Adaptive grid refinement for numerical weather prediction

An adaptive atmospheric flow model is described and results of integrations with this model are presented. The adaptive technique employed is that of Berger and Oliger. The technique uses a finite difference method to integrate the dynamical equations first on a coarse grid and then on finer grids which have been placed based on a Richardson-type estimate of the truncation error in the coarse grid solution. By correctly coupling the integrations on the various grids, periodically re-estimating the error, and recreating the finer grids, uniformily accurate solutions are economically produced. The "primitive" hydrostatic equations of meteorology are solved for the advection of a barotropic cyclone and for the development of a baroclinic disturbance which results from the perturbation of an unstable jet. These integrations demonstrate the feasibility of using multiple, rotated, overlapping fine grids. Direct computations of the truncation error are used to confirm the accuracy of the Richardson-type truncation error estimates.