A Generalized Sigma-Coordinate System for the MM5

A generalized sigma-coordinate system is presented that allows for a rapid vertical decay of small-scale topographic structures in the coordinate surfaces. Its properties are similar to the smooth-level vertical-coordinate system recently introduced by Schär et al., but it is designed for the coordinate definition used in the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5). An idealized advection test demonstrates that the accuracy of the horizontal advection greatly benefits from the reduced slope of the coordinate surfaces at some vertical distance from the topography. Moreover, a test considering an atmosphere at rest in the vicinity of an isolated mountain shows that the new coordinate system strongly reduces the numerical noise appearing in such a configuration. The noise turns out to be related to a local numerical instability triggered by computing the horizontal temperature diffusion along sloping coordinate surfaces. When the temperature diffusion is computed truly horizontally, the noise disappears completely.