AN OPTIMAL REGIONAL AVERAGING METHOD WITH ERROR-ESTIMATES AND A TEST USING TROPICAL PACIFIC SST DATA

This paper provides a systematic procedure for computing the regional average of climate data in a subregion of the earth surface using the covariance function written in terms of empirical orthogonal functions (EOFs). The method is optimal in the sense of minimum mean square err or (mse) and ives an mse estimate of the averaging results. The random measurement error is also included in the total mse. Since the EOFs c an account for spatial inhomogeneities, the method can be more accurat e than those that assume a homogeneous covariance matrix;This study sh ows how to further improve the accuracy of optimal averaging (OA) by i mproving the accuracy of the eigenvalues of the covariance function th rough an extrapolation method. The accuracy of the authors' procedure is tested using cross-validation techniques, which simulate past sampl ing conditions on the recent, well-sampled tropical Pacific SST and us e the EOFs independent to the month being tested. The true sampling er ror of the cross-validated tests is computed with respect to the 1 deg rees X 1 degrees data for various sampling conditions. The theoretical sampling error is computed from the authors' derived formula and comp ared to the true error from the cross-validation tests. The authors' n umerical results show that (i) the extrapolation method can sometimes improve the accuracy of the eigenvalues by 10%, (ii) the optimal avera ging consistently yields smaller mse than the arithmetic averaging, an d (iii) the theoretical formula for evaluating the OA error gives esti mates that compare well with the true error.