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.Comment: 15 pages, 7 figure
