Multivariate Recurrence Analysis

Abstract

Recurrence analysis was introduced to infer the degree of separation between a “control” and an “anomaly” ensemble of, say, seasonal means simulated in general circulation model (GCM) experiments. The concept of recurrence analysis is described as a particular application of a statistical technique called multiple discriminant analysis (MDA). Using MDA, univariate recurrence is easily generalized to multicomponent problems. Algorithms that can be used to estimate the level of recurrence and tests that can be used to assess the confidence in a priori specified levels of recurrence are presented. Several of the techniques are used to reanalyze a series of El Niño sensitivity experiments conducted with the Canadian Climate Centre GCM. The simulated El Niño response in DJF mean 500 mb height are all estimated to be more than 94% recurrent in the tropics and are estimated to be between 90% and 959b recurrent in the Northern Hemisphere between 20° and 60°N latitude. Discrimination rules that can be used to classify individual realizations of climate as members of the control or “experimental” ensemble are obtained as a by-product of the multiple recurrence analysis. We show that it is possible to make reasonable inferences about the state of the eastern Pacific sea surface temperature by classifying observed DJF 500 mb height fields with discrimination rules derived from the GCM experiments.