Table of Contents
ISRN Applied Mathematics
Volume 2012 (2012), Article ID 465320, 20 pages
http://dx.doi.org/10.5402/2012/465320
Research Article

Inverse Dispersion for an Unknown Number of Sources: Model Selection and Uncertainty Analysis

Defence R&D Canada – Suffield, P.O. Box 4000 Stn Main, Medicine Hat, AB, Canada T1A 8K6

Received 20 June 2012; Accepted 10 July 2012

Academic Editors: Y. Dimakopoulos, J. R. Fernandez, and T. Y. Kam

Copyright © 2012 Her Majesty the Queen in Right of Canada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. Porta, T. H. Illangasekare, P. Loden, Q. Han, and A. P. Jayasumana, “Continuous plume monitoring using wireless sensors: proof of concept in intermediate scale tank,” Journal of Environmental Engineering, vol. 135, no. 9, pp. 831–838, 2009. View at Publisher · View at Google Scholar · View at Scopus
  2. L. Robertson and J. Langner, “Source function estimate by means of variational data assimilation applied to the ETEX-I tracer experiment,” Atmospheric Environment, vol. 32, no. 24, pp. 4219–4225, 1998. View at Google Scholar · View at Scopus
  3. M. Bocquet, “Reconstruction of an atmospheric tracer source using the principle of maximum entropy. I: theory,” Quarterly Journal of the Royal Meteorological Society, vol. 131, no. 610 B, pp. 2191–2208, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. L. C. Thomson, B. Hirst, G. Gibson et al., “An improved algorithm for locating a gas source using inverse methods,” Atmospheric Environment, vol. 41, no. 6, pp. 1128–1134, 2007. View at Publisher · View at Google Scholar · View at Scopus
  5. C. T. Allen, G. S. Young, and S. E. Haupt, “Improving pollutant source characterization by better estimating wind direction with a genetic algorithm,” Atmospheric Environment, vol. 41, no. 11, pp. 2283–2289, 2007. View at Publisher · View at Google Scholar · View at Scopus
  6. J. P. Issartel, M. Sharan, and S. K. Singh, “Identification of a point source by use of optimal weighted least squares,” Pure and Applied Geophysics, vol. 169, pp. 467–482, 2012. View at Google Scholar
  7. A. Keats, E. Yee, and F. S. Lien, “Bayesian inference for source determination with applications to a complex urban environment,” Atmospheric Environment, vol. 41, no. 3, pp. 465–479, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. A. Keats, E. Yee, and F. S. Lien, “Efficiently characterizing the origin and decay rate of a nonconservative scalar using probability theory,” Ecological Modelling, vol. 205, no. 3-4, pp. 437–452, 2007. View at Publisher · View at Google Scholar · View at Scopus
  9. F. K. Chow, B. Kosović, and S. Chan, “Source inversion for contaminant plume dispersion in urban environments using building-resolving simulations,” Journal of Applied Meteorology and Climatology, vol. 47, no. 6, pp. 1533–1572, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. E. Yee, F. S. Lien, A. Keats, and R. D'Amours, “Bayesian inversion of concentration data: source reconstruction in the adjoint representation of atmospheric diffusion,” Journal of Wind Engineering and Industrial Aerodynamics, vol. 96, no. 10-11, pp. 1805–1816, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. E. Yee, “Bayesian probabilistic approach for inverse source determination from limited and noisy chemical or biological sensor concentration measurements,” in Chemical and Biological Sensing VIII, A. W. Fountain III, Ed., vol. 6554, 65540W, of Proceedings of the SPIE, p. 12, April 2007. View at Publisher · View at Google Scholar · View at Scopus
  12. M. Sharan, S. K. Singh, and J. P. Issartel, “Least square data assimilation for identification of the point source emissions,” Pure and Applied Geophysics, vol. 169, pp. 483–497, 2012. View at Google Scholar
  13. E. Yee, “Theory for reconstruction of an unknown number of contaminant sources using probabilistic inference,” Boundary-Layer Meteorology, vol. 127, no. 3, pp. 359–394, 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. E. Yee, “Probability theory as logic: data assimilation for multiple source reconstruction,” Pure and Applied Geophysics, vol. 169, pp. 499–517, 2012. View at Google Scholar
