Risk-based Optimization of Flood Diversion System of Karun4 Dam under Hydraulic and Hydrologic Uncertainties

Document Type : Research Paper


1 Dept. of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Dept. of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

3 Department of Civil Engineering, University of Tehran, Tehran, Iran


Risk-based optimization in flood diversion system is a framework that allows the designer to involve uncertainties in the decision-making process and determine the reliability of the hydraulic structure. This study was conducted to incorporate hydrological and hydraulic uncertainties in the probabilistic design of Karun-4 diversion system in Khuzestan province, southwestern Iran. The risk-based multivariate probabilistic model was developed for determining the effect of uncertainty sources on the characteristics of the flow diversion system. For this purpose, the time series of annual maximum peak flow and maximum flood volume data for a period of 37 years were prepared and evaluated. Archimedean copula function and non-dominated sorting genetic algorithm were adopted to minimize the overtapping risk and construction cost as objective functions. Diameter, slope, wall covering and tunnel entrance height, cofferdam height at upstream and downstream were searched as decision variables in the possible space of the problem. The results show that optimal values of upstream cofferdam height, downstream cofferdam height and the diameter of the first and second tunnels were estimated as 44.5, 12.5, 10.5 and 9.9 m, respectively, all corresponding to 25-year return period. Moreover, the results suggest that the proposed framework could be valuable for decision makers when economic, hydraulic and hydrological uncertainties are expected.


