Applicability of Bayesian inference approach for pollution source identification of river chemical spills: A tracer experiment based analysis of algorithmic parameters, impacts and comparison with Frequentist approaches

JIANG Ji-ping1,2 DONG Fu-jia1 LIU Ren-tao1 YUAN Yi-xing1

(1.School of Environment, Harbin Institute of Technology, Harbin, China 150090)
(2.School of Environmental Science and Engineering, Southern University of Science and Technology, Shenzhen, China 518055)

【Abstract】Based on Bayes theorem and combined variance assumptions on pollutant concentration time series with Adaptive-Metropolis sampling, a modular Bayesian approach was established targeting at pollutant source identification during spills. This probability approach updated the prior knowledge on source information by combining experiments and monitoring and was able to directly characterize uncertainty due to the inversion process by probability distribution. Source inversion test results from field tracer experiments were investigated to determine the validity of this Bayesian inference approach, correlation of posterior parameter and impact factors. Results indicated that Bayesian approach was successful in identifying the source parameters and could effectively reduce the emergency decision risks. It is shown that the skewness of posterior distribution of source parameters and variation were sensitive to assumed variance. Using RMSE as objective function, test results also suggested that the default parameters for the established Bayesian source inversion method, were as follows: heteroscedasticity setting stabilization factors λ1 = 0, and λ2 = 0.1–0.5, and AM sampling proposal scale factor Comparisons between the Bayesian approach and optimization approach on aspects of solution methodology, computing process and inverse results were made and differentiation were highlighted. This work provides valuable references for the practical usage of Bayesian approach in surface water pollution source identification.

【Keywords】 Bayesian inference; source inversion; river chemical spill; Adaptive-Metropolis sampling; river tracer experiments;

【DOI】

【Funds】 Key Special Fund for Science and Technology on National Water Pollution Control and Treatment (Grant No. 2012ZX07205-005) China Postdoctoral Science Foundation (Grant No. 2014M551249)

Download this article

    References

    [1] Xue P, Zeng W. Trends of environmental accidents and impact factors in China [J]. Frontiers of Environmental Science & Engineering in China, 2011, 5 (2): 266–276.

    [2] Qu J H, Meng X L, You H. A two-stage evaluation system to identify optimum emergency disposal technology schemes of sudden water source pollutions [J]. China Environmental Science, 2015, 35 (10): 3193–200 (in Chinese).

    [3] Staff Reporter. Crocodile River water affected by toxic spill[M/OL].2005[2017-03-05]. http://mg.co.za/article/2005-12-23-crocodile-river-water-affected-by-toxic-spill.

    [4] India Environment Portal[M/OL]. 2017[2017-03-05] http://www.indiaenvironmentportal.org.in/category/thesaurus/water-pollution.

    [5] NRC. National Response Center (NRC) data download[M/OL]. [2017-03-05] http://www.nrc.uscg.mil/download.html.

    [6] Wang S R, Zhang R, Guo L G, et al.Study on the water ecological risk prevention and control technology system of dongting lake [J]. China Environmental Science, 2017, 37 (5): 1896–905 (in Chinese).

    [7] Chen Y H, Wang P, Jiang J P. Contaminant point source identification of rivers chemical spills based on correlation coefficients optimization method [J]. China Environmental Science, 2011, 31 (11): 1802–1807 (in Chinese).

    [8] Peng Y M, Liu C F, Yang A M. Genetic algorithm to two-dimensional steady inverse problem of convection-diffusion equation [J]. Journal of North China University of Science and Technology (Natural Science Edition), 2008, 30 (2): 84–87. (in Chinese).

    [9] Xin X K, Han X B, Li J. Pollutant source identification model of water pollution incident based on genetic algorithm [J]. Water Resources and Power, 2014, 32 (7): 52–55. (in Chinese).

    [10] Mou X Y. Research on inverse problem of pollution source term identification based on differential evolution algorithm [J]. Chinese Journal of Hydrodynamics, 2011, 26 (1): 24–30. (in Chinese).

    [11] Boano F, Revelli R, Ridolfi L. Source identification in river pollution problems:A geostatistical approach [J]. Water Resources Research, 2005, 41 (7): 1–13

    [12] Cheng W P, Jia Y.Identification of contaminant point source in surface waters based on backward location probability density function method [J]. Advances in Water Resources, 2010, 33 (4): 397–410.

