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Particle filter-based data assimilation technique for the evaluation of transport of pollutants in small rivers

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Abstract

The discharge of pollutants into water resources has caused many undesirable effects on human health and the environment. In this context, meta-heuristic methods, such as the Simulated Annealing algorithm, allow for only offline estimation of the concentration and dispersion coefficient of pollutant. However, online data assimilation is a very important for decision support in real time. In this regard, the present paper focuses on the use of the so-called Particle Filter as an online observer. Our studies were performed through the algorithms Sampling Importance Resampling (SIR) and Liu and West (LW), using tracer experimental observations from a small river in Brazil. Such approach allowed for tracking satisfactorily the pollutant concentration, longitudinal dispersion coefficient, flow velocity, pollutant load released and distance from the pollution source. The results can be enhanced ever more through the LW filter, which reduces the impoverishment of the samples as well as the computational time due to the use of a smoothing kernel.

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References

  • Abderrezzak KEK, Ata R, Zaoui F (2015) One-dimensional numerical modelling of solute transport in streams: the role of longitudinal dispersion coefficient. J Hydrol 527:978–989

    Google Scholar 

  • Abi T, Nwosu P (2009) The effect of oil spillage on the soil of Eleme in Rivers State of the Niger Delta Area of Nigeria. Res J Environ Sci 3(3):316–320

    Google Scholar 

  • Alapati S, Kabala Z (2000) Recovering the release history of a groundwater contaminant using a non-linear least-squares method. Hydrol Process 14(6):1003–1016

    Google Scholar 

  • Allison C, Oriabure G, Ndimele PE, Shittu JA (2018) Dealing with oil spill scenarios in the Niger Delta: lessons from the past. In: The political ecology of oil and gas activities in the Nigerian aquatic ecosystem, Elsevier, Amsterdam, pp 351–368

  • Amirabdollahian M, Datta B (2014) Identification of pollutant source characteristics under uncertainty in contaminated water resources systems using adaptive simulated anealing and fuzzy logic. Int J GEOMATE 6(1):757–762

    Google Scholar 

  • Ani EC, Wallis S, Kraslawski A, Agachi PS (2009) Development, calibration and evaluation of two mathematical models for pollutant transport in a small river. Environ Model Softw 24(10):1139–1152

    Google Scholar 

  • Arulampalam MS, Maskell S, Gordon N, Clapp T (2002) A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking. IEEE Trans Signal Process 50(2):174–188

    Google Scholar 

  • Ayvaz MT (2016) A hybrid simulation-optimization approach for solving the areal groundwater pollution source identification problems. J Hydrol 538:161–176

    Google Scholar 

  • Baek KO, Seo IW (2016) On the methods for determining the transverse dispersion coefficient in river mixing. Adv Water Resour 90:1–9

    Google Scholar 

  • Baek KO, Seo IW (2017) Estimation of the transverse dispersion coefficient for two-dimensional models of mixing in natural streams. J Hydroenviron Res 15:67–74

    Google Scholar 

  • Benedini M, Tsakiris G (2013) Water quality modelling for rivers and streams. Springer, Berlin

    MATH  Google Scholar 

  • Bieroza M, Heathwaite A (2015) Seasonal variation in phosphorus concentration-discharge hysteresis inferred from high-frequency in situ monitoring. J Hydrol 524:333–347

    Google Scholar 

  • Boënne W, Desmet N, Van Looy S, Seuntjens P (2014) Use of online water quality monitoring for assessing the effects of WWTP overflows in rivers. Environ Sci Process Impacts 16(6):1510–1518

    Google Scholar 

  • Chen T, Morris J, Martin E (2005) Particle filters for state and parameter estimation in batch processes. J Process Control 15(6):665–673

    Google Scholar 

  • Chen D, Dahlgren RA, Shen Y, Lu J (2012) A Bayesian approach for calculating variable total maximum daily loads and uncertainty assessment. Sci Total Environ 430:59–67

    Google Scholar 

  • DeChant CM, Moradkhani H (2012) Examining the effectiveness and robustness of sequential data assimilation methods for quantification of uncertainty in hydrologic forecasting. Water Resour Res 48(4)

  • de Oliveira Neves AC, Nunes FP, de Carvalho FA, Fernandes GW (2016) Neglect of ecosystems services by mining, and the worst environmental disaster in Brazil. Natureza & Conserva o 1(14):24–27

