Canonical Correlation Analysis for Hydroclimatic Datasets with Known Measurement Uncertainties

Canonical correlation analysis (CCA) is a linear dimensionality reduction method applied to pairs of multi-dimensional random variables. It has found applications in many areas of hydrology including regional flood frequency analysis, long-range rainfall forecasting, and statistical downscaling of general circulation models. The solutions to CCA are conventionally expressed as eigenvector problems. This standard formulation is oblivious to the measurement uncertainties in the data and assumes that the dimensionality of the reduced space, i.e. the number of canonical components is known a priori. Since many hydro-climatic datasets, like streamflow and sea surface temperature, have large measurement uncertainties and the number of canonical components is not known a priori, the standard CCA formulation may not be appropriate for such variables. In this study, the CCA is formulated as a linear latent variable model and its solutions are obtained using Bayesian learning. The proposed algorithm accounts for the measurement uncertainties in the data and determines the number of canonical components using the principle of automatic relevance determination. The effectiveness of the proposed algorithm and its advantages over the standard CCA algorithm are illustrated using synthetic examples and real-world hydrologic data.