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A computer-implemented method to provide stabilized and spatially smooth regression coefficients for weather forecast error correction from small training data sets. In accordance with the present invention, an MOS estimate of the regression coefficient calculated from a small data set can be optimally combined with a smooth prior estimate of the regression coefficient, an estimate of the spatial error covariance of that prior estimate, and an estimate of the spatial error covariance of the MOS estimate. The result is a filtered MOS (FMOS) regression coefficient which can be used to more accurately estimate and correct errors in weather forecasts even using only small data sets.