Testing methods of pattern extraction for climate data using synthetic modes

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.