Some Developments in the Use of Empirical Orthogonal Functions for Mapping Meteorological Fields

Abstract

Some current uses of empirical orthogonal functions (EOF) are briefly summarized, together with some relations with spectral and principal component analyses. Considered as a mean square estimation technique of unknown values within a random process or field, the optimization of error variance leads to a Fredholm integral equation. Its kernel is the autocorrelation function, which in many practical cases is only known as discrete values of interstation correlation coefficients computed from a sample of independent realizations. The numerical solution in one or two dimensions of this integral equation is approximated in a new and more general framework that requires, in practice, the a priori choice of a set of generating functions. Developments are provided for piecewise constant, facetlike linear, and thin plate type spline functions. The first part of the paper ends with a review of the mapping, archiving and stochastic simulating possibilities of the EOF method. A second part includes a case study concerning precipitation fields, previously worked out by optimal interpolation methods.