Assessment of Conceptual Model Uncertainty in Groundwater Modeling (Case Study: Najafabad Aquifer of Gavkhouni Basin)

Document Type : Research Article


1 Department of Water Engineering, College of Aburaihan, University of Tehran, Iran.

2 Department o Water Resources, Water Research Institute (WRI), Tehran, Iran

3 Department of Water Engineering, College of Aburaihan, University of Tehran, Iran


Groundwater‌ modeling is the foundation for quantitative analysis of groundwater resources, the successful assessment of which depends on its stable and reliable simulation. Because groundwater models are‌ an approximation‌ of reality, it is impossible to quite determine a system's properties through modeling or to mathematically describe the complex properties of a hydrogeological system. Therefore, inherently, all models have a degree of uncertainty, and as a result, the existence of uncertainty in the groundwater model sets managerial decisions in relation to it at risk of failure. The purpose of this study is to explain a method for quantitative recognition of groundwater uncertainty and how model uncertainty can be used as a tool to better realize the modeled system and provide the information needed to help make more informed decisions. A quantitative investigation of groundwater modeling was performed in Najafabad located in Isfahan province. Three conceptual models were‌ created for Najafabad aquifer by different geological settings, recharging, and model boundaries. Conceptual models were developed in steady-state for 2018-2019 and calibrated using observational data. All models were validated using available water level data of 2018-2019. The models reliably simulated the water level in the aquifer. To select the best model, the model selection criteria (AIC, AICC, BIC, and KIC) was used. The results showed that model number 1 with the highest weight and the least uncertainty was introduced as the best model.


  • Neuman S.P, Maximum likelihood Bayesian averaging of uncertain model predictions. Stochastic Environmental Research and Risk Assessment. 2003; 17(5): 291-305.
  • Rojas R, F. L. Conceptual model uncertainty in groundwater modeling: Combining generalized likelihood uncertainty estimation and Bayesian model averaging. Water Resour Res. 2008; 44: W12418.
  • Brendecke C. Comments on Model Uncertainty Memo. For consideration by the Eastern Snake Hydrologic Modeling Committee. 2009.
  • Wu J.Ch , & Zeng X. Review of the uncertainty analysis of groundwater numerical simulation. Chinese Science Bulletin. 2013; 58(25): 3044-3052.
  • Zeng X, Wu J, Wang D, Zhu X‌, & Long Y. Assessing Bayesian model averaging uncertainty of groundwater modeling based on information entropy method. Journal of Hydrology. 2016; 538: 689–704. doi:10.1016/j.jhydrol.2016.04.038
  • Parrish M. A , Moradkhani H, & DeChant C. M. Toward reduction of model uncertainty: Integration of Bayesian model averaging and data assimilation. WATER RESOURCES RESEARCH. 2012; 48. doi:10.1029/2011WR011116
  • Samani S, Asghari Moghaddam A, & Ye M. Investigating the effect of complexity on groundwater flow modeling uncertainty. Stoch Environ Res Risk Assess. 2018; 32(3): 643–659. doi:10.1007/s00477-017-1436-6
  • Engelhardt I, De Aguinaga J, Mikat H, Schu¨th C, & Liedl R. Complexity vs. simplicity: groundwater model ranking using. Ground Water. 2014; 52:573–583. doi:10.1111/ gwat.12080
  • Lukjan A, Swasdi S, & Chalermyanont T. Importance of Alternative Conceptual Model for Sustainable Groundwater Management of the Hat Yai Basin, Thailand. Procedia Engineering, 2016; 154: 308 – 316.
  • Touhidul Mustafa S. Md , Nossent J, Ghysels G, Huysmans M. Integrated Bayesian Multi-model approach to quantify input, parameter and conceptual model structure uncertainty in groundwater modeling. Journal of Hydrology. 2020;
  • Malmir M, Javadi S, Moridi A, Neshat A, & Razdar B. A new combined framework for sustainable development using the DPSIR approach and numerical modeling. Geoscience Frontiers. 2021;12(4)
  • Zayandab Consulting Engineers, updating the balance of water resources in the case study of Gavkhooni catchment in 2011-2012, Volume 5: Water Resources Assessment, Appendix 6: Water Resources Balance Report Najafabad Case Study (4206). 2015. (In Persian)
  • Holder J. J. E. Olsen and Philip Z. Experimental determination of subcritical crack growth parameters in sedimentary rock: Geophysical Research Letters 2001; 28(4): 599-602


  • Singhal B. B. S. and Gupta R. P. Applied Hydrogeology of Fractured Rocks. Springer Publication. 2010; United States.
  • Akaike H. A new look at the statistical model identification. IEEE Trans Automat Contr. 1974; 19: 716–723.
  • Hurvich C.M, and Tsai C.L. Regression and time series model selection in small samples. Biometrika. 1989;76(2): 297-307.
  • Rissanen, J., Modeling by shortest data description. Automatica 1978; 14(5): 465-471.
  • Schwarz G. Estimating the dimension of a model. The annals of statistics.1978;6(2):461-464.
  • Kashyap R.L. Optimal choice of AR and MA parts in autoregressive moving average models. IEEE Transactions on Pattern Analysis and Machine Intelligence. 1982; (2): 99-104.
  • Ye M, Meyer PD, Neuman SP. On model selection criteria in multi model analysis. Water Resour Res. 2008a; doi:10.1029/2008WR006803.
  • Carrera J and Neuman S.P. Estimation of aquifer parameters under transient and steady state conditions: 2. Uniqueness, stability, and solution algorithms. Water Resources Research. 1986b; 22(2): 211-227.
  • Samper F.J, & Neuman Sh.P. Estimation of spatial covariance structures by adjoint state maximum likelihood cross validation: 1. Theory. Water Resources Research. 1989a; 25(3): 351-362.
  • Carrera J. and Neuman S.P. Estimation of aquifer parameters under transient and steady state conditions: 1. Maximum likelihood method incorporating prior information. Water Resources Research. 1986a; 22(2): 199-210.
  • Ye M, Meyer PD, Neuman SP. On model selection criteria in multi model analysis. Water
    Resour Res. 2008a; doi:10.1029/2008WR006803.
  • Ye M, Neuman S.P, Meyer‌ P.D, Pohlmann K. Sensitivity analysis and assessment of prior model probabilities in MLBMA with application to unsaturated fractured tuff. Water Resources Research. 2005; 41(12).
  • 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.
  • Kass R.E, and Raftery A.E. Bayes factors. Journal of the American statistical association 90; 1995: (430)773-795.
  • Liu P, Elshall A.S , Ye M , Beerli P, Zeng X, Lu D and Tao Y. Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods. Water Resources Research. 2016.
  • Hill C.M, Tiedeman C.R. Effective Groundwater Model Calibration: With Analysis of Data, Sensitivities, Predictions, and Uncertainty. John Wiley & Sons, Inc., Hoboken, New Jersey. 2007; 455 pp.
  • Hill M.C. Methods and guidelines for effective model calibration: with application to UCODE, a computer code for universal inverse modeling, and MODFLOWP, a computer code for inverse modeling with MODFLOW: U.S.Geological Survey Water-Resources Investigations Report; 1998: 98-4005
  • Diks C.G.H, Vrugt J.A. Comparison of point forecast accuracy of model averaging methods in hydrologic applications, Stochastic Environmental Research and Risk Assessment. 2010; 24: 809-820.
  • Duan Q, Ajami N, Gao X, and Sorooshian S. Multi-model ensemble hydrologic prediction using Bayesian model averaging. Advances in Water Resources. 2007; 30(5): 1371–1386.