A two-dimensional analytical model for the dispersion of air-pollutants in the atmosphere with a capping inversion

Abstract

A two-dimensional steady-state mathematical model has been developed for the pollutant released from an elevated source in an inversion layer by parameterizing vertical eddy diffusion coefficient as a generalized functional form of downwind distance from the source and wind speed as power-law function of the height above the ground. A closed form analytical solution of the resulting partial differential equation with the physically relevant boundary conditions is obtained. The developed model is validated with the data sets obtained at the Northern part of Copenhagen and from the EPRI (Electric Power Research Institute) field experiment conducted at Kincaid in unstable conditions. In stable conditions, the performance of the present model is analyzed with the data set obtained at the Hanford diffusion grid. The present model is performing better to Gaussian model in case of Copenhagen and gives comparable prediction for EPRI data set. For the Hanford data set in stable conditions, present model gives under predicting trend. A slight variation (upto 1°) in the value of σ φ observed in Hanford diffusion experiment, the performance of the present model improves significantly. The proposed model can also be used for computing the concentration distribution of a pollutant released from an infinite line source perpendicular to the direction of the mean wind.