Multi-Source Atmospheric Dispersion Event Reconstruction Using Bayesian Inference and Composite Model Ranking

When hazardous materials are released into the atmosphere intentionally or accidentally, dispersion of contaminants by local winds creates a hazard zone for the population. A network of well-placed sensors has been envisioned and implemented in major cities to monitor harmful contaminant concentrations. This information can be used in source term estimation methods to reconstruct the dispersion event in terms of its location and emission strength. Event reconstruction tools coupled with an appropriate forward dispersion model can estimate the quantity and nature of the source(s) responsible for the release. An added complexity occurs when the contaminant is released from more than one location at a time. To date, most event reconstruction tools have focused on single source releases. In this study we extend the Stochastic Event Reconstruction Tool (SERT) that is capable of estimating the source locations and strengths for single source releases to multiple source releases. Our proposed approach adopts the Gaussian plume model as the forward model to estimate the locations and emission strengths of multiple source releases. Bayesian inference with Markov chain Monte Carlo (MCMC) sampling is used to produce estimates of model parameters within minutes on a conventional processor. Prior probabilities used in the Bayesian formulation are specified based on certain beliefs about the individual source parameters. With multi-source estimations, it is possible to obtain reasonable predictions from a model with the incorrect number of sources. Determining the correct number of sources is challenging and critical because an incorrect estimation of the number of sources could mislead and delay emergency response efforts. To reconstruct the number of source locations correctly, we propose a composite model ranking system to quantitatively select the estimation with the correct number of source terms. The ranking formula takes into consideration the following performance metrics: the l2 norm of relative error for concentration data, the Fractional Bias (FB), and Pearson's correlation coefficient (R). Rather than choosing a single metric to decide model performance, this composite formulation allows the model to be evaluated for error, bias, and correlation together. Using field data sets and synthetically generated data, the method is tested and found to produce accurate source estimates for single and dual release dispersion events. The ranking system successfully assigns a higher rank to the estimation with the correct number of sources in each case tested, and the overall method produces reasonable parameter estimation results.