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Simultaneous Model Calibration and Source Inversion in Atmospheric Dispersion Models

  • Juan G. García
  • Bamdad HosseiniEmail author
  • John M. Stockie
Article
  • 33 Downloads

Abstract

We present a cost-effective method for model calibration and solution of source inversion problems in atmospheric dispersion modelling. We use Gaussian process emulations of atmospheric dispersion models within a Bayesian framework for solution of inverse problems. The model and source parameters are treated as unknowns and we obtain point estimates and approximation of uncertainties for sources while simultaneously calibrating the forward model. The method is validated in the context of an industrial case study involving emissions from a smelting operation for which cumulative monthly measurements of zinc particulate depositions are available.

Keywords

Atmospheric dispersion particle deposition inverse source identification Bayesian estimation uncertainty quantification 

Mathematics Subject Classification

62F15 65M08 65M32 86A10 

Notes

Acknowledgements

This work was partially supported by the Natural Sciences and Engineering Research Council of Canada through a Postdoctoral Fellowship (BH) and a Discovery Grant (JMS). We are grateful to the Environmental Management Group at Teck Resources Ltd. (Trail, BC) for providing data and for many useful discussions.

References

  1. Arora, R. K. (2015). Optimization: Algorithms and applications. Boca Raton, FL: CRC Press.CrossRefGoogle Scholar
  2. Chatwin, P. C. (1982). The use of statistics in describing and predicting the effects of dispersing gas clouds. Journal of Hazardous Materials, 6(1–2), 213–230.CrossRefGoogle Scholar
  3. Colbeck, I. (2009). Identification of air pollution sources via modelling techniques. In S . M. Mudge (Ed.), Methods in environmental forensics (pp. 309–352). Boca Raton, FL: CRC Press. chapter 10.Google Scholar
  4. Conti, S., Gosling, J. P., Oakley, J. E., & O’Hagan, A. (2009). Gaussian process emulation of dynamic computer codes. Biometrika, 96(3), 663–676.CrossRefGoogle Scholar
  5. Cooper Environmental. (2015). Ambient Monitoring: Xact 625 (product description), Beaverton, OR. http://cooperenvironmental.com/xact-625/.
  6. Dupuy, D., Helbert, C., Franco, J., et al. (2015). DiceDesign and DiceEval: Two R packages for design and analysis of computer experiments. Journal of Statistical Software, 65(11), 1–38.CrossRefGoogle Scholar
  7. Enting, I . G., & Newsam, G . N. (1990). Inverse problems in atmospheric constituent studies: II. Sources in the free atmosphere. Inverse Problems, 6(3), 349–362.CrossRefGoogle Scholar
  8. Fang, K.-T., Lin, D. K. J., Winker, P., & Zhang, Y. (2000). Uniform design: Theory and application. Technometrics, 42(3), 237–248.CrossRefGoogle Scholar
  9. García, J. G. (2018) Parameter estimation and uncertainty quantification applied to advection–diffusion problems arising in atmospheric source inversion. PhD thesis, Department of Mathematics, Simon Fraser University.Google Scholar
  10. Gilchrist, W. (2000). Statistical modelling with quantile functions. Boca Raton, FL: CRC Press.CrossRefGoogle Scholar
  11. Haario, H., Saksman, E., & Tamminen, J. (2001). An adaptive Metropolis algorithm. Bernoulli, 7(2), 223–242.CrossRefGoogle Scholar
  12. Haupt, S. E., & Young, G. S. (2008) Paradigms for source characterization. In Proceedings of the 15th joint conference on the applications of air pollution meteorology with A&WMA (p. J6.1), New Orleans, LA: American Meteorological Society.Google Scholar
  13. Hester, R. E., & Harrison, R. M., (Eds.) (2008). Environmental forensics. Issues in Environmental Science and Technology. Cambridge: The Royal Society of ChemistryGoogle Scholar
  14. Hosseini, B., & Stockie, J. M. (2016). Bayesian estimation of airborne fugitive emissions using a Gaussian plume model. Atmospheric Environment, 141, 122–138.CrossRefGoogle Scholar
  15. Hosseini, B., & Stockie, J. M. (2017). Estimating airborne particulate emissions using a finite-volume forward solver coupled with a Bayesian inversion approach. Computers & Fluids, 154, 27–43.CrossRefGoogle Scholar
  16. Isakov, V. (1990). Inverse source problems volume 34 of mathematical surveys and monographs. Providence, RI: American Mathematical Society.Google Scholar
  17. Johnson, M. E., Moore, L. M., & Ylvisaker, D. (1990). Minimax and maximin distance designs. Journal of Statistical Planning and Inference, 26(2), 131–148.CrossRefGoogle Scholar
  18. Jones, B., & Johnson, R. T. (2009). Design and analysis for the Gaussian process model. Quality and Reliability Engineering International, 25(5), 515–524.CrossRefGoogle Scholar
  19. Kaipio, J., & Somersalo, E. (2005). Statistical and computational inverse problems, volume 160 of applied mathematical sciences. New York, NY: Springer.Google Scholar
  20. Keats, A., Yee, E., & Lien, F.-S. (2007). Bayesian inference for source determination with applications to a complex urban environment. Atmospheric Environment, 41(3), 465–479.CrossRefGoogle Scholar
  21. Kennedy, M. C., & O’Hagan, A. (2001). Bayesian calibration of computer models. Journal of the Royal Statistical Society, Series B - Statistical Methodology, 63(3), 425–464.CrossRefGoogle Scholar
  22. Kim, Y., & Platt, U. (Eds.). (2007). Advanced environmental monitoring. New York, NY: Springer.Google Scholar
