYNCLINE),
Bad Honnef (Germany),
May 26-29, 2010,
Poster.
» Abstract
When network and graph theory are used in the study of complex systems, the typically finite set of nodes of the network under consideration is frequently either explicitly or implicitly considered representative of a much larger finite or infinite set of objects of interest. The selection procedure, e. g., formation of a subset or some kind of discretization or aggregation, typically results in individual nodes of the studied network representing quite differently sized regions of the domain of interest. This heterogenous sampling may induce substantial biases in derived network statistics.
To avoid these problems, we propose an axiomatic scheme based on the idea of node splitting invariance to derive consistently weighted variants of various commonly used statistical network measures which approximate the corresponding properties of the underlying domain of interest.
The practical relevance and applicability of our approach is demonstrated for the example of climate networks – networks constructed from climate data on grids with heterogenous mesh cell areas.
A. Radebach, J. Runge, J. Zscheischler, J. F. Donges, N. Marwan, J. Kurths:
Evolving complex networks from global climatological fields on geodesic grids,
458th WE-Heraeus-Seminar on Theory and Applications in Neuroscience and Climatology (SYNCLINE),
Bad Honnef (Germany),
May 26-29, 2010,
Poster.
» Abstract
Recent research has revealed the applicability of complex network approaches for data analysis of global climatological fields. Designating points of a regular grid (of measurement stations, respectively reanalysis data sites) as nodes of a network and creation of edges between them using similarity measures (e.g., cross correlation, mutual information) leads to a network representation of the underlying dynamics. We use a geodesic grid (with roughly 2.5?x2.5? resolution), where each grid point covers approx. the same area. This approach inhibits biases due to the variable local node density, which appear in grids such as the frequently used regular latitude-longitude grid. The datasets of daily surface air temperature and pressure, covering the last 60 years, are split into partially overlapping windows (their width ranging from half a year up to decades), allowing to construct evolving networks, i.e., changing network topologies in time. Hereby, we are able to analyze correspondences in the temporal evolution of network properties and classical climate indices, e.g., SOI, NAO index. The spatiotemporally resolved network measures also highlight climatological phenomena such as ENSO or the impact of vulcanic eruptions.
R. V. Donner, Y. Zou, J. F. Donges, N. Marwan, J. Kurths:
Recurrence networks – A novel paradigm for nonlinear time series analysis,
458th WE-Heraeus-Seminar on Theory and Applications in Neuroscience and Climatology (SYNCLINE),
Bad Honnef (Germany),
May 26-29, 2010,
Poster.
» Abstract
This paper presents a new approach for analyzing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network, which links different points in time if the considered states are closely neighbored in phase space. In comparison with similar network-based techniques, the new approach has important conceptual advantages and can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases.
It is demonstrated that there are fundamental relationships between many topological properties of recurrence networks and different non-trivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related with the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis. The performance of our approach is illustrated for different model systems as well as some real-world geoscientific time series.
J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
On the backbone of climate networks,
458th WE-Heraeus-Seminar on Theory and Applications in Neuroscience and Climatology (SYNCLINE),
Bad Honnef (Germany),
May 26-29, 2010,
Poster.
» Abstract
We propose a method to reconstruct and analyze a complex network from data generated by a spatio-temporal dynamical system, relying on the nonlinear mutual information of time series analysis and betweenness centrality of complex network theory. We show, that this approach reveals a rich internal structure in complex climate networks constructed from reanalysis and model surface air temperature data. Our novel method uncovers peculiar backbone-like structures of high energy flow, that we relate to global surface ocean currents. This points to a major role of the oceanic surface circulation in coupling and stabilizing the global temperature field in the long term mean (140 years for the model run and 60 years for reanalysis data). We find that these results cannot be obtained using classical linear methods of multivariate data analysis, and have ensured their robustness by intensive significance testing.
H. Schultz, J.F. Donges, N. Marwan, J. Kurths:
Coupled climate networks,
458th WE-Heraeus-Seminar on Theory and Applications in Neuroscience and Climatology (SYNCLINE),
Bad Honnef (Germany),
May 26-29, 2010,
Poster.
» Abstract
The idea of constructing climate networks from climate time series taken at geographical grid points states a quite young and promising approach to provide novel insights into the dynamics of the climate system. Here we want to introduce the method of constructing networks out of coupled climate patterns in order to investigate their interdependence. Analyzing the networks' topological properties we aim at a better understanding of general atmospheric circulation phenomena and lower troposphere dynamics related to extreme events. In this work we focus on geopotential height layers and surface climate patterns using NCAR/NCEP reanalysis data.
N. Marwan:
Hot Topics in Recurrence Plot Analysis,
Seminar at the Freiburg Center for Data Analysis and Modeling,
Freiburg (Germany),
April 27, 2010,
Talk invited.
N. Marwan, J Donges, N. Wessel, J. Kurths:
Complex network approach for recurrence analysis of cardiovascular oscillations,
6th Conference of the European Study Group on Cardiovascular Oscillations (ESGCO 2010),
Berlin (Germany),
April 12-14, 2010,
» Talk (PDF, 11.37M).
» Abstract
Recurrence quantification analysis has been successfully applied to cardiovascular time series for the study of diseases. A recent development in recurrence studies unifies two different areas in complex systems analysis: complex network theory and recurrence plots. The recurrence matrix (calculated from time series) can be identified with the adjacency matrix of a complex network, hence enabling a complex network analysis of time series. We illustrate similarities and differences between the recurrence quantification analysis and the complex network analysis and demonstrate the potential of the complex network measures for the characterisation of time series. Finally, we apply the proposed approach to analyse cardiovascular oscillations in order to predict pre-eclampsia.
N. Malik, N. Marwan, J. Kurths:
Spatial structures and directionalities in precipitation over South Asia,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
Poster.
» Abstract
Due to the underlying dynamics of atmospheric circulations and varied topography, precipitation during monsoon over the Indian subcontinent tends to occur in form of enormously complex spatiotemporal patterns. Employing methods from nonlinear time series analysis we studied the spatial structures of the rainfall field during the summer monsoon and identified the principle regions where the dynamics of monsoonal rainfall is more coherent or homogeneous and also, we estimated the time delay patterns of rain events. We have applied our method on two separate high resolution gridded data sets of daily rainfall covering the Indian subcontinent. Using the method of event synchronization, we have estimated the regions where heavy rain events during monsoon happen in some lag synchronized form. Active (Break) phase of monsoon is characterised by increase(decrease) of rainfall over certain regions of Indian subcontinent. We propose that our method is able to identify regions of such coherent rainfall activity. Further using the delay behaviour of rainfall events we estimate the directionalities involved in the progress of major rainfall events. We have been able to show that these directions are very similar to wind directions during these type of rainfall events. Employing the same method on a high resolution TRMM rainfall data we also show the path ways of precipitation over the Himalayas during different seasons.
H. C. H. Schultz, J. F. Donges, N. Marwan, J. Kurths:
Coupled patterns in complex climate networks,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
Poster.
» Abstract
The idea of constructing climate networks from climate time series taken at geographical grid points states a quite young and promising approach to provide novel insights into the dynamics of the climate system. In order to investigate the relation and mutual influence of superposed climate patterns we introduce the method of constructing three-dimensional networks. By means of analyzing their topological properties we aim at mapping atmospheric circulation phenomena (e.g. Hadley Cells) or even revealing structures which might be related to extreme events. We focus on different levels of geopotential height using reanalysis data ranging from 1948 to 2008.)
A. Radebach, J. Runge, J. Zscheischler, J. F. Donges, N. Marwan, J. Kurths:
Evolving complex networks from global climatological fields on geodesic grids,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
» Poster (PDF, 27.02M).
» Abstract
Recent research has revealed the applicability of complex network approaches for data analysis of global climatological fields. Designating points of a regular grid (of measurement stations, respectively reanalysis data sites) as nodes of a network and creation of edges between them using similarity measures (e.g., cross correlation, mutual information) leads to a network representation of the underlying dynamics. We use a geodesic grid (with roughly 2.5?x2.5? resolution), where each grid point covers approx. the same area. This approach inhibits biases due to the variable local node density, which appear in grids such as the frequently used regular latitude-longitude grid. The datasets of daily surface air temperature and pressure, covering the last 60 years, are split into partially overlapping windows (their width ranging from half a year up to decades), allowing to construct evolving networks, i.e., changing network topologies in time. Hereby, we are able to analyze correspondences in the temporal evolution of network properties and classical climate indices, e.g., SOI, NAO index. The spatiotemporally resolved network measures also highlight climatological phenomena such as ENSO or the impact of vulcanic eruptions.
K. Rehfeld, J. F. Donges, N. Marwan, J. Kurths:
Correlation-based similarity networks for unequally sampled data,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
Poster.
» Abstract
Complex networks present a promising and increasingly popular paradigm for the description and analysis of interactions within complex spatially extended systems in the geosciences. Typically, a network is constructed by thresholding a similarity matrix which is based on a set of time series representing the system's dynamics at different locations. In geoscientific applications such as paleoclimate records derived from ice and sediment cores or speleothems, however, researchers are inherently faced with irregularly and heterogenously sampled time series. For this type of data, standard similarity measures, e.g., Pearson correlation or mutual information, must fail. Most attention has been placed on frequency-based methods focussing on the derivation of power spectra, such as the Lomb-Scargle periodogram. In the context of paleoscientific network research correlation estimation is of high interest, but available methods require interpolation prior to analysis. Here we present a generalization of the Pearson correlation coefficient adapted to irregularly sampled time series and show that it has advantages over the standard approach. Characterizing the method in the application to model systems we further extend our scope to real world data and show that it offers new options for network research and provide novel insights into the functioning of the earth system.
