Comparison of nonlinear and linear PCA on surface wind, surface height, and SST in the South China Sea

We compared nonlinear principal component analysis （NLPCA） with linear principal component analysis （LPCA） with the data of sea surface wind anomalies （SWA）, surface height anomalies （SSHA）, and sea surface temperature anomalies （SSTA）, taken in the South China Sea （SCS） between 1993 and 2003. The SCS monthly data for SWA, SSHA and SSTA （i.e., the anomalies with climatological seasonal cycle removed） were pre-filtered by LPCA, with only three leading modes retained. The first three modes of SWA, SSHA, and SSTA of LPCA explained 86%, 71%, and 94% of the total variance in the original data, respectively. Thus, the three associated time coefficient functions （TCFs） were used as the input data for NLPCA network. The NLPCA was made based on feed-forward neural network models. Compared with classical linear PCA, the first NLPCA mode could explain more variance than linear PCA for the above data. The nonlinearity of SWA and SSHA were stronger in most areas of the SCS. The first mode of the NLPCA on the SWA and SSHA accounted for 67.26% of the variance versus 54.7%, and 60.24% versus 50.43%, respectively for the first LPCA mode. Conversely, the nonlinear SSTA, localized in the northern SCS and southern continental shelf region, resulted in little improvement in the explanation of the variance for the first NLPCA.