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 integra- tions 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 hemis- pheric 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. Pres- ently, 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.