Js. Lin et Lm. Hildemann, A GENERALIZED MATHEMATICAL SCHEME TO ANALYTICALLY SOLVE THE ATMOSPHERIC DIFFUSION EQUATION WITH DRY DEPOSITION, Atmospheric environment, 31(1), 1997, pp. 59-71
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