Geoscience Reference
In-Depth Information
measures, a statistical test should be applied (Marwan 2011). Other more
complex measures that quantify other aspects of the dynamics (e.g.,
predictability, or laminar phases) are included in the Cross Recurrence Plot
Toolbox for MATLAB, available from
http://tocsy.pik-potsdam.de/CRPtoolbox/
Bivariate and multivariate extensions of recurrence plots allow nonlinear
correlation tests and synchronization analyses to be carried out. A detailed
introduction to methods based on recurrence plots can be found on the
following web site:
http://www.recurrence-plot.tk
h e analysis of recurrence plots has already been applied to many problems
in earth sciences. h e comparison of the dynamics of modern precipitation
data with paleo-rainfall data inferred from annual-layered lake sediments in
the northwestern Argentine Andes provides a good example of such analyses
(Marwan et al. 2003). In this instance the recurrence plot method was applied
to red-color intensity transects across varved lake sediments that were
approximately 30 kyrs old (Section 8.7). Comparing the recurrence plots
from the sediments with those from modern precipitation data revealed that
the reddish layers document the more intense rainy seasons that occurred
during La Niña years. h e application of linear techniques was, however,
not able to link the increased l ux of reddish clays with either the El Niño or
La Niña phase of the El Niño/Southern Oscillation. Moreover, recurrence
plots helped to prove the hypothesis that longer rainy seasons, enhanced
precipitation, and the stronger inl uence of the El Niño/Southern Oscillation
caused an increase in the number of landslides 30 kyrs ago (Marwan et al.
2003, Trauth et al. 2003).
Recommended Reading
Ansari AR, Bradley RA (1960) Rank-Sum Tests for Dispersion. Annals of Mathematical
Statistics, 31:1174-1189. [Open access]
Blackman, RB, Tukey, JW (1958) h e Measurement of Power Spectra. Dover NY
Cooley JW, Tukey JW (1965) An Algorithm for the Machine Calculation of Complex Fourier
Series. Mathematics of Computation 19(90):297-301.
Donner RV, Heitzig J, Donges JF, Zou Y, Marwan N, Kurths J (2011) h e Geometry of Chaotic
Dynamics - A Complex Network Perspective. European Physical Journal B, 84:653-672
Eckmann JP, Kamphorst SO, Ruelle D (1987) Recurrence Plots of Dynamical Systems.
Europhysics Letters 5:973-977
Grenander U (1958) Bandwidth and variance in estimation of the spectrum. Journal of the
Royal Statistical Society Series B 20:152-157
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