Bayesian inversion of concentration data: Source reconstruction in the adjoint representation of atmospheric diffusion

In this paper, we address the problem of the recovery of the location and strength of a contaminant source from concentration data measured by an array of sensors. To solve this difficult problem, we develop a novel Bayesian probabilistic inferential solution that provides a natural and logically consistent method for source reconstruction from a limited number of noisy concentration data. The methodology enables a rigorous determination of the uncertainty in the inference of the source parameters (e.g., location, emission rate). A model (or, source–receptor relationship) that relates the source distribution to the concentration data is formulated, and Bayesian probability theory is used to derive the posterior probability density function of the source parameters. A computationally efficient methodology for determination of the likelihood function for the problem, based on an adjoint representation of the source–receptor relationship, is described. This representation is formulated in both the Eulerian and Lagrangian descriptions of turbulent dispersion, the former in terms of a partial differential equation (advection–diffusion equation) and the latter in terms of an Ito stochastic differential equation. The Bayesian inferential methodology for source reconstruction is illustrated using two sets of real concentration data involving contaminant dispersion in highly disturbed flows over urban and complex environments.