A Theoretically Lossless Method for Deriving Empirical Orthogonal Functions from Unevenly Sampled Data

Abstract

The Lomb-Scargle discrete Fourier transform (LSDFT) is a fairly popular technique for analyzing time series within the astronomy community. However, this algorithm is largely unknown in many other disciplines, despite many potential applications. In particular, the atmospheric sciences stand to benefit substantially from implementing it, since much of the corpus of observational data is irregularly sampled. In this study, a solution for empirical orthogonal functions (EOFs) based on irregularly sampled data is derived from the LSDFT. It is demonstrated that this particular algorithm has no hard limit on its accuracy, and yields results comparable to those of complex Hilbert EOF analysis. Three LSDFT algorithms are compared in terms of their performance in evaluating EOFs for data from the Tropical Rainfall Measuring Mission. All three are shown to be able to capture the pattern of the diurnal cycle, and also show other consistent features in the zero to twelve day frequency band. The feasibility of implementing these algorithms is also investigated, and it is found that the programming language R is only about 2.2 ± 0.1 times as slow as CUDA C/C++ in this particular application.