Analysis of the Uncertainty of the Simulation-Optimization Model using the Monte Carlo Markov Chain Algorithm

Document Type : Research Article


1 Ph. D Student, School of Environment, College of Engineering, University of Tehran, Iran

2 Associate Professor, School of Environment, College of Engineering, University of Tehran, Iran

3 Assistant Professor, School of Environment, College of Engineering, University of Tehran, Iran


Uncertainty analysis is an inseparable step in the process of hydrological modeling. Quantitative assessment of the uncertainty in the simulation model outputs and its parameters lead to an increase of confidence in the results of modeling and understanding of the sources of uncertainty.  Due to the increasing use of groundwater management model and predicting the behavior of the aquifer, this research is seeking to analyze the uncertainty in quantitative-qualitative aquifer simulation and its effect on optimization results. Using SWAT hydrologic model, the amount of recharge is specified and inserted into MODFLOW groundwater flow model and MT3DMS transmission model. In this research, the DREAM (zs) algorithm (based on Monte Carlo Markov chain algorithms) was used to examine the uncertainty of MODFLOW model parameters. Then by linking the model with MOPSO, the optimum head and salinity are obtained in the aquifer. The results show that the accuracy of the inputs of the model leads to the desirability of the results in relation to the intended purpose of reducing the water table.