  15. D. J. Thomson, “Criteria for the selection of stochastic models for particle trajectories in turbulent flows,” Journal of Fluid Mechanics, vol. 180, pp. 529–556, 1987. View at Google Scholar · View at Scopus
  16. M. C. Kennedy and A. O'Hagan, “Bayesian calibration of computer models,” Journal of the Royal Statistical Society B, vol. 63, no. 3, pp. 425–464, 2001. View at Publisher · View at Google Scholar
  17. J. Sacks, W. J. Welch, T. J. Mitchell, and H. P. Wynn, “Design and analysis of computer experiments,” Statistical Science, vol. 4, no. 4, pp. 409–435, 1989. View at Google Scholar
  18. D. Higdon, J. Gattiker, B. Williams, and M. Rightley, “Computer model calibration using high-dimensional output,” Journal of the American Statistical Association, vol. 103, no. 482, pp. 570–583, 2008. View at Publisher · View at Google Scholar
  19. T. K. Flesch, J. D. Wilson, and E. Yee, “Backward-time Lagrangian stochastic dispersion models and their application to estimate gaseous emissions,” Journal of Applied Meteorology, vol. 34, no. 6, pp. 1320–1332, 1995. View at Google Scholar · View at Scopus
  20. E. T. Jaynes, Probability Theory: The Logic of Science, Cambridge University Press, Cambridge, Mass, USA, 2003. View at Publisher · View at Google Scholar
  21. H. Haario, E. Saksman, and J. Tamminen, “An adaptive Metropolis algorithm,” Bernoulli, vol. 7, no. 2, pp. 223–242, 2001. View at Publisher · View at Google Scholar
  22. C. J. F. Ter Braak, “A Markov chain Monte Carlo version of the genetic algorithm differential evolution: easy Bayesian computing for real parameter spaces,” Statistics and Computing, vol. 16, no. 3, pp. 239–249, 2006. View at Publisher · View at Google Scholar
  23. J. A. Vrugt, C. J. F. Ter Braak, C. G. H. Diks, B. A. Robinson, J. M. Hyman, and D. Higdon, “Accelerating Markov chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, no. 3, pp. 273–290, 2009. View at Google Scholar · View at Scopus
  24. J. S. Liu, F. Liang, and W. H. Wong, “The multiple-try method and local optimization in Metropolis sampling,” Journal of the American Statistical Association, vol. 95, no. 449, pp. 121–134, 2000. View at Publisher · View at Google Scholar
  25. J. Berntsen, T. O. Espelid, and A. Genz, “An adaptive algorithm for the approximate calculation of multiple integrals,” ACM Transactions on Mathematical Software, vol. 17, no. 4, pp. 437–451, 1991. View at Publisher · View at Google Scholar
  26. M. A. Newton and A. E Rafferty, “Approximate Bayesian inference by the weighted likelihood bootstrap,” Journal of the Royal Statistical Society B, vol. 3, pp. 3–48, 1994. View at Google Scholar
  27. A. Gelman and X.-L. Meng, “Simulating normalizing constants: from importance sampling to bridge sampling to path sampling,” Statistical Science, vol. 13, no. 2, pp. 163–185, 1998. View at Publisher · View at Google Scholar
  28. J. Skilling, “Nested sampling for general Bayesian computation,” Bayesian Analysis, vol. 1, no. 4, pp. 833–859, 2006. View at Google Scholar
  29. F. Feroz, M. P. Hobson, and M. Bridges, “MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics,” Monthly Notices of the Royal Astronomical Society, vol. 398, no. 4, pp. 1601–1614, 2009. View at Publisher · View at Google Scholar · View at Scopus
  30. H. Jeffreys, Theory of Probability, Oxford University Press, Oxford, UK, 3rd edition, 1961.
  31. D. P. Storwold, Detailed Test Plan for Fusing Sensor Information from Observing Networks (FUSION) Field Trial 2007 (FFT-07), WDTC-TP-07-078, West Desert Test Center, US Army Dugway Proving Ground, 2007.
  32. R. B. Stull, An Introduction to Boundary-Layer Meteorology, Kluwer Academic Publishers, 1988.
  33. J. D. Wilson, T. K. Flesch, and L. A. Harper, “Micro-meteorological methods for estimating surface exchange with a disturbed windflow,” Agricultural and Forest Meteorology, vol. 107, no. 3, pp. 207–225, 2001. View at Publisher · View at Google Scholar · View at Scopus