N. Marwan, J. Donges, Y. Zou, R. Donner, J. Kurths:
Complex network approach for recurrence analysis of time series,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
» Poster (PDF, 8.51M).
» Abstract
We propose a novel approach for analysing time series using complex network theory. We identify the recurrence matrix (calculated from time series) with the adjacency matrix of a complex network and apply measures for the characterisation of complex networks to this recurrence matrix. We illustrate similarities and differences between the recurrence quantification analysis and the complex network analysis. By using the logistic map, we demonstrate the potential of the complex network measures for the detection of dynamical transitions. Finally, we apply the proposed approach to a marine palaeo-climate record and identify the subtle changes to the climate regime.
Y. Zou, R. V. Donner, J. F. Donges, N. Marwan, J. Kurths:
Identifying shrimps in continuous dynamical systems using recurrence-based methods,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
Poster.
» Abstract
The identification of specific periodic islands (so-called shrimps) in the two-dimensional parameter space of certain complex systems has recently attracted considerable interest. While for discrete systems, a discrimination between periodic and chaotic windows can be easily made based on the maximum Lyapunov exponent of the system, this remains a challenging task for continuous systems, especially if only short time series are available (e.g., in case of experimental data).
In this work, we demonstrate that nonlinear measures based on recurrence plots obtained from individual trajectories provide a practicable alternative for automatically distinguishing periodic and chaotic dynamics and, hence, numerically detecting shrimps. Traditional diagonal line-based measures of recurrence quantification analysis as well as measures from complex network theory are shown to allow an excellent classification of periodic and chaotic behavior in parameter space. Average path length and clustering coefficient of the resulting recurrence networks are found to be particularly powerful discriminatory statistics for the identification of shrimps.
Our results are illustrated in detail for the Roessler system. Implications for detecting bifurcations between regular and chaotic dynamics in other models of geophysical phenomena (such as the Lorenz-84 system) are discussed.
R. V. Donner, Y. Zou, J. F. Donges, N. Marwan, J. Kurths:
Recurrence networks – A novel paradigm for nonlinear time series analysis,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
Poster.
» Abstract
We present a novel approach for analysing structural properties of time series from complex systems. Starting from the concept of recurrences in phase space, the recurrence matrix of a time series is interpreted as the adjacency matrix of an associated complex network, which links different points in time if the considered states are closely neighboured in phase space. In comparison with similar network-based techniques, this new approach has important conceptual advantages and can be considered as a unifying framework for transforming time series into complex networks that also includes other existing methods as special cases.
It is demonstrated that there are fundamental relationships between many topological properties of recurrence networks and different non-trivial statistical properties of the phase space density of the underlying dynamical system. Hence, this novel interpretation of the recurrence matrix yields new quantitative characteristics (such as average path length, clustering coefficient, or centrality measures of the recurrence network) related with the dynamical complexity of a time series, most of which are not yet provided by other existing methods of nonlinear time series analysis. The potentials of recurrence networks are illustrated for different dynamical systems with low-dimensional deterministic chaos, including paradigmatic models for geophysical systems such as the Lorenz oscillator.
N. Malik, N. Marwan, J. Kurths:
Distinct dynamical regimes in monsoonal paleo-records and the role of solar forcing,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
Talk.
» Abstract
Monsoons tend to fluctuate between regimes of different dynamics over varied time scales. So it is important to not only identify the transitions in monsoonal systems but also the multiple dynamical states of a monsoonal system and there corresponding time scales.We present a method to identify distinct dynamical regimes in a time series by comparing different segments of the time series using recurrence plots. We use this method on paleo-records from lakes and speleothems from East Africa and South Asia respectively to identify the time periods of similar dynamics of monsoon. Further we try to compare the identified regimes with changes in solar forcing.
K. Rehfeld, N. Marwan, J. Kurths, D. Wagenbach, S. Preunkert, S. Breitenbach:
A correlation estimation algorithm adapted to irregular sampling applied to ice core and speleothem time series,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
Talk.
» Abstract
Geoscientific time series providing information over timescales from years to centuries are constructed from geoarchives and are prone to errors in time and signal dimension. Sampling is often inherently irregular which for frequency-based analysis requires interpolation prior to analysis or methods adapted to it. Spectral analysis of irregularly sampled data has received much interest especially in the field of astrophysics, but most research has been focussed on power spectrum estimators such as the Lomb-Scargle Periodogram. Cross- and autocorrelation estimation of unequally sampled data has received little attention up to now. However, it offers new possibilities for correlation-based similarity network analysis and we show that our approach can highlight cyclical patterns lost in the interpolation process. This feature can be extremely useful in the chronology building process, where annual lamination can provide restraints for radiometric dates and time horizons as used for the dating of speleothems and ice cores. Here, a correlation estimation algorithm adapted to irregular sampling is presented, validated against common routines for equidistant sampling and its robustness regarding common sampling artifacts is shown. Results of the analysis of a speleothem record and a Mont Blanc summit ice core record are presented.
J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
The backbone of climate networks,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
Talk.
» Abstract
We propose a method to reconstruct and analyze a complex network from data generated by a spatio-temporal dynamical system, relying on the nonlinear mutual information of time series analysis and betweenness centrality of complex network theory. We show, that this approach reveals a rich internal structure in complex climate networks constructed from reanalysis and model surface air temperature data. Our novel method uncovers peculiar wave-like structures of high energy and information flow, that we relate to global surface ocean currents. This points to a major role of the oceanic surface circulation in coupling and stabilizing the global temperature field in the long term mean (140 years for the model run and 60 years for reanalysis data). We find that these results cannot be obtained using classical linear methods of multivariate data analysis, and have ensured their robustness by intensive significance testing.
J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
Significance tests for spatially embedded complex networks,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
Poster.
» Abstract
The analysis of spatially embedded complex networks, i.e., networks with vertices embedded in a metric space, is of increasing interest in many fields of science, particularly in the geosciences. Examples are climate networks in meteorology, earthquake networks in geology or recurrence networks for time series analysis. In many cases, there is some degree of uncertainty about the network structure, e.g., edges might be missing in the network that exist in the system under study (the opposite may also be true). This is particularly true for networks constructed from multivariate data using tools of time series analysis. Given this uncertainty, it is very important to evaluate the significance of measured network properties such as clustering coefficient, average path length, degree distribution or various vertex centrality sequences with respect to a given null hypothesis. Here we present different types of surrogates for spatially embedded networks, i.e., random networks with prescribed spatial constraints such as fixed edge distance distribution or a fixed average edge distance sequence, and show how to use them for testing the associated null hypotheses.We demonstrate the proposed significance tests for a global climate network constructed from coupled model surface air temperature data.
J. Heitzig, N. Marwan, Y. Zou, J. F. Donges, J. Kurths:
Consistently weighted measures for complex network topologies,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
Talk.
» Abstract
Most measures of the structural and topological properties of a complex network are of a combinatorial nature, basically counting certain nodes, edges, triangles, paths, etc. But the typically finite set of nodes of the studied network is often either explicitly or implicitly considered representative of a much larger finite or infinite set of objects of interest, either by being a subset of this larger set or by being some kind of discretisation or aggregation of it. Examples are networks consisting of a statistically sampled number of members of a large social or scientific community, networks of discrete regular grid points on a surface or of irregular mesh cells in some manifold, or networks constructed from recurrence plots of time series with regular or irregular time intervals. This selection procedure typically results in individual nodes of the studied network representing quite differently sized regions of the domain of interest, inducing substantial biases in derived network statistics.
To avoid these problems, we propose an axiomatic scheme based on the idea of node splitting invariance to derive consistently weighted variants of various commonly used statistical network measures which approximate the corresponding properties of the underlying domain of interest. The practical relevance and applicability of our approach is demonstrated for the example of climate networks – networks constructed from climate data on grids with heterogenous mesh cell areas
.
J. F. Donges, N. Marwan, S. Breitenbach:
Recurrence structure of speleothem isotope records from Asia hints at simultaneous transitions in climate dynamics during the Holocene,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
Poster.
» Abstract
Speleothems are important archives of past climate variability. We study isotope records of stalagmites from three caves at different locations in Asia: Oman, Northeastern India and China. The isotope records present proxies for the precipitation variability at these locations and cover a time span of 3-11 kyr before present. The large spatial separation of the considered caves results in a distinct influence of the Intertropical Convergence Zone and, therefore, mutually different summer and winter monsoon dynamics.
Recurrence analysis exploits a phenomenon frequently observed in nature – the tendency of a system's state to closely resemble an earlier state after some finite time of arbitrary evolution. Statistically analysing the stalagmite isotope time series' recurrence structure unveils synchronous transitions at all locations, although the records themselves do not linearly correlate. This finding suggests that at these times the entire Asian monsoon system underwent qualitative changes which are visible in the isotope time series despite the locally different climatic and environmental conditions.
A more detailed history of large scale monsoon dynamics in the recent geological past in context with other known climatic and environmental factors is essential for a deeper understanding of the underlying physical mechanisms. This in turn may prove useful for assessing the probability of the monsoon system undergoing a major qualitative transition (passing a tipping point) in the near future.
R. V. Donner, J. F. Donges, N. Marwan, Y. Zou, J. Kurths:
Epochs of synchronous changes and dynamical transitions in African dust flux variability over the past 5 Ma detected by recurrence network analysis,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
Talk.
