Some Aspects of the Computer Modelling of Pollution From An Atmospheric Source
Authors: Wallis J. , Aziz K. 
Published: March 2010

Abstract
This study evaluates the effect of several parameters on the prediction of pollutant dispersion from a stationary atmospheric source under atmospheric conditions similar to those experienced by emission stacks in Alberta. Differences and similarities between Gaussian models and commonly wed numerical computer models are discussed. It is shown that the two approaches do not correspond exactly. Both are compared on a consistent basis. This study shows that discretisation error from the numerical model, is considerable initially, but that it decreases significantly for increasing downwind distance. It is also shown that discretization error is much greater and less predictable for simulations where transport coefficients and velocity vary with height. A second-order explicit method was found to be superior to an implicit and other explicit methods for steady-state simulations.

Introduction
SOCIETY is placing increasing emphasis on better air and water quality, one one important facet in the improvement of these resources is the computer model for pollutant dispersion. Although the model does not "clean up" the pollution, it is extremely useful in predicting whether an effluent will be noxious in the surrounding environment.
Air pollution models are generally restricted in their range of applicability, and are generally developed from very simplified forms of the conservation equations of mass, energy and momentum in a. turbulent atmosphere. Even when simplified, they are often non-linear, transient and strongly coupled three-di-mensional partial differential equations. The solution of these equations (see Aziz and Hellums, 1967, for numerical problems associated with the solution of the corresponding laminar flow equations) is often beyond the capability of present computers. Assuming that the conservation equations are sufficiently simplified, one still has the problem of determining appropriate boundary conditions, not an easy task because of the lack of detailed information about the atmosphere at any given time.
The starting point for most studies is the convection-diffusion equation (Carr, 1973):
(Equation in full paper)
The classical and most common approach is to solve Equation 1 at steady-state with v, w, DI and R equal to zero. For flat terrain, constant u, and Dy and DZ constant or functions of downwind distance, the solution is the well-known Gaussian plume distribution. Many different methods have been used to estimate the plume standard deviations (related to Dy and DZ); e.g. Smith and Singer (1966), Pasquill (1961) and Sutton (1947).
Because of the flat-terrain restriction, some people have tried to adapt the Gaussian model to irregular terrain; e.g. Hunt and Mulhearn (1973). They analyzed pollutant dispersion from a line source over a cylindrical ridge where the wind distribution was governed by potential flow. From their analysis, they concluded that the ridge had little effect on ground-level concentration if the height of the ridge was relatively small in comparison with the hill's distance from the stack. This implies that the flat-terrain restrictions on the Gaussian model are not necessarily severe.
In contrast, Turbulent Transport theory (with simplifying assumptions) shows D. and u are functions only of vertical distance; e.g. Monin and Yaglom (1965).