An Alternative Approach to Nonhydrostatic Modeling

Abstract

An alternative approach to the design of nonhydrostatic numerical weather prediction (NWP) models is presented. Instead of extending mesoscale nonhydrostatic modeling concepts to the synoptic scales and beyond, a hydrostatic NWP model using the mass-based σ vertical coordinate has been extended to include the nonhydrostatic motions, preserving the favorable features of the hydrostatic formulation. In order to do so, the system of nonhydrostatic equations was split into two parts: (a) the part that corresponds to the hydrostatic system, except for higher-order corrections due to the vertical acceleration, and (b) the system of equations that allows computation of the corrections appearing in the first system due to the vertical acceleration. This procedure does not require any linearization or approximation. With this approach, the nonhydrostatic dynamics has been introduced through an add-on nonhydrostatic module. The separation of the nonhydrostatic contributions shows in a transparent way where, how, and to what extent relaxing the hydrostatic approximation affects the hydrostatic equations. The nonhydrostatic module can be turned on and off depending on resolution, so that the model can be run in the hydrostatic mode at lower resolutions with no extra cost. This also allows easy comparison of hydrostatic and nonhydrostatic solutions obtained using otherwise identical model. The nonhydrostatic model developed appears to be computationally robust at all resolutions and efficient in NWP applications. With the current coding, the extra computational effort needed due to the nonhydrostatic extension is of the order of 20% of that required by the hydrostatic dynamics, both in terms of computer time and memory. Compared to the hydrostatic version of the model, no additional computational boundary conditions are needed in real data runs. At lower resolutions, in the hydrostatic limit, the forecasts of traditional meteorological parameters obtained using the hydrostatic and the nonhydrostatic modes are almost indistinguishable. The model also demonstrated the presence of important two-dimensional nonhydrostatic effects at very high horizontal resolutions. At these scales, the nonhydrostatic model was generally more robust than the hydrostatic one and produced smoother solutions. The impact of the nonhydrostatic dynamics appears to be weak at the horizontal resolutions of about 8 km. However, a visible effect on the orographic precipitation was detected. In addition to that, the nonhydrostatic deviation of pressure made a significant small-scale contribution to the pressure gradient force at places. The proposed approach appears well suited for models designed for a wide range of horizontal resolutions, and in particular for unified global and regional forecasting systems. Being developed from an existing model, the new model requires only minimal changes to the existing preprocessing and postprocessing infrastructure.