» Abstract
In the last decades, increasing interest has been spent on deciphering changes in the environmental conditions in Central and Eastern Africa during the last several millions of years and their relationship with the evolution of the human race. Among other sources of information, the atmospheric dust flux recorded in marine sediments serves as an excellent proxy for changes in land cover, vegetation, and atmospheric circulation. Like for other palaeoclimate records, the analysis of such data is however strongly challenged by properties such as long-term non-stationarity and unequal sampling in time domain.
In this work, we demonstrate the potential of recurrence networks, a recently developed method of nonlinear time series analysis, for tracing and quantitatively characterising changes of the environmental variability encoded in dust flux records. Since this method does not rely on the temporal order of observations, but is exclusively based on the mutual similarity of individual values or embedded state vectors (i.e., recurrences of values in some abstract phase space), it can be directly applied even to unequally sampled time series. Moreover, the topological properties of recurrence networks associated with a time series can already be estimated for rather short data segments in a meaningful way, which makes this approach especially suitable for detecting changes in the recorded variability by using running windows in time.
We apply our method to the dust flux records from ODP sites 659, 721/722, and 967, corresponding to three locations off Northwestern Africa, in the Eastern Mediterranean, and in the Northwestern Indian Ocean. Complex network measures such as average path length and clustering coefficient computed for the recurrence networks obtained for sliding windows in time identify hidden dynamical transitions in the environmental conditions. Comparing the overall temporal variability of these measures between the three considered records reveals epochs of synchronous behaviour, which indicates a large-scale impact of the corresponding changes in the temporal variability of vegetation patterns and/or atmospheric circulation.
J. Kurths, J. F. Donges, R. V. Donner, N. Marwan, Y. Zou:
Nonlinear Time Series Analysis in Earth Sciences – Potentials and Pitfalls,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
Talk invited.
» Abstract
The application of methods of nonlinear time series analysis has a rich tradition in Earth sciences and has enabled substantially new insights into various complex processes there. However, some approaches and findings have been controversially discussed over the last decades. One reason is that they are often bases on strong restrictions and their violation may lead to pitfalls and misinterpretations.
Here, we discuss three general concepts of nonlinear dynamics and statistical physics, synchronization, recurrence and complex networks and explain how to use them for data analysis. We show that the corresponding methods can be applied even to rather short and non-stationary data which are typical in Earth sciences.
N. Marwan, J. F. Donges, S. Breitenbach:
Synchronous climate transitions during the Holocene in Asia derived from speleothems,
EGU General Assembly,
Vienna (Austria),
May 2-7, 2010,
» Poster (PDF, 4.97M).
» Abstract
Speleothems offer rich archives of past climate variability. We analyse isotope records of stalagmites from three caves at different locations in Asia: Oman, Northeastern India and China. These records are proxies for the rainfall variability at these locations and cover a tthirdpartyime range of approx. 3-11 kyr. Due to the large spatial separation of the considered caves, the influence of the Intertropical Convergence Zone and, hence, the summer and winter monsoon is quite distinct at each location.
Recurrence is a fundamental property of dynamical systems. The recurrence behaviour of processes is captured by the binary recurrence matrix. Interpreting the recurrence matrix either as a recurrence plot or a recurrence network yields powerful methods of nonlinear data analysis based on recurrence quantification analysis and complex network theory, respectively. The statistical analysis of recurrence plots and recurrence networks can uncover hidden transitions in data series, which cannot be found by linear methods of time series analysis.
Analysis of the recurrence structure of the stalagmite isotope records unveils synchronous transitions at all locations, even though the data series themselves do not correlate. This result suggests that at these times the entire monsoon system underwent changes which are visible in the isotope records despite the locally different dependence of rainfall on the summer and winter monsoon dynamics.
><2009
Y. Zou, J. F. Donges, N. Marwan, J. Kurths:
The Backbone of the Climate Networks,
AGU Fall Meeting,
San Francisco (USA)),
December 14-18, 2009,
Talk.
» Abstract
We propose a method to reconstruct and analyze a complex network from data generated by a spatio-temporal dynamical system, relying on the nonlinear mutual information of time series analysis and betweenness centrality of complex network theory. We show, that this approach reveals a rich internal structure in complex climate networks constructed from reanalysis and model surface air temperature data. Our novel method uncovers peculiar wave-like structures of high energy flow, that we relate to global surface ocean currents. This points to a major role of the oceanic surface circulation in coupling and stabilizing the global temperature field in the long term mean (140 years for the model run and 60 years for reanalysis data). We find that these results cannot be obtained using classical linear methods of multivariate data analysis. Furthermore, we introduce significance tests to quantify the robustness of measured network properties to uncertainties.
In the last years, recurrence plot based techniques have been intensely studied and received a steep progress. For example, a recurrence based approach was proposed for the study of coupling directions or delayed synchronisation, for the effective dynamical construction of a long time-series, or as a surrogate test for couplings – just to mention some of these new developments. Meanwhile, it was mathematically proven that a recurrence plot contains the dynamics of the underlying system, and that it is possible to reconstruct a phase space trajectory from the recurrence plot. Moreover, using a recurrence plot of a measured time-series from driven system, even the driving force can be reconstructed.
Meanwhile, another method for the analysis of complex systems, the complex network theory, has received increasing attention and popularity. Both techniques, recurrence plots and complex networks exhibit astonishing similarities, as both approaches are based on a binary square matrix, either representing recurrences or links. Therefore, it is not a surprise that both techniques come together and that approaches from complex network theory have found their way into the recurrence analysis.
The practical and interactive introduction in the MATLAB CRP Toolbox enlightens the potentials and applicability of the toolbox for the analysis of various problems in different scientific fields, in particular in cardiology, cognitive science, image analysis and palaeo-climatology. The participants of the workshop will be tutored and supervised in order to be able to solve own problems with the toolbox.
R. Donner, J. Donges, Y. Zou, N. Marwan, J. Kurths:
The complex network approach and recurrence quantification analysis,
3rd International Symposium on Recurrence Plots,
Montreal (Canada),
August 25, 2009,
Talk.
» Abstract
The possibility of characterising time series by means of complex networks has been proposed recently in different works. The recurrence matrix as derived from a time series is an ideal candidate for being interpreted as an adjacency matrix of a complex network. We discuss similarities and differences between recurrence quantification analysis and complex network theory. Measures of complex network theory applied on a recurrence matrix provide a new quantitative approach to recurrence analysis by quantification of different local and global topological features in the recurrence structure. We show how we can interpret these measures in terms of state space properties and why they bear new and complementary insights, not yet covered by the standard recurrence quantification analysis. Future directions related to specific practical questions of time series analysis are outlined.
S. Schinkel, N. Marwan, J. Kurths:
Confidence bounds of recurrence-based complexity measures,
3rd International Symposium on Recurrence Plots,
Montreal (Canada),
August 25, 2009,
Talk.
» Abstract
Recurrence quantification analysis (RQA) has become an established tool for data analysis in various research areas. The complexity measures the RQA provides have been useful in describing and analysing a broad range of data. The RQA is known to be rather robust to noise and nonstationarities. Yet, one key question in empirical research concerns the confidence bounds of measured data or any derived quantities. In this talk we suggest a method for estimating the confidence bounds of recurrence-based complexity measures. We will show that this method allows us to investigate EEG measurements obtained during cognitive tasks (ERPs) on the scale of single measurements.
Y. Zou, M. C. Romano, M. Thiel, N. Marwan, J. Kurths:
Extracting indirect coupling by means of probabilities of recurrence: revisited,,
3rd International Symposium on Recurrence Plots,
Montreal (Canada),
August 25, 2009,
Talk.
» Abstract
The identification of the coupling direction from time series taking place in a group of interacting components is an important challenge for many experimental studies. We propose a method to uncover the coupling configuration by means of conditional probabilities of recurrence, which was originally introduced to detect and quantify the weak coupling direction between two interacting systems. Here, we extend this approach to the case of multivariate time series, where the indirect interaction is present. We test our method for three Lorenz systems coupled via delays. Furthermore, some important issues about the implementation of this approach will be also discussed.
N. Marwan:
Modern nonlinear approaches for data analysis,
Course Global Change Management Studies, University of Applied Science Eberswalde,
Eberswalde (Germany),
June 8, 2009,
Lecture.
N. Marwan:
Recurrence plots for the analysis of complex systems,
Brainstorm meeting on Unconventional Energy Machine,
Kloster Bronbach (Germany),
April 23-25, 2009,
Talk invited.
Recurrence is a fundamental property of dynamical systems, which can be exploited to characterise the system's behaviour in phase space. A powerful tool for their visualisation and analysis is the recurrence plot. Methods basing on recurrence plots have been proven to be very successful especially in analysing short, noisy and nonstationary data, as they are typical in Earth sciences. Recurrence Plots (RPs) have found applications in such diverse fields as life sciences, astrophysics, earth sciences, meteorology, biochemistry, and finance, where they are used to provide measures of dynamical properties, complexity or dynamical transitions. Theoretical results show how closely RPs are linked to dynamical invariants like entropies and dimensions. Moreover, they are successful tools for synchronisation analysis and advanced surrogate tests.
J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
The backbone of the climate network,
EGU General Assembly,
Vienna (Austria),
April 20-24, 2009,
Poster.
