A Nonhydrostatic Model Based on a New Approach

Considerable experience with nonhydrostatic models has been accumulated on the scales of convective cloudsand storms. However, numerical weather prediction (NWP) deals with motions on a much wider range of temporal and spatial scales. Thus, difficulties that may not be significant on the small scales, may become important in NWP applications. Having in mind these considerations, a new approach has been proposed and applied in developing nonhydrostatic models intended for NWP applications. Namely, instead of extending the cloud models to synoptic scales, the hydrostatic approximation is relaxed in a hydrostatic NWP model. In this way the model validity is extended to nonhydrostatic motions, and at the same time favorable features of the hydrostatic formulation are preserved.

In order to apply this approach, the system of nonhydrostatic equations is split into two parts: (a) the part thatcorresponds to the hydrostatic system, except for corrections due to vertical acceleration, and (b) the system of equations that allows computation of the corrections appearing in the first system. This procedure does not require any additional approximation.

In the model, isotropic horizontal finite differencing is employed that conserves a number of basic and deriveddynamical and quadratic quantities. The hybrid pressure-sigma vertical coordinate has been chosen as the primary option. The forward-backward scheme is used for horizontally propagating fast waves, and an implicit scheme is used for vertically propagating sound waves. The Adams-Bashforth scheme is applied for the advection of the basic dynamical variables and for the Coriolis terms. In real data runs, the nonhydrostatic dynamics does not require extra computational boundary conditions at the top. The philosophy of the physical package and possible future developments of physical parameterizations are also reviewed.

A two-dimensional model based on the described approach successfully reproduced classical nonhydrostaticsolutions, thereby demonstrating the soundness of the formulation. Similarly, in high resolution NWP applications, the models developed have been fully competitive with other nonhydrostatic models, as well as with mature hydrostatic models.

In high resolution NWP applications, the efficiency of the described computational algorithm far exceeds those of most established state-of-the-art nonhydrostatic models. The high computational efficiency has been achieved primarily due to the time-stepping procedure. The remarkable computational efficiency observed demonstrates that meaningful nonhydrostatic forecasting/simulations have become feasible even on workstations and PC s.

Forecast examples obtained using the capability of the models to be run in both hydrostatic and nonhydrostatic modes demonstrate that significant differences between hydrostatic and nonhydrostatic forecasts can develop even at the resolution of 8 km. Also, the nonhydrostatic dynamics is computationally more robust.