    Google Scholar 

  • Doucet A, Johansen AM (2009) A tutorial on particle filtering and smoothing: fifteen years later. Handb Nonlinear Filter 12(656–704):3

    MATH  Google Scholar 

  • Doucet A, De Freitas N, Gordon N (2001) An introduction to sequential Monte Carlo methods. In: Sequential Monte Carlo methods in practice. Springer, Berlin, pp 3–14

  • Freni G, Mannina G (2010) Bayesian approach for uncertainty quantification in water quality modelling: the influence of prior distribution. J Hydrol 392(1–2):31–39

    Google Scholar 

  • Gordon NJ, Salmond DJ, Smith AF (1993) Novel approach to nonlinear/non-Gaussian Bayesian state estimation. In: IEE proceedings F (radar and signal processing), IET, vol 140, pp 107–113

  • Guo J, Zheng L (2005) A modified simulated annealing algorithm for estimating solute transport parameters in streams from tracer experiment data. Environ Model Softw 20(6):811–815

    Google Scholar 

  • Gustafsson F (2010) Particle filter theory and practice with positioning applications. IEEE Aerosp Electron Syst Mag 25(7):53–82

    Google Scholar 

  • Isermann R, Balle P (1997) Trends in the application of model-based fault detection and diagnosis of technical processes. Control Eng Pract 5(5):709–719

    Google Scholar 

  • Jirka GH, Weitbrecht V (2005) Mixing models for water quality management in rivers: continuous and instantaneous pollutant releases. In: Water quality hazards and dispersion of pollutants. Springer, Berlin, pp 1–34

  • Julier SJ, Uhlmann JK (1997) New extension of the kalman filter to nonlinear systems. In: Signal processing, sensor fusion, and target recognition VI, vol 3068. International Society for Optics and Photonics, pp 182–193

  • Kaipio J, Somersalo E (2007) Statistical inverse problems: discretization, model reduction and inverse crimes. J Comput Appl Math 198(2):493–504

    MathSciNet  MATH  Google Scholar 

  • Kashefipour SM, Falconer RA (2002) Longitudinal dispersion coefficients in natural channels. Water Res 36(6):1596–1608

    Google Scholar 

  • Kirkpatrick S, Gelatt C, Vecchi M (1983) Science 220:671 (1983). https://doi.org/10.1126/science.220.4598 (Google Scholar Crossref, CAS)

  • Leibundgut C, Maloszewski P, Külls C (2011) Tracers in hydrology. Wiley, New York

    Google Scholar 

  • Leisenring M, Moradkhani H (2012) Analyzing the uncertainty of suspended sediment load prediction using sequential data assimilation. J Hydrol 468:268–282

    Google Scholar 

  • Liu J, West M (2001) Combined parameter and state estimation in simulation-based filtering. In: Sequential Monte Carlo methods in practice. Springer, Berlin, pp 197–223

  • Ljung L, Pflug G, Walk H (2012) Stochastic approximation and optimization of random systems, vol 17. Birkhäuser, Basel

    MATH  Google Scholar 

  • Lugon J, Silva Neto AJ, Rodrigues PPGW (2008) Assessment of dispersion mechanisms in rivers by means of an inverse problem approach. Inverse Probl Sci Eng 16(8):967–979

    MathSciNet  MATH  Google Scholar 

  • Luo X, Hoteit I, Duan L, Wang W (2011) Review of nonlinear Kalman, ensemble and particle filtering with application to the reservoir history matching problem

  • Marta-Almeida M, Mendes R, Amorim FN, Cirano M, Dias JM (2016) Fundão dam collapse: oceanic dispersion of River Doce after the greatest Brazilian environmental accident. Mar Pollut Bull 112(1–2):359–364

    Google Scholar 

  • Martin JL, McCutcheon SC (2018) Hydrodynamics and transport for water quality modeling. CRC Press, Boca Raton

    Google Scholar 

  • Meyer AM, Klein C, Fünfrocken E, Kautenburger R, Beck HP (2019) Real-time monitoring of water quality to identify pollution pathways in small and middle scale rivers. Sci Total Environ 651:2323–2333

    Google Scholar 

  • Mori J, Yu J (2014) Quality relevant nonlinear batch process performance monitoring using a kernel based multiway non-Gaussian latent subspace projection approach. J Process Control 24(1):57–71

    Google Scholar 

  • Newman M, Hatfield K, Hayworth J, Rao P, Stauffer T (2005) A hybrid method for inverse characterization of subsurface contaminant flux. J Contam Hydrol 81(1–4):34–62