» Abstract
Betweenness centrality reveals a rich internal structure in complex climate networks constructed from reanalysis and model surface air temperature data using the nonlinear mutual information. Our novel approach uncovers peculiar wave-like structures of high information flow (the backbone), that we relate to global surface ocean currents. This points to a major role of the oceanic surface circulation in coupling and stabilizing the global temperature field in the long term mean (140 years for the model run and 60 years for reanalysis data). The authors have ensured the robustness of these results by intensive significance testing on the level of time series analysis and complex network theory. It is found that using the linear Pearson correlation coefficient for climate network construction yields similar, but less pronounced backbone structures.
Y. Zou, N. Marwan, M. C. Romano, M. Thiel, J. Kurths:
Extracting indirect coupling by means of recurrences,
EGU General Assembly,
Vienna (Austria),
April 20-24, 2009,
Poster.
» Abstract
The identification of correct couplings from measured time series taking place in a group of interacting components is a non-trivial problem. This is also interesting for extracting the interacting topology of complex networks from real data sets, in particular with the driver-response relationships. We propose a method to uncover the coupling configuration by means of recurrence properties. The approach hinges on a generalization of conditional probability of recurrence, which was originally introduced to detect and quantify the weak coupling directionality between two interacting subsystems. Here, we extend this approach to the case of multivariate time series, where the indirect interaction is present. We test our method by considering three coupled Van der Pol oscillators contaminated with normal distributed noise. Furthermore, we extract the correct time delay information contained in the three coupled Lorenz systems. Our results confirm that the proposed method could be used to identify the indirectionality, which shows relevance for experimental time series analysis.
J. F. Donges, Y. Zou, N. Marwan, J. Kurths:
Statistical significance tests for spatially embedded complex networks,
EGU General Assembly,
Vienna (Austria),
April 20-24, 2009,
Poster.
» Abstract
The analysis of spatially embedded complex networks, i.e. networks with vertices embedded in a metric space, is of increasing interest in many fields of science. Examples are power grids in electrical engineering, the internet and world wide web in computer science or social networks in social science. In many cases, there is some degree of uncertainty about the network structure, e.g. edges might be missing in the network that exist in the system under study (the opposite may also be true). This is particularly true for networks constructed from multivariate data using the tools of time series analysis. Given this uncertainty, it is very important to evaluate the significance of measured network properties such as clustering coefficient, average path length, degree distribution or various vertex centrality sequences with respect to a given null hypothesis. Here we present different types of surrogates for spatially embedded networks, i.e. random networks with prescribed spatial constraints such as fixed edge distance distribution or a fixed average edge distance sequence, and show how to use them for testing the associated null hypotheses.We demonstrate the proposed significance tests for a global climate network constructed from coupled model surface air temperature data.
N. Malik, N. Marwan, J. Kurths:
Characteristics, patterns and synchronization of monsoonal precipitation over India,
EGU General Assembly,
Vienna (Austria),
April 20-24, 2009,
Poster.
» Abstract
We employ the methods of nonlinear time series analysis on a high resolution daily rainfall gridded data set from 1951 to 2004 for India to understand varied features and mechanisms of monsoonal precipitation over India. Based on measures like lagged cross-correlation, mutual information and interdependence we use a clustering algorithm to find regions having homogeneous variability of monsoonal precipitation. We further show that major rainfall events occurring in some of these regions in north India are lag synchronised with rainfall received in coastal regions and hence establishing that precipitation received in two distinct regions are coupled and interdependent.
J. Kurths, N. Marwan:
Synchronization and Recurrence: Are Nonlinear Approaches Useful in Geophysical Time Series Analysis?,
EGU General Assembly,
Vienna (Austria),
April 20-24, 2009,
Talk invited.
» Abstract
Various approaches in nonlinear time series analysis have enabled substantially new insights into complex processes in many fields ranging from lasers via electrochemistry to earth sciences and even economy. However, they are often basing on strong restrictions; their violation may lead to pitfalls and misinterpretations.
Here, we discuss two general concepts of nonlinear dynamics, synchronization and recurrence and discuss how to use them for data analysis. We show that corresponding methods for time series analysis can be applied even to rather short and somewhat non-stationary data.
Finally applications are presented to study dynamic teleconnections, such as El Nino – Monsoon interactions.
H. Schultz, J. F. Donges, N. Marwan, J. Kurths:
Global warming trend in climate networks,
EGU General Assembly,
Vienna (Austria),
April 20-24, 2009,
» Poster (PDF, 1.31M).
><2008
N. Marwan, S. Schinkel, M. Trauth, J. Kurths:
Significance for a recurrence based transition analysis,
International Workshop on Extreme Events – Theory, Observations, Modeling, and Prediction (EXEV 08),
Palma de Mallorca (Spain),
November 10-14, 2008,
Talk.
N. Marwan, S. Breitenbach:
Detection of abrupt climate change using recurrence plots,
Dynamics Days Berlin-Brandenburg,
Potsdam (Germany),
October 8-10, 2008,
Talk.
N. Marwan:
Cross recurrence plot toolbox: Recurrence plots for data analysis in geosciences,
Workshop on Data analysis and modeling in Earth sciences (DAMES),
Potsdam (Germany),
September 29-October 1, 2008,
Talk.
N. Malik, N. Marwan, J. Kurths:
Lag synchronization between precipitation data of different meteorological stations during Indian Monsoon,
Workshop on Data analysis and modeling in Earth sciences (DAMES),
Potsdam (Germany),
September 29-October 1, 2008,
Talk.
» Abstract
We propose that there exist a lag synchronization between the precipitation received in two different regions of India. We show that major rainfalls received during monsoon in some parts of Indo-Gangetic plains are lag synchronized with rainfall received in western coastal region of India. This phenomena could used for short range prediction of rainfall in these regions of north India during Monsoon months.
N. Marwan, S. Schinkel, J. Kurths:
A significance test for a recurrence based transition analysis,
NOLTA conference,
Budapest (Hungary),
September 7-12, 2008,
Talk invited.
» Abstract
The recurrence of states is a fundamental behaviour of dynamical systems. A modern technique of nonlinear data analysis, the recurrence plot, visualises and analyses the recurrence structure and allows us to detect transitions in the system's dynamics by using recurrence quantification analysis (RQA). In the last decade, the RQA has become popular in many scientific fields. However, a sufficient significance test was not yet developed.
We propose a statistical test for the RQA which is based on bootstrapping of characteristic small scale structures in the recurrence plot. Using this test we can present significance levels for the detected transitions and, hence, get a more reliable result. We demonstrate the new technique on marine dust records from the Atlantic which were used to infer climate changes in Africa for the last 4 Ma.
N. Marwan, S. Schinkel:
A statistical test for a recurrence based transition analysis of brain signals,
DGBMT-Workshop Biosignalverarbeitung,
Potsdam (Germany),
July 16-18, 2008,
» Poster (PDF, 1.14M).
» Abstract
The recurrence of states is a fundamental behaviour of dynamical systems. A modern technique of nonlinear data analysis, the recurrence plot, visualises and analyses the recurrence structure and allows us to detect transitions in the system's dynamics by using recurrence quantification analysis (RQA). In the last decade, the RQA has become popular in many scientific fields. However, a sufficient significance test was not yet developed. We propose a statistical test for the RQA which is based on bootstrapping of characteristic small scale structures in the recurrence plot. Using this test we can present confidence bounds for the detected transitions and, hence, get a more reliable result.
We apply this approach to EEG data obtained in a study of event-related potentials (ERP). We show that using the RQA it is possible to detect statistically significant transitions in the brain's dynamics reflecting the event-related activity.
S. Schinkel, N. Marwan, J. Kurth:
Symbol-based recurrence analysis of EEG data,
DGBMT-Workshop Biosignalverarbeitung,
Potsdam (Germany),
July 16-18, 2008,
Poster.
N. Marwan, S. Schinkel, J. Kurths, M. Trauth:
Significance for a recurrence based transition analysis,
EGU General Assembly,
Vienna (Austria),
April 14-18, 2008,
» Talk (MOV, 3.19M).
» Abstract
The recurrence of states is a fundamental behaviour of dynamical systems. A modern technique of nonlinear data analysis, the recurrence plot, visualises and analyses the recurrence structure and allows us to detect transitions in the system's dynamics by using recurrence quantification analysis (RQA). In the last decade, the RQA has become popular in many scientific fields. However, a sufficient significance test was not yet developed.
We propose a statistical test for the RQA which is based on bootstrapping of characteristic small scale structures in the recurrence plot. Using this test we can present significance levels for the detected transitions and, hence, get a more reliable result.
We demonstrate the new technique on marine dust records from the Atlantic which were used to infer climate changes in Africa for the last 4 Ma.
N. Marwan, J. Kurths, M. Trauth:
Detection of extreme events in palaeo-climate proxy data using recurrence plots,
EGU General Assembly,
Vienna (Austria),
April 14-18, 2008,
» Poster (PDF, 2.14M).
N. Marwan, P. Saparin, J. S. Thomsen, J. Kurths:
Measuring changes of 3D structures in high-resolution $\mu$CT images of trabecular bone,
Biosignals Conference 2008 (BIOSTEC 2008),
Funchal (Portugal),
Januar 28-31, 2008,
» Talk (PDF, 5.17M).
