CANONICAL CORRELATION-ANALYSIS AND ITS METEOROLOGICAL APPLICATIONS

Linear statistical prediction of the values of some predictants from the available values of predictors is contained. The reasons that do not permit one to use too many different predictors are given. The application of the method of empirical orthogonal functions (EOFs) to the selection of a small number of the most valuable predictors is discussed. The main results of the canonical correlation analysis developed by A. M. Obukhov and H. Hotelling in the mid-30ies are presented. It is noted that this analysis makes it possible to determine most efficently which of the predictors contain the greatest amount of information about the predictant values. A review of many papers where the canonical correlation analysis is applied to the meteorological problems is given. Generalization of the canonical correlation analysis to the case of infinite families of fluctuating varibles - random processes and fields - is considered; special attention is given to the cases where there is only a finite number of non-zero canonical correlations between past and future of a time series.