Investigation of uncertainty due to model complexity in groundwater modeling

Document Type : Research paper

Authors

1 1. Ph.D Candidate, Department of Water Engineering, College of Aburaihan, University of Tehran, Pakdasht, Iran

2 2. Associate Professor, Department of Water Engineering, College of Aburaihan, University of Tehran, Pakdasht, Iran

3 3. Assistant Professor of Hydrogeology, Department of Water Resources Study and Research, Water Research Institute, Tehran, Iran

4 4. Associate Professor, Department of Water Engineering, College of Aburaihan, University of Tehran, Pakdasht, Iran

Abstract

One of the factors that lead to uncertainty in the mathematical model of groundwater flow is the uncertainty due to the complexity of the conceptual model that results from the increase of model parameters. Considering the complexity of groundwater modeling can aid in selecting an optimal model, and can avoid model uncertainty and misleading conclusions. The purpose of this study is to investigate the uncertainty of the complexity of the mathematical model of the Najafabad aquifer. In this regard, six conceptual models with five different degrees of complexity with the number of calibrated model parameters (4, 16, 20, 22, 26, and 26 parameters) with the same observational data in Najafabad aquifer located in Isfahan province in a steady-state and for the year 2018-2019 were developed and model selection criteria (AIC, AICC, BIC, and KIC) were used to evaluate the probability of models. The results showed that model #1 with four parameters, which is the simplest model, was selected as the best model and has the least uncertainty. But models 5 and 6, which are the most complex models, have the most uncertainty and the least level of confidence. Therefore, it can be said that in defining the conceptual model of an aquifer, determining the optimal number of parameters will decrease the uncertainty of the mathematical model. 