» Abstract
The appearances of pathological changes of bone can be various. Determination of apparent bone mineral density is commonly used for diagnosing bone pathological conditions. However, in the last years the structural changes of trabecular bone have received more attention because bone densitometry alone cannot explain all variation in bone strength. The rapid progress in high resolution 3D micro Computed Tomography ($\mu$CT) imaging facilitates the development of new 3D measures of complexity for assessing the spatial architecture of trabecular bone. We have developed a novel approach which is based on 3D complexity measures in order to quantify spatial geometrical properties of bone architecture. These measures evaluate different aspects of organization and complexity of trabecular bone, such as complexity of its surface, node complexity, or local surface curvature. In order to quantify the differences in the trabecular bone architecture at different stages of osteoporotic bone loss, the developed complexity measures were applied to 3D data sets acquired by $\mu$CT from human proximal tibiae and lumbar vertebrae. The results obtained by the complexity measures were compared with results provided by static histomorphometry. We have found clear relationships between the proposed measures and different aspects of bone architecture assessed by the histomorphometry.
N. Marwan:
Recurrence plots for the analysis of complex systems,
IITM Colloquium Indian Institute for Tropical Meteorology,
Pune (India),
January 18, 2008,
Talk.
N. Marwan:
Recurrence plots for the analysis of complex systems,
Hands-on research on complex systems,
Gandhinagar (India),
January 6-18, 2008,
» Lecture (MOV, 5.29M).
><2007
S. Breitenbach, B. Plessen, H. Oberhänsli, N. Marwan, D. Lund, J. Adkins, D. Günther, M. Fricker, G. H. Haug:
The Holocene Indian Summer Monsoon variability recorded in a stalagmite from NE India,
AGU Fall Meeting,
San Francisco (USA),
December 10–14, 2007,
Talk.
» Abstract
South Asian economies depend on the timely onset of the Indian Summer Monsoon (ISM), but understanding of the ISM variability is incomplete, due to lack of information on past ISM. Our stalagmite is the first well-dated climate record from the heart of the ISM region spanning the past 11,000 years. The speleothem was collected from Krem Umsynrang Cave, located 825 m above sea level in NE India. This region is influenced by the ISM, with more than 75% of annual rainfall falling during the monsoon season. The chronology of the stalagmite is based on 36 U/Th multi-collector ICP MS dates. Our data reveal profound changes in ISM rainfall and moisture balance. A strong increase of the ISM between 11.4 and 9.3 kyr BP is followed by a gradual decline over the course of the Holocene. This may be best explained by a strong coupling between ISM and the Intertropical Convergence Zone (ITCZ), with a stronger ISM during a more northerly position of the ITCZ. This long-term trend is punctuated by centennial to multi- to sub-decadal events of a weaker ISM. The most pronounced events occurred at 10.7, 8.5-8.1, 7.4, 4.4-4.0, 3.5, 1.4, 0.3 kyr BP. The δ13C record is interpreted to reflect centennial to decadal changes in the drip rate of the stalagmite. δ13C fractionation during periods of higher drip rates (i.e. times of longer residence time of percolating water) correspond with periods of a weaker ISM as inferred from our δ18O record. Our record shows in great detail periods of weaker ISM. They provide new insights on the sensitivity of terrestrial climate archives on the Indian subcontinent. Drought events recorded in our stalagmite correspond well with intervals of severe aridity known from other regions of the Asian monsoon. Moreover, our 11,000 year climate record shows that NE India experienced its driest conditions during the last three millennia.
N. Marwan, M. C. Romano, M. Thiel, J. Kurths:
Recurrence Plots for the Analysis of Complex Systems,
Final meeting DFG SPP 1114 on Mathematical methods for time series analysis and digital image processing,
Münzingen (Germany),
November 7-9, 2007,
Talk.
N. Marwan, S. Breitenbach:
Detection of climate transitions in Asia derived from speleothems,
3rd Physcon Conference,
Potsdam (Germany),
September 3-7, 2007,
Talk.
» Abstract
Speleothems offer archives of climatic variability in the past. We analyse isotope records of stalagmites from several caves at different locations in Asia: Oman, NW and NE India and China. These records are proxies for the monsoon rainfall variability at these locations and cover a time range between today and about 12 kyr. At these locations, the influences of the summer and winter monsoon are rather different.
Recurrence is a fundamental property of dynamical systems. A statistical analysis of recurrence plots can uncover hidden transitions in data series, which are not obvious using linear statistical methods.
The analyses of the recurrence structure of the different isotope records of the stalagmites reveals simultaneous transitions at same times, although the data series itself do not correlate. These transitions are also not obvious considering the data by eye. This result suggests that at certain times the entire monsoon system underwent changes which are visible in the isotope records despite the different reaction of the local rainfall on the summer and winter monsoon. Therefore, these changes were probably of global nature.
Speleothems offer archives of climatic variability in the past. We analyse isotope records of stalagmites from three caves at different locations in Asia: Oman, Northern India and China. These records are proxies for the rainfall variability at these locations and cover a time range between about 3 and 4 kyr. At these locations, the influences of the summer and winter monsoon are rather different. Recurrence is a fundamental property of dynamical systems. A statistical analysis of recurrence plots can uncover hidden transitions in data series, which are not obvious using linear statistical methods.
The analyses of the recurrence structure of the isotope records of the stalagmites reveals transitions at the same times, although the data series itself do not correlate. This result suggests that at these times the entire monsoon system underwent changes which are visible in the isotope records despite the different reaction of the local rainfall on the summer and winter monsoon.
G. Litak, A. Syta, N. Marwan, J. Kurths:
Dynamics of the cutting process by recurrence plots,
2nd International Recurrence Plot Workshop,
Siena (Italy),
September 9-12, 2007,
Poster.
» Abstract
The cutting process is a highly nonlinear phenomenon where dry friction is combined with possible contact loss and time delay effects. Unwanted and harmful vibrations may appear during cutting which may have a regular or chaotic nature depending on the system parameters. We have examined the cutting process by using a two degrees of freedom non-smooth model with a dry friction component. Using nonlinear time series embedding approach and recurrence plots analysis we identify the cutting forces that may lead to a chaotic motion.
N. Marwan, A. Junginger, M. Trauth, A. Bergner, Y. Garcin:
Recurrence in climate variability – A comparison of modern climate data from Nakuru, Kenya, with Early Holocene palaeo-climate records,
EGU General Assembly,
Vienna (Austria),
April 16-20, 2007,
» Poster (PDF, 12.33M).
» Abstract
Modern climate in tropical East Africa is mainly controlled by the Intertropical Convergence Zone (ITCZ) and the African-Asian summer monsoon, both being very sensitive to the El Niño/ Southern Oscillation (ENSO). Climate change and climatic variability are reflected in well preserved lacustrine sediments exposed in basins within the larger rift depression. In the past, ENSO related influences may have changed and led to fluctuations in the mean-annual precipitation and the intra- and inter-annual variations of rainfall. In order to study past precipitation variability, we compare the recurrence structure of a laminated lakesediment sequence from Lake Nakuru, Kenya, with the recurrence structure of modern regional rainfall data.
The recurrence of states is a fundamental behaviour of dynamical systems. A modern technique of nonlinear data analysis, the recurrence plot, visualises and analyses the recurrence structure and allows us to compare different systems using recurrence statistics. The studied lake sediment sequence was deposited immediately south of the equator during the East African humid period between 16 to 6 kyr BP. This interval was characterised by 25-30% more precipitation, and eventually a much stronger influence of the summer monsoon compared to the present. A comparison of the recurrence statistics of modern and past climate data help to understand the relative importance of the main drivers of the tropical climate and their behaviour in the course of global climate change.
N. Marwan, S. Breitenbach:
Detection of climate transitions in Asia derived from speleothems,
EGU General Assembly,
Vienna (Austria),
April 16-20, 2007,
» Poster (PDF, 4.35M).
» Abstract
Speleothems offer archives of climatic variability in the past. We analyse isotope records of stalagmites from three caves at different locations in Asia: Oman, Northern India and China. These records are proxies for the rainfall variability at these locations and cover a time range between about 3 and 4 kyr. At these locations, the influences of the summer and winter monsoon are rather different.
Recurrence is a fundamental property of dynamical systems. A statistical analysisof recurrence plots can uncover hidden transitions in data series, which are not obvious using linear statistical methods.
The analyses of the recurrence structure of the isotope records of the stalagmites reveals transitions at the same times, although the data series itself do not correlate. This result suggests that at these times the entire monsoon system underwent changes which are visible in the isotope records despite the different reaction of the local rainfall on the summer and winter monsoon.
N. Marwan, S. Breitenbach:
Can nonlinear data analysis help to understand climate changes in Asia during the Holocene?,
EGU General Assembly,
Vienna (Austria),
April 16-20, 2007,
» Poster (PDF, 5.22M).
» Abstract
Speleothems offer archives of climatic variability in the past. We analyse isotope records of stalagmites from several caves at rather different locations in Asia. These records are proxies for the rainfall variability at these locations and cover a time range between about 2 and 5 kyr. At these locations, the influences of the Intertropical Convergence Zone (ITCZ) and, hence, the summer and winter monsoon are rather different.
Recurrence is a fundamental property of dynamical systems. Recurrence plots are modern methods of nonlinear data analysis and allows us to study the recurrence behaviour in processes. A statistical analysis of recurrence plots can uncover hidden transitions in data series, which are not obvious using linear statistical methods.
The analyses of the recurrence structure of the isotope records of the stalagmites reveals transitions at the same times, although the data series themselves do not correlate. This result suggests that at these times the entire monsoon system underwent changes which are visible in the isotope records despite the different reaction of the local rainfall on the summer and winter monsoon.
