A mixed spectral finite-difference model for pollutant concentrations over a hill

Given incident logarithmic profiles of wind and pollutant concentration above a rough, absorbing surface, the three-dimensional distribution of pollutant concentration over a hill of gentle slope is determined from a linearized model. The model is applied in neutrally stratified flow, without chemistry, and is integrated using spectral methods in the horizontal and a finite-difference scheme in the vertical. This approach allows for flexibility in choosing a closure scheme and a variety of surface boundary conditions. This was not possible in the analytic approach of Padro (1987) who added pollutant concentration and flux to the MS3DJH/1 model of Walmsley et al. (1980). The present model requires as input the turbulent kinetic energy, E, dissipation, , and the perturbation vertical velocity, w, from the three-dimensional boundary-layer flow model of Beljaars et al. (1987), hereinafter referred to as MSFD, The latter model also supplies wind velocity perturbations at the upper boundary, as input to upper boundary conditions on the pollutant flux perturbations.The present study describes applications of the model to idealized terrain features: isolated two- and three-dimensional hills and ridges and an infinite series of ridges. (Application to real terrain, however, presents no difficulties.) Comparisons were made with different (though uniform) surface roughnesses. Tests were performed to examine the effect of upstream terrain features in the periodic domain and to illustrate the importance of the vertical resolution of the output for interpreting results from the sinusoidal terrain case.