A mathematical model has been proposed for computing crosswind-integrated concentration in a capping inversion layer by considering the eddy diffusivity as a function of down wind distance from the source. An analytical solution of the resulting partial differential equation with the physically relevant boundary conditions has been obtained for the general functional form of eddy diffusivity using the method of eigen-function expansion.
The model with eddy diffusivity as a linear function of downwind distance is validated with the available data in the literature from Copenhagen in Denmark and plume validation experiment conducted by Electric Power Research Institute at Kincaid in USA. The agreement is found to be good between the computed and the observed concentrations in both the experiments. In fact, majority of the concentrations predicted from the model are with in a factor of two to observations.