Abstract
Groundwater system is a complex and open system, which is affected by natural conditions and human activities. Natural hydrological processes is conceptualized through relatively simple flow governing equations in groundwater models. Moreover, observation data is always limited in field hydrogeological conditions. Therefore, the predictive results of groundwater simulation often deviate from true values, which is attribute to the uncertainty of groundwater numerical simulation. According to the process of system simulation, the uncertainty sources of groundwater numerical simulation can be divided into model parameters, conceptual model and observation data uncertainties. In addition, the uncertainty stemmed from boundary conditions is sometimes refered as scenario uncertainty. In this paper, the origination and category of groundwater modeling uncertainty are analyzed. The recent progresses on the methods of groundwater modeling uncertainty analysis are reivewed. Furthermore, the researches on the comprehensive analysis of uncertainty sources, and the predictive uncertainty of model outputs are discussed. Finally, several prospects on the deveolpment of groundwater modeling uncetainty analysis are proposed.
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Zadeh L A. Toward a generalized theory of uncertainty (GTU)—An outline. Inform Sci, 2005, 172: 1–40
Hassan A E, Bekhit H M, Chapman J B. Using Markov Chain Monte Carlo to quantify parameter uncertainty and its effect on predictions of a groundwater flow model. Environ Modell Softw, 2009, 24: 749–763
Hassan A E, Bekhit H M, Chapman J B. Uncertainty assessment of a stochastic groundwater flow model using GLUE analysis. J Hydrol, 2008, 362: 89–109
Zeng X K, Wang D, Wu J C. Sensitivity analysis of the probability distribution of groundwater level series based on information entropy. Stoch Env Res Risk A, 2012, 26: 345–356
Ajami N K, Hornberger G M, Sunding D L. Sustainable water resource management under hydrological uncertainty. Water Resour Res, 2008, 44: W11406
Rojas R, Feyen L, Dassargues A. Conceptual model uncertainty in groundwater modeling: Combining generalized likelihood uncertainty estimation and Bayesian model averaging. Water Resour Res, 2008, 44: W12418
Yen B C, Cheng S T, Melching C S. Stochastic and Risk Analysis in Hydraulic Engineering. Littleton: Water Resources Publications, 1986
Van Asselt M. Perspectives on Uncertainty and Risk: The PRIMA Approach to Decision Support. Dordrecht: Kluwer Academic Publishers, 2000
Liu P G, Shu L C. Uncertainty on numerical simulation of groundwater flow in the riverside well field (in Chinese). J Jilin Univ (Earth Science Edition), 2008, 38: 639–644
Merz B, Thieken A H. Flood risk curves and uncertainty bounds. Nat Hazards, 2009, 51: 437–458
Yang P H, Yuan D X, Yuan W H, et al. Formations of groundwater hydrogeochemistry in a karst system during storm events as revealed by PCA. Chin Sci Bull, 2010, 55: 1412–1422
Helton J C, Oberkampf W L. Alternative representations of epistemic uncertainty. Reliab Eng Syst Safe, 2004, 85: 1–10
Katz R W, Parlange M B, Naveau P. Statistics of extremes in hydrology. Adv Water Resour, 2002, 25: 1287–1304
Singh A, Mishra S, Ruskauff G. Model averaging techniques for quantifying conceptual model uncertainty. Ground Water, 2010, 48: 701–715
Blasone R S, Vrugt J A, Madsen H, et al. Generalized likelihood uncertainty estimation (GLUE) using adaptive Markov Chain Monte Carlo sampling. Adv Water Resour, 2008, 31: 630–648
Wu J C, Lu L, Tang T. Bayesian analysis for uncertainty and risk in a groundwater numerical model’s predictions. Hum Ecol Risk Assess, 2011, 7: 1310–1331
Jin X L, Xu C Y, Zhang Q, et al. Parameter and modeling uncertainty simulated by GLUE and a formal Bayesian method for a conceptual hydrological model. J Hydrol, 2010, 383: 147–155
Ajami N K, Duan Q Y, Sorooshian S. An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction. Water Resour Res, 2007, 43: W01403
Zeng X K, Wang D, Wu J C, et al. Reliability analysis of the groundwater conceptual model. Hum Ecol Risk Assess, 2013, 19: 515–525
Xu X W, Li B W, Wang X J. Progress in study on irrigation practice with saline groundwater on sandlands of Taklimakan Desert Hinterland. Chin Sci Bull, 2006, 51: 161–166
Renard B, Kavetski D, Kuczera G, et al. Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors. Water Resour Res, 2010, 46: W05521
Refsgaard J C, Christensen S, Sonnenborg T O, et al. Review of strategies for handling geological uncertainty in groundwater flow and transport modeling. Adv Water Resour, 2012, 36: 36–50
