A K-theory of dispersion, settling and deposition in the atmospheric surface layer

The classical analytical treatments of dispersion developed in the period 1940 to 1960 included “non-Gaussian” effects such as particle settling (b), deposition (g) and the vertical gradient in diffusivity (K(z)=K0 + mz). Unfortunately, they used an unphysical lower boundary condition linking b with g. These “non-Gaussian” effects, and the interaction between them, can be evaluated correctly 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 Lb=K0*U/b^2 , Lg = K0*U/g^2 and Lm = K0*U/m^2 respectively. In this case, the ratio b/m plays a central role and when b/m=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 formula for the case when all three non-Gaussian effects are strong. A more general result is that surface concentration scales as C(x)~g^-2 whenever deposition is strong. Categorization of dispersion problems using b/m , Lg and Lb is proposed.