Step-Mountain Technique Applied to an Atmospheric C-Grid Model, or How to Improve Precipitation near Mountains

Abstract

Starting with Arakawa and Lamb?s second-order C-grid scheme, this paper describes the modifications made to the dynamics to create a C-grid atmospheric model with a variable number of cells for each vertical column. Where mountains exist, grid cells are discarded at the bottom of the column so that the mass per square meter of retained cells is more nearly equal to that of horizontally adjacent cells. This leads to the following chain of causes and effects: decreased mass variations reduce the numerically induced alternating patterns in the horizontal velocity components, which reduce erroneous vertical mass fluxes, which reduce erroneous precipitation. In addition, horizontal flows above mountains are smoother, the Ferrel cell is stronger, and the polar cell is better organized. The C-grid performs geostrophic adjustment best among the gridpoint schemes, being the most sensitive to condensation-released heating perturbations. It also overreacts more egregiously to numerical errors, particularly with respect to the vertical mass flux, and consequently is often not used. Mesinger et al. applied the step-mountain (eta coordinate) technique to an E-grid scheme with excellent results. Its application to the C-grid reduces numerical errors in the vertical mass flux resulting in improvements in precipitation and other quantities.