Evaluating EOF modes against a stochastic null hypothesis

In this paper it is suggested that a stochastic isotropic diffusive process, representing a spatial first order auto regressive process (AR(1)-process), can be used as a null hypothesis for the spatial structure of climate variability. By comparing the leading empirical orthogonal functions (EOFs) of a fitted null hypothesis with EOF modes of an observed data set, inferences about the nature of the observed modes can be made. The concept and procedure of fitting the null hypothesis to the observed EOFs is in analogy to time analysis, where an AR(1)-process is fitted to the statistics of the time series in order to evaluate the nature of the time scale behavior of the time series. The formulation of a stochastic null hypothesis allows one to define teleconnection patterns as those modes that are most distinguished from the stochastic null hypothesis. The method is applied to several artificial and real data sets including the sea surface temperature of the tropical Pacific and Indian Ocean and the Northern Hemisphere wintertime and tropical sea level pressure.