Extraction of Nonlinear Dynamical Modes Underlying Climate Variability

Abstract:

In this report we suggest a new method for reducing the dimension of space-distributed climate data. The main idea of the method is an improving the traditional linear methods for data decomposition by taking into account nonlinear couplings between the variables. Actually, the method is aimed to reveal a few hidden dynamical signals which explain an essential part of data and are interpreted as dominant internal modes driving the observed multivariate dynamics. Bayesian optimality is used for selecting relevant structure of the nonlinear transformation, including both the number of principal modes and the degree of nonlinearity. We applied the expansion to monthly SST data covering the Globe. It is shown that the obtained nonlinear modes capture more part of SST variability than principal components (PCs) constructed by either EOF decomposition or its spatio-temporal extension. In particular, only a few modes explain a set of key SST-based Pacific and Atlantic indices with correlation coefficient more than 0.7. A relation of the obtained modes to decadal natural climate variability including current hiatus in global warming is exhibited and discussed in the report. Advances of the proposed expansion in relation to phase space reconstruction for data-driven stochastic modeling are demonstrated.

This research was supported by the Government of the Russian Federation (Agreement No. 14.Z50.31.0033 with the Institute of Applied Physics RAS)