Experiments with an adaptive multigrid shallow-water tropical cyclone model

The adaptive multigrid tropical cyclone track model MUDBAR achieves higher resolution near the vortex by superimposing nested overlapping grids with different mesh sizes. Unlike conventional nested-grid methods, multigrid processing allows optimal solution speed and accurate estimates of truncation error; the latter are used in an adaptive mesh refinement scheme to provide just the resolution needed at each point. Previous versions of the model were based on the nondivergent barotropic vorticity equation; we now consider the extension of the model to the shallow-water equations.

The discretization is based on the Arakawa C-grid, and uses semi-implicit (leapfrog/trapezoidal) time differencing. The implicit equations at each time step are converted to a single Helmholtz equation for the geopotential, which is solved by an FAS-FMG multigrid method. Grid interfaces are treated with open boundary conditions to minimize the effects of wave reflection.

Numerical results are used to compare the performance of the shallow-water model to that of the previous nondivergent version. Sensitivity of tropical cyclone tracks to model dynamics, resolution, and vortex structure are investigated.