# IRMACS: The Interdisciplinary Colloquium: "The Mathematics of Atmospheric Pollutant Dispersion"

*Dr. John Stockie*

### Abstract

Atmospheric dispersion refers to the transport of contaminants in the atmosphere under the influence of advection (due to the wind) and turbulent diffusion. The advection-diffusion equation is a parabolic partial differential equation that is commonly used to model such pollutant dispersion problems. When a contaminant is emitted from a stationary point source, then the governing equations admit an analytical solution commonly known as the "Gaussian plume" solution. This plume solution has been exploited by environmental engineers for decades and forms the basis of many of efficient and robust software packages for estimating contaminant concentrations assuming that the emission rates are known.

Our work focuses on the corresponding inverse problem, in which we aim to estimate the source emission rate based on ground-level contaminant measurements. We describe a least squares optimization approach for source estimation, and pay particular attention to the ill-conditioning of the inverse problem. Our results will be illustrated using an actual study of a large zinc smelting operation in British Columbia, in which zinc emission rates are estimated for several sources distributed around the smelter site. This approach is a general one that can be applied to a wide range of applications involving airborne particles such as biological agents (seeds and insects), natural hazards (volcanic eruptions and forest fires), and terrorist attacks (radioactive fall-out and infectious microbes).