ANALYTICAL SOLUTIONS OF THE ATMOSPHERIC DIFFUSION EQUATION WITH MULTIPLE SOURCES AND HEIGHT-DEPENDENT WIND-SPEED AND EDDY DIFFUSIVITIES

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.