An Implicit Time Integration Scheme for Baroclinic Models of the Atmosphere

Abstract

A semi-implicit time integration algorithm developed earlier for a barotropic model resulted in an appreciable economy of computing time. An extension of this method to baroclinic models is formulated, including a description of the various steps in the calculations. In the proposed scheme, the temperature is separated into a basic part dependent only on the vertical coordinate and a corresponding perturbation part. All terms involving the perturbation temperature are calculated from current values of the variables, while a centered finite-difference time average is applied to the horizontal pressure gradient, the divergence, and the vertical motion in the remaining terms. This method gives computationally stable integrations with relatively large time steps. The model used to test the semi-implicit scheme does not include topography, precipitation, diabatic heating, and other important physical processes. Five-day hemispheric integrations from real data with time steps of 60 and 30 min show differences of the order of 3 m. These errors are insignificant when compared to other sources of error normally present in most numerical models. Presently, this model produces relatively good short-range predictions, and this is a strong factor in favor of inserting the major physical processes as soon as possible.