We derived a finite-difference scheme of primitive equations for the staggered coordinate system as well as for the ordinary one. This scheme is supposedly reasonable from the standpoint of compatibility with the system of original differential equations. We also formulated computational boundary conditions with a great care.
In order to test the usefulness of this computation scheme, the forecastings of wave motions in a channel with the balance Barotropic model and with the non-balance barotropic model of the atmosphere were attempted. The finite-difference form we used was computationally stable for both models and caused no trouble in 48-hour forecast of the height field which was given mathematically at the initial time. The budget of energy within the forecasting domain could be estimated accurately. Besides, the results of the forecasting agree well with what can be expected theoretically from the model atmosphere.
Since the numerical test of the finite-difference form gave fairly satisfactory result in the forecasting of simple pattern, we tried to apply the scheme for the non-balance model to the barotropic forecasting of 500-mb height over the northern hemisphere. There occurred no trouble in this case, either.
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