Testing Methods of Pattern Extraction for Climate Data Using Synthetic Modes

Abstract

In this paper we develop a method to quantify the accuracy of different pattern extraction techniques for the additive space–time modes often assumed to be present in climate data. It has previously been shown that the standard technique of principal component analysis (PCA; also known as empirical orthogonal functions) may extract patterns that are not physically meaningful. Here we analyze two modern pattern extraction methods, namely dynamical mode decomposition (DMD) and slow feature analysis (SFA), in comparison with PCA. We develop a Monte Carlo method to generate synthetic additive modes that mimic the properties of climate modes described in the literature. The datasets composed of these generated modes do not satisfy the assumptions of any pattern extraction method presented. We find that both alternative methods significantly outperform PCA in extracting local and global modes in the synthetic data. These techniques had a higher mean accuracy across modes in 60 out of 60 mixed synthetic climates, with SFA slightly outperforming DMD. We show that in the majority of simple cases PCA extracts modes that are not significantly better than a random guess. Finally, when applied to real climate data these alternative techniques extract a more coherent and less noisy global warming signal, as well as an El Niño signal with a clearer spectral peak in the time series, and more a physically plausible spatial pattern.

Classification of synoptic circulation patterns with a two-stage clustering algorithm using the modified structural similarity index metric (SSIM)

“…The reason for this statement was the common assumption that the first few modes returned by PCA are physically interpretable and match the underlying signal in the data. However, Fulton and Hegerl (2021) tested this signal-extraction 365 method and demonstrated that it has serious deficiencies when extracting multiple additive synthetic modes (false dipoles instead of monopoles, which may lead to serious misinterpretation of extracted modes). They also found that PCA tends to mix independent spatial regions into single modes.…”

A regional attentive empirical orthogonal function analysis: An application to North Atlantic Oscillation

“…Previous oceanic and atmospheric studies have made significant efforts in geographic data analysis to extract patterns from simulated and observed gridded geographic data sets (Hannachi, 2007; Meehl et al, 2005). These patterns can further aid the investigation of the physical mechanisms behind these signals and thus to improve understanding of the physical processes that generate oceanic and climate variability and teleconnections (Fulton & Hegerl, 2021). Empirical orthogonal functions (EOFs) are the one of the most widely used methods to find patterns of variability from high‐dimensional geographic data.…”

“…understanding of the physical processes that generate oceanic and climate variability and teleconnections (Fulton & Hegerl, 2021). Empirical orthogonal functions (EOFs) are the one of the most widely used methods to find patterns of variability from high-dimensional geographic data.…”

Localized injections of interactive volcanic aerosols and their climate impacts in a simple general circulation model

“…Although the development of verification datasets for advanced data analytic techniques in the climate community is nascent, there are a few examples. Fulton and Hegerl (2021) generated synthetic climate modes to test the accuracy of distinct pattern extraction techniques and show that the most commonly used principal component analysis technique does not perform well. Mamalakis et al (2022) worked to develop an "attribution benchmark dataset" for which the ground truth is known to enable evaluation of different explainable artificial intelligence (AI) methods.…”