An ISOMAP Analysis of Sea Surface Temperature for the Classification and Detection of El Niño & La Niña Events

Isometric feature mapping (ISOMAP) is a nonlinear dimensionality reduction method used for extracting features from spatiotemporal data. The traditional principal component analysis (PCA), a linear dimensionality reduction method, measures the distance between two data points based on the Euclidean distance (line segment), which cannot reflect the actual distance between the data points in a nonlinear space. By contrast, the ISOMAP measures the distance between two data points based on the geodesic distance, which more closely reflects the actual distance by the view of tracing along the local linearity in the original nonlinear structure. Thus, ISOMAP-reconstructed data points can reflect the features of real structures and can be classified more accurately than traditional PCA-reconstructed data points. Moreover, these ISOMAP-reconstructed data points can be used for cluster analysis by emphasizing the differences among the points more than those by the traditional PCA. In this study, sea surface temperature (SST) data points reconstructed using the traditional PCA and ISOMAP were compared. The classification based on these reconstructed SST points was tested using the Niño 3.4 index, which labels El Niño, La Niña, or normal events. The mean differences from the ISOMAP data points were larger than those from the traditional PCA data points. The ISOMAP not only helped differentiate the points in two different events but also provided better difference measurement of the points belonging to the same class (e.g., 82/83 and 97/98 El Niño events). On examining the evolution of the leading three temporal eigen components of the SST PCA, or especially the SST ISOMAP, we found that the trajectories were similar to the Lorenz 63 model on a phase space figure. This implies that NWP perturbations can be traced using the ISOMAP to measure growing unstable behaviors. Spatial eigenmodes (empirical orthogonal function) between the traditional PCA and ISOMAP were also determined and compared herein