Detecting spatial patterns with the cumulant function. Part II: An application to El Nino

TL;DR

This paper introduces a nonlinear technique called Maxima of Cumulant Function (MCF) to detect spatial patterns in climate data, specifically applied to El Nino, revealing asymmetric temperature patterns and extreme value behaviors.

Contribution

The paper presents MCF as a new nonlinear method for identifying spatial patterns that deviate from the mean, outperforming PCA and NLPCA in reliability and capturing complex mixtures.

Findings

MCF effectively detects El Nino and La Nina temperature patterns.

MCF captures asymmetric spatial patterns not identified by PCA.

Extreme value analysis shows bounded tails during La Nina and unbounded during El Nino.

Abstract

The spatial coherence of a measured variable (e.g. temperature or pressure) is often studied to determine the regions where this variable varies the most 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 the 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 Nino/Southern Oscillation and its spatial patterns. We find nonsymmetric temperature patterns corresponding to El Nino and La Nina, 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 Nina episodes is bounded, while the tail during El Ninos 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.