S. Breitenbach, B. Plessen, N. Marwan, H. Oberhänsli, S. Prasad, B. S. Kotlia, D. Fernandez, J. Adkins, G. Haug:
North Atlantic cold events pushed ITCZ southward and weakened Indian summer Monsoon in northern India,
EGU General Assembly,
Vienna (Austria),
April 16-20, 2007,
Poster.
N. Marwan:
Recurrence plots for the analysis of complex systems,
Colloquium of the School of Physical Science, JNU,
New-Delhi (India),
March 10, 2007,
Talk.
><2006
N. Marwan, N. Wessel, S. Schinkel, P. Saparin:
Recurrence Plot basierte Biosignalverarbeitung,
DGBMT-Workshop Biosignalverarbeitung,
Potsdam (Germany),
July 13-14, 2006,
Talk.
» Abstract
In vielen biologischen Prozessen läßt sich die Wiederkehr von bestimmten Zuständen beobachten. Die Wiederkehr (engl: recurrence) ist eine typische Eigenschaft von komplexen dynamischen Systemen. Die Methode der Recurrence-Plots untersucht verschiedene Aspekte des Wiederkehrverhaltens auf der Basis von Zeitreihen. Die Quantifizierung von Recurrence-Plots erlaubt eine Untersuchung von Übergängen zwischen verschiedenen Regimes, die Typisierung von Prozessen und sogar das Auffinden von nichtlinearen Korrelationen oder Synchronisations-Phänomenen zwischen verschiedenen Systemen. Eine Generalisierung von Recurrence-Plots kann zur Analyse von wiederkehrenden Strukturen in räumlichen Daten (z. B. in Bildern) benutzt werden.
Die Möglichkeiten der Anwendung von Recurrence-Plots in der Biosignalverarbeitung werden anhand von Beispielen demonstriert. Die Quantifizierung von laminaren Zustäen durch Recurrence-Plots der Herzschlagvariabilität erlaubt dessen Differenzierung und potentielle Vorhersagbarkeit von ventrikulären Tachykardien. Neu entwickelte Ordnungsmuster-Recurrence-Plots werden für die Untersuchung von ereigniskorrelierten Potentialen (EEG-Messungen) verwendet und ermöglichen deren Nachweis bereits in Einzelversuchen. Die Ausdehnung von Recurrence-Plots auf räumliche Daten wird anhand von pQCT-Aufnahmen des trabekulären Knochens der proximalen Tibia demonstriert. Diese Methode zeigt einen deutlichen Zusammenhang zwischen der Komplexität der trabekulären Strukturen und des Stadiums von Osteoporose.
Das Spektrum der Beispiele demonstriert die Universalität der Recurrence-Plot-basierten Methoden in der Medizin. Diese Methoden haben jedoch auch schon Anwendung in vielen anderen wissenschaftlichen Disziplinen gefunden, wie in chemischen, Geo- und Ingenieurwissenschaften.
N. Marwan:
Hot Topics in the Recurrence Plot Developments with Illustrations and Applications,
CSC Seminar, University of Siena,
Siena (Italy),
June 15, 2006,
Talk.
N. Marwan:
Höhlenforschung im Alpinen Karst,
Lange Nacht der Wissenschaften,
Dresden (Germany),
June 2006,
Talk.
><2005
N. Marwan, P. Saparin, J. Kurths:
Generalisation of recurrence plot analysis for spatial data,
NOLTA conference,
Bruges (Belgium),
October 18-21, 2005,
» Talk (PDF, 4.25M).
» Abstract
Classically introduced recurrence plots (RPs) can only be applied to one-dimensional data like phase space vectors and time series. We develop an extended and generalized RP approach which enables to analyze spatial (higher-dimensional) data regarding recurrent structures. Resulting RPs have higher dimensions (e.g. 4). Hence, the measures used to evaluate classic RPs are extended to assess higher-dimensional recurrence plots. Developed approach is applied to assess bone structure from 2D pQCT images of human proximal tibia.
N. Marwan, P. Saparin, J. S. Thomsen, J. Kurths:
A new quantitative approach for measuring changes of 3D structures in trabecular bone,
3rd European Congress "Achievements in Space Medicine into Healthcare Practice and Industry",
Berlin (Germany),
September 28-30, 2005,
» Talk (PDF, 7.09M).
» Abstract
Changes in trabecular bone composition during the development of osteoporosis were used as a model of bone loss under microgravity conditions during long-term space flights. Structural changes of trabecular bone have received more attention in the last years as bone densitometry alone cannot explain all variation in bone strength. We have previously successfully developed and applied a set of measures of complexity, which quantify the trabecular bone architecture from 2D Computed Tomography (CT) images. The rapid progress in high resolution 3D microCT imaging facilitates the development of new 3D measures of complexity, which should be able to assess the spatial architecture of trabecular bone.
We have developed a novel approach which is based on 3D complexity measures in order to quantify spatial geometrical properties (like local ratio of volume/surface of bone, marching cubes distribution, or local bone surface curvatures and their distributions). These measures evaluate different aspects of organization and complexity of trabecular bone spatial architecture, such as complexity of its surface, node complexity, or trabecular bone surface curvature.
In order to quantify the differences in the trabecular bone architecture at different stages of osteoporosis, the developed complexity measures were applied to 3D data sets acquired by micro-CT from human proximal tibiae and lumbar vertebrae. The results obtained by the complexity measures were compared with results provided by static histomorphometry and with compression bone strength of the vertebrae obtained from biomechanical testing. We have found clear relationships between the proposed measures and different aspects of bone architecture assessed by the histomorphometry (e.g. complexity of bone surface). Using the newly introduced measures, we were able to find significant differences in 3D bone architecture at various stages of osteoporosis. Therefore, we conclude that this approach designed to quantify bone loss in microgravity can be directly applied for diagnostics of pathological changes in bone structure in patients on Earth as well as to the evaluation of medical treatment results.
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the phase-space trajectory. This provides us a better understanding of the structures occuring in recurrence plots. The relationship between the time-scales and line structures are of practical importance in cross recurrence plots. Using this relationship within cross recurrence plots, the time-scales of differently sampled or time-transformed measurements can be adjusted. An application to geophysical measurements illustrates the capability of this method for the adjustment of time-scales in different measurements.
M. H. Trauth, N. Marwan, J. Kurths:
Comparing modern and Pleistocene ENSO-like influences in NW Argentina using cross recurrence plot analysis,
1st International Recurrence Plot Workshop,
Potsdam (Germany),
September 22-24, 2005,
Talk.
» Abstract
Climatic changes are of major importance in landslide generation in the Argentine Andes. Increased humidity as a potential influential factor was inferred from the temporal clustering of landslide deposits during a period of significantly wetter climate, 30,000 years ago. A change in seasonality was tested by comparing past (inferred from annual-layered lake deposits, 30,000 years old) and modern (present-day observations) precipitation changes. Quantitative analysis of cross recurrence plots has been developed to compare the influence of the El Niño/Southern Oscillation (ENSO) on present and past rainfall variations. This analysis has revealed a stronger influence of NE trades in the location of landslide deposits in the intra-andean basin and valleys, what caused a higher contrast between summer and winter rainfall and an increasing of precipitation in La Niña years. This is believed to reduce thresholds for landslide generation in the arid to semiarid intra-andean basins and valleys.
N. Marwan, P. Saparin, J. Kurths:
Recurrence plot extension for 2D spatial data,
1st International Recurrence Plot Workshop,
Potsdam (Germany),
September 22-24, 2005,
Talk.
» Abstract
Classically introduced recurrence plots (RPs) can only be applied to one-dimensional data like phase space vectors and time series. We develop an extended and generalized RP approach which enables us to analyze spatial (higher-dimensional) data regarding recurrent structures. Resulting RPs have higher dimensions (e.g. 4). Hence, the measures used to evaluate classic RPs are extended to assess higher-dimensional recurrence plots. Developed approach is applied to assess bone structure from 2D pQCT images of human proximal tibia.
Recent applications of recurrence quantification analysis on EEG data have emphasized the potential of investigation event related potentials on a single trial base. With an innovative modification of recurrence plots, based on rank order structures in the data, the recurrence quantification analysis can be further improved. We present new results using order pattern recurrence plots applied on data of event related potentials and the found improvement in comparison with the common recurrence plots.
The alignment of the time scales of geological data series to a geological reference time series is of major interest in many investigations, e.g., geophysical borehole data should be correlated to a given data series whose time scale is known in order to achieve an age-depth function or the sedimentation rate for the borehole data. Instead of using the "wiggle matching" by eye, we present the application of cross recurrence plots for such tasks. Using this method, the synchronization and time-rescaling of geological data to a given time scale is much easier, objective and faster than by hand. The application of this method to the rock magnetic data of two different sediment cores from the Makarov Basin (central Arctic Ocean) adjusts them to each other, and makes them comparable. This procedure was perfomed using the CRP toolbox.
N. Wessel, N. Marwan, A. Schirdewan, J. Kurths:
Recurrence plot analysis of heart rate variability before the onset of ventricular tachycardia,
1st International Recurrence Plot Workshop,
Potsdam (Germany),
September 22-24, 2005,
Talk.
