Js. Lin et Lm. Hildemann, ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND-SPEED AND EDDY DIFFUSIVITIES, Atmospheric environment, 30(2), 1996, pp. 239-254
Three-dimensional analytical solutions of the atmospheric diffusion eq
uation with multiple sources and height-dependent wind speed and eddy
diffusivities are derived in a systematic fashion. For homogeneous Neu
mann (total reflection), Dirichlet (total adsorption), or mixed bounda
ry conditions, the solutions for a single source are comprised of thre
e components: a source strength, a crosswind dispersion factor, and a
vertical dispersion factor. The two dispersion factors together consti
tute a Green's function - the concentration response due to a unit dis
turbance (source). When the general point source Green's functions are
derived for a bounded domain (inversion effect) with various boundary
conditions and arbitrary power-law profiles for wind speed and eddy d
iffusivities, previously published equations are found to be simplifie
d versions of this more general case. A methodology based on the super
position of Green's functions is proposed, which enables the estimatio
n of ambient concentrations not only from a single source, but also fr
om multiple point, line, or area releases.