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

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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 that part 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 isentropic potential vorticity possibly becoming ill‐defined in the regions of planetary boundary layer is thus circumvented. The divergence equation is a companion to the (pseudo) potential vorticity equation and the model is thus called 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 computational stability of long Rossby waves; a semi‐Lagrangian semi‐implicit treatment of both the linear and the nonlinear terms; the use of an unstaggered grid in the horizontal; the use of a nonlinear multigrid technique to solve the nonlinear implicit equations. A linear numerical stability analysis of the model's gravity–inertia waves indicates that the potential temperature needs to be separated into horizontal mean and perturbation parts. This allows an implicit treatment of the vertical advection associated with the mean in the thermodynamic equation. Numerical experiments with developing baroclinic waves have been carried out and give realistic results.
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Document Type: Research Article

Affiliations: 1: Data Assimilation Office and Joint Center for Earth System Technology, NASA/Goddard Space Flight Center, Greenbelt, Maryland 20771, USA; 2: Front Range Scientific Computation, and University of Colorado, USA; 3: University of Copenhagen, Copenhagen, Denmark; 4: Weizmann Institute of Science, Israel

Publication date: March 1, 2000

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