Higher Order Finite-Differencing Experiments with a Semi-Implicit Model at the National Meteorological Center

Abstract

Real data experiments are conducted using a semi-implicit version of NMC's six-layer primitive equation model to investigate reduction in spatial truncation error by higher order finite-differencing. The higher order approximations are applied to advection terms in the equations. Detailed results art presented for two developing winter storm cases over North America. Comparisons between second- and fourth-order versions of the coarse-mesh (381 km) model show that the higher order scheme produces improved predicted translational speeds of meteorological features. Forty-eight hour forecasts made by the fourth-order model are more accurate in both mass field and accumulated precipitation predictions. Fine-mesh (one-half the grid distance) forecasts have been made for one of the cases with both second- and fourth-order differencing. Second-order fine-mesh results are remarkably similar to those from the coarse-mesh fourth-order model, although the finer mesh does produce a more accurate forecast of precipitation. Fourth-order differencing in the fine mesh produces further improvements. The computational efficiency of the higher order coarse-mesh alternative to the fine mesh is an attractive feature to be considered in operational forecast environments.