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

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.