A generalized mathematical scheme to analytically solve the atmospheric diffusion equation with dry deposition

Abstract

A generalized mathematical scheme is developed to simulate the turbulent dispersion of pollutants which are adsorbed or deposit to the ground. The scheme is an analytical (exact) solution of the atmospheric diffusion equation with height-dependent wind speed and eddy diffusivities, and with a Robin-type boundary condition at the ground. Unlike published solutions of similar problems where complex or non-programmable (e.g., hypergeometric or Kummer) functions are obtained, the analytical solution proposed herein consists of two previously derived Green's functions (modified Bessel functions) expressed in an integral form that is amenable to numerical integration. In the case of invariant wind speed and turbulent eddies with height (i.e., Gaussian deposition plume), the solution reduces to an equivalent well-known heat conduction solution. The physical behavior represented by the Green's functions comprising the solution can be interpreted. This generalized scheme can be modified further to account for inversion effects or other meteorological conditions. The solution derived is useful for examining the accuracy 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.