Design of an Atmospheric Model Based on a Generalized Vertical Coordinate

Abstract

Although there are important advantages in the use of an isentropic vertical coordinate in atmospheric models, it requires overcoming computational difficulties associated with intersections of coordinate surfaces with the earth?s surface. In this paper, the authors present a model based on the generalized vertical coordinate, ? = F(?, p, pS), in which an isentropic coordinate can be combined with a terrain-following σ coordinate near the surface with a smooth transition between the two. One of the key issues in developing such a model is to satisfy consistency between the predictions of the pressure and the potential temperature. In the model presented in this paper, consistency is maintained by the use of an equation that determines the vertical mass flux. A procedure to properly choose ? = F(?, p, pS) is also presented, which guarantees that ? is a monotonic function of height even when unstable stratification occurs. In the vertical discretization, the Charney?Phillips grid is used since, with this grid, it is straightforward to satisfy the thermodynamic equation when ? = ?. In the generalized vertical coordinate, determining the pressure gradient force requires both the Montgomery potential and the geopotential at the same levels. The discrete hydrostatic equation is designed to maintain consistency between the two. The vertically discrete equations also satisfy two important integral constraints. With these features, the model becomes identical to the isentropic coordinate model developed by Hsu and Arakawa when ? = ?. To demonstrate the performance of the model, the simulated nonlinear evolution of a midlatitude disturbance starting from random disturbances is presented. In the simulation, physical processes are represented by simple thermal forcing in the form of Newtonian heating and friction in the form of Rayleigh damping. During the evolution of the disturbance, the model generates sharp fronts both at the surface and in the upper and middle troposphere. No serious computational difficulties are found in this simulation.