Empirical Orthogonal Function Analysis of SST Image Series: A Physical Interpretation

Abstract

Abstract The physical implications underlying the empirical orthogonal function (EOF) decomposition of a series of sea surface temperature (SST) images are discussed. Neglecting vertical advection, and in the hypothesis of slowly time-varying horizontal advection, it is proven that EOFs multiplied by temporal amplitudes are particular solutions of the heat diffusion equation with advection. The normal-mode equation for EOFs with eigenvalues fixed by the boundary condition for the SST is derived from the heat equation. In addition, it is proven that in the continuous limit the covariance matrix is a Green’s function for the EOFs normal-mode equation. By using these ideas, the equivalence between spatial and temporal EOF analysis is shown. A practical application of the theory is presented by decomposing a series of 72 objective SST maps obtained from 187 Advanced Very High Resolution Radiometer SST images collected over the Channel of Sicily in 1992 (1 January–31 December).