Example: Detection of an El Niño impact on local rainfall
in NW Argentina, 30000 years ago

The Santa Maria Basin in NW Argentina is located between opposite
El Niño influences. These influences have changed for the Santa
Maria Basin during the Holocene.
Varved lake sediments from the Santa Maria Basin offer an archive
of variations in the rainfall 30000 years ago.

Cross recurrence plots (CRPs) reveal epochs of a similar dynamics
in precipitation (present-day and past) and the El Niño. Here the
CRP between the present-day rainfall in Salta and the Southern
Oscillation Index (SOI) is shown. From a statistical investigation
of the CRPs between modern/past precipitation and El Niño data (SOI)
the existence of an El Niño-like impact on the local climate in NW
Argentina 30000 years ago can be inferred.

Reference:

Marwan, N., Trauth, M. H., Vuille, M., Kurths, J.:
Comparing modern and Pleistocene ENSO-like influences in NW Argentina using nonlinear time series analysis methods,
Climate Dynamics, 21(3-4), 2003, 317-326,
doi:10.1007/s00382-003-0335-3, Article (PDF).

An optical feedback experiment. The dynamic of the laser intensity
can be described with two coupled differential equations. However,
for large delays the dynamics can be described with one equation.
The delay components of this equation can be determined by using
the ACE algorithm.

The maximal-correlation function (right) exhibits the typical
delays in the system more significant than the auto-correlation
function (right).

The optimal transformations, which are used for the model. Where the
term f_{0}(y_{t}) is strong non-linear,
the feedback term f_{2}(y_{t}) is linear.

Reference:

Voss, H., Kurths, J.:
Reconstruction of nonlinear time delay models from data by
the use of optimal transformations, Phys. Lett. A, 234, 1997, 336-344,
doi:10.1016/S0375-9601(97)00598-7, Article (PDF).