A Global Semi-Implicit Semi-Lagrangian Shallow-Water Model on Locally Refined Grids

Abstract

A variable-resolution global shallow-water model has been developed. The scheme makes use of a two-time-level semi-implicit semi-Lagrangian discretization, and the variable-resolution grid is composed of a basic global uniform coarser grid, employing successive local refinements to obtain high resolution over a region of interest. The algorithm on the locally refined grid is implemented in an efficient way with the help of a multigrid method, employed in the solution of the (nonlinear) elliptic equation resulting from the semi-implicit discretization. The model is very stable and attains high resolution over the area of interest at considerably lower costs than that of a global model with uniform high resolution. The results of comparisons are presented. The use of local refinement techniques is shown to be an effective way to obtain variable resolution in finite-difference global models.