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.
