1. The European Physical Journal — Special Topics, 232(1), 2023: Trends in Recurrence Analysis of Dynamical Systems
2. Quaternary Science Reviews, 2022: Special issue on Time Series Analysis for Earth, Climate and Life Interactions
3. Chaos, 28(8), 2018: Focus issue on Recurrence quantification analysis for understanding complex systems
4. C. L. Webber, Jr., C. Ioana, N. Marwan (ed.): Springer Proceedings in Physics: Recurrence Plots and Their Quantifications: Expanding Horizons, ISBN 978-3-319-29921-1, Springer International Publishing, Cham, 2016
5. C. L. Webber, Jr. and N. Marwan (ed.): Understanding Complex Systems: Recurrence Quantification Analysis — Theory and Best Practices, ISBN 978-3-319-07154-1, Springer International Publishing, Cham, 2015
6. N. Marwan, M. Riley, A. Giuliani, C. L. Webber, Jr. (ed.): Springer Proceedings in Mathematics & Statistics: Translational Recurrences — From Mathematical Theory to Real-World Applications, ISBN 978-3-319-09530-1, Springer International Publishing, Cham, 2014
7. International Journal of Bifurcation and Chaos, 21(4), 2011: Recurrence Plots at the Crossroad Between Theory and Application
8. The European Physical Journal — Special Topics, 174(1), 2009: Understanding the Earth as a Complex System
9. The European Physical Journal — Special Topics, 164(1), 2008: 20 Years of Recurrence Plots: Perspectives for a Multi-purpose Tool of Nonlinear Data Analysis
10. Bodenlos – Forschung im alpinen Karst, since 1997
11. Spektakel – das völlig abgehangene Blatt zum Kurs Einseiltechnik am USZ Dresden, No. 1–3, 1997/ 1998

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><2019

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   ozturk2019

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.

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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.

G. Chopra, V. R. Unni, P. Venkateshan, S. M. Vallejo-Bernal, N. Marwan, J. Kurths, R. I. Sujith: Classification of Tropics Based on the Spatio-Temporal Dynamics of the Intertropical Convergence Zone from a Complex Networks Perspective, American Meteorological Society’s 37th Conference on Climate Variability and Change/ 104th Annual Meeting of the American Meteorological Society, Baltimore (USA), Jan 30, 2024, Talk. » Abstract

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.

N. Marwan: New Time-series Analysis Concepts for Analysing Event Data, Paleoclimate research on the Telegrafenberg campus and within the Geo.X network, PIK Potsdam, Potsdam (Germany), Jan 29, 2024, Talk. » Abstract

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.

M. Mannone, N. Marwan, A. Chella, V. Seidita, A. Giacometti, P. Fazio: Entangled Gondolas. Design of Multi-Layer Networks of Quantum-Driven Robotic Swarms, XVII International Workshop on Artificial Life and Evolutionary Computation (WIVACE 2023), Venice (Italy), Sep 6, 2023, Talk. » Abstract

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.

N. Marwan, T. Braun: Power spectrum estimation for extreme events data, 10th International Congress on Industrial and Applied Mathematics (ICIAM), Tokyo (Japan), Aug 23, 2023, » Talk (PDF, 5.27M) . » 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).

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.

N. Marwan, K. H. Kraemer: Recurrences of movement, Workshop on Biomarkers arising from nonlinear analysis of movement variability, Zurich (Switzerland), July 5, 2023, Lecture and workshop. » Abstract

Hands-on workshop on recurrence analysis.

N. Marwan: Recurrence analysis for complex systems, Workshop on Biomarkers arising from nonlinear analysis of movement variability, Zurich (Switzerland), July 5, 2023, Talk invited. » Abstract

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.

J. Zhang, J. Klose, M. Sierralta, S. Tsukamoto, D. Scholz, N. Marwan, S. Breitenbach: Isothermal thermoluminescence (ITL) dating of a speleothem from Bleßberg Cave, 17th International Luminescence and Electron Spin Resonance Dating conference (LED2023), Copenhagen (Denmark), Jun 29, 2023, Talk. » Abstract

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.

