24 - Empirical Orthogonal Function Analysis

Summary

The analyses we have discussed in previous chapters include the use of base functions, such as sinusoidal functions with specified frequencies, i.e. harmonic analysis; sinusoidal base functions with a frequency range from 0 to the Nyquist frequency with an interval inversely proportional to the total length of time of the data, i.e. Fourier analysis; and wavelet base functions for wavelet analysis. These base functions, however, are chosen regardless of the nature of the variability of the data themselves. In this chapter, we will discuss a different method, in which the base functions are determined empirically, that is dependent on the nature of the data. In other words, this method will find the base functions from the data and these base functions describe the nature of the data. The method is applicable to many types of data, especially to time series data at multiple locations, e.g. a sequence of weather maps or satellite images. There are several variants of the method, but here we will only provide an introduction for the basics.