A Method of Upgrading a Hydrostatic Model to a Nonhydrostatic Model

Abstract

As the sigma-p coordinate under hydrostatic approximation can be interpreted as the mass coordinate with out the hydro static approximation, we propose a method that up grades a hydro static model to a nonhydrostatic model with relatively less effort. The method adds to the primitive equations the extra terms omitted by the hydro static approximation and two prognostic equations for vertical speed w and nonhydrostatic part pres sure p'. With properly formulated governing equations, at each time step, the dynamic part of the model is first integrated as that for the original hydro static model and then nonhydrostatic contributions are added as corrections to the hydro static solutions. In applying physical parameterizations after the dynamic part integration, all physics pack ages of the original hydro static model can be directly used in the nonhydrostatic model, since the up graded nonhydrostatic model shares the same vertical coordinates with the original hydro static model. In this way, the majority codes of the nonhydrostatic model come from the original hydro static model. The extra codes are only needed for the calculation additional to the primitive equations. In order to handle sound waves, we use smaller time steps in the nonhydrostatic part dynamic time integration with a split-explicit scheme for horizontal momentum and temperature and a semi-implicit scheme for w and p'. Simulations of 2-dimensional mountain waves and density flows associated with a cold bubble have been used to test the method. The idealized case tests demonstrate that the pro posed method realistically simulates the nonhydrostatic effects on different atmospheric circulations that are revealed in the oretical solutions and simulations from other nonhydrostatic models. This method can be used in upgrading any global or mesoscale models from a hydrostatic to nonhydrostatic model.

Keywords

• Nonhydrostatic model
• Hydrostatic to nonhydrostatic