The Gaussian Plume Model Equation for Atmospheric Dispersion Corrected for Multiple Reflections at Parallel Boundaries: A Mathematical Rewriting of the Model and Some Numerical Testing

The well-known Gaussian plume model has proven to be very useful in simulating the atmospheric dispersion of air pollutants (both gaseous and particulates). Nevertheless, the nature of the model presents problems in the actual computation of concentrations when the plume is confined between two parallel boundaries due to the occurrence of multiple reflections. The ground and temperature inversion lid (especially, when the inversion layer is at low levels in the atmosphere) with a chimney stack releasing the effluent below the latter, is one contextual example of horizontal parallel reflecting boundaries. A second example is buildings confining a roadway on either side, with motor vehicles emitting pollution within the street canyon (or urban notch). In such cases, multiple reflections should be accounted for, otherwise the model underpredicts the resulting concentration. This paper presents a mathematical rewriting of the Gaussian plume model equation corrected for multiple reflections when the pollution source is confined between parallel boundaries. The obtained result is most appropriate when the parallel boundaries are rigid, and near-complete reflection is achieved, e.g., street canyon environment (second quoted example). It is worth noting that the relevant mathematical derivations and definitions are all included in the paper to facilitate reading and to ensure comprehensiveness in the presentation. Additionally, the outcome of some preliminary numerical testing is presented. The latter indicates that the new formulation is mathematically stable and yields interesting results. Further numerical investigation and experimental evaluation are merited.