Identification of pollution sources in rivers using a hydrodynamic diffusion wave model and improved Bayesian-Markov chain Monte Carlo algorithm

Abstract

● A hydrodynamic-Bayesian inference model was developed for water pollution tracking.

● Model is not stuck in local optimal solutions for high-dimensional problem.

● Model can estimate source parameters accurately with known river water levels.

● Both sudden spill incident and normal sewage inputs into the river can be tracked.

● Model is superior to the traditional approaches based on the test cases.

Water quality restoration in rivers requires identification of the locations and discharges of pollution sources, and a reliable mathematical model to accomplish this identification is essential. In this paper, an innovative framework is presented to inversely estimate pollution sources for both accident preparedness and normal management of the allowable pollutant discharge. The proposed model integrates the concepts of the hydrodynamic diffusion wave equation and an improved Bayesian-Markov chain Monte Carlo method (MCMC). The methodological framework is tested using a designed case of a sudden wastewater spill incident (i.e., source location, flow rate, and starting and ending times of the discharge) and a real case of multiple sewage inputs into a river (i.e., locations and daily flows of sewage sources). The proposed modeling based on the improved Bayesian-MCMC method can effectively solve high-dimensional search and optimization problems according to known river water levels at pre-set monitoring sites. It can adequately provide accurate source estimation parameters using only one simulation through exploration of the full parameter space. In comparison, the inverse models based on the popular random walk Metropolis (RWM) algorithm and microbial genetic algorithm (MGA) do not produce reliable estimates for the two scenarios even after multiple simulation runs, and they fall into locally optimal solutions. Since much more water level data are available than water quality data, the proposed approach also provides a cost-effective solution for identifying pollution sources in rivers with the support of high-frequency water level data, especially for rivers receiving significant sewage discharges.

Graphical abstract

Keywords

Identification of pollution sources / Water quality restoration / Bayesian inference / Hydrodynamic model / Inverse problem

References

[1] Addepalli B , Sikorski K , Pardyjak E R , Zhdanov M S . (2011). Source characterization of atmospheric releases using stochastic search and regularized gradient optimization. Inverse Problems in Science and Engineering, 19(8): 1097–1124

[2] Atmadja J , Bagtzoglou A C . (2001). State of the art report on mathematical methods for groundwater pollution source identification. Environmental Forensics, 2(3): 205–214

[3] Ayvaz M T . (2016). A hybrid simulation-optimization approach for solving the areal groundwater pollution source identification problems. Journal of Hydrology (Amsterdam), 538: 161–176

[4] Bekele E G, Nicklow J W (2007). Multi-objective automatic calibration of SWAT using NSGA-II. Journal of Hydrology (Amsterdam), 341(3–4): 165–176

[5] Bu Q , Wang D , Zheng Y , Wang Z , Gu J . (2014). Identification and ranking of the risky organic contaminants in the source water of the Danjiangkou reservoir. Frontiers of Environmental Science & Engineering, 8(1): 42–53

[6] Chen D , Dahlgren R A , Lu J . (2013). A modified load apportionment model for identifying point and diffuse source nutrient inputs to rivers from stream monitoring data. Journal of Hydrology (Amsterdam), 501: 25–34

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

[8] Das S , Mullick S S , Suganthan P N . (2016). Recent advances in differential evolution: an updated survey. Swarm and Evolutionary Computation, 27(4): 1–30

[9] Datta B , Chakrabarty D , Dhar A . (2011). Identification of unknown groundwater pollution sources using classical optimization with linked simulation. Journal of Hydro-environment Research, 5(1): 25–36

[10] Faulkner B R . (2008). Bayesian modeling of the assimilative capacity component of nutrient total maximum daily loads. Water Resources Research, 44(8): 218–227

[11] Freni G, Mannina G (2010). Bayesian approach for uncertainty quantification in water quality modelling: The influence of prior distribution. Journal of Hydrology (Amsterdam), 392(1–2): 31–39

