Bayesian inference for source determination with applications to a complex urban environment |
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| Institution: | 1. Department of Mechanical Engineering, University of Waterloo, Waterloo, Ont., Canada N2L 3G1;2. Defence R&D Canada—Suffield, P.O. Box 4000, Medicine Hat, AB, Canada T1A 8K6;1. Advanced Concepts Team of the European Space Agency, ESTEC, The Netherlands;2. Faculty of Aerospace Engineering, Delft University of Technology, The Netherlands;3. Department of Mechanical and Aerospace Engineering of Carleton University, Canada;1. State Key Laboratory of Multiphase Flow in Power Engineering, Xi''an Jiaotong University, No. 28 Xianning West Road, Xi''an 710049, PR China;2. School of Chemical Engineering and Technology, Xi''an Jiaotong University, No. 28 Xianning West Road, Xi''an 710049, PR China;1. Laboratory of Mechanics and Energy, Universite d''Evry-Val d''Essonne, 40 Rue Du Pelvoux, 91080 Courcouronnes, Evry Cedex, France;2. Centre for Atmospheric Sciences, Indian Institute of Technology Delhi 110016, India;1. Aeris LLC, Louisville, CO, USA;2. Department of Meteorology and Atmospheric Science, Pennsylvania State University, University Park, PA, USA;3. Research Applications Laboratory, National Center for Atmospheric, Boulder, CO, USA;1. LMEE, Universite d''Evry-Val d''Essonne, 40 Rue Du Pelvoux, 91080 Courcouronnes, France;2. Centre for Atmospheric Sciences, IIT Delhi, Hauz Khas, New Delhi 110016, India |
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| Abstract: | 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. |
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