A simple model containing gravity waves of phase speed C and a basic current U is used to test the hypothesis that in a nested grid system of different mesh sizes a better computation on the fine grid results if the outer, coarse-grid forecast is not made independently of the limited-area, fine-grid forecast but interacts with the fine grid throughout the integration. This hypothesis, which is based on an appeal to the characteristics of the differential equation, is verified by the tests, especially when C is less than U. A two-step Lax-Wendroff scheme with the staggered arrangement of variables suggested by Eliassen is used in both grids.

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