Nonlinear principal component analysis of the tidal dynamics in a shallow sea

Abstract

A nonlinear, neural‐network‐based extension of the principal component analysis (PCA) is applied to the water level and current fields in a shallow tidal sea at the German North Sea coast. Contrary to the linear PCA, which tends to split patterns in the data among several modes difficult to interpret, the nonlinear PCA enables to identify the nonlinear spatial patterns in the data with only a single mode. The first nonlinear principal component (PC) corresponds well with the joint probability distribution of the linear PCs and can be argued to represent a ‘typical’ tidal cycle in the study area.

Nonlinear Principal Component Analysis: Neural Network Models and Applications

“…Kirby and Miranda [5] constrained network units to work in a circular manner resulting in a circular PCA whose components are closed curves. In the fields of atmospheric and oceanic sciences, circular PCA is applied to oscillatory geophysical phenomena, for example, the oceanatmosphere El Niño-Southern oscillation [6] or the tidal cycle at the German North Sea coast [7]. There are also applications in the field of robotics in order to analyse and control periodic movements [8].…”

Validation of Nonlinear PCA

“…Detecting and describing nonlinear structures is especially important for analysing time series. Nonlinear PCA is therefore frequently used to investigate the dynamics of different natural processes [4,5,6]. But validating the model complexity of nonlinear PCA is a difficult task [7].…”