Computational dispersion properties of vertically staggered grids for atmospheric models

Abstract

It is shown that the best vertical grids have computational dispersion properties corresponding to a regular (equidistant, unstaggered) grid with twice the vertical resolution. These best vertical grids are: 1) two well-known vertically staggered grids, namely, the widely used Lorenz grid and the Charney-Phillips grid; 2) two other vertically staggered grids carrying both horizontal and vertical velocity components at the same levels; and 3) the new time-staggered versions of all the aforementioned grids, and the time-staggered regular vertical grid, if used with either the appropriate version of an economical explicit scheme or a semi-implicit scheme for approximations with these time-staggered grids. The time-vertically staggered grids considered here provide twice the effective vertical resolution of comparable vertically staggered grids for finite-difference approximations of the vertical derivatives in vertical advection and vertical diffusion terms. -from Author