A Three-Layer Diffusion Model as Applied to Unstable Atmospheric Conditions

Abstract

A three-layer numerical model, incorporating the ideas of forced, free, and windless convection, is constructed for use in the two-dimensional diffusion equation for steady state conditions. The eddy diffusivity of momentum Km in the first layer is that given by Monin and Obukhov, while in the second layer Km is proportional to the 4/3; power of the height z. In the third layer Km ? z2. The wind velocity profiles developed for the model are consistent with the definition of the eddy diffusivity of momentum for the layer of constant shearing stress. The numerical model is tested for its reliability by comparing numerical results with analytic results attained under the same conditions. The model is then applied to the unstable Project Prairie Grass gas diffusion data in order to see if the model can account for the observed cross-wind integrated concentration c?. A satisfactory comparison between the predicted and the observed field of c? is obtained. The exceptions are those cases exhibiting great instability. The comparisons achieved were an improvement over those obtained by Elliott in a study of the unstable Project Prairie Grass data.