Non-linear principal component analysis of nearshore bathymetry

Abstract

Spatially and temporally extensive nearshore bathymetric datasets have recently been analyzed with complex principal component analysis (CPCA) to extract propagating spatial patterns that constitute most to the dominant lower-dimensional structure in the datasets. CPCA assumes this structure to be linear, which may be an oversimplification of the true structure as the nearshore is a strongly non-linear system. Here we investigate whether a neural network-based circular non-linear principal component analysis (NLPCA.cir) provides a more representative approximation of the underlying lower-dimensional structure of nearshore depth data than possible with CPCA. To that end, NLPCA.cir was applied to three datasets characterized by interannual offshore-directed sandbar behavior, coming from Egmond (The Netherlands), Hasaki Coast (Japan) and Duck (North Carolina, USA). The main difference between these datasets is the temporal variation in sandbar amplitude, which is smallest at Egmond and largest at Duck. We find that the first NLPCA.cir mode 1 at Egmond and Hasaki leads to a more complete characterization of the lower-dimensional data structure than possible with CPCA (i.e. the underlying low-dimensional structure of bathymetric data at Egmond and Hasaki is indeed non-linear). This is not the case at Duck, where the temporal variations in sandbar amplitude are so large that the non-linear lower-dimensional structure in the data, should it exist, is no longer visually apparent and can no longer be detected by NLPCA.cir. This suggests that a simple visual check of the data suffices to decide whether one should resort to NLPCA.cir or to the more simple and computationally quicker CPCA.