Predicting the track of a moving hurricane accurately requires resolving the flow field adequately on both the large scale surrounding the storm and the small scale within the storm itself. Since the scales involved may differ by two orders of magnitude, models using uniform resolution are inappropriate.
In this paper we describe a simple numerical model which uses an adaptive multigrid scheme to automatically refine the mesh around the storm as it moves. Based on the nondivergent barotropic vorticity equation on a section of the sphere, the model uses the Arakawa Jacobian in space and an efficient Runge-Kutta scheme in time. Careful attention is paid to maintaining conservation properties locally in the discretization. Estimates of the local truncation error obtained during multigrid processing are used to decide where to refine or coarsen the grid.
We will present the details of the model formulation, focusing on the grid structure and the mesh refinement algorithm, and exploring differences between the MLAT and FAC approaches. Numerical results will be shown comparing the accuracy of the fully adaptive solution to that obtained with a uniform high-resolution grid and demonstrating the savings in computation time.