A Mesoscale Numerical Model Using the Nonhydrostatic Pressure-based Sigma-Coordinate Equations: Model Experiments with Dry Mountain Flows

Abstract

A nonhydrostatic numerical model suitable for simulating mesoscale meteorological phenomena is developed and described here. The model is the first to exploit the nonhydrostatic equation system in σ (normalized pressure) coordinates. In addition to the commonly recognized advantages of σ-coordinate models, this model is potentially advantageous in nesting with large-scale σ-coordinate models. The equation system does not support sound waves but it presents the internal gravity waves accurately. External gravity waves are the fastest wave modes in the system that limit the integration time step. However, since short nonhydrostatic external waves are much slower than the speed of shallow-water waves and because fast hydrostatic long waves imposes less severe restriction on the time step when they are resolved by many grid points, a large time step (compared to that determined by the speed of hydrostatic shallow-water waves) can be used when horizontal grid spacing is on the order of 1 km. The system is solved in a way analogous to the anelastic system in terrain-following height coordinates. The geopotential height perturbation is diagnosed from an elliptic equation. Conventional finite-differencing techniques are used based on Arakawa C grid, The flux-corrected transport (FCT) scheme is included as an option for scalar advection. The model has been used to study a variety of problems and here the simulations of dry mountain waves are presented. The resists of simulations of the 11 January 1972 Boulder severe downslope windstorm are reported and the wave development mechanism discussed.