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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 15, issue 1
Nonlin. Processes Geophys., 15, 169–177, 2008
https://doi.org/10.5194/npg-15-169-2008
© Author(s) 2008. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: Extreme Events: Nonlinear Dynamics and Time Series Analysis

Nonlin. Processes Geophys., 15, 169–177, 2008
https://doi.org/10.5194/npg-15-169-2008
© Author(s) 2008. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  19 Feb 2008

19 Feb 2008

Detecting spatial patterns with the cumulant function – Part 2: An application to El Niño

A. Bernacchia1, P. Naveau2, M. Vrac2, and P. Yiou2 A. Bernacchia et al.
  • 1Dipartimento di Fisica, Università "La Sapienza", Roma, Italy
  • 2Laboratoire des Sciences du Climat et de l'Environnement, IPSL-CNRS, France

Abstract. The spatial coherence of a measured variable (e.g. temperature or pressure) is often studied to determine the regions of high variability or to find teleconnections, i.e. correlations between specific regions. While usual methods to find spatial patterns, such as Principal Components Analysis (PCA), are constrained by linear symmetries, the dependence of variables such as temperature or pressure at different locations is generally nonlinear. In particular, large deviations from the sample mean are expected to be strongly affected by such nonlinearities. Here we apply a newly developed nonlinear technique (Maxima of Cumulant Function, MCF) for detection of typical spatial patterns that largely deviate from the mean. In order to test the technique and to introduce the methodology, we focus on the El Niño/Southern Oscillation and its spatial patterns. We find nonsymmetric temperature patterns corresponding to El Niño and La Niña, and we compare the results of MCF with other techniques, such as the symmetric solutions of PCA, and the nonsymmetric solutions of Nonlinear PCA (NLPCA). We found that MCF solutions are more reliable than the NLPCA fits, and can capture mixtures of principal components. Finally, we apply Extreme Value Theory on the temporal variations extracted from our methodology. We find that the tails of the distribution of extreme temperatures during La Niña episodes is bounded, while the tail during El Niños is less likely to be bounded. This implies that the mean spatial patterns of the two phases are asymmetric, as well as the behaviour of their extremes.

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