Bayesian identification of a single tracer source in an urban-like environment using a deterministic approach

Abstract

This paper presents a two-step deterministic approach for identifying an unknown point source with a constant emission rate in built-up urban areas. The analytic form of the marginal posterior probability density function of the source location is derived to estimate the source location. The emission rate is then estimated using the conditional posterior distribution. Such a procedure deconstructs the calculation of the joint posterior distribution of the source parameters into calculations of two separate distributions and can thus be easily calculated directly and accurately without stochastic sampling. The proposed method is tested using real data obtained in two wind tunnel scenarios of contaminant dispersion in typical urban geometries represented by block arrays. Computational fluid dynamics (CFD) modeling and the adjoint equations are used to calculate the building-resolving source-receptor relationship required in the identification. The estimated source parameters in both cases are close to true values. In both cases, the source locations are identified with errors less than half of the block size, and the emission rates are well estimated, with only slight overestimation. Moreover, in this paper, we test two potential performance indicators for a posteriori evaluation of the credibility of a certain estimation. One indicator is the size of the highest probability density region, and the other is the angle between the observed and predicted concentration vectors, which is derived from the analytic form of the marginal posterior distribution of the source location. Synthetic concentration data are generated to test the validity of both indicators. It is found that the former is not appropriate for denoting the credibility of estimations but that the latter shows a strong correlation with estimation performance and is likely to be an effective performance indicator for Bayesian source term estimation.