The mixed spectral finite-difference (MSFD) model : improved upper boundary conditions

The Mixed Spectral Finite-Difference (MSFD) model for neutrally stratified, turbulent surface-layer flow has been shown to produce accurate, computationally economical predictions of flow in complex terrain as long as certain conditions are met. Since the model is based on linearized equations, variations in the surface roughness must not be extreme and terrain slopes must, in practice, be of order 0.3 or less. This paper summarizes modifications to the MSFD model since the original description appeared in Beljaars et al. (1987a) and Karpik (1988). A significant improvement is the formulation of the upper boundary conditions. This new approach follows from an asymptotic form of the model equations where vertical diffusion terms are neglected. The resulting differential equations have an explicit, analytically expressible solution. The asymptotic solution derived in this way is shown to match very well with the solution to the full equation set within the computational domain. We illustrate that the improved upper boundary conditions permit the use of a computational top boundary that is lower than was previously possible, thus increasing computing efficiency without sacrificing accuracy. The paper concludes with a brief description of MSFD-PC, the personal computer version of the model, and an outline of future development plans for the MSFD model.