Exploring a multi-resolution modeling approach within the shallow-water equations

We find that potential vorticity is conserved to within machine precision and total available energy is conserved to within time-truncation error. This finding holds for the full suite of meshes, ranging from quasi-uniform resolution and highly-variable resolution meshes. Using shallow-water test cases 2 and 5, we find that solution error is controlled primarily by the grid resolution in the coarsest part of the model domain.

This finding is consistent with results obtained by others. When these variable resolution meshes are used for the simulation of an unstable zonal jet, we find that the core features of the growing instability are largely unchanged as the variation in mesh resolution increases. The main differences between the simulations occur outside the region of mesh refinement and these differences are attributed to the additional truncation error that accompanies increases in grid spacing.

Overall, the results demonstrate support for this approach as a path toward multi-resolution climate system modeling.