Statistical Corrections to Numerical Prediction Equations

Abstract

A procedure for statistical correction of numerical prediction equations at the end of each predictive time step is described and tested with a one-dimensional prediction model. The model equation is a modified Burgers equation that allows the formation of shocks, analogous to atmospheric fronts, and which contains a space and velocity-dependent source of energy to maintain the flow against dissipation. The detailed flow is calculated from a fine-grid numerical integration. Coarse-grid values, for testing a coarse-grid prediction scheme, are obtained by space-time averages. Since the coarse-grid prediction equation cannot represent the sub-grid-scale motions, statistical corrections are added in the form of parametric terms as a pragmatic substitute for the missing sub-grid-scale effects. Tests with different versions of the model show that substantial improvement over the straight- forward coarse-grid prediction can he obtained when the coefficients of appropriate parametric terms are determined by a multiple regression procedure.