  23. Leelössy, Á., Molnár, F., Izsák, F., Havasi, Á., Lagzi, I., & Mészáros, R. (2014). Dispersion modeling of air pollutants in the atmosphere: A review. Open Geosciences, 6(3), 257–278.CrossRefGoogle Scholar
  24. Lewellen, W. S., & Sykes, R. I. (1989). Meteorological data needs for modeling air quality uncertainties. Journal of Atmospheric and Oceanic Technology, 6(5), 759–768.CrossRefGoogle Scholar
  25. Lin, C.-H., & Chang, L.-F. W. (2002) Relative source contribution analysis using an air trajectory statistical approach. Journal of Geophysical Research: Atmospheres, 107(D21):ACH 6–1–ACH 6–10.Google Scholar
  26. Lushi, E., & Stockie, J. M. (2010). An inverse Gaussian plume approach for estimating atmospheric pollutant emissions from multiple point sources. Atmospheric Environment, 44(8), 1097–1107.CrossRefGoogle Scholar
  27. Matson, M., & Dozier, J. (1981). Identification of subresolution high temperature sources using a thermal IR sensor. Photogrammetric Engineering and Remote Sensing, 47(9), 1311–1318.Google Scholar
  28. McGill, R., Tukey, J. W., & Larsen, W. A. (1978). Variations of box plots. The American Statistician, 32(1), 12–16.Google Scholar
  29. McKay, M. D., Beckman, R. J., & Conover, W. J. (1979). Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2), 239–245.Google Scholar
  30. Morrison, R. D. (2000). Application of forensic techniques for age dating and source identification in environmental litigation. Environmental Forensics, 1(3), 131–153.CrossRefGoogle Scholar
  31. Mudge, S. M. (2007). Multivariate statistical methods in environmental forensics. Environmental Forensics, 8(1–2), 155–163.CrossRefGoogle Scholar
  32. Mudge, S. M. (2008) Environmental forensics and the importance of source identification. In Environmental forensics, volume 26 of issues in environmental science and technology (pp. 1–16). The Royal Society of Chemistry: Cambridge.Google Scholar
  33. Murphy, K. P. (2012). Machine learning: A probabilistic perspective. Cambridge, MA: MIT Press.Google Scholar
  34. O’Hagan, A. (2006). Bayesian analysis of computer code outputs: A tutorial. Reliability Engineering and System Safety, 91(10), 1290–1300.CrossRefGoogle Scholar
  35. Osborne, M. A., Garnett, R., & Roberts, S. J. (2009). Gaussian processes for global optimization. In Proceedings of the 3rd international conference on learning and intelligent optimization (LION3) (pp. 1–15).Google Scholar
  36. Pujol, G., Iooss, B., Janon, A., et al. (2016). Sensitivity: Global sensitivity analysis of model outputs. R package version 1.12.1.Google Scholar
  37. Rao, K. S. (2005). Uncertainty analysis in atmospheric dispersion modeling. Pure and Applied Geophysics, 162(10), 1893–1917.CrossRefGoogle Scholar
  38. Rao, K. S. (2007). Source estimation methods for atmospheric dispersion. Atmospheric Environment, 41, 6964–6973.CrossRefGoogle Scholar
  39. Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian processes for machine learning. Cambridge, MA: MIT Press.Google Scholar
  40. Saltelli, A., Chan, K., & Scott, E. M. (2000). Sensitivity analysis volume 134 of Wiley series in probability and statistics. New York, NY: Wiley.Google Scholar
  41. Sebastiani, P., & Wynn, H. P. (2002). Maximum entropy sampling and optimal Bayesian experimental design. Journal of the Royal Statistical Society, Series B—Statistical Methodology, 62(1), 145–157.CrossRefGoogle Scholar
  42. Seinfeld, J. H., & Pandis, S. N. (1997). Atmospheric chemistry and physics: From air pollution to climate change. New York, NY: Wiley.Google Scholar
  43. Skiba, Y. N. (2003). On a method of detecting the industrial plants which violate prescribed emission rates. Ecological Modelling, 159(2), 125–132.CrossRefGoogle Scholar
  44. Sobol, I. M. (1993). Sensitivity estimates for non-linear mathematical models. Mathematical Modelling and Computational Experiments, 1(4), 407–414.Google Scholar
  45. Sohn, M. D., Reynolds, P., Singh, N., & Gadgil, A. J. (2002). Rapidly locating and characterizing pollutant releases in buildings. Journal of the Air and Waste Management Association, 52(12), 1422–1432.CrossRefGoogle Scholar
  46. Spikmans, V. (2019). The evolution of environmental forensics: From laboratory to field analysis. Wiley Interdisciplinary Reviews: Forensic Science, 1, e1334.Google Scholar
  47. Stuart, A. M., & Teckentrup, A. L. (2018). Posterior consistency for Gaussian process approximations of Bayesian posterior distributions. Mathematics of Computation, 87(310), 721–753.CrossRefGoogle Scholar
  48. Sullivan, T. J. (2015). Introduction to uncertainty quantification. New York, NY: Springer.CrossRefGoogle Scholar
  49. Thermo Scientific. (2015) High-volume air samplers (product description), Waltham, MA. http://www.thermoscientific.com/en/product/high-volume-air-samplers.html.
  50. Turner, D. B. (1994). Workbook of atmospheric dispersion estimates: An introduction to dispersion modeling. Boca Raton, FL: CRC Press.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Juan G. García
    • 1
  • Bamdad Hosseini
    • 3
    Email author
  • John M. Stockie
    • 2
  1. 1.3DM Devices Inc.AldergroveCanada
  2. 2.Department of MathematicsSimon Fraser UniversityBurnabyCanada
  3. 3.Computing and Mathematical SciencesCalifornia Institute of TechnologyPasadenaUSA

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