Trend Singular Value Decomposition Analysis and Its Application to the Global Ocean Surface Latent Heat Flux and SST Anomalies

Given the complexity of trends in the actual climate system, distinguishing between different trends and different trend modes is important for climate research. This study introduces a new method called "trend singular value decomposition (TSVD) analysis," which is designed for systematically extracting coupled trend modes, albeit small, by performing an eigenanalysis of the inverse-rank covariance matrix between two fields. Applications to simple time series models and annual mean surface latent heat flux (LHF) and SST data for 1958–2006 are presented and discussed. Results show that the TSVD analysis can capture different coherent trends into different leading modes. The first TSVD mode between the global LHF and SST anomalies, similar to the first conventional SVD mode, generally represents a large-scale increasing LHF trend induced by a warming SST trend; whereas, interestingly, unlike the second SVD mode that is mainly associated with the familiar ENSO, the second TSVD mode is mainly associated with the Pacific decadal oscillation (PDO). TSVD analysis casts the (global) long-term and (Pacific) decadal trends into the leading two modes, respectively. Compared to SVD analysis, the advantages of the TSVD analysis in detecting coupled low-frequency modes are even more evident in the tropical Pacific (TP), where the coherent trend signals (i.e., the long-term trends and the decadal trends) are smaller than the ENSO-related signals. Thus, TSVD analysis performs better than SVD analysis when focusing on trends rather than on maximum covariance patterns, particularly on relatively small coherent trend patterns, such as the coupled long-term trends and decadal trends in the TP.