Bayesian inference for source determination with applications to a complex urban environment

The problem of determining the source of an emission from the limited information provided by a finite and noisy set of concentration measurements obtained from real-time sensors is an ill-posed inverse problem. In general, this problem cannot be solved uniquely without additional information. A Bayesian probabilistic inferential framework, which provides a natural means for incorporating both errors (model and observational) and prior (additional) information about the source, is presented. Here, Bayesian inference is applied to find the posterior probability density function of the source parameters (location and strength) given a set of concentration measurements. It is shown how the source–receptor relationship required in the determination of the likelihood function can be efficiently calculated using the adjoint of the transport equation for the scalar concentration. The posterior distribution of the source parameters is sampled using a Markov chain Monte Carlo method. The inverse source determination method is validated against real data sets acquired in a highly disturbed flow field in an urban environment. The data sets used to validate the proposed methodology include a water-channel simulation of the near-field dispersion of contaminant plumes in a large array of building-like obstacles (Mock Urban Setting Trial) and a full-scale field experiment (Joint Urban 2003) in Oklahoma City. These two examples demonstrate the utility of the proposed approach for inverse source determination.