EOFs of Harmonizable Cyclostationary Processes

While approximate cyclostationary processes are commonly found in climatic and geophysical studies, one great disincentive in using cyclostationary empirical orthogonal functions is their computational burden. This is especially so for three-dimensional, spacetime case. This paper discusses a simple method of computing approximate cyclostationary empirical orthogonal functions based on the theory of harmonizable cyclostationary processes. The new method is computationally much more efficient than that by Kim et al. (1996a). In the new method cyclostationary empirical orthogonal functions are easier to understand. Namely, they are naturally defined as the products of Bloch functions (inner modes) and Fourier functions (outer modes), which otherwise is the result of the factorization theorem (Smith 1969). Bloch functions are simply the principal components (PC) of the coefficient time series, which are generally correlated. They represent the normal modes of the nested fluctuations of ha...