    [13] Wang J B, Lei X H, Liao W H. Source identification for river sudden water contamination based on coupled probability density function method [J]. Journal of Hydraulic Engineering, 2015, 46 (11): 1280–1289. (in Chinese).

    [14] Wu Z K, Fan H M, Chen X R. The numerical study of the inverse problem in reverseprocess of convection-diffusion equation with adjoint assimilation method [J]. Chinese Journal of Hydrodynamics, 2008, 23 (2): 111–115. (in Chinese).

    [15] Hamdi A.Inverse source problem in a 2D linear evolution transport equation:detection of pollution source [J]. Inverse Problems in Science and Engineering, 2012, 20 (3): 401–421.

    [16] Hamdi A. Identification of point sources in two-dimensional advection-diffusion-reaction equation: application to pollution sources in a river.Stationary case [J]. Inverse Problems in Science & Engineering, 2007, 15 (8): 855–870.

    [17] Hamdi A. The recovery of a time-dependent point source in a linear transport equation: application to surface water pollution [J]. Inverse Problems, 2009, 25 (7): 6–23.

    [18] Wu Y Y, Jin W L, Wu Y B. Inverse problem of instantaneous source in wide and shallow rivers and analysis on main influencing factors of inversion accuracy [J]. Water Resources Protection, 2015, 31 (5): 58–61. (in Chinese).

    [19] Gao Q, Han L X, Chen L N. Instantaneous Source Inversion based on Horizontal 2D Flow Model and Inversion Precision Impact Analysis [J]. Sichuan Environment, 2016, 35 (3): 67–72. (in Chinese).

    [20] Marshall L, Nott D, Sharma A.A comparative study of Markov chain Monte Carlo methods for conceptual rainfall-runoff modeling [J]. Water Resources Research, 2004, 40 (2): 1–11.

    [21] Campbell E P, Fox D R, Bates B C.A Bayesian Approach to parameter estimation and pooling in nonlinear flood event models [J]. Water Resources Research, 1999, 35 (1): 211–220.

    [22] Bates B C, Campbell E P.A Markov Chain Monte Carlo Scheme for parameter estimation and inference in conceptual rainfall runoff modeling [J]. Water Resources Research, 2001, 37 (4): 937–947.

    [23] Loos M, Krauss M, Fenner K.Pesticide Nonextractable Residue Formation in Soil: Insights from Inverse Modeling of Degradation Time Series [J]. Environmental Science & Technology, 2012, 46 (18): 9830–9837.

    [24] Zhu S. Research on inverse problems of environmental hydraulics by Bayesian inference [D]. Zhejiang University, 2008. (in Chinese).

    [25] Zhu S, Liu G H, Mao G H. Application of Bayesian Inference to Estimate the Parameters in 2D Convection-diffusion Equation with Source [J]. Journal of Sichuan University (Engineering Science Edition), 2008, 40 (2): 38–43. (in Chinese).

    [26] Zhu S, Liu G H, Wang L Z. A Bayesian approach for the indentification of pollution source in water quality model coupled with hydrodynamics [J]. Journal of Sichuan University (Engineering Science Edition), 2009, 41 (5): 30–35. (in Chinese).

    [27] Mao X. 基于贝叶斯理论的事故场景重建技术 [D]. Tianjin: Nankai University, 2009. (in Chinese).

    [28] Chen H Y, Teng Y G, Wang J S. Event source identification of water pollution based on Bayesian-MCMC [J]. Journal of Hunan University(Natural Sciences), 2012, 39 (6): 74–78. (in Chinese).

    [29] Cao X Q, Song J Q, Zhang W M. MCMC method on an inverse problem of source term identification for convection-diffusion equation [J]. Chinese Journal of Hydrodynamics, 2010, 25 (2): 127–136. (in Chinese).

    [30] Wei G, Chi Z, Yu L, et al. Source identification of sudden contamination based on the parameter uncertainty analysis [J]. Journal of Hydroinformatics, 2016, 18 (6): 919–927.