Keywords

References

حیدری، ج.، چیت‌سازان، م.، میرزایی، س.ی.، 1398. مدل‌سازی رابطه هیدروژئولوژیکی آبخوان دشت صحنه-بیستون با رودخانه گاماسیاب و مدیریت آبخوان. هیدروژئولوژی، 4(1): 140-152.
عرب عامری، ع.، شیرانی، ک.، رضایی، خ.، 1397. ارزیابی آسیب‌پذیری آب زیرزمینی به روش دراستیک (مطالعه موردی: دشت نجف­آباد). علوم و مهندسی آبخیزداری ایران، 12(43): 80-88.
کرد، م.، اصغری مقدم، ا.، نخعی، م.، 1398. مدل­سازی عددی آبخوان دشت اردبیل و مدیریت آن با استفاده از بهینه‌سازی برداشت آب زیرزمینی. هیدروژئولوژی، 4(1): 153-167.
گلابی، م.ر.، زینعلی، م.، نیک­سخن، م. ح.، آذری، آ.، 1397. بررسی عملکرد مدل مفهومی مادفلو و فرا مدل شبیه‌ساز بیان ژن در مدل‌سازی هیدروگراف معرف آبخوان (مطالعه موردی: دشت لور-اندیمشک). هیدروژئولوژی، 3(2): 33-45.
Akaike, H., 1974. A new look at the statistical model identification. IEEE Trans Automat Contr, 19: 716–723.
Arkesteijn, L., Pande, S., 2013. On hydrological model complexity, its geometrical interpretations and prediction uncertainty. Water Resour. Res, 49(10): 7048-7063.
Asl-Rousta, B., Mousavi, S.J., Ehtiat, M., Ahmadi, M., 2018. SWAT-Based Hydrological Modelling Using Model Selection Criteria. Water Resour Manage, 32:2181–2197.
Brooks, R. J., Tobias, A.M.,­ 1996. Choosing the best model: Level of detail, complexity, and model performance. Math. Comput. Model, 24(4): 1-14.
Carrera, J., Neuman, S.P., 1986. Estimation of aquifer parameters under transient and steady state conditions: 2. Uniqueness, stability, and solution algorithms. Water Resources Research, 22(2): 211-227.
Clement, T.P., 2011. Complexities in hindcasting models-when should we say enough is enough?. Ground water, 49(5): 620-629.
Collyer, C.E., 1985. Comparing strong and weak models by fitting them to computer-generated data. Attention, Perception, & Psychophysics, 38(5): 476-481.
Gómez-Hernández, J., 2006. Complexity. Groundwater, 44(6): 782-785.
Helton, J.C., Oberkampf, W.L., 2004. Alternative representations of epistemic uncertainty. Reliab Eng Syst Safe, 85: 1–10.
Hill, C.M., Tiedeman, C.R., 2007. Effective Groundwater Model Calibration: With Analysis of Data, Sensitivities, Predictions, and Uncertainty. John Wiley & Sons, Inc., Hoboken, New Jersey. 455 pp.
Hill, M. C., 2006. The practical use of simplicity in developing ground water models. Groundwater, 44(6): 775-781.
Hill, M.C., 1998. 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, pp. 98-4005.
Holder, J., Olsen­, J.E., Philip, Z., 2001. Experimental determination of subcritical crack growth parameters in sedimentary rock: Geophysical Research Letters, 28/4: 599-602.
Hunt, R.J., C. Zheng., 1999. Debating complexity in modeling. Eos, Transactions of the American Geophysical Union, 80(3): 29-29.
Hunt, R.J., Doherty, J., Tonkin, M.J., 2007. Are models too simple? Arguments for increased parameterization. Ground Water, 45(3): 254-262.
Hurvich, C.M., Tsai, C.L., 1989. Regression and time series model selection small samples. Biometrika, 76: 297–307.
Jakeman, A. J., Hornberger, G.M., 1993. How much complexity is warranted in a rainfall-runoff model? Water Resour. Res, 29(8):2637-2649.
Kashyap, R.L., 1982. Optimal choice of AR and MA parts in autoregressive moving average models. IEEE Transactions on Pattern Analysis and Machine Intelligence, (2): 99-104.
Kass, R.E., Raftery, A.E., 1995. Bayes factors. Journal of the American statistical association 90; (430):773-795.
Kumar, P. 2011. Typology of hydrologic predictability. Water Resour. Res, 47(3): 167-177.
Li, X., Tsai, F.-C., 2009. Bayesian model averaging for groundwater head prediction and uncertainty analysis using multimodel and multimethod. Water Resour. Res­, 45, W09403.
Liu,  P., Elshall,  A.S., Ye,  M., Beerli,  P., Zeng,  X., Lu,  D., Tao, Y., ­2016. Evaluating marginal likelihood with thermodynamic integration method and comparison with several other numerical methods. Water Resources Research.52(2): 734-758.
Lukjan, A., Swasdi, S., Chalermyanont, T., 2016. Importance of Alternative Conceptual Model for Sustainable Groundwater Management of the Hat Yai Basin, Thailand. Procedia Engineering, 154: 308-316.
Malmir,  M, Javadi,  S, Moridi,  A, Neshat,  A, Razdar,  B. A. 2021. new combined framework for sustainable development using the DPSIR approach and numerical modeling. Geoscience Frontiers, 12(4).
McDonald, M.G., Harbaugh, A.W., 1988. A modular three-dimensional finite-difference ground-water flow model, U. S. Geological survey, Techniques of Water-Resources Investigation, book 6, chap. A1, 586 pp.
Meyer, P., Ye, M., Neuman, S., Rockhold, M., Cantrell, K., Nicholson, T., 2007. Combined estimation of hydrogeologic conceptual. Washington, DC: U.S. Nucl. Regul. Comm.
Nettasana, T., 2012. Conceptual Model Uncertainty in the Management of the Chi River Basin, Thailand. Thesis, University of Waterloo.
Popper, K. R., 1982. The Open Universe: An Argument for Indeterminism (From the Postscript to the Logic of Scientific Discovery, ed. WW Bartley III). Hutchinson, London.
Refsgaard, J.C., Sluijs, J.P., Brown, J.,  Keur , P.,  2006. A framework for dealing with uncertainty due to model structure error. Adv Water Resour, 29: 1586–1597.
Rissanen, J., 1978. Modeling by shortest data description, 14: 465-471.
Rojas, R., Feyen, L., Dassargues, A., 2008. Conceptual model uncertainty in groundwater modeling: Combining generalized likelihood uncertainty estimation and Bayesian model averaging. Water Resour Res, 44(12): W12418.
Schoups, G., van de Giesen, N. C., Savenije, H.G., 2008. Model complexity control for hydrologic prediction. Water Resour. Res, 44(12): 370-380.
Schwartz, F.W., Liu, G., Aggarwal, P., Schwartz, C.M., 2017. Naïve simplicity: the overlooked piece of the complexity-simplicity paradigm. Groundwater, 55(5): 703-711.
Schwarz, G., 1978. Estimating the dimension of a model. Ann Stat, 6: 46-464.
Simmons, C.T., Hunt, R.J., 2012. Updating the debate on model complexity. GSA Today, 22(8): 28-29.
Singhal, B.B.S., Gupta R.P., 2010. Applied Hydrogeology of Fractured Rocks. Springer Publication. United States.
Todd, D.K., Mays, L.W., 2005. Groundwater Hydrology. Third Ed., John Wiley & Sons Inc., U.S.A. 636 pp.
Viaroli, S., Lotti, F, Mastrorillo., L, Paolucci., V, Mazza., R., 2019. Simplified two-dimensional modelling to constrain the deep groundwater contribution in a complex mineral water mixing area, Riardo Plain, southern Italy. Hydrogeology Journal, 27: 1459-1478.
Ye,  M., Neuman, S.P., Meyer,  P.D., 2004. Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff. Water Resour Res, 40(5): W05113.
Ye, M., Meyer, P., Neuman, S., 2008. On model selection criteria in multimodel analysis. Water Resour. Res, 44(3): 380-384.
Ye, M., Neuman, S.P., Meyer, P.D., 2004. Maximum likelihood Bayesian averaging of spatial variability models in unsaturated fractured tuff. Water Resour Res, 40(5): W05113.
Ye M, Pohlmann KF, Chapman JB, Pohll GM, Reeves DM. 2010. A model-averaging method for assessing groundwater conceptual model uncertainty. Ground Water. 48(5): 716-28.
Yeh, W.W.G., Yoon, Y.S., 1981. Aquifer parameter identification with optimum dimension in parameterization. Water Resources Research, 17(3): 664-672.
Yin, J., Tsai, F., Kao, Shih-Chieh. 2021. Accounting for uncertainty in complex alluvial aquifer modeling by Bayesian multi-model approach. United States.  Journal of Hydrology, 601: 126682.
Young, P., Parkinson, S., Lees, M., 1996. Simplicity out of complexity in environmental modeling: Occam's Razor revisited. J. Appl. Stat, 23(2-3): 165-210.
Hydrogeology
Volume 6, Issue 2
Publisher
March 2022
Pages 132-150

Files

Share

How to cite

Statistics