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We describe the development of a general, predictive, hydrostatic meteorological model. The model is three-dimensional and is suitable for a wide variety of problems, ranging from the synoptic scale to the small end of the mesoscale. The model contains provisions for variable terrain, a moisture cycle, sensible heat addition at the earth's interface, and high- and low-resolution boundary layer physics. This paper presents the mathematical and numerical formulation used in the various options of the model. First we write the basic equations on a Lambert conformal projection. Then we describe the horizontal and vertical grid structure, the finite-difference equations, and the energetics of the three-dimensional model and its two-dimensional analog. We consider the role of the lateral boundary conditions for limited area forecasts, with emphasis on their effect on the mean motion over the domain. Two options for including the frictional and diabatic effects at the earth's surface are presented. These include a bulk parameterization and a high-resolution model of the planetary boundary layer. Both models use a predictive surface energy equation developed by Blackadar to determine the time-dependent surface heat flux. The water vapor cycle and the parameterization of cumulus convection are summarized. Both stable non-convective (grid-scale relative humidity equal to 100%) and unstable convective (grid-scale relative humidity less than 100%) precipitation are modeled. We present several preliminary simulations with the two-dimensional analog, in order to investigate the sensitivity of the model to the finite-differencing scheme, the treatment of the upper boundary condition, and the effect of the horizontal diffusion on the solutions forced by moderate flow over steep terrain. The model is shown to be energetically consistent to a good approximation, and capable of simulating hydro-static mountain waves realistically. Three-dimensional experiments are discussed in a separate paper by Warner et al. (1978).
Anthes et al. (Tue,) studied this question.