[12] García L , Barreiro-Gomez J , Escobar E , Tellez D , Quijano N , Ocampo-Martinez C . (2015). Modeling and real-time control of urban drainage systems: A review. Advances in Water Resources, 85: 120–132

[13] Gelman A , Rubin D B . (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7(4): 457–472

[14] Ghane A , Mazaheri M , Mohammad Vali Samani J . (2016). Location and release time identification of pollution point source in river networks based on the Backward Probability. Journal of Environmental Management, 180: 164–171

[15] Gill J (2014). Bayesian Methods: A Social and Behavioral Sciences Approach. Boca Raton: CRC Press

[16] Harvey I . (2011). The microbial genetic algorithm. In: Kampis G, Karsai I, Szathmáry E, eds. Advances in Artificial Life: Darwin Meets von Neumann (Part II). Budapest: Springer-Verlag Berlin Heidelberg, 126–133

[17] Huang J , Yin H , Chapra S C , Zhou Q . (2017). Modelling dissolved oxygen depression in an urban river in China. Water (Basel), 9(7): 520–538

[18] Huang J , Yin H , Jomma S , Rode M , Zhou Q . (2016). Identification of Pollutant Sources in a Rapidly Developing Urban River Catchment in China. Vienna: EGU General Assembly, EPSC2016–13299

[19] Jia H , Xu T , Liang S , Zhao P , Xu C . (2018). Bayesian framework of parameter sensitivity, uncertainty, and identifiability analysis in complex water quality models. Environmental Modelling & Software, 104: 13–26

[20] Jiang J P , Han F , Zheng Y , Wang N N , Yuan Y X . (2018). Inverse uncertainty characteristics of pollution source identification for river chemical spill incidents by stochastic analysis. Frontiers of Environmental Science & Engineering, 12(5): 6

[21] Jing P , Yang Z , Zhou W , Huai W , Lu X . (2019). Inversion of multiple parameters for river pollution accidents using emergency monitoring data. Water Environment Research, 91(8): 731–738

[22] Laloy E , Vrugt J A . (2012). High-dimensional posterior exploration of hydrologic models using multiple-try DREAM_ZS and high-performance computing. Water Resources Research, 48(1): W01526

[23] Massoudieh A , Kayhanian M . (2013). Bayesian chemical mass balance method for surface water contaminant source apportionment. Journal of Environmental Engineering, 139(2): 250–260

[24] Mazaheri M , Mohammad Vali Samani J , Samani H M V . (2015). Mathematical model for pollution source identification in rivers. Environmental Forensics, 16(4): 310–321

[25] Mirghani B Y , Mahinthakumar K G , Tryby M E , Ranjithan R S , Zechman E M . (2009). A parallel evolutionary strategy based simulation-optimization approach for solving groundwater source identification problems. Advances in Water Resources, 32(9): 1373–1385

[26] Mirza I A , Vieru D . (2017). Fundamental solutions to advection–diffusion equation with time-fractional Caputo–Fabrizio derivative. Computers & Mathematics with Applications (Oxford, England), 73(1): 1–10

[27] Nag R , Markey B K , Whyte P , O’flaherty V , Bolton D , Fenton O , Richards K G , Cummins E . (2021). A Bayesian inference approach to quantify average pathogen loads in farmyard manure and slurry using open-source Irish datasets. Science of the Total Environment, 786: 147474

[28] Neuman S P , Xue L , Ye M , Lu D . (2012). Bayesian analysis of data-worth considering model and parameter uncertainties. Advances in Water Resources, 36: 75–85

[29] Opara K , Arabas J . (2018). Comparison of mutation strategies in Differential Evolution–A probabilistic perspective. Swarm and Evolutionary Computation, 39(4): 53–69

[30] Oubanas H , Gejadze I , Malaterre P O , Mercier F . (2018). River discharge estimation from synthetic SWOT-type observations using variational data assimilation and the full Saint-Venant hydraulic model. Journal of Hydrology (Amsterdam), 559: 638–647

