A Diffusion Model for an Urban Area

The purpose of this paper is to present a working model for the diffusion of gases from multiple sources in an urban area. Since 24-hr sulfur dioxide measurements were made at 32 sampling stations in Nashville, Tenn., during a 12-month study, this was the city chosen for investigation. A diffusion equation modified to use area instead of point sources was used with a source inventory of sulfur dioxide emissions to calculate 24-hr concentrations at 1-mile intervals. Wind velocity and stability were averaged by 2-hr periods to evaluate the diffusion equation. One average effective source height was used. Sulfur dioxide was assumed to be oxidized or adsorbed on particulates exponentially with a half-life of 4 hr. By averaging twelve 2-hr calculated concentrations, 24-hr concentrations were determined. Maps with lines of equal concentration were drawn from the calculated point concentrations for 35 test periods. From these, concentrations were determined for the locations having observed concentrations. Fifty-eight per cent of all calculated concentrations were within ±1 pphm of the observed concentrations. Excluding zero values of both calculated and observed concentrations, 70 per cent of the calculated values are within a factor of 2 of the observed values. There is a general tendency toward overcalculation (calculated values greater than observed) especially downwind of major sources. Undercalculation which was noted upwind of major sources is probably because calculated concentrations at the center of a square-mile area received no contribution from sources within that area but only from other areas. Results show that 24-hr concentrations and their areal extent in urban areas from multiple sources may be estimated for a variety of meteorological conditions using the source inventory—diffusion approach.