Analytical Parameterizations of Diffusion: The Convective Boundary Layer

Abstract

A brief review is made of data bases which have been used for developing diffusion parameterizations for the convective boundary layer (CBL). A variety of parameterizations for lateral and vertical dispersion, σy and σz, are surveyed; some of these include mechanical turbulence, source height, or buoyancy effects. Recommendations are made for choosing among these alternatives, depending on the type of source. Because observations of passive plumes indicate that the Gaussian model does a poor job of describing vertical diffusion in the CBL, alternative models for predicting dimensionless crosswind integrated ground concentration, Cy, are reviewed and compared. These include an analytical equation which closely approximates laboratory results; this equation can be applied to any source height > 0.04zi, where zi is the mixing depth. An analysis of a limited amount of buoyant plume data indicates that a radically different approach is needed when the dimensionless buoyancy flux, F*, exceeds 0.1. Such plumes impinge on the ?lid? of the mixing layer before ground impact occurs, and residual plume buoyancy causes enhanced lateral spreading under the lid; the observations indicate that σy approximates the x? law that applies to buoyant plume rise when F* > 0.06. The residual buoyancy also causes a delay in downward mixing that is proportional to F*. The main consequence of these two effects is that maximum ground concentration is reduced, compared to that from passive plumes, and is independent of wind speed. For smaller F*, the observations indicate that, with an assumed plume rise ?h = 3ziF*?, several different Cy parameterizations give satisfactory results, including a Gaussian model.