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

Abstract

A 2-time-level finite difference atmospheric general circulation model based on the semi-Lagrangian advection of pseudo potential vorticity (which becomes potential vorticity in thatpart of the domain where the hybrid vertical coordinate becomes isentropic) has been formulated.At low levels, the hybrid vertical coordinate is terrain following. The problem of isentropicpotential vorticity possibly becoming ill-defined in the regions of planetary boundary layer isthus circumvented. The divergence equation is a companion to the (pseudo) potential vorticityequation and the model is thus called a PV-D model. Many features of a previously developedshallow water PV-D model are carried over: a modification of the PV equation needed to givecomputational stability of long Rossby waves; a semi-Lagrangian semi-implicit treatment ofboth the linear and the nonlinear terms; the use of an unstaggered grid in the horizontal; theuse of a nonlinear multigrid technique to solve the nonlinear implicit equations. A linearnumerical stability analysis of the model’s gravity–inertia waves indicates that the potentialtemperature needs to be separated into horizontal mean and perturbation parts. This allowsan implicit treatment of the vertical advection associated with the mean in the thermodynamicequation. Numerical experiments with developing baroclinic waves have been carried out andgive realistic results.