Main Subjects

[1].               Mirzaei M, Huang Y.F, and El-Shafie A. Applicati on of the generalized likelihood uncertainty estimation (GLUE) approach for assessing uncertainty in hydrological models. A review, Stochastic Environmental Research and Risk Assessment. 2015; 29(5): 1265-1273.
[2].               Rojas R, Kahunde S. Application of a multimodel approach to account for conceptual model and scenario uncertainties in groundwater modeling. Journal of Hydrology.2010; 394(3)416-435.
[3].               Montanari A, Grossi G. Estimating the uncertainty of hydrological forecasts. A statistical approach, Water Resources Research. 2008; 44: W00B08.
[4].               Blazkova S, Beven K. A limits of acceptability approach to model evaluation and uncertainty estimation in flood frequency estimation by continuous simulation: Skalka catchment, Czech Republic, Water Resources Research. 2009; 45: W00B16.
[5].               Blasone R.S, Parameter estimation and uncertainty assessment in hydrological modelling. 2007; Technical university of Denmark.
[6].               Johnson J. Framework to effectively quantify and communicate groundwater model uncertainty to management and client, U.S. department of the Interior Urea of Reclamation. Pacific Northwest Regional Office Boise. 2010; Idaho, U.S.A.
[7].               Vrugt JA, Gupta HV, Bouten W, Sorooshian S. A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic parameter estimation. Water Resources Research. 2003; 39(8):1201.
[8].               Kanso A, Chebbo G, Tassin B. Application of MCMC–GSA model calibration method to urban runoff quality modeling, Reliability Engineering & System Safety. 2004; 91(10-11):1398–1405.
[9].               Dotto C.B.S, Mannina G, Kleidorfen M, Vezzaro L, Henrichs M, cCarthy, et al. Comparison of different uncertainty techniques in urban stormwater quantity and quality modeling, Water Research. 2012; 46(8):2545-2558.
[10].            Talebizadeh M, Morid S, Ayyoubzadeh SA, Ghasemzadeh M. ncertainty Analysis in Sediment Load Modeling Using ANN and SWAT Model. Water Resources Management. 2009; 24(9):1747-1761.
[11].            Pohll G. Pohlmann K, Hassan A, Chapman J, Mihvec T. Assessing groundwater model uncertainty for the central Nevada test area. Spectrum 2002.
[12].            Hassan AE, Bekhit HB, Chapmann JB. Uncertainty assessment of a stochastic groundwater flow model using GLUE analysis. Journal of Hydrology. 2008; 362:89-109.
[13].            Blasone R.S, Vrugt J.A, Madsen H, Rosberg D, Robinson B.A, Zyvoloski, G.A. Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling, Advances in Water Resources. 2008; 31:630–648.
[14].            Fu J, Gomez-Hernandez JJ. Uncertainty Assessment and data worth in groundwater flow and mass transport modeling using a blocking markov chain montecarlo method. Journal of Hydrology. 2009; 364:328-341.
[15].            Sepúlveda N. Doherty J. Uncertainty Analysis of a Groundwater Flow Model in East-Central Florida. Groundwater. 2015; 53(3):464–474.
[16].            Keating EH, Doherty J, Vrugt JA, Kang Q. Optimization and uncertainty assessment of strongly non-linear groundwater models with high parameter dimensionality. Water Resources Research. 2010; W10517(46).
[17].            Rojas R, Feyen L, Dassargues A. Conceptual model uncertainty in groundwater modeling: Combining generalized likelihood uncertainty estimation and Bayesian model averaging. Water Resources Research. 2008; W12418 44(12):619-624.
[18].            McKinney DC, Lin MD. Genetic algorithm solution of groundwater management models. Water Resources Research. 1994; 30(6):1897.
[19].            Huang C, Mayer AS. Pump-and-treat optimization using well locations and pumping rates as decision variables. Water Resources Research. 1997; 33(5):1001–1012.
[20].            Storck P, Eheart JW, Valocchi AJ. A method for the optimal location of monitoring ells for detection of groundwater contamination in threedimensional heterogeneous aquifers. Water Resources Research. 1997; 33(9):2081.
[21].            Das, Datta. Application of optimisation techniques in groundwater quantity and quality management. Sadhana: Academy Pro- ceedingsin Enging. 2001; 26 (4).293-316.
[22].            Hsiao CT, Chang LC. Dynamic optimal groundwater management with inclusion of fixed costs. Journal of Water Resources Planning and Management. 2002; 128(1):57–65.
[23].            Loaiciga HA. Analytical game theoretic approach to groundwater extraction. Journal of Hydrology. 2004; 297:22–33.
[24].            Reed PM, Minsker BS. Striking the balance: Long-term groundwater monitoring design for conflict objectives. Journal of Water Resources Planning and Management. 2004; 130(2):140-149.
[25].            Tran TM. Multi-Objective Management of Saltwater in Groundwater. Optimization under Uncertainty. 2004; TU Delft University of Technology.
[26].            Wu J, Zheng C, Chein C.C, Zheng L. A comprative study of Monte Carlo simple genetic algorithm and noisy genetic algorithm for cost-effective sampling network design under uncertainty. Advance in Water Resources. 2005;29(1) 899-911.
[27].            Karamouz M, Tabari M. M, Kerachian R. Application of artificial neural networks and generic algorithms in conjunctive use of surface and groundwater resources. Water International. 2007; 32(1): 163-176.
[28].            Salazar R, Szidarouszky F, Coppola EJr, Rojana A. Application of game theory for groundwater conflict in Mexico. Journal of Environmental Management. 2007; 84: 560-571.
[29].            Bazargan-Lari MR, Kerachian R, Mansoori A. A conflictresolution model for the onjunctive use of surface and groundwater resources that considers water-quality issues: A case study. Environmental Management. 2009; 43:470–482.
[30].            Mahjoub MA, Ammar S, Edziri H, Bouraoui A, Zine Mighri, Z. Antiin- flamatory and antioxidant activities of some extracts and pure natural products isolated from Rhus tripartitum (Ucria) leaves, stems and fruits. Med. Chem. Res. 2010; 19: 271–282.
[31].            Ketabchi H, Ataie-Ashtiani B. Development of Combined Ant Colony Optimization Algorithm and Numerical Simulation for Optimal Management of Coastal Aquifers. Iran-Water Resources Research. 2011; 7(1):1-12 (In Persian).
