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Hydrological risk analysis of dam overtopping using bivariate statistical approach: a case study from Geheyan Reservoir, China

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Abstract

Hydrological risk analysis is essential and provides useful information for dam safety management and decision-making. This study presents the application of bivariate flood frequency analysis to risk analysis of dam overtopping for Geheyan Reservoir in China. The dependence between the flood peak and volume is modelled with the copula function. A Monte Carlo procedure is conducted to generate 100,000 random flood peak-volume pairs, which are subsequently transformed to corresponding design flood hydrographs (DFHs) by amplifying the selected annual maximum flood hydrographs (AMFHs). These synthetic DFHs are routed through the reservoir to obtain the frequency curve of maximum water level and assess the risk of dam overtopping. Sensitive analysis is performed to investigate the influence of different AMFH shapes and correlation coefficients of flood peak and volume on estimated overtopping risks. The results show that synthetic DFH with AMFH shape characterized by a delayed time to peak results in higher risk, and therefore highlight the importance of including a range of possible AMFH shapes in the dam risk analysis. It is also demonstrated that the overtopping risk is increased as the correlation coefficient of flood peak and volume increases and underestimated in the independence case (i.e. traditional univariate approach), while overestimated in the full dependence case. The bivariate statistical approach based on copulas can effectively capture the actual dependence between flood peak and volume, which should be preferred in the dam risk analysis practice.

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References

  • Apel H, Merz B, Thieken AH (2008) Quantification of uncertainties in flood risk assessments. Int J River Basin Manag 6(2):149–162

    Article  Google Scholar 

  • Callau Poduje AC, Belli A, Haberlandt U (2014) Dam risk assessment based on univariate versus bivariate statistical approaches: a case study for Argentina. Hydrol Sci J 59(12):2216–2232

    Article  Google Scholar 

  • Chen JH, Guo SL, Li Y, Liu P, Zhou YL (2013) Joint operation and dynamic control of flood limiting water levels for cascade reservoirs. Water Resour Manag 27(3):749–763

    Article  CAS  Google Scholar 

  • Cheng ST, Yen BC, Tang WH (1982) Overtopping risk for an existing dam. Department of Civil Engineering, University of Illinois at Urbana-Champaign, Illinois

    Google Scholar 

  • De Michele C, Salvadori G, Canossi M, Petaccia A, Rosso R (2005) Bivariate statistical approach to check adequacy of dam spillway. J Hydrol Eng 10(1):50–57

    Article  Google Scholar 

  • Erdik T, Duricic J, Van Gelder PHAJM (2013) The probabilistic assessment of overtopping reliability on Akyayik dam. KSCE J Civil Eng 17(7):1810–1819

    Article  Google Scholar 

  • Favre AC, El Adlouni S, Perreault L, Thiémonge N, Bobée B (2004) Multivariate hydrological frequency analysis using copulas. Water Resour Res 40:W01101

    Article  Google Scholar 

  • Gebregiorgis AS, Hossain F (2012) Hydrological risk assessment of old dams: case study on Wilson dam of Tennessee River basin. J Hydrol Eng 17(1):201–212

    Article  Google Scholar 

  • Genest C, Rémillard B, Beaudoin D (2009) Goodness-of-fit tests for copulas: a review and a power study. Insur Math Econ 44(2):199–213

    Article  Google Scholar 

  • Goodarzi E, Mirzaei M, Ziaei M (2012) Evaluation