[31] Sharifi S , Haghshenas M M , Deksissa T , Green P , Hare W , Massoudieh A . (2014). Storm water pollution source identification in Washington, DC, using Bayesian chemical mass balance modeling. Journal of Environmental Engineering, 140(3): 04013015

[32] Shi B , Jiang J , Sivakumar B , Zheng Y , Wang P . (2018). Quantitative design of emergency monitoring network for river chemical spills based on discrete entropy theory. Water Research, 134: 140–152

[33] Singh S K , Rani R . (2014). A least-squares inversion technique for identification of a point release: application to Fusion Field Trials 2007. Atmospheric Environment, 92: 104–117

[34] Siriwardene N R, Perera B J C (2006). Selection of genetic algorithm operators for urban drainage model parameter optimisation. Mathematical and Computer Modelling, 44(5–6): 415–429

[35] Thomann R V, Mueller J A (1987). Principles of Surface Water Quality Modeling and Control. New York: Harper & Row Publishers

[36] Umer S . (2015). Investigation into mutation operators for microbial genetic algorithm. In: 2015 7th International Joint Conference on Computational Intelligence (IJCCI). Lisbon: IEEE, 299–305

[37] Vrugt J A . (2016). Markov chain monte carlo simulation using the DREAM software package: theory, concepts, and MATLAB implementation. Environmental Modelling & Software, 75: 273–316

[38] Wani O , Scheidegger A , Carbajal J P , Rieckermann J , Blumensaat F . (2017). Parameter estimation of hydrologic models using a likelihood function for censored and binary observations. Water Research, 121(9): 290–301

[39] Xu Z , Qu Y , Wang S , Chu W . (2021). Diagnosis of pipe illicit connections and damaged points in urban stormwater system using an inversed optimization model. Journal of Cleaner Production, 292: 126011

[40] Xu Z , Wang L , Yin H , Li H , Schwegler B R . (2016). Source apportionment of non-storm water entries into storm drains using marker species: modeling approach and verification. Ecological Indicators, 61: 546–557

[41] Yang H , Shao D , Liu B , Huang J , Ye X . (2016). Multi-point source identification of sudden water pollution accidents in surface waters based on differential evolution and Metropolis-Hastings-Markov chain Monte Carlo. Stochastic Environmental Research and Risk Assessment, 30(2): 507–522

[42] Zhang G , Liu X , Wu S , Hua Z , Zhao L , Xue H , Wang P . (2021). Identification of pollution sources in river based on particle swarm optimization. Journal of Hydrodynamics, 33(6): 1303–1315

[43] Zhao Y , Sharma A , Sivakumar B , Marshall L , Wang P , Jiang J . (2014). A Bayesian method for multi-pollution source water quality model and seasonal water quality management in river segments. Environmental Modelling & Software, 57: 216–226

[44] Zhao Y , Zheng B , Jia H , Chen Z . (2019). Determination sources of nitrates into the Three Gorges Reservoir using nitrogen and oxygen isotopes. Science of the Total Environment, 687: 128–136

[45] Zhao Z , Yin H , Xu Z , Peng J , Yu Z . (2020). Pin-pointing groundwater infiltration into urban sewers using chemical tracer in conjunction with physically based optimization model. Water Research, 175: 115689

[46] Zhi W , Li L , Dong W , Brown W , Kaye J , Steefel C , Williams K H . (2019). Distinct source water chemistry shapes contrasting concentration-discharge patterns. Water Resources Research, 55(5): 4233–4251

[47] Zhu Q , Gu A , Li D , Zhang T , Xiang L , He M . (2021a). Online recognition of drainage type based on UV-vis spectra and derivative neural network algorithm. Frontiers of Environmental Science & Engineering, 15(6): 136

[48] Zhu Y , Chen Z , Asif Z . (2021b). Identification of point source emission in river pollution incidents based on Bayesian inference and genetic algorithm: inverse modeling, sensitivity, and uncertainty analysis. Environmental Pollution, 285: 117497

RIGHTS & PERMISSIONS

Higher Education Press