A proposed adiabatic formulation of 3-dimensional global atmospheric models based on potential vorticity

A 2-time-level finite difference atmospheric general circulation model base d on the semi-Lagrangian advection of pseudo potential vorticity (which bec omes potential vorticity in that parr of the domain where the hybrid vertic al coordinate becomes isentropic) has been formulated. At low levels, the h ybrid vertical coordinate is terrain following. The problem of isentropic p otential vorticity possibly becoming ill-defined in the regions of planetar y boundary layer is thus circumvented. The divergence equation is a compani on to the (pseudo) potential vorticity equation and the model is thus calle d a PV-D model. Many features of a previously developed shallow water PV-D model are carried over: a modification of the PV equation needed to give co mputational stability of long Rossby waves; a semi-Lagrangian semi-implicit treatment of both the linear and the nonlinear terms; the use of an unstag gered grid in the horizontal; the use of a nonlinear multigrid technique to solve the nonlinear implicit equations. A linear numerical stability analy sis of the model's gravity-inertia waves indicates that the potential tempe rature needs to be separated into horizontal mean and perturbation parts. T his allows an implicit treatment of the vertical advection associated with the mean in the thermodynamic equation. Numerical experiments with developi ng baroclinic waves have been carried out and give realistic results.