A Puff-on-Cell Model for Computing Pollutant Transport and Diffusion

Abstract

A scheme is developed to minimize the pseudo-diffusion which arises in numerical solutions of finite-difference equations of turbulent diffusion and transport. In the present model, the subgrid scale distribution of the pollutant concentration is parameterized by a Gaussian puff. At each time step the concentration within each grid volume is characterized by a Lagrangian puff. The center of each Lagrangian puff is advected by the mean wind and its boundaries are expanded or contracted by diffusive displacements, computed from the values of concentration, atmospheric turbulent diffusivity, and the gradient of pollutant concentration between the adjacent grid volumes. The standard deviation of the puff is parameterized as a linear combination of the grid length and the diffusive displacement. The constants in the parameterization are determined by calibrating the standard deviation of the puff width predicted by the numerical model against that of an analytical solution. The pollutant is then distributed back to the surrounding Eulerian grid volumes, preserving the first and the second moments of the concentration distribution. The use of the model is illustrated by predicting the vertical concentration distribution of sulfur dioxide and sulfate for a period of 5 days. Furthermore, the requirement for realistic surface-layer parameterization in such numerical models is demonstrated by comparing the results of the constant-flux layer parameterization based upon the modern similarity theory with those of the conventional linear-profile approximation.