Rojas R, Kahunde S, Peeters L, et al. Application of a multimodel approach to account for conceptual model and scenario uncertainties in groundwater modelling. J Hydrol, 2010, 394: 416–435
Ye M, Pohlmann K F, Chapman J B, et al. A model-averaging method for assessing groundwater conceptual model uncertainty. Ground Water, 2010, 48: 716–728
Montanari A. What do we mean by ‘uncertainty’? The need for a consistent wording about uncertainty assessment in hydrology. Hydrol Process, 2007, 21: 841–845
Beven K, Binley A. The future of distributed models-Model calibration and uncertainty prediction. Hydrol Process, 1992, 6: 279–298
Beven K, Freer J. Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the GLUE methodology. J Hydrol, 2001, 249: 11–29
Vazquez R F, Beven K, Feyen J. GLUE based assessment on the overall predictions of a MIKE SHE application. Water Resour Manag, 2009, 23: 1325–1349
Brazier R E, Beven K J, Anthony S G, et al. Implications of model uncertainty for the mapping of hillslope-scale soil erosion predictions. Earth Surf Proc Land, 2001, 26: 1333–1352
Mertens J, Madsen H, Feyen L, et al. Including prior information in the estimation of effective soil parameters in unsaturated zone modelling. J Hydrol, 2004, 294: 251–269
Aronica G, Hankin B, Beven K. Uncertainty and equifinality in calibrating distributed roughness coefficients in a flood propagation model with limited data. Adv Water Resour, 1998, 22: 349–365
Mantovan P, Todini E. Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology. J Hydrol, 2006, 330: 368–381
Mantovan P, Todini E, Martina M L V. Reply to comment by Keith Beven, Paul Smith and Jim Freer on “Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology”. J Hydrol, 2007, 338: 319–324
Beven K, Smith P, Freer J. Comment on “Hydrological forecasting uncertainty assessment: Incoherence of the GLUE methodology” by Pietro Mantovan and Ezio Todini. J Hydrol, 2007, 338: 315–318
Beven K, Smith P, Freer J. So just why would a modeller choose to be incoherent? J Hydrol, 2008, 354: 15–32
Vrugt J A, Gupta H V, Bouten W, et al. A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters. Water Resour Res, 2003, 39: Artn 1201
Metropolis N, Rosenbluth A W, Rosenbluth M N, et al. Equation of state calculations by fast computing machines. J Chem Phys, 1953, 21: 1087–1092
Hastings W K. Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 1970, 57: 97–109
Haario H, Saksman E, Tamminen J. Adaptive proposal distribution for random walk Metropolis algorithm. Comput Stat, 1999, 14: 375–395
Haario H, Saksman E, Tamminen J. An adaptive Metropolis algorithm. Bernoulli, 2001, 7: 223–242
Bates B C, Campbell E P. A Markov chain Monte Carlo scheme for parameter estimation and inference in conceptual rainfall-runoff modeling. Water Resour Res, 2001, 37: 937–947
Marshall L, Nott D, Sharma A. A comparative study of Markov chain Monte Carlo methods for conceptual rainfall-runoff modeling. Water Resour Res, 2004, 40: W02501
Gelfand A E, Hills S E, Racine-Poon A, et al. Illustration of Bayesian inference in normal data models using Gibbs sampling. J Am Stat Assoc, 1990, 85: 972–985
Duan Q Y, Sorooshian S, Gupta V. Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resour Res, 1992, 28: 1015–1031
Braak C. A Markov Chain Monte Carlo version of the genetic algorithm Differential Evolution: Easy Bayesian computing for real parameter spaces. Stat Comput, 2006, 16: 239–249
Vrugt JA, ter Braak C J F, Diks C G H, et al. Accelerating Markov Chain Monte Carlo simulation by differential evolution with self-adaptive randomized subspace sampling. Int J Nonlin Sci Num, 2009, 10: 273–290
Vrugt J A. DREAM(D): An adaptive markov chain monte carlo simulation algorithm to solve discrete, noncontinuous, posterior parameter estimation problems. Hydrol Earth Syst Sci, 2011, 8: 4025–4052
Laloy E, Vrugt J A. High-dimensional posterior exploration of hydrologic models using multiple-try DREAM((ZS)) and high-performance computing. Water Resour Res, 2012, 48: W01526
Yoon H, Hart D B, McKenna S A. Parameter estimation and predictive uncertainty in stochastic inverse modeling of groundwater flow: Comparing null-space monte carlo and multiple starting point methods. Water Resour Res, 2013, 49: 536–553
Thiemann M, Trosset M, Gupta H, et al. Bayesian recursive parameter estimation for hydrologic models. Water Resour Res, 2001, 37: 2521–2535
Poeter E P, Hill M C. UCODE, a computer code for universal inverse modeling. Comput Geosci, 1999, 25: 457–462
