Nonlinear Dimensionality Reduction Methods in Climate Data Analysis

TL;DR

This paper evaluates three nonlinear dimensionality reduction techniques—NLPCA, Isomap, and Hessian LLE—for climate data analysis, specifically studying El Nino variability, and finds they are useful for exploratory purposes despite similar results to PCA.

Contribution

It applies and compares three nonlinear dimensionality reduction methods to climate data, assessing their effectiveness in analyzing El Nino variability.

Findings

Nonlinear methods are effective for exploratory data analysis.

These methods do not outperform PCA in this application.

They provide additional insights into climate data structure.

Abstract

Linear dimensionality reduction techniques, notably principal component analysis, are widely used in climate data analysis as a means to aid in the interpretation of datasets of high dimensionality. These linear methods may not be appropriate for the analysis of data arising from nonlinear processes occurring in the climate system. Numerous techniques for nonlinear dimensionality reduction have been developed recently that may provide a potentially useful tool for the identification of low-dimensional manifolds in climate data sets arising from nonlinear dynamics. In this thesis I apply three such techniques to the study of El Nino/Southern Oscillation variability in tropical Pacific sea surface temperatures and thermocline depth, comparing observational data with simulations from coupled atmosphere-ocean general circulation models from the CMIP3 multi-model ensemble. The three methods used here are a nonlinear principal component analysis (NLPCA) approach based on neural networks, the Isomap isometric mapping algorithm, and Hessian locally linear embedding. I use these three methods to examine El Nino variability in the different data sets and assess the suitability of these nonlinear dimensionality reduction approaches for climate data analysis. I conclude that although, for the application presented here, analysis using NLPCA, Isomap and Hessian locally linear embedding does not provide additional information beyond that already provided by principal component analysis, these methods are effective tools for exploratory data analysis.