A NUMERICAL GLOBAL SHALLOW WATER MODEL BASED ON THE
               SEMI-LAGRANGIAN ADVECTION OF POTENTIAL VORTICITY

                                       
                          J. R. Bates and Yong Li  
                   NASA/Goddard Laboratory for Atmospheres
                             Greenbelt, Maryland.

                                  A. Brandt 
               Weizmann Institute of Science, Rehovot, Israel.

                           S. McCormick and J. Ruge
                  University of Colorado, Boulder, Colorado.


   
    Potential vorticity (PV) is coming to be seen as the most important
dynamical quantity in large scale atmospheric dynamics. Existing numerical
atmospheric models that use primitive equations do not predict the PV
directly.  

    We are engaged in a project aimed at predicting the PV directly, by
using its evolution equation as one of the governing equations in the 
primitive equation set.  The semi-Lagrangian approach is used, thus giving
high accuracy for PV advection and offering the prospect of a more 
faithful simulation of the PV evolution than is otherwise possible.
The approach is made feasible by the use of an efficient multigrid 
method for solving the nonlinear implicit finite-difference equations
that arise at each time step.

The model is integrated for periods of up to 50 days using a variety of
initial conditions.  Comparisons with an existing semi-Lagrangian finite
difference shallow water model and an Eulerian spectral model indicate the
advantages of the PV approach, especially in cases of highly nonlinear flow.