Modelling multivariate data systems: Application to El Niño and the Annual Cycle

Abstract

We propose a general procedure for the analysis of noisy high dimensional dynamical systems, potentially with time delay. This procedure combines novel dimensionality reduction techniques, nonlinear time series analysis for dynamical systems and nonparametric statistical estimation of functional dependencies. To check the feasibility of our method, we apply it to the sea surface temperature (SST) field in the tropical Pacific Ocean, in order to build a model for the interaction of El Niño/Southern Oscillation (ENSO) and the Annual Cycle coupled system. This dynamical representation is shown to be reducible to three dimensions by applying Isomap, a recent method of dimensionality reduction. From the resulting time series, we construct a stochastic dynamical system by using nonparametric estimation. This dynamical system is numerically integrated and compared with measured data a posteriori. The use for prediction of the joint system of ENSO and the Annual Cycle is discussed. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.