[32].            Fallah mahdipour A, Bozorg Hadad A, Alimohammadi S. Optimal Operation of the Conjunctive Aquifers - Dam system: The Genetic Programming Approach. Water resource engineering. 2014; 7(21):51-66 (In Persian).
[33].            Ayvaz MT, Elçi A. A groundwater management tool for solving the pumping cost minimization problem for the Tahtali watershed (Izmir-Turkey) using hybrid hs-solver optimization algorithm. Journal of Hydrology. 2013; 478:63–76.
[34].            Narula K, Gosain, A. K. Modeling hydrology, groundwater recharge and non-point nitrate loadings in the Himalayan Upper Yamuna basin. Science of The Total Environment. 2013; 468, S102-S116.
[35].            Elçi A, Ayvaz MT. Differential-evolution algorithm based optimization for the site selection of groundwater production wells with the consideration of the vulnerability concept. Journal of Hydrology. 2014; 511:736–749.
[36].            Nakhaei M, Mohammadi M, Rezaie M. Optimizing of aquifer withdrawal numerical model using genetic algorithm (case study: Uromiyeh coastal aquifer). Iran-Water Resources Research. 2014; 10(2):94-97 (In Persian).
[37].            El Alfy M. Numerical groundwater modelling as an effective tool for management of water resources in arid areas. Hydrological Sciences Journal. 2014; 59(6), 1259-1274.
[38].            Izady A, Davary K, Alizadeh A, Ziaei AN, Akhavan S, Alipoor, et al. Groundwater conceptualization and modeling using distributed SWAT-based recharge for the semi-arid agricultural Neishaboor plain, Iran. Hydrogeology Journal. 2015; 23(1): 47-68.
[39].            Raei E, Nikoo MR, Pourshahabi S. A multi-objective simulation-optimization model for in situ bioremediation of groundwater contamination: Application of bargaining theory Journal of Hydrology.2017; 551: 407-422.
[40].            Thomas A. Simulation optimization model for aquifer parameter estimation using coupled meshfree point collocation method and cat swarm optimization. Engineering Analysis with Boundary Elements. 2018; 91: 60-72.
[41].            Bates BC, Campbell EP. A Markov Chain Monte Carlo scheme for parameter estimation and inference in conceptual rainfall - runoff modeling. Water Resources Research. 2001; 37: 937-947.
[42].            Neal R. Probabilistic inference using Markov Chain Monte Carlo methods, Technical Report CRG-TR-93-1, Department of Computer Science. University of Toronto. Toronto. Canada. 1993; 144.
[43].            Kuczera G, Parent E. Monte Carlo assessment of parameter uncertainty in conceptual catchment models: The Metropolis algorithm. Journal of Hydrology. 1998; 211: 69-85.
[44].            Metropolis N, Rosenbluth A.W, Rosenbluth M.N, Teller A.H, Teller E. Equations of state calculations by fast computing machines. Journal of Chemical Physics. 1953; 21: 1087-1091.
[45].            Hastings W.K. Monte Carlo sampling methods using Markov Chains and their applications. Biometrika. 1970; 57: 97-109.
[46].            Laloy E, Vrugt J.A. High-dimensional posterior exploration of hydrologic models using multiple-try DREAM (ZS) and high-performance computing. Water Resources Research. 2012; 48: W01526.
[47].            Vrugt, JA, Ter Braak CJF, Diks CGH, Robinson BA, Hyman JM, Higdon D. Accelerating Markov Chain Monte Carlo simulation using self-adaptative differential evolution with randomized subspace sampling. International Journal of Nonlinear Sciences and Numerical Simulation. 2009; 10: 273-290.
[48].            Kuczera G, Kavetski D, Renard B, Thyer M. A limited-memory acceleration strategy for MCMC sampling in hierarchical Bayesian calibration of hydrological models. Water Resources Research. 2010; 46: W07602.
[49].            Ter Braak CJF. A Markov chain Monte Carlo version of the genetic algorithm differential evolution: Easy Bayesian computing for real parameter spaces. Statistics and Computing. 2006; 16: 239-249.
[50].            Vrugt JA, Ter Braak CJF, Clark MP, Hyman JM, Robinson BA. Treatment of input uncertainty in hydrologic modeling: Doing hydrology backward with Markov chain Monte Carlo simulation. Water Resources Research. 2008; 44: W00B09.
[51].            Montanari A, Koutsoyiannis D. A blueprint for process-based modeling of uncertain hydrological systems. Water Resources Research. 2012; 48: W09555.
[52].            Schoups G, Vrugt J.A. A formal likelihood function for parameter and predictive inference of hydrologic models with correlated, heteroscedastic and non-Gaussian errors. Water Resources Research. 2010; 46: W10531.
[53].            Koskela JJ, Croke BWF, Koivusalo H, Jakeman AJ, Kokkonen T. Bayesian inference of uncertainties in precipitation-streamflow modeling in a snow affected catchment. Water Resources Research. 2012; 48: W11513.
[54].            Kamali A, Niksokhan MH. Development of a Model for Calculation of Sustainability Index of Groundwater Resources. Ecohydrology. 2017; 4(4): 1071-1087. (In Persian)
[55].            Studies of gavkhuni water balance, groundwater report, zayanderoud consulting company.2015.
[56].            McDonald M, Harbaugh GAW. A modular three-dimensional finite-difference ground-water flow model.1988.
[57].            Storn R, Price K. Differential evolution-A simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization.1997; 11: 341-359.
[58].            Price K.V, Storn R.M, Lampinen J.A. Differential evolution, A practical approach to global optimization, Springer. Berlin. 2005; 538 pp.
[59].            Gelman A, Rubin D.B. Inference from iterative simulation using multiple sequences, Statistical Science.1992; 7: 457-472.
[60].            Eberhart RC, Kennedy J. A new optimizer using particle swarm theory. In: Proc. of the Sixth International Symposium on Micro Machine and Human Science; 1995; 4-6 October, Nagoya, Japan, 39-43.
[61].            Alemayehu T, van Griensven A, Woldegiorgis B.T, Bauwens W. An improved SWAT vegetation growth module and its evaluation for four tropical ecosystems. Hydrol. Earth Syst. Sci. 2017; 21, 4449–4467.
[62].            Nourali M, Ghahraman B, Pourreza-Bilondi M, Davary K. Effect of formal and informal likelihood functions on uncertainty assessment in a single event rainfall-runoff model. Journal of Hydrology. 2016;540: 549–564.
Volume 6, Issue 1
April 2019
Pages 137-151
  • Receive Date: 22 September 2018
  • Revise Date: 01 December 2018
  • Accept Date: 01 December 2018
  • First Publish Date: 21 March 2019