Currently, Gaussian type dispersion modeling and point source approximation are combined to estimate the ambient air concentrations of pollutants dispersed downwind of an areawide emission source, using the approach of virtual point source approximation. The Gaussian dispersion modeling becomes less accurate as the receptor comes closer to the source, and becomes inapplicable for the estimation of on-site ambient air concentrations at disposal sites. Partial differential equations are solved with appropriate boundary conditions for use in estimating the on-site concentrations in the ambient air impacted by emissions from an area source such as land disposal sites. Two variations of solution techniques are presented, and their predictions are compared.