Approximating dispersion from a finite line source

We examine the basis of the approximation suggested by Calder [1973. On estimating air pollution concentrations from a highway in an oblique wind. Atmospheric Environment 7, 863–868], Luhar and Patil [1989. A general finite line source model for vehicular pollution prediction. Atmospheric Environment 23, 555–562], and Esplin [1995. Approximate explicit solution to the general line source problem. Atmospheric Environment 29, 1459–1463] for the concentration downwind of a finite line source when the wind blows at an angle to the source. The Luhar–Esplin (LE) approximation is equivalent to replacing the varying source–receptor distances in the integral representing the concentration caused by the line source by an effective distance along the wind direction between the receptor and the line source. This approximation performs poorly when the wind approaches a direction parallel to the line source. It can be improved by retaining the effective-distance approximation only for evaluation of vertical diffusion and approximating the resulting line source integral with the assumption of small cross-wind distance. The resulting Horst–Venkatram approximation has much smaller errors than those of the LE approximation for the range of receptor locations considered in this paper.