Although a great deal of research effort has been focused on the forward prediction of the transport and dispersion of contaminants released into the turbulent atmosphere, much less work has been directed towards the “inverse prediction” of contaminant source location and strength from the measured concentration, even though the importance of this problem for a number of practical applications is obvious. In general, the inverse problem of source reconstruction is ill-posed and unsolvable without additional information. In this paper, the inverse problem of source reconstruction for the difficult case of multiple sources when the number of sources is unknown a priori is addressed. The problem is solved using a Bayesian probabilistic inferential framework in which Bayesian probability theory is used to derive the probability density function for the number of sources and for the parameters (e.g., location, emission rate, initial release time, release duration) that characterize each source. It is shown that Bayesian inference provides a natural and logically consistent method for source reconstruction from a limited number of noisy concentration data. The latter enables a rigorous determination of the uncertainty in the inference of the source distribution (e.g., number of sources, spatial location and emission rate of each source, etc.), hence extending the potential of the methodology as a tool for quantitative source reconstruction.

A mapping (or, source-receptor relationship) that relates the multiple source distribution to the concentration data measured by an array of sensors is formulated based on a source-oriented approach using a forward-time Lagrangian stochastic model. A computationally efficient methodology for determination of the likelihood function for the problem, based on an adjoint representation of the source-receptor relationship (receptor-oriented approach) and realized in terms of a backward-time Lagrangian stochastic model is described.[1] An efficient computational algorithm based on a reversible jump Markov chain Monte Carlo (MCMC) method is formulated and implemented to draw samples from the posterior density function of the source parameters. The methodology allows the MCMC method to jump between the hypothesis spaces corresponding to different numbers of sources in the source distribution, and thereby allows a sample from the full joint posterior distribution for the number of sources and source parameters to be obtained. The proposed methodology for source reconstruction is tested using synthetic concentration data generated for cases involving multiple sources.