Theoretical foundation of cyclostationary EOF analysis for geophysical and climatic variables: Concepts and examples

Natural variability is an essential component of observations of all geophysical and climate variables. In principal component analysis (PCA), also called empirical orthogonal function (EOF) analysis, a set of orthogonal eigenfunctions is found from a spatial covariance function. These empirical basis functions often lend useful insights into physical processes in the data and serve as a useful tool for developing statistical methods. The underlying assumption in PCA is the stationarity of the data analyzed; that is, the covariance function does not depend on the origin of time. The stationarity assumption is often not justifiable for geophysical and climate variables even after removing such cyclic components as the diurnal cycle or the annual cycle. As a result, physical and statistical inferences based on EOFs can be misleading. Some geophysical and climatic variables exhibit periodically time-dependent covariance statistics. Such a dataset is said to be periodically correlated or cyclostationary. A proper recognition of the time-dependent response characteristics is vital in accurately extracting physically meaningful modes and their space–time evolutions from data. This also has important implications in finding physically consistent evolutions and teleconnection patterns and in spectral analysis of variability—important goals in many climate and geophysical studies. In this study, the conceptual foundation of cyclostationary EOF (CSEOF) analysis is examined as an alternative to regular EOF analysis or other eigenanalysis techniques based on the stationarity assumption. Comparative examples and illustrations are given to elucidate the conceptual difference between the CSEOF technique and other techniques and the entailing ramification in physical and statistical inferences based on computational eigenfunctions.