An Improved Method for Computing Horizontal Diffusion in a Sigma-Coordinate Model and Its Application to Simulations over Mountainous Topography

Abstract A set of modifications is presented to reduce the unphysical impact of horizontal diffusion in numerical models with a terrain-following sigma-coordinate system. At model levels sufficiently far away from the ground, vertical interpolation is used to compute diffusion truly horizontally when the coordinate surfaces are sloping. Close to the ground, where truly horizontal computation of diffusion is not everywhere possible without intersecting the topography, a combination of one-sided truly horizontal diffusion and orography-adjusted diffusion along the sigma surfaces is used for most of the variables. The latter means that the diffusion coefficient is reduced strongly when the grid points involved in the computation of horizontal diffusion are located at greatly different heights. For temperature, one-sided horizontal diffusion is not used because it damps the slope wind circulation in an unphysical way. However, a temperature gradient correction is applied to the terrain-following part of the t...