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

Gianluca Borzelli, Roberto Ligi
1999 Journal of Atmospheric and Oceanic Technology  
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
more » ... 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
doi:10.1175/1520-0426(1999)016<0682:eofaos>2.0.co;2 fatcat:b5ocrkauxbfy5loh52s5r5fm3a