Estimating airborne particulate emissions using a finite-volume forward solver coupled with a Bayesian inversion approach

Abstract

We consider the problem of estimating emissions of particulate matter from point sources. Dispersion of the particulates 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 to solve this equation and apply our algorithm 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.

Simultaneous Model Calibration and Source Inversion in Atmospheric Dispersion Models

“…We further observe that our estimate of the total emission is consistent with previous studies, with the exception of (H&S) which appears to have a higher estimate. This is mostly due to the over-estimation of q 1 which, as was mentioned before, is likely due to a lack of calibration in [12]. By allowing the model parameters to be calibrated automatically we have obtained estimates that are consistent with two previous studies that used very different methodologies, namely the engineering estimates and (L&S).…”

“…In comparison to the previous approaches of [12] and [22] our total computational cost (including the training of the emulator and design of experiment) is higher. For example, [22] uses a Gaussian plume model which is much cheaper than the finite volume solver but comes at the cost of major simplifications to the physics.…”

“…First of all, there is a notable difference between the estimates for q 1 . In [12], the parameters p, z 0 , L are fixed at 0.2, 0.05 and −10, respectively. But these values depend strongly on environmental conditions, so a mis-assessment in the environmental conditions might lead to sub-optimal predictions.…”

“…For example, [22] uses a Gaussian plume model which is much cheaper than the finite volume solver but comes at the cost of major simplifications to the physics. On the other hand, [12] uses a finite volume forward solver of the original PDEs, which is only evaluated four times. However, neither of these two approaches provides an automated calibration procedure, and so we claim that the extra computations in our methodology are a small price to pay for a richer solution structure with more realistic uncertainty estimates and rigorous model calibration.…”

“…We apply the atmospheric dispersion model (3), as adapted in [12] for this specific zinc smelter site with n = 4 sources:…”