N. Marwan, T. Braun: Power Spectrum Estimation for (Extreme) Events Data, EGU General Assembly, Vienna (Austria), Apr 25, 2023, DOI:10.5194/egusphere-egu23-7730, » Talk (PDF, 6.39M) . » 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. 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).

S. Gupta, Z. Su, A. Banerjee, N. Boers, N. Marwan, L. Magnusson, C. Lopez, E. Hernandez-Garcia, F. Pappenberger, J. Kurths: Spatial synchronization patterns of extreme rainfall and convection in the Asian Summer Monsoon region, Conference on Nonlinear Data Analysis and Modeling: Advances, Applications, Perspectives, PIK Potsdam, Potsdam (Germany), Mar 17, 2023, Poster. » 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. The impact of El Nino-Southern Oscillation on the convective sources of the two monsoon subsystems, and thus their interannual variability is investigated.

M. Gelbrecht, K. H. Krämer, N. Marwan: TreeEmbedding: Optimal state space reconstruction via Monte Carlo decision tree search, Conference on Nonlinear Data Analysis and Modeling: Advances, Applications, Perspectives, PIK Potsdam, Potsdam (Germany), Mar 17, 2023, Poster. » Abstract

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.

S. M. Vallejo-Bernal, T. Braun, N. Marwan, J. Kurths: Synchronized heavy rainfall events in Europe: the role of atmospheric rivers, Conference on Nonlinear Data Analysis and Modeling: Advances, Applications, Perspectives, PIK Potsdam, Potsdam (Germany), Mar 17, 2023, Poster. » Abstract

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.

T. Braun, S. M. Vallejo-Bernal, D. Traxl, N. Marwan, J. Kurths: A spatio-temporal analysis of global atmospheric rivers, Conference on Nonlinear Data Analysis and Modeling: Advances, Applications, Perspectives, PIK Potsdam, Potsdam (Germany), Mar 17, 2023, Poster. » Abstract

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.

T. Haselhoff, T. Braun, N. Marwan, S. Moebus: Complex networks for the urban acoustic environment, Conference on Nonlinear Data Analysis and Modeling: Advances, Applications, Perspectives, PIK Potsdam, Potsdam (Germany), Mar 17, 2023, Poster. » Abstract

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.

J. Wassmer, B. Merz, N. Marwan: Resilience of emergency infrastructure networks after flooding events, Conference on Nonlinear Data Analysis and Modeling: Advances, Applications, Perspectives, PIK Potsdam, Potsdam (Germany), Mar 17, 2023, Poster. » 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.

N. Antary, N. Marwan: Interpolation effects an RQA measures, Conference on Nonlinear Data Analysis and Modeling: Advances, Applications, Perspectives, PIK Potsdam, Potsdam (Germany), Mar 17, 2023, Poster. » Abstract

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.

M. R. Sales, M. Mugnaine, J. D. Szezech Jr., R. L. Viana, I. L. Caldas, N. Marwan, J. Kurths: Characterizing stickiness using recurrence time entropy, Conference on Nonlinear Data Analysis and Modeling: Advances, Applications, Perspectives, PIK Potsdam, Potsdam (Germany), Mar 17, 2023, Poster. » Abstract

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.

C. Özdes, D. Eroglu, N. Marwan, T. Braun: Multi-stable synchronization patterns and switching dynamics of paleoclimate networks, Conference on Nonlinear Data Analysis and Modeling: Advances, Applications, Perspectives, PIK Potsdam, Potsdam (Germany), Mar 17, 2023, Talk. » Abstract

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.

N. Marwan, T. Braun, K. H. Kraemer, A. Banerjee, D. Eroglu: Recurrence plots for analysing extreme events data, Conference on Nonlinear Data Analysis and Modeling: Advances, Applications, Perspectives, PIK Potsdam, Potsdam (Germany), Mar 17, 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.

><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.

