An Adaptive Multigrid Barotropic Tropical Cyclone Track Model

This paper describes the application of adaptive multigrid techniques to the problem of tropical cyclone track prediction. Based on the nondivergent barotropic vorticity equation, the model uses an adaptive multigrid method to refine the mesh around the moving vortex. Like conventional nested-grid models, this model achieves nonuniform resolution by superimposing uniform grids of different mesh sizes. Unlike nested-grid models, multigrid processing uses the interplay between solutions on fine and coarse grids—in regions where they overlap—to 1) solve the implicit problem for the streamfunction with optimum efficiency, 2) automatically achieve two-way interaction at the grid interfaces, and 3) provide accurate truncation error estimates for use in determining where to refine or coarsen the grids. An exchange rate algorithm accomplishes the latter task, approximately optimizing the grid selection based on a user-specified trade-off between accuracy and computational work. Numerical results demonstrate that the model chooses reasonable grids with minimal user intervention. Using adaptive mesh refinement is at least an order of magnitude more efficient than using a single uniform grid, and the overhead cost of adaptive regridding is less than 2% of the total execution time. The adaptive multigrid approach allows track prediction errors due to discretization to be essentially eliminated from the problem at a reasonable computational cost.