Derivation of an eddy diffusivity depending on source distance for vertically inhomogeneous turbulence in a convective boundary layer

Accounting for the current knowledge of the convective boundary layer structure and characteristics, a new formulation for the eddy diffusivities to be used in atmospheric dispersion models has been derived. That is, expressions for the eddy diffusivities, depending on source distance, for inhomogeneous turbulence are proposed. The classical statistical diffusion theory, the observed spectral properties, and observed characteristics of energy-containing eddies are used to estimate these parameters. In addition, a vertical eddy diffusivity was introduced into an air pollution model, validated with the data of Copenhagen experiments, and compared with an improved Gaussian model. The results of this new method are shown to agree with the measurements of Copenhagen and also with those of the Gaussian model. Furthermore, the current study suggests that the inclusion of the memory effect, important in regions near an elevated continuous point source, improves the description of the turbulent transport process of atmospheric contaminants. The major advance shown in this paper is the necessity of including the downwind distance-dependent eddy diffusivity in air quality modeling, and it is demonstrated that such theory would suggest that it should yield better results than the asymptotic solution alone. It, in fact, does yield better results in the near and intermediate fields.