N. Marwan: Ways to Quantitative Recurrence Plot Analysis, Complexity Lab Seminar, Rochester Institute of Technology, Rochester (US), Nov 15, 2022, Lecture. » Abstract

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.

N. Marwan: Investigating palaeoclimate conditions with nonlinear time series analysis, Colloquium on Complex and Biological Systems, University of Potsdam, Potsdam (Germany), Jun 24, 2022, Talk. » Abstract

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.

N. Marwan: Bleßberghöhle – Schatzkammer für die Wissenschaft, VdHK-Symposium: Wissenschaft unter Tage – Höhlenforschung im Dialog, Truckenthal (Germany), Jun 15, 2022, » Talk (PDF, 8.96M) .

N. Marwan, J. F. Donges, R. V. Donner, D. Eroglu: Integrative multivariate study of past African climate variability, EGU General Assembly, Vienna (Austria), May 24, 2022, DOI:10.5194/egusphere-egu22-6559, » Talk (PDF, 7.01M) . » Abstract

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
• Complex networks, network models, measures, network representations
• 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.

N. Marwan: Reconstructing Complex Networks from Data, Seminar Networks Unit, IMT School For Advanced Studies, Lucca (Italy), February 4, 2021, Talk invited. » 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.

><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.

K. H. Kraemer, N. Marwan, K. Wiesner, J. Kurths: Recurrence Plot based entropies and their ability to detect transitions, (Virtual) EGU General Assembly, Vienna (Austria), May 4-8, 2020, DOI:10.5194/egusphere-egu2020-10861, Talk. » Abstract

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

1. die Bedeutung der Strukturen und Informationen in recurrence plots,
2. die Erweiterung zur Beschreibung räumlich und raumzeitlich wiederkehrender Muster, deren Anwendung zur Identifizierung von
3. abrupten Änderungen in der Dynamik und
4. äußeren Einflüssen auf die Dynamik eines Systems als auch
5. Kopplungen zwischen verschiedenen Systemen,
6. eine Kombination mit der Methodik der komplexen Netzwerke,
7. Modifikationen zur Behandlung typischer Probleme mit geowissenschaftlichen Daten, wie unregelmäßiges Datensampling und Unsicherheiten in den Daten,
8. die Entwicklung eines Signifikanztests und schließlich
9. 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.

N. Marwan: Co-authorship network of the recurrence plot domain, 8th International Symposium on Recurrence Plots, Zhenjiang (China), August 21-23, 2019, Poster. » Abstract

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.

N. Marwan: What can you see? Perception problems of recurrence plots, 7th International Symposium on Recurrence Plots, São Paulo (Brazil), August 23-25, 2017, » Talk (PDF, 3.44M) . » Abstract

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.

D. Eroglu, N. Marwan: Multiplex Recurrence Networks, 7th International Symposium on Recurrence Plots, São Paulo (Brazil), August 23-25, 2017, Poster. » Abstract

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.

D. Eroglu, N. Marwan: Multiplex Recurrence Networks, EGU General Assembly, Vienna (Austria), April 23-28, 2017, » Poster (PDF, 5.64M) . » Abstract

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:

1. GlobalAirTrafficNetwork(fromopenflights.org) with information on airports, airportlocation, directflight connection, airplane type
2. Global population dataset (from SEDAC, NASA)
3. 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.
4. 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.

N. Marwan: Recurrence Plots for the Analysis of Complex Systems, Chapman Chair Seminar "Complex Systems Science Meets Arctic Science", University of Fairbanks, Fairbanks (USA), March 2, 2017, Lecture.

N. Marwan: Caves as scientific archives, Chapman Chair Seminar "Complex Systems Science Meets Arctic Science", University of Fairbanks, Fairbanks (USA), March 2, 2017, Lecture.

><2016

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.

N. Marwan: Analysing spatially extended high-dimensional dynamics by Recurrence plots, Conference Perspectives in Nonlinear Dynamics (PNLD2016), Berlin (Germany), July 24-26, 2016, Talk. » 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: 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.

