Response to small‐scale forcing on two staggered grids used in finite‐difference models of the atmosphere

‘Source‐sink’ shallow water integrations are performed, using two limited area models with the Coriolis terms included. One of the models was defined on the staggered C grid, and the other on the semi‐staggered E/B grid. For each grid, experiments were performed with grid sizes of 250, 125 and 62.5 km. A source and a sink, of constant intensity, were placed symmetrically in the central part of the domain. They covered, for the three resolutions considered, areas of one, four and sixteen grid points, respectively. At the sink ‘point’, after 24 hours, substantial differences in the depth of the water existed between the lowest resolution experiments on the two grids. The differences were very much reduced in the two 125 km experiments, and were virtually absent in the highest resolution, 62.5 km, experiments. With increasing resolution, the depths at the sink on the two grids converged with about equal rapidity towards a value in between the two lowest resolution values. As to be expected on the basis of the geostrophic adjustment theory when applied to the spatially discretized systems, the depth on the low resolution C grid solution was found to be an underestimate, and that on the E grid an overestimate, of the true value. It is demonstrated that the rate of convergence on the E grid can be improved by increasing the weight of the modification introduced to cope with the grid separation problem. An implication of the results obtained in the simple experiments reported here is that forcing schemes should be considered which would avoid forcing at single grid points. Where appropriate, simultaneous forcing at several neighbouring points may be an attractive alternative approach.