» Abstract
The knowledge of transitions between regular, laminar or chaotic behaviour is essential to understand the underlying mechanisms behind complex systems. While several linear approaches are often insufficient to describe such processes, there are several nonlinear methods which however require rather long time observations. To overcome these difficulties, we propose measures of complexity based on vertical structures in recurrence plots and apply them to the logistic map as well as to heart rate variability data. For the logistic map these measures enable us not only to detect transitions between chaotic and periodic states, but also to identify laminar states, i.e. chaos-chaos transitions. The traditional recurrence quantification analysis fails to detect the latter transitions. Applying our new measures to the heart rate variability data, we are able to detect and quantify the laminar phases before a life-threatening cardiac arrhythmia thereby facilitating a prediction of such an event. The maximal vertical line length using an embedding dimension of 6 and a radius of 110 ms is 283.7±190.4 before ventricular tachycardia vs. 179.5±134.1 at a control time ($p<0.01$). A comparison to the previous applied methods from symbolic dynamics and the finite-time growths rates is given. Our findings could be of importance for the therapy of malignant cardiac arrhythmias.
N. Marwan, N. R. Nowaczyk, M. Thiel, J. Kurths:
Re-alignment of geological time series using the Cross Recurrence Plot Toolbox,
13th NDES meeting,
Potsdam (Germany),
September 18-22, 2005,
» Poster (PDF, 453.11K).
» Abstract
The alignment of the time scales of geological data series to a geological reference time series is of major interest in many investigations, e. g., geophysical borehole data should be correlated to a given data series whose time scale is known in order to achieve an age-depth function or the sedimentation rate for the borehole data. Instead of using the "wiggle matching" by eye, we present the application of cross recurrence plots for such tasks. Using this method, the synchronization and time-rescaling of geological data to a given time scale is much easier, objective and faster than by hand. The application of this method to the rock magnetic data of two different sediment cores from the Makarov Basin (central Arctic Ocean) adjusts them to each other, so that they are comparable. This procedure was perfomed using the CRP toolbox, available from http://tocsy.agnld.uni-potsdam.de.
An introduction in the application of the CRP toolbox will be presented at the recurrence plot workshop after the NDES meeting.
N. Marwan, P. Saparin, J. S. Thomsen, J. Kurths:
An innovative approach for the assessment of 3D structures in trabecular bone,,
13th NDES meeting,
Potsdam (Germany),
September 18-22, 2005,
» Poster (PDF, 10.14M).
» Abstract
Changes in trabecular bone composition during the development of osteoporosis are used as a model of bone loss in microgravity. The structural changes of trabecular bone have received more attention in the last years as bone densitometry alone cannot explain all variation in bone strength. We have previously successfully developed and applied a set of measures of complexity, which quantify the trabecular bone architecture using 2D Computed Tomography (CT) images. The rapid progress in high resolution 3D microCT imaging facilitates the development of new 3D measures of complexity, which should be able to assess the spatial architecture of trabecular bone.
We have developed a novel approach which is based on 3D complexity measures in order to quantify the distribution of 3D geometrical properties (like local ratio of volume/surface of bone, marching cubes distribution, or local bone surface curvatures and their distributions). These measures evaluate different aspects of organization and complexity of trabecular bone architecture, such as surface complexity, node complexity, or surface curvature.
In order to quantify the deterioration of the trabecular bone architecture due to different osteoporotic stages, the developed complexity measures were applied to 3D data sets of human proximal tibiae and lumbar vertebrae acquired by microCT. We have found clear relationships between the proposed measures and different aspects of bone architecture (e.g. complexity of bone surface). The results obtained by the complexity measures were compared with the outcome of a static histomorphometric analysis. Using the newly introduced measures, we were able to find significant changes in 3D bone architecture at various stages of osteoporosis. Therefore, we propose that these measures of complexity will be able to successfully describe the deterioration of the trabecular bone network that takes place under microgravity conditions as well.
N. Marwan, P. Saparin, J. S. Thomsen, J. Kurths:
An innovative approach for the assessment of 3D structures in trabecular bone,
Joint Life Science Conference "Life in Space for Life on Earth",
Cologne (Germany),
June 26-30, 2005,
» Poster (PDF, 10.14M).
» Abstract
Changes in trabecular bone composition during the development of osteoporosis are used as a model of bone loss in microgravity. The structural changes of trabecular bone have received more attention in the last years as bone densitometry alone cannot explain all variation in bone strength. We have previously successfully developed and applied a set of measures of complexity, which quantify the trabecular bone architecture using 2D Computed Tomography (CT) images. The rapid progress in high resolution 3D microCT imaging facilitates the development of new 3D measures of complexity, which should be able to assess the spatial architecture of trabecular bone.
We have developed a novel approach which is based on 3D complexity measures in order to quantify the distribution of 3D geometrical properties (like local ratio of volume/surface of bone, marching cubes distribution, or local bone surface curvatures and their distributions). These measures evaluate different aspects of organization and complexity of trabecular bone architecture, such as surface complexity, node complexity, or surface curvature.
In order to quantify the deterioration of the trabecular bone architecture due to different osteoporotic stages, the developed complexity measures were applied to 3D data sets of human proximal tibiae and lumbar vertebrae acquired by microCT. We have found clear relationships between the proposed measures and different aspects of bone architecture (e.g. complexity of bone surface). The results obtained by the complexity measures were compared with the outcome of a static histomorphometric analysis. Using the newly introduced measures, we were able to find significant changes in 3D bone architecture at various stages of osteoporosis. Therefore, we propose that these measures of complexity will be able to successfully describe the deterioration of the trabecular bone network that takes place under microgravity conditions as well.
N. Marwan, A. Groth:
Improved recurrence quantification analysis for the investigation of ERP data,
Tandem Workshop on Advanced Methods of Electrophysiological Signal Analysis and Symbol Grounding – Dynamical Systems Approaches to Language,
Potsdam (Germany),
March 14–17, 2005,
Poster.
» Abstract
Recent applications of recurrence quantification analysis on EEG data have emphasized the potential of investigation event related potentials on a single trial base. With an innovative modification of recurrence plots, based on rank order structures in the data, the recurrence quantification analysis can be further improved. We present new results using order pattern recurrence plots applied on data of event related potentials and the found improvement in comparison with the common recurrence plots.
><2004
N. Marwan:
Das Karstgebiet des Boljshoj Thac im Nordkaukasus,
Karstrunde der Universität Tübingen,
Tübingen (Germany),
November 24, 2004,
» Talk invited (PDF, 8.27M).
N. Marwan, P. Saparin, W. Gowin, J. Kurths:
3D measures of complexity for the assessment of complex trabecular bone structures,
2nd Meeting Complexity in the Living,
Rome (Italy),
September 28, 2004,
» Talk (PDF, 744.30K).
» Abstract
Structural changes in trabecular bone received more attention in the last years as bone densitometry alone cannot explain all reasons for the variation in strength of bone. Measures of complexity defined for 2D Computed Tomography (CT) images were successfully developed to quantify the changes in bone architecture. Recently available high-resolution 3D data from micro-CT challenge the development of new 3D measures of complexity, which should be able to assess structural changes in spatial architecture of bone.
We develop new 3D complexity measures by using spatial correlation and distribution of 3D geometrical properties. The Moran's Index was introduced for measuring the two-dimensional spatial autocorrelation of populations in an eco-system, but was successfully applied to 2D image analysis. We extend this measure onto 3D and apply it to quantify spatial bone images acquired by micro-CT. The second proposed measure, the Shape Index, uses the relationship between the ratio of volume/surface and the corresponding geometrical shape.
To test these measures, we use specially developed artificial bone models where the direction and the amount of architectural changes can be controlled. Our experiments confirm the stability and sensitivity of the proposed measures of complexity. Finally, the developed structural measures are applied to quantify the changes in 3D datasets of human proximal tibia bone biopsies acquired by micro-CT. We find significant changes in 3D bone architecture (spatial correlation, complexity of the Shape Index distribution) at various stages of osteoporosis.
N. Marwan, P. Saparin, W. Gowin, J. Kurths:
On the way to new 3D measures of complexity for bone assessment,
2nd Meeting Complexity in the Living,
Rome (Italy),
September 28, 2004,
» Poster (PDF, 677.82K).
» Abstract
Structural changes in trabecular bone are more important for the strength of the bone than bone mineral density. Measures of complexity defined for 2D bone images are successfully used for the study of changes in bone structure. However, these measures cannot be easily adopted to 3D images.
New measures of complexity for 3D bone images are developed using approaches of recurrence plot analysis, spatial auto-correlation (Moran Index) and fractal measures (lacunarity). The investigation of these new measures of complexity using artificial models under controlled structural changes confirmes their suitability as measures for structural changes. Their application to 3D bone images reveals significant changes in the bone structure due to various stages of osteoporosis.
N. Marwan, P. Saparin, W. Gowin, J. Kurths:
On the way to new 3D measures of complexity for bone assessment,
8th Experimental Chaos Conference,
Florence (Italy),
June 14–17, 2004,
» Poster (PDF, 677.82K).
» Abstract
Structural changes in trabecular bone are more important for the strength of the bone than bone mineral density. Measures of complexity defined for 2D bone images are successfully used for the study of changes in bone structure. However, these measures cannot be easily adopted to 3D images.
New measures of complexity for 3D bone images are developed using approaches of recurrence plot analysis, spatial auto-correlation (Moran Index) and fractal measures (lacunarity). The investigation of these new measures of complexity using artificial models under controlled structural changes confirmes their suitability as measures for structural changes. Their application to 3D bone images reveals significant changes in the bone structure due to various stages of osteoporosis.
N. Marwan, J. Kurths:
Geometric structures in recurrence plots,
EGU General Assembly,
Nice (France),
April 25–30, 2004,
» Poster (PDF, 134.36K).
N. Marwan:
Independent Component Analysis (ICA) und ihre Möglichkeiten in den Geowissenschaften,
Kolloquium of Deptartment of Geophysics, University of Kiel,
Kiel (Germany),
February 2004,
Talk.
