Airborne contaminant source estimation using a finite-volume forward solver coupled with a Bayesian inversion approach

TL;DR

This paper introduces a finite-volume numerical algorithm combined with Bayesian inversion to accurately estimate airborne contaminant emissions, demonstrating improved uncertainty bounds over traditional Gaussian plume models in a real industrial scenario.

Contribution

The paper presents a novel finite-volume solver integrated with Bayesian inversion for source estimation, improving accuracy and uncertainty quantification in atmospheric dispersion modeling.

Findings

Finite-volume solver yields tighter emission rate uncertainty bounds.

Algorithm effectively estimates zinc emissions from industrial sources.

Bayesian framework enhances model robustness to data noise.

Abstract

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.