    Google Scholar 

  • Ngo TB, Nguyen TA, Vu NQ, Chu TTH, Cao MQ (2012) Management and monitoring of air and water pollution by using GIS technology. J Vietnam Environ 3(1):50–54

    Google Scholar 

  • Parolin RdS, Rodrigues P, Domínguez D, Santiago O, Neto AdS (2015) Análise de sensibilidade e estimação de uma fonte de contaminantes no estuário do rio macaé. Rev Bras Recur Hídricos 20:24–33

    Google Scholar 

  • Rodrigues PPGW, González YM, de Sousa EP, Neto FDM (2013) Evaluation of dispersion parameters for river São Pedro, Brazil, by the simulated annealing method. Inverse Probl Sci Eng 21(1):34–51

    MATH  Google Scholar 

  • Salamon P, Feyen L (2010) Disentangling uncertainties in distributed hydrological modeling using multiplicative error models and sequential data assimilation. Water Resour Res 46(12)

  • Samuel J, Coulibaly P, Dumedah G, Moradkhani H (2014) Assessing model state and forecasts variation in hydrologic data assimilation. J Hydrol 513:127–141

    Google Scholar 

  • Schwaab M (2007) Análise de Dados Experimentais: I. Fundamentos de Estatística e Estimação de Parâmetros, Editora E-papers

  • Segura FR, Nunes EA, Paniz FP, Paulelli ACC, Rodrigues GB, Braga GÚL, dos Reis Pedreira Filho W, Barbosa Jr F, Cerchiaro G, Silva FF, et al (2016) Potential risks of the residue from Samarco’s mine dam burst (Bento Rodrigues, Brazil). Environ Pollut 218:813–825

  • Seo IW, Choi HJ, Kim YD, Han EJ (2016) Analysis of two-dimensional mixing in natural streams based on transient tracer tests. J Hydraul Eng 142(8):04016020

    Google Scholar 

  • Singh SK, Beck M (2003) Dispersion coefficient of streams from tracer experiment data. J Environ Eng 129(6):539–546

    Google Scholar 

  • Smith T, Marshall L, Sharma A (2015) Modeling residual hydrologic errors with Bayesian inference. J Hydrol 528:29–37

    Google Scholar 

  • Socolofsky SA, Jirka GH (2005) Special topics in mixing and transport processes in the environment. Engineering-lectures, 5th edn. Texas A&M University, College Station pp 1–93

  • Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    MathSciNet  MATH  Google Scholar 

  • Telles WR, Rodrigues PPGW, da Silva Neto AJ, Santiago OL, Mesa MI, Junior JL (2013) Simulação de uma pluma de contaminantes no rio macaé utilizando redes neurais artificiais. Revista Brasileira de Recursos Hidricos 18(2):165–174

    Google Scholar 

  • West M (1993) Approximating posterior distributions by mixtures. J R Stat Soc Ser B (Methodol) 55(2):409–422

    MathSciNet  MATH  Google Scholar 

  • Wolsey LA (1998) Integer programming. Wiley, New York

    MATH  Google Scholar 

  • Wu H, Huang G, Meng Q, Zhang M, Li L (2016) Deep tunnel for regulating combined sewer overflow pollution and flood disaster: a case study in Guangzhou City, China. Water 8(8):329

    Google Scholar 

  • Yeh HD, Chang TH, Lin YC (2007) Groundwater contaminant source identification by a hybrid heuristic approach. Water Resour Res 43(9)

  • Yeh HD, Lin CC, Chen CF (2016) Reconstructing the release history of a groundwater contaminant based on AT123D. J Hydroenviron Res 13:89–102

    Google Scholar 

  • 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. Environ Model Softw 57:216–226

    Google Scholar 

  • Zhou Q, Ren Y, Xu M, Han N, Wang H (2015) Adaptation to urbanization impacts on drainage in the city of Hohhot, China. Water Sci Technol 73(1):167–175

    Google Scholar 

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Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001.

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Correspondence to Julio Cesar Sampaio Dutra.

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Communicated by Apala Majumdar.

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Faria, R.R., da Silva, W.B., Dutra, J.C.S. et al. Particle filter-based data assimilation technique for the evaluation of transport of pollutants in small rivers. Comp. Appl. Math. 39, 243 (2020). https://doi.org/10.1007/s40314-020-01289-2

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