Abstract: The design and development of a general primitive equation model is described in this paper. The model is three-dimensional and is particularly suitable for complex terrain and planetary boundary layer(PBL) processes as well as atmospheric diffusion. The model utilizes a high resolution parameterization, which includes surface heat, moisture and momentum fluxes. The ground temperature is predicted from a surface energy budget and a slab model. Short-and long-wave radiation is considered in the surface energy budget. In order to improve the description of high resolution PBL physical processes, a turbulence kinetic energy(TKE) equation is derived and K-e closure is adopted.The basic and averaged equations is first presented in this paper. Then a consistent set of the averaged equations was derived in terrain-following coordinate systems, in which the Exner function was applied to pressure gradient force. After introducing TKE equation and K-e closure, we discuss particularly the PBL parameterization. In the numerical method, and implicit cubic spline-function method was developed to compute the advection terms.In order to test the consideration of physical processes, the PBL-parameterization, the finite-differencing scheme and the boundary condition, we conducted a comparison of observational and simulative results of two-dimensional model with high spatial resolution. The horizontal resolution both the real terrain data and themodel are 1km. The results of 12-h and 24-h simulations for the PBL processes and the contaminant(TSP, S02) diffusion in Lanzhou Basin during the winter showed that this model is capable of successful simulating the PBL and contaminant diffusion processes under a stable zonal flow weather condition. However, it is necessary to run three-dimensional model for complex weather condition.

Key words: boundary layer parameterization, K-e closure, atmospheric diffusion, mesoscale numerical model, implicit cubic spline function