Analysis of the error associated with grid representation of point sources

The steady-state, three-dimensional transport equation for inert pollutant dispersion in the atmosphere is solved analytically to obtain expressions for pollutant concentrations from both a point source and a rectangular area source. The results of this analysis have application to numerical grid models in which the smallest resolvable source is the size of a single grid. The concentrations at ground level along the plume centerline from the two types of sources are in close agreement with each other at distances greater than 10 km downwind when the horizontal dimension of the rectangular source is not less than 100 m. The dimension of the source in the vertical direction is held constant at 50 m. Similar results are obtained for concentrations along the plume centerline at the effective stack height. When the size of the source in the crosswind direction is increased to 1 km, good agreement between the two concentrations is obtained for downwind distances over 60 km for the ground level case and over 140 km for the concentration at stack height level. For the horizontal dimension equal to 10 km, good agreement between the two cases is only obtained at extremely large downwind distances at both the stack height and ground levels.