An Implicit Time Integration Scheme for Baroclinic Models of the Atmosphere

semi-implicit time integration algorithm developed earlier for a barotropic model resulted in a n 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.