An Intercomparison of Methods for Finding Coupled Patterns in Climate Data

TLDR

In geophysical datasets, sampling times are often comparable to spatial points, and methods such as SVD and CPCA are preferred for their ease of implementation and lack of user‑chosen parameters. The study proposes a conceptual framework to compare methods that isolate coupled modes of variability between two field time series. The authors compare CPCA, CCA, BP‑CCA, SFPCA, and SVD within a simple geophysical model, varying spatial points, sample size, and signal‑to‑noise ratio to evaluate each method’s ability to detect coupled signals. In the model, CPCA generally outperforms SVD, BP, and SFPCA in accurately extracting coupled patterns, though it suffers from a mean bias toward individual field EOFs at low signal‑to‑noise ratios; under longer time series or when the coupled signal differs from EOFs, SVD and BP become more reliable.

Abstract

This paper introduces a conceptual framework for comparing methods that isolate important coupled modes of variability between time series of two fields. Four specific methods are compared: principal component analysis with the fields combined (CPCA), canonical correlation analysis (CCA) and a variant of CCA proposed by Barnett and Preisendorfer (BP), principal component analysis of one single field followed by correlation of its component amplitudes with the second field (SFPCA), and singular value decomposition of the covariance matrix between the two fields (SVD). SVD and CPCA are easier to implement than BP, and do not involve user-chosen parameters. All methods are applied to a simple but geophysically relevant model system and their ability to detect a coupled signal is compared as parameters such as the number of points in each field, the number of samples in the time domain, and the signal-to-noise ratio are varied. In datasets involving geophysical fields, the number of sampling times may not be much larger than the number of observing locations or grid points for each field. In a model system with these characteristics, CPCA usually extracted the coupled pattern somewhat more accurately than SVD, BP, and SFPCA, since the patterns it yielded exhibit smaller sampling variability; SVD and BP gave quite similar results; and CCA was uncompetitive due to a high sampling variability unless the coupled signal was highly localized. The coupled modes derived from CPCA and SFPCA exhibit an undesirable mean bias toward the leading EOFs of the individual fields; in fact, for small signal-to-noise ratios these methods may identify a coupled signal that is similar to a dominant EOF of one of the fields but is completely orthogonal to the true coupled signal within that field. For longer time series, or in situations where the coupled signal does not resemble the EOFs of the individual fields, these biases can make SVD and BP substantially superior to CPCA.