A K-Theory of Dispersion, Settling and Deposition in the Atmospheric Surface Layer

Dispersion estimates with a Gaussian plume model are often incorrect because of particle settling (beta), deposition (gamma) or the vertical gradient in diffusivity (K (v) (z) = K (0) + mu z). These "non-Gaussian" effects, and the interaction between them, can be evaluated with a new Hankel/Fourier method. Due to the deepening of the plume downwind and reduced vertical concentration gradients, these effects become more important at greater distance from the source. They dominate when distance from the source exceeds L (beta) = K (0) U/beta 2, L (gamma) = K (0) U/gamma 2 and L (mu) = K (0) U/mu 2 respectively. In this case, the ratio beta/mu plays a central role and when beta/mu = 1/2 the effects of settling and K gradient exactly cancel. A general computational method and several specific closed form solutions are given, including a new dispersion relation for the case when all three non-Gaussian effects are strong. A more general result is that surface concentration scales as C(x) similar to gamma 2 whenever deposition is strong. Categorization of dispersion problems using beta/mu, L (gamma) and L (mu) is proposed.