A GENERALIZED MATHEMATICAL SCHEME TO ANALYTICALLY SOLVE THE ATMOSPHERIC DIFFUSION EQUATION WITH DRY DEPOSITION

A generalized mathematical scheme is developed to simulate the turbule nt dispersion of pollutants which are adsorbed or deposit to the groun d. The scheme is an analytical (exact) solution of the atmospheric dif fusion equation with height-dependent wind speed and eddy diffusivitie s, and with a Robin-type boundary condition at the ground. Unlike publ ished solutions of similar problems where complex or non-programmable (e.g., hypergeometric or Kummer) Functions are obtained, the analytica l solution proposed herein consists of two previously derived Green's functions (modified Bessel functions) expressed in an integral form th at is amenable to numerical integration. In the case of invariant wind speed and turbulent eddies with height (i.e., Gaussian deposition plu me), the solution reduces to an equivalent well-known heat conduction solution. The physical behavior represented by the Green's functions c omprising the solution can be interpreted. This generalized scheme can be modified further to account for inversion effects or other meteoro logical conditions. The solution derived is useful for examining the a ccuracy and performance of sophisticated numerical dispersion models, and is particularly suitable for modeling the transport of pollutants undergoing strong surface adsorption or high depositional losses. Copy right (C) 1996 Elsevier Science Ltd