Pseudospectral simulation of dry deposition from a point source

Abstract

A pseudospectral, two-dimensional model for dispersion and dry deposition of atmospheric pollutants is developed on the basis of gradient-transfer theory (K-theory). A symmetrical transform is developed for the vertical direction satisfying the condition of mass conservation. The deposition to the ground is represented by a sink term at the surface and according to this the model is called the surface depletion model. Comparison with analytical solutions is performed in the case of constant wind and diffusivity profiles. Agreement between numerical and analytical results is within 2–5% even with only 17 grid points in the vertical direction. The error can be further reduced by application of more grid points. The pseudospectral method is more accurate than finite difference methods, especially with respect to advection. Multiple sources and time-dependent physically realistic, e.g. measured wind and diffusivity profiles can easily be treated. Sources between gridpoints can be accurately represented. The pseudospectral model is used for calculation of deposition rates with diffusivity and wind profiles for different atmospheric stability conditions. Comparison is made with the conventional. Gaussian source depletion method for estimates of dry deposition from a point source. The discrepancy between the two models increases with increasing atmospheric stability. In the stable case with a deposition velocity of 1 cms −1 and a point source at a height of 25m, the Gaussian source depletion model underestimates the suspension ratio by a factor of 1.5 at a downwind distance of 22 km from the source. The surface concentration is overestimated by nearly a factor of 2 at the same distance. Contrary to other, more simple surface depletion models which do not take wind and diffusivity profiles into account, it is found that the suspension ratio is smaller for the surface depletion than the source depletion model at short distances, while the opposite relation occurs only at larger distances. This effect is ascribed to the low wind velocity at the surface which results in stronger deposition close to the source, while at larger distances the vertical diffusive transport becomes more important for the rate of dry deposition. The present results are especially relevant for dispersion and deposition in cases of low diffusivities, where the difference between the two-dimensional pseudospectral surface depletion model and other less sophisticated deposition models is most pronounced.