Singular Value Decomposition of Wintertime Sea Surface Temperature and 500-mb Height Anomalies

Abstract

Single field principal component analysis (PCA), direct singular value decomposition (SVD), canonical correlation analysis (CCA), and combined principal component analysis (CPCA) of two fields are applied to a 39-winter dataset consisting of normalized seasonal mean sea surface temperature anomalies over the North Pacific and concurrent 500-mb height anomalies over the same region. The CCA solutions are obtained by linear transformations of the SVD solutions. Spatial patterns and various measures of the variances and covariances explained by the modes derived from the different types of expansions are compared, with emphasis on the relative merits of SVD versus CCA. Results for two different analysis domains (i.e., the Pacific sector versus a full hemispheric domain for the 500-mb height field) are also compared in order to assess the domain dependence of the two techniques. The SVD solution is also compared with the results of 28 Monte Carlo simulations in which the temporal order of the SST grids is randomized and found to be highly significant. As expected, the leading SVD modes explain substantially more of the squared covariance between the two fields than any of the CCA modes, while the paired expansion coefficients of the leading CCA modes are more strongly correlated than any of the SVD modes. The expansion coefficient for the leading SVD mode is almost identical to the leading principal component of the SST field, regardless of whether the 500-mb height field is hemispheric or restricted to the Pacific sector. SST patterns strongly resembling the second and third EOFs are also recovered among the three leading SVD modes. The leading CCA mode in the expansion based on the three leading singular value vectors for the Pacific sector resembles the pattern of anomalies observed in association with ENSO. The other modes more closely resemble the patterns derived from PCA of the 500-mb height field than those for the SVD modes on which they are based. The SVD and CPCA solutions for the first three modes proved to be quite similar. The SVD and CCA solutions based on the hemispheric 500-mb height field are indicative of a coupling between the interannual variability of North Pacific and North Atlantic SST by virtue of their mutual relationship to one of the atmosphere's most prominent planetary wave patterns.