A simple algorithm to modify the National Meteorological Center (NMC) Nested Grid Model (NGM) from second-order finite differencing and interpolation on a staggered grid to fourth order is derived and evaluated for operational application. A surprising result of a linear computational stability analysis that predicts long- wave instability is also elucidated. A linear computational stability analysis including a smoothing term, however, is stable for long waves. Thus, numerous forecasts with the fourth-order scheme show no sign of instability because the NGM includes a smoothing term.
Twenty-four NGM forecasts with fourth-order finite differencing and interpolation were compared to the operational second-order runs. The results show consistent improvement of all forecast fields by the fourth- order scheme in terms of average anomaly correlation. The average anomaly correlation during the entire period shows much more improvement in the lower layers than the upper layers.
Results for one case are presented in detail. The operational forecast failed to predict the location of a synoptic low over the Great Lakes. The fourth-order model more accurately predicted the location and intensity of the storm. Furthermore, most of the pressure centers in the sea level pressure field show intensity in the fourth- order model that is stronger than or equal to those in the second order.