A Semi-Analytical Model for Short Range Near Ground Dispersion

A semi-analytical model for dispersion of passive scalar from continuous ground sources up to distances of a few hundred meters is presented. The model is based on an equation for the cross wind integrated concentration (CWIC) with a vertical turbulent diffusion coefficient that depends on the distance from the source, and on an equation for the lateral width of the cloud.

We present a formal analytical solution for the CWIC, assuming a distance dependent power law (in Z) form of the vertical turbulent diffusivity. This solution, based on the parametrix method, is of the form of an infinite series. The first term in this series is taken as an approximate solution of the CWIC. For the cloud lateral width we propose a Langevin stochastic model, that depends on the cloud height. The formal analytical solution of this equation is used to derive a set of two equations for , which are easily solved numerically.

The model was tested against Prairie Grass Project data. Very good agreement was achieved for and for the near ground CWIC without applying any data fitting. Based on the model results, we present simple analytical formulas for the distance dependent vertical diffusion coefficient which result in a very close fit to the model results. Implementation of this simple formulas to the solution of the CWIC is extremely simple and computationally efficient.