Main Subjects

Afshar, A., and Marino, M.A., (1990) Optimizing spillway capacity with uncertainty in flood estimator, Journal of Water Resources Planning and Management, 116 (l): 71–83.
Afshar, A., Barkhordary, A., and Marino, M.A., (1994) Optimizing river diversion under hydraulic and hydrologic
uncertainties. Journal of Water Resources Planning and Management,120 (1): 36–47.
Afshar, A., Rasekh, A., and Afshar, M.H., (2009) Risk-based optimization of large flood diversion systems, using genetic algorithms, Journal of Engineering Optimization, 41(3):259–273.
Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6): 716-722.
Akhlaghi, M. (2015). Risk analysis of flood diversion system (Case study: KarunIV). M.Sc. Thesis. Science and Reseach Branch, Islamic Azad University. Pp:122. (In Farsi)
Behrooz, M., Alimohammadi, S. and Atari, J. (2014). Sensitivity analysis of hydrologic, hydraulic and economic uncertainties in design of flood control systems. Iran Water Resources Research. 10(2): 69-81. (In Farsi)
Behrooz, M., and Alimohammadi, S. (2018). Uncertainty analysis of flood control measures including epistemic and aleatory uncertainties: probability theory and evidence theory. J. Hydrol. Eng., 23(8): 04018033
Biglarbeigi P, Giuliani M, Castelletti A (2018) Partitioning the impacts of streamflow and evaporation uncertainty on the operations of multipurpose reservoirs in arid regions. J Water Resour Plann Manage 144(7): 05018008
Chen L, Guo, S. (2019) Copulas and Its Application in Hydrology and Water Resources. Springer https://doi.org/10.1007/978-981-13-0574-0
Chow V.T. (1959) Open channel hydraulics, McGraw-Hill, New York
Clayton, D.G. (1978). A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence. Bimetrika.65: 141 -151.
Davtalab R, Mirchi A, Khatami S, Gyawali R, Massah AR, Farajzadeh M, Madani K (2017) Improving continuous hydrologic modeling of data-poor river basin using hydrologic engineering center’s hydrologic modelling system: case study of Karkheh River basin. J Hydrol Eng, 05017011-1
Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transaction on Evolutionary Computation 6:181-197
Dehghani, M. Saghafian, B. and Zargar, M. (2019). Probabilistic hydrological drought index forecasting based on meteorological drought index using Archimedean copulas. Hydrology Research. 50: 1230-1251.
Fotakis, D. and Sidiropoulos, E. (2012). A new multi-objective self-organizing optimization algorithm (MOSOA) for spatial optimization problems. Applied Mathematics and Computation. 218: 5268-5180.
Gao L, Zhang L, Li X, Zhou S (2019) Evaluating metropolitan flood coping capabilities under heavy storms. J Hydrol Eng 24(6): 05019011.
Goldberg, D. E. (1989). Genetic algorithms in search optimization and machine learning, Addision-Wesley, Reading, Mass. Pp: 399.
Goodarzi E., Mirzaei, M., Shui, L.T., and Ziaei, M. (2011). Evaluation dam overtopping risk based on univariate and bivariate flood frequency analysis. Hydrol., Earth Syst. Sci. Discuss., 8: 9757–9796.
Haghighi A, Zahedi A (2014) Uncertainty analysis of water supply networks using the fuzzy set theory and NSGA-II. Eng App Art Int 32: 270–282
International Commission on Large Dams (ICOLD). (1973). Lessons from dam incidents (reduced edition). ICOLD, Paris.
Iran Ministry of Energy (2008) Karun IV dam and power planet report Rep No. 338202/3290/13363, Tehran, Iran
Karamouz M, Doroudi S, Moridi A (2018) Developing a model for optimizing the geometric characteristics of water diversion systems. J Irrig Drain Eng 144(2): 04017062
Kojadinovic, I. and Yan, J. (2010). Package Copula. Version 0.9-7, May 28, 2010. Available in: http://cran.r-project.Org/web/packages/copula/coupla.
Kong XM, Huang GH, Li YP, Fan YR, Zeng XT, Zhu Y (2018) Inexact copula-based stochastic programming method for water resources management under multiple uncertainties. J Water Resour Plann Manage 144(11): 04018069
Kwon, H.H., Moon, Y.I., (2006), Improvement of overtopping risk evaluations using probabilistic concepts for existing dams, Journal of Stoch Environ Res Risk Assess, 20: 223–237
Lalehzari R (2017) Closure to “Multi-objective management of water allocation to sustainable irrigation planning and optimal cropping pattern”. J Irri Drain Eng 07016024 DOI: 10.1061/(ASCE)IR.1943-4774.0001144.
Lalehzari R, Boroomand-Nasab S, Moazed H, Haghighi A (2016) Multi-objective management of water allocation to sustainable irrigation planning and optimal cropping pattern. J Irri Drain Eng 142(1): 05015008
Lund, J.R., (1991) Random variables versus uncertain values: stochastic modeling and design, Journal of Water Resources Planning and Management, 117 (2), 179–194.
Mahab-Ghods Consulting Engineers. (2004). Design of the upstream cofferdam of Karun4 Dam, Final report. (In Farsi).
Marengo, H. (2006). Case study: dam safety during construction, lessons of the overtopping diversion works at Aguamilpa dam. Journal of Hydraulic Engineering, 132(11), 1121-1127.
Marengo, H., Arregiun F. L., Aldama, A. A, Morals, V. (2013). Case Study: Risk analysis by overtopping of diversion works during dam construction: The La Yasca hydroelectric project, Mexico. Structural Safety 42: 26-34.
Maurer EP, Kayser G, Doyle L, Wood AW (2018) Adjusting flood peak frequency changes to account for climate change impacts in the western United States. J Water Resour Plann Manage 144(3): 05017025.
Mays, L.W. and Travis, Q.B., (2005) Optimizing Retention Basin Networks, Journal of Water Resour. Plan. Manage., 134(5): 432-439.
McCann, M.M.Jr., Franzini, J.B., and Shah, H.C., 1984. Preliminary safety evaluation of existing dams.Vol. 1. Washington, D.C: Federal Emergency Management Agency.
Rasekh A, Afshar A, Afshar MH (2010) Risk-cost optimization of hydraulic structures: methodology and case study. Water Resour Manage 24 (11): 2833-2851
Salas, J.D., Obeysekera, J. (2019) Probability distribution and risk of the first occurrence of k extreme hydrologic events. J Hydrol Eng 24(10): 04019032
Schwarz, G. (1978). Estimating the dimension of a model. Annalys of Statistics, 6(2): 461-464.
Sklar, A., (1959). Fonction de re’partition a’n dimensions et leurs marges. [Distribution functions, dimensions and margins]. Publications of the Institute of Statistics, University of Paris, Paris, pp. 229–231. (In French)
Sreekanth, J., and Datta, B. (2010). Multi-objective management of saltwater intrusion in coastal aquifers using genetic programming and modular neural network based surrogate models. Journal of Hydrology. 393: 245–256.
Srinivas, N., and Deb, K. (1994) Multi-objective optimization using non-dominated sorting in genetic algorithms. Evol Com 2: 221-248
Thompson, K.D., Stedinger, J.R., and Heath, D.C. (1997) Evaluation and presentation of dam failure and flood risks. Journal of Water Resources Planning and Management, 123 (4): 216-227.
Tung, Y.K. (2017). Uncertainty analysis and risk-based design of detention basin without damage function. Water Resour. Res. 53, 3576–3598
Tung, Y.K. and Mays, L.W. (1981) Optimal risk-based design of flood levee systems, Journal of Water Resources Research, 17(4): 843-852.
Tung, Y.K., Yen, B.C., Melching, C.S. (2006) Hydrosystems engineering reliability assessments and risk analysis, McGraw-Hill, New York
Tung, Y.K., and Bao, Y., (1990) On the optimal risk-based design of highway drainage structures, Journal of Stochastic Environmental Research and Risk Assessment, 4 (4): 295–308.
USACE (US Army Corps of Engineers) (1996) Risk-based analysis for flood damage reduction studies. Engineer Manual EM 1110-2-1619, Washington, DC
Yazdi, J., Zahraie, B., Salehi Neyshabouri, S.A.A. (2016) A stochastic optimization algorithm for optimizing flood risk management measures including rainfall uncertainties and nonphysical flood damages. J Hydrol Eng 04016006
Zhang C, Ding W, Ming F, Fu G (2019) Cost-benefit framework design of water transfer systems. J Water Resour Plann Manage 145(5): 04019007
Zhu X, Zhang C, Yin J, Zhou H, Jiang Y (2014) Optimization of water diversion based on reservoir operating rules: analysis of the Biliu River reservoir, China. J Hydrol Eng 19: 411-421.