The CCA selects pairs of spatial patterns of two variables X & Y, such that their time evolution is optimally correlated (Preisendorfer 1988; Zorita et al. 1992; Bretherton, 1992; Kharin, 1994; Von Storch 1995).

where Cxx and Cyy are the elements of covariance matrices for the data fields X and Y, Cxy are the elements of cross-covariance matrix associated with X and Y. U and V are the new, best correlated, time series. The spatial patterns associated to them are determined from: