A stable numerical integration scheme for the primitive meteorological equations

Abstract A stable numerical integration scheme is applied to the non‐divergent barotropic vorticity equation. Integrations are performed with time steps ranging from 15 min to 4 h. The root‐mean‐square differences between the forecasts are calculated in order to measure the sensitivity of the predictions to the size of the time step. These experiments show that the truncation errors remain reasonably small with time steps as large as two hours. This scheme is then associated with the semi‐implicit algorithm in the integration of the shallow water equations. Integrations are carried out with large time steps and the resulting predictions are presented in order to demonstrate that the scheme is perfectly stable.