Bayesian inference and wind field statistical modeling applied to multiple source estimation

Abstract

We present a methodology to identify multiple pollutant sources in the atmosphere that combines a data-driven dispersion model with Bayesian inference and uncertainty quantification. The dispersion model accounts for a realistic wind field based on the output of a multivariate dynamic linear model (DLM), estimated from measured wind components time series. The forward problem solution, described by an adjoint transient advection-diffusion partial differential equation, is then obtained using an appropriately stabilized finite element formulation. The Bayesian inference tool accounts for uncertainty in the concentration data and automatically states the balance between the prior and the likelihood. The source parameters are estimated by a Metropolis in Gibbs Monte Carlo Markov chain (MCMC) algorithm with adaptive steps. The MCMC algorithm is initialized with a maximum a posteriori estimator obtained with particle swarm optimization to accelerate convergence. Finally, the proposed methodology seems to outperform inversion techniques from previous works.

Keywords: Atmospheric dispersion; Bayesian inference; MCMC algorithms; Metropolis in Gibbs sampler; Source estimation; Uncertainty quantification.