    [31] Thomann R V, Mueller J A. Principal of surface water quality modelling and control [M]. Prentice Hall, 1987.

    [32] Xie G X. Research of uncertainty theory and methodology in water environment--A case study of Three-George Reservior [D]. Changsha: Hunan University, 2005. (in Chinese).

    [33] Runkel R L.One-dimensional transport with inflow and storage (OTIS): a solute transport model for streams and rivers [M/OL]. Water-Resource Investigations Report, 1998.

    [34] Scales J A, Tenorio L. Prior information and uncertainty in inverse problems [J]. Geophysics, 2001, 66 (2): 389–397.

    [35] Ntzoufras I.Bayesian modeling using Win BUGS [M]. Hoboken, New Jersey: John Wiley & Sons, 2009.

    [36] Keats A, Yee E, Lien F-S. Bayesian inference for source determination with applications to complex urban environment [J]. Atmospheric Environment, 2007, 41 (3): 465–479.

    [37] Keats A, Yee E, Lien F S. Information-driven receptor placement for contaminant source determination [J]. Environmental Modelling & Software, 2010, 25 (9): 1000–1013.

    [38] Box G E P, Cox D R. An Analysis of Transformations [J]. Journal of the Royal Statistical Society, 1964, 26 (2): 211–252.

    [39] Metropolis N, Rosenbluth A W, Rosenbluth M N, et al. Equation of state calculations by fast computing machines [J]. Journal of Chemical Physics, 1953, 21 (10): 87–92.

    [40] Hasting W K.Monte Carlo sampling methods using Markov chains and their applications [J]. Biometrika, 1970, 57 (1): 97–109.

    [41] Geman S, Geman D.Stochastic relaxtion, Gibbs distirubtions and the Bayesian restoration of images [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, 6: 721–741.

    [42] Liu J S.Monte Carlo Strategies in Scientific Computing [M]. New York: Springer-Verlag, 2001.

    [43] Haario H, Saksman E, Tamminen J.An adaptive Metropolis algorithm [J]. Bernoulli, 2001, 7 (2): 223–242.

    [44] Haario H, Saksman E, Tamminen J. Componentwise adaptation for high dimensional MCMC [J]. Computational Statistics, 2005, 20 (2): 265–273.

    [45] Cowles M K, Carlin B P. Markov chain Monte Carlo convergence diagnostics:a comparative review [J]. Journal of the American Statistical Association, 1996, 91 (434): 883–904.

    [46] Rathbun R E, Shultz D J, Stephens D W. Preliminary experiments with a modified tracer technique for measuring stream reaeration coefficients [M/OL].USGS Open-File Report, 1975.http://pubs.er.usgs.gov/publication/ofr75256.

    [47] Crompton J. Traveltime Data for the Truckee River Between Tahoe City, California, and Vista, Nevada, 2006 and 2007.USGSOFR 2008-1084 [M]. 2008.

    [48] Rivord J, Saito L, Miller G, et al. Modeling Contaminant Spills in a Regulated River in the Western United States [J]. Journal of Water Resources Planning and Management, 2014, 140 (3): 343–354.

    [49] Reid S E, Mackinnon P A, Elliot T. Direct measurements of reaeration rates using noble gas tracers in the River Lagan, Northern Ireland [J]. Water and Environment Journal, 2007, 21 (3): 182–191.

    [50] Efron B. Why Isn’t Everyone a Bayesian? [J]. The American Statistician, 1986, 40 (1): 1–5.

    [51] Lindley D V.The Future of Statistics: A Bayesian 21st Century [J]. Advances in Applied Probability, 1975: 7.

    [52] Efron B. Bayesian inference and the parametric bootstrap [J]. The Annals of Applied Statistics, 2012, 6 (4): 1971–1997.

This Article

ISSN:1000-6923

CN:11-2201/X

Vol 37, No. 10, Pages 3813-3825

October 2017

Downloads:0

Share
Article Outline

Abstract

  • 1 Construction of Bayesian inference based uncertain pollution source identification method
  • 2 Field tracerexperiment based pollution source identification
  • 3 Impacts of Bayesian inference based emergency source identification
  • 4 Comparison of Bayesian inference source identification method and deterministic optimization method
  • 5 Conclusions
  • References