A first-order WKB approximation for air pollutant dispersion equation

In this work, we used a combined first-order Wentzel–Kramers–Brillouin (WKB) approximation and the Sturm–Liouville theory to solve the air pollutant dispersion equation. In the light of previous works, we extended the investigation by considering the eddy diffusion coefficient as a function of height and downwind distance. We derived the analytical solution in finite boundary layer, when the wind speed is a generalized function of height. The convergence of the solution is numerically verified. We used the solution to evaluate the model against Prairie Grass and Hanford experiments. It predicts 89% and 84% cases within a factor of two respectively. The results obtained with Prairie Grass experiment are also compared with those from the Danish OML model, their statistical performances are comparable.

► Air pollutant dispersion equation
► A first-order WKB method
► Eigen-function expansion
► Analytical solution
► Model is evaluated using Prairie and Hanford diffusion data sets, compared with OML.