><2003
N. Marwan, J. Kurths, U. Schwarz:
Independent component analysis (ICA) of sedimentary rock magnetic data,,
28th General Assembly of EGS,
Nice (France),
April 7–11, 2003,
» Poster (PDF, 1.59M).
» Abstract
Rock-magnetic measurements contain a mixture of signals of the regional palaeo climate and the palaeo Earth' magnetic field. The Earth' magnetic field, eg. the palaeo field intensity, is of special interest. However, it is not easy to separate. Methods which can decomposite the mixed signal could be suitable for our purpose. We focus on the Independent Component Analysis (ICA) and apply them on the rock-magnetic data of three cores gained from sediments of two lakes in Italia. With this method we obtain independent components, which should contain a clear climate signal and a signal which corresponds to the intensity of the Earth' magnetic field. This way the climate component can be evaluated by comparing with global climate proxy data (e.g. Δ18O). Unfortunately the signal of the Earth magnetic field can not be evaluated.
N. Marwan, U. Schwarz, J. Kurths:
The Earth' magnetic field in the past 100 kyr (based on ICA),
28th General Assembly of EGS,
Nice (France),
April 7–11, 2003,
» Poster (PDF, 339.50K).
» Abstract
Rock-magnetic and palaeo-magnetic data from sediments of two Italian lakes provide a reconstruction of the Earth' magnetic field in the last 100 kyr. Since the measurements contain also the climate signal, we apply the Independent Component Analysis in order to extract the signal of the Earth' magnetic field.
N. Marwan:
Independent component analysis of rock magnetic measurements,
PhD Day AGNLD, University of Potsdam,
Potsdam (Germany),
March, 2003,
» Talk (PDF, 2.39M).
N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths:
Recurrence plot based analysis of heart rate variability before the onset of ventricular tachycardia,
…,
,
January, 2003,
» Poster (PDF, 92.67K).
><2002
N. Marwan, N. R. Nowaczyk, M. Thiel:
Cross recurrence plot based rescaling of geological time series,
27th General Assembly of EGS,
Nice (France),
April 22–26, 2002,
» Poster (PDF, 123.55K).
» Abstract
The adjustment of the time scales of geological data series to a geological reference time series is of major interest in many investigations, e. g., geophysical borehole data should be correlated to a given data series whose time scale is known in order to achieve an age-depth function or the sedimentation rate for the borehole data. Instead of using the `wiggle matching' by eye, we present the application of cross recurrence plots for such tasks. Using this method, the synchronization and time-rescaling of geological data to a given time scale is much easier, objective and faster than by hand. The application of this method to the rock magnetic data of two different sediment cores from the Makarov Basin (central Arctic Ocean) adjusts them to each other, so that they are comparable.
N. Marwan, M. C. Romano, M. Thiel, J. Kurths:
Significance of complexity measures based on cross recurrence plots,
27th General Assembly of EGS,
Nice (France),
April 22–26, 2002,
» Poster (PDF, 90.59K).
» Abstract
Cross recurrence plots (CRPs) can become a useful tool for studying similarities between the dynamics of natural systems. Complexity measures based on geometrical structures in CRPs enable us to assess these similarities. However, an important point is the relevance of these measures. A first approach of a significance test is based on a surrogate data test. The results are compared with the theoretical distributions of the CRP complexity measures.
><2001
N. Marwan, A. Meinke, P. beim Graben:
Recurrence plots – Exemplary application to ERP data,
Workshop on Analyzing and Modelling Event-Related Brain Potentials – Cognitive and Neural Approaches,
Potsdam (Germany),
November 2001,
» Poster (PDF, 532.74K).
N. Marwan, N. Nowaczyk, J. Kurths, M. Thiel:
Cross recurrence plot based rescaling of geological time series,
26th General Assembly of EGS,
Nice (France),
March 25–30, 2001,
» Talk (PDF, 436.25K).
» Abstract
The rescaling of geological data series to a geological reference time series is of major interest in many investigations. For example, geophysical borehole data should be correlated to a given data series whose time scale is known in order to achieve an age-depth function or the sedimentation rate for the borehole data. Usually this synchronization is performed visually and by hand. Instead of using this 'wiggle matching' by eye, we present the application of cross recurrence plots for such tasks. Using this method, the synchronization and rescaling of geological data to a given time scale is much easier and faster than by hand.
N. Marwan, M. Trauth, U. Schwarz, J. Kurths, M. R. Strecker:
El Niño impact on lake deposits in NW Argentina 30 000 14C years ago,
26th General Assembly of EGS,
Nice (France),
March 25–30, 2001,
» Poster (PDF, 162.23K).
» Abstract
Lake deposits at location of El Paso (Santa Maria Basin, NW Argentina) and an age of 30,000 14C years show a characteristic colouration structure. Because of terrific geological conditions one can use the red colour intensity of these varved sediments as a precipitation time series and for analysis of the climate conditions 30,000 14C years ago. We have investigated this palaeo-precipitation with the method of cross recurrence plots in order to find the impact of the El Niño on the weather at this area in the past. The quantitative analysis of the cross recurrence plots reveals a significant influence of ENSO on the palaeo-precipitation, which obtains the impact of northeasterly trade winds in the past.
><2000
H. Fuchs, J. Kurths, N. Marwan, J. F. W. Negendank, K.-H. Rädler, M. Rheinhardt, U. Schwarz, N. Seehafer:
Geomagnetic Variations – Spatio-Temporal Variations, Processes and Impacts on the System EarthENSO Impact on Landslide Generation in Northwestern Argentina,
Europa 2000 im Zeichen der Physik, University of Potsdam,
Potsdam (Germany),
May 5, 2000,
» Poster (PDF, 0.00P).
» Abstract
The aim of this project is to apply and develop modern techniques of nonlinear data analysis to study complex dy-namical relationships between the variations of the Earth's magnetic field and of the climate during the last 100,000 years. We mainly intend to study phase stability and nonlinear correlations of these multivariate data based on new approaches of synchronization analysis and maximal correlations. Problems of special interests are to test for a possible phase delay between climate signals and the relative palaeointensity, to study the influence of long-term variations, especially in the sub-Milankovitch range, and to analyse excursions of relative palaeointensity in detail. The nonlinear analysis of sediment data will be mainly ba-sed on the sediment investigations performed in the group of Prof. Negendank (Geo For-schungs Zentrum Potsdam) and in the group of Prof. Bleil (University of Bremen). We will also build up a toolbox of data analysis techniques including modern as well as standard methods; it will be avail-able for other projects in this special research programme.
The variations of the geomagnetic main field such as drifts, excursions or reversals reflect the complex nature of the motions in the Earth's core. The observed features of these variations should be understood on the basis of sufficiently detailed simulations of the dynamo process in the Earth's core, which consists in very complex interactions of the magnetic field with fluid motions caused by thermal or other instabilities. Our project aims to study the time behavior of the geodynamo on the simpler level of mean-field dynamo models. However, a new mean-field concept is used, with mean fields defined by filtering of the multipole spectra of the original fields. In our models patterns of the convective motions are used originating from simulations under conditions which are realistic for the situation to be assumed in the Earth's core. The main result we expect from the proposed work is a contribution to understanding the time variations of the geomagnetic field and their connection with the fluid motions in the Earth's core.
N. Marwan, M. Trauth, J. Kurths, U. Schwarz:
ENSO Impact on Landslide Generation in Northwestern Argentina,
25th General Assembly of EGS,
Nice (France),
April 24–29, 2000,,
Talk.
» Abstract
Climatic changes are of major importance in landslide generation in the Argentine Andes. Increased humidity as a potential influential factor was inferred from the temporal clustering of landslide deposits during a period of significantly wetter climate, 30,000 years ago. A change in seasonality was tested by comparing past (inferred from annual-layered lake deposits, 30,000 years old) and modern (present-day observations) precipitation changes. Quantitative analysis of cross recurrence plots were developed to compare the influence of the El Niño/Southern Oscillation (ENSO) on present and past rainfall variations. This analysis has shown the stronger influence of NE trades in the location of landslide deposits in the intra-andean basin and valleys, what caused a higher contrast between summer and winter rainfall and an increasing of precipitation in La Niña years. This is believed to reduce thresholds for landslide generation in the arid to semiarid intra-andean basins and valleys.
N. Marwan, M. H. Trauth, J. Kurths, U. Schwarz:
Climate dynamics of varved Pleistocene lake sediments in NW Argentina,
24th General Assembly of EGS,
Den Haag (The Netherlands),
April 19–21, 1999,
Talk.
» Abstract
Climatic changes are of major importance in landslide generation in the Argentine Andes. Increased humidity as a potential influential factor was inferred from the temporal clustering of landslide deposits during a period of significantly wetter climate, 30,000 years ago. A change in seasonality was tested by comparing past (inferred from annual-layered lake deposits, 30,000 years old) and modern (present-day observations) precipitation changes. Nonlinear time-series analyses were used to compared the influence of two major climate oscillator, the El Niño/Southern Oscillation (ENSO) and the Atlantic Sea-Surface Temperature Dipole (ASSTD) on present and past rainfall variations. This comparison reveals significant cyclicities of 3 to 4 years (ENSO) and about 12 years (ASSTD) in precipitation. However, in contrast to the ASSTD influence, the ENSO influence seems to be different today and in the past in the sense of increasing or decreasing rainfall In addition to increased humidity, this change could be important in landslide generation 30,000 years ago.