Doherty J E. PEST, Model-independent Parameter Estimation, User Manual 5th Edition, 2010
Bredehoeft J. The conceptualization model problem-surprise. Hydrogeol J, 2005, 13: 37–46
Troldborg L, Refsgaard J C, Jensen K H, et al. The importance of alternative conceptual models for simulation of concentrations in a multi-aquifer system. Hydrogeol J, 2007, 15: 843–860
Poeter E, Anderson D. Multimodel ranking and inference in ground water modeling. Ground Water, 2005, 43: 597–605
Refsgaard J C, van der Sluijs J P, Brown J, et al. A framework for dealing with uncertainty due to model structure error. Adv Water Resour, 2006, 29: 1586–1597
Draper D. Assessment and propagation of model uncertainty. J Roy Stat Soc B Met, 1995, 57: 45–97
Kass R E, Raftery A E. Bayes factors. J Am Stat Assoc, 1995, 90: 773–795
Akaike H. A new look at the statistical model identification. IEEE Trans Automat Contr, 1974, 19: 716–723
Hurvich C M, Tsai C L. Regression and time series model selection in small samples. Biometrika, 1989, 76: 297–307
Schwarz G. Estimating the dimension of a model. Ann Statist, 1978, 6: 461–464
Hannan E J, Quinn B G. The Determination of the order of an autoregression. J Roy Stat Soc Ser B-Stat Met, 1979, 41: 190–195
Kashyap R L. Optimal choice of AR and MA parts in autoregressive moving average models. IEEE Trans Patt Anal Mach Int, 1982, 4: 99–104
Neuman S P, Wierenga P J. A comprehensive strategy of hydrogeologic modeling and uncertainty Analysis for nuclear facilities and sites. NUREG/CR-6805, u.s. Nucl Regul Comm, Washington D C, 2003
Neuman S P. Maximum likelihood Bayesian averaging of uncertain model predictions. Stoch Env Res Risk A, 2003, 17: 291–305
Ye M, Neuman S P, Meyer P D. Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff. Water Resour Res, 2004, 40: W05113
Tsai FTC, Li X. Inverse groundwater modeling for hydraulic conductivity estimation using Bayesian model averaging and variance window. Water Resour Res, 2008, 44: W09434
Yustres A, Asensio L, Alonso J, et al. A review of Markov Chain Monte Carlo and information theory tools for inverse problems in subsurface flow. Computat Geosci, 2012, 16: 1–20
Foglia L, Mehl SW, Hill MC, et al. Evaluating model structure adequacy: The case of the maggia valley groundwater system, southern switzerland. Water Resour Res, 2013, 49: 260–282
Ye M. MMA: A computer code for multimodel analysis. Ground Water, 2010, 48: 9–12
Rojas R, Feyen L, Batelaan O, et al. On the value of conditioning data to reduce conceptual model uncertainty in groundwater modeling. Water Resour Res, 2010, 46: W08520
Rojas R, Feyen L, Dassargues A. Sensitivity analysis of prior model probabilities and the value of prior knowledge in the assessment of conceptual model uncertainty in groundwater modeling. Hydrol Process, 2009, 23: 1131–1146
Troldborg M, Nowak W, Tuxen N, et al. Uncertainty evaluation of mass discharge estimates from a contaminated site using a fully Bayesian framework. Water Resour Res, 2010, 46: W12552
Raftery A E, Gneiting T, Balabdaoui F, et al. Using Bayesian model averaging to calibrate forecast ensembles. Mon Weather Rev, 2005, 133: 1155–1174
Harp D R, Vesselinov V V. Analysis of hydrogeological structure uncertainty by estimation of hydrogeological acceptance probability of geostatistical models. Adv Water Resour, 2012, 36: 64–74
Post J, Hattermann F F, Krysanova V, et al. Parameter and input data uncertainty estimation for the assessment of long-term soil organic carbon dynamics. Environ Modell Softw, 2008, 23: 125–138
Renard B, Kavetski D, Kuczera G. Comment on “An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction” by Newsha K. Ajami et al. Water Resour Res, 2009, 45: W03603
Krzysztofowicz R. Bayesian theory of probabilistic forecasting via deterministic hydrologic model. Water Resour Res, 1999, 35: 2739–2750
Kavetski D, Kuczera G, Franks S W. Bayesian analysis of input uncertainty in hydrological modeling: 2. Application. Water Resour Res, 2006, 42: W03408
Kavetski D, G Kuczera, SW Franks. Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory. Water Resour Res, 2006, 42: W03407
Ebrahimi N, Soofi E S, Soyer R. Information measures in perspective. Int Stat Rev, 2010, 78: 383–412
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Wu, J., Zeng, X. Review of the uncertainty analysis of groundwater numerical simulation. Chin. Sci. Bull. 58, 3044–3052 (2013). https://doi.org/10.1007/s11434-013-5950-8
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DOI: https://doi.org/10.1007/s11434-013-5950-8