N. Marwan, S. Foerster, J. Kurths: Recurrence plot analysis of spatially extended high-dimensional dynamics, 6th International Symposium on Recurrence Plots, Grenoble (France), June 17-19, 2015, » Talk (PDF, 5.77M) . » 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.

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 (RR_c, L_c, DET_c and DIV_c) of these measures on the chaos threshold of the logistic map, firstly, we verify that a scaling law of type RR-RR_c ∝ (a-a_c)^α is evident with the critical exponent α=0.47 ±0.01. Secondly, we show that the quantity L scales as | L - L_c| ∝ (a-a_c)^β, where the exponent is β=0.46±0.02. Thirdly, we numerically verify that DET exhibits a scaling law of type | DET-DET_c | ∝ (a-a_c)^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-a_c)^ν and DIV ∝ (a-a_c)^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.

N. Marwan, J. Donges, R. Donner, J. Kurths: Recurrence plots and complex networks for time series analysis, International Symposium Topical Problems of Nonlinear Wave Physics, Nizhny Novgorod/Saratov (Russia), July 17-23, 2014, Talk invited. » Abstract

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.

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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.

N. Marwan: Potential Pitfalls in Recurrence Plot Analysis, 5th International Symposium on Recurrence Plots, Chicago (USA), August 14-16, 2013, » Talk invited (PDF, 3.28M) . » Abstract

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.

N. Marwan: Practical Tutorial CRP Toolbox for MATLAB and RQA Software, 5th International Symposium on Recurrence Plots, Chicago (USA), August 14-16, 2013, Lecture and workshop.

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) .

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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.

N. Marwan: Recent achievements in recurrence plot research, 4th International Symposium on Recurrence Plots, Hong Kong (China), December 5-8, 2011, Talk invited. » Abstract

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.

E. J. Ngamga, N. Marwan, J. Donges, J. Kurths: Network approach for unvealing subtle transitions in dynamical systems, 4th International Symposium on Recurrence Plots, Hong Kong (China), December 5-8, 2011, » Poster (PDF, 719.17K) . » Abstract

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

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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.

N. Marwan: Hot topics in the recurrence plot field, 3rd International Symposium on Recurrence Plots, Montreal (Canada), August 25, 2009, » Talk invited (PDF, 1.87M) . » Abstract

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.

N. Marwan: Introduction in the CRP Toolbox, 3rd International Symposium on Recurrence Plots, Montreal (Canada), August 25, 2009, Lecture and workshop. » Abstract

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.

N. Marwan, J. Kurths: Recurrence plots in Earth sciences, EGU General Assembly, Vienna (Austria), April 20-24, 2009, » Talk invited (PDF, 7.93M) . » Abstract

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.

N. Marwan, S. Breitenbach: Detection of climate transitions in Asia derived from speleothems, 2nd International Recurrence Plot Workshop, Siena (Italy), September 9-12, 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 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.

N. Marwan, J. Kurths: Line structures in recurrence plots, 1st International Recurrence Plot Workshop, Potsdam (Germany), September 22-24, 2005, Talk. » Abstract

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.

N. Marwan, A. Groth: Improved recurrence quantification analysis for the investigation of ERP data, 1st International Recurrence Plot Workshop, Potsdam (Germany), September 22-24, 2005, » Poster (PDF, 3.15M) . » 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.

N. Marwan, N. R. Nowaczyk, M. Thiel, J. Kurths: Re-alignment of geological time series using the Cross Recurrence Plot Toolbox, 1st International Recurrence Plot Workshop, Potsdam (Germany), September 22-24, 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, 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: Einfluß ozeanischer Telekonnexionen auf den Niederschlag in NW Argentinien vor 30 000 Jahren – Untersuchungen mit nichtlinearen Methoden der Datenanalyse, Seminar of the Sonderforschungsbereich 267/ Deformation Processes in the Andes, Berlin (Germany), February 2, 2000, Talk.

><1999

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.

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