  We propose a numerical algorithm for solving the atmospheric dispersion
problem with elevated point sources and ground-level deposition. The problem is
modelled by the 3D advection-diffusion equation with delta-distribution source
terms, as well as height-dependent advection speed and diffusion coefficients.
We construct a finite volume scheme using a splitting approach in which the
Clawpack software package is used as the advection solver and an implicit time
discretization is proposed for the diffusion terms. The algorithm is then
applied to an actual industrial scenario involving emissions of airborne
particulates from a zinc smelter using actual wind measurements. We also
address various practical considerations such as choosing appropriate methods
for regularizing noisy wind data and quantifying sensitivity of the model to
parameter uncertainty. Afterwards, we use the algorithm within a Bayesian
framework for estimating emission rates of zinc from multiple sources over the
industrial site. We compare our finite volume solver with a Gaussian plume
solver within the Bayesian framework and demonstrate that the finite volume
solver results in tighter uncertainty bounds on the estimated emission rates.
