Comparative evaluation of fine-mesh, limited-area grid schemes

An extensive investigation has been made of a one-level, fine-mesh, limited area, primitive equation numerical weather prediction (NWP) model. The aim of the investigation was to determine the relative merits of a variety of finite-difference schemes, boundary conditions and methods of initialisation, in anticipation of the development of a multi-level model. Two types of time-differencing schemes were studied, namely, the leapfrog method and the semi-implicit scheme of McPherson (1971). The semi-implicit scheme proved to be nearly four times as fast as the leapfrog method and displayed less raggedness at the two grid length level. Forecasts were also made on both a regular grid and the staggered grid of Eliassen (l956). The staggered grid forecasts required slightly longer computation time but provided an effective resolution equal to one-half that of the regular grid. The associated decrease in truncation errors resulted in improved forecasts. However the complexity of the code even at the one-level stage is a significant factor weighing against the staggered grid. Gravity waves reflected and generated at the lateral boundaries are of considerable concern in limited-area NWP experiments with the primitive equations. The procedures of Charney (1962), Gerrity and McPherson (1969) and Bushby (1969) were all successfully tested. It is suggested that the Gerrity and McPherson approach is the most desirable, essentially because of its extreme simplicity. Initialisation with the balance equation and dynamic initialisation were each tested. Little difference was observed in the quality of the forecasts, suggesting that both procedures should be retained for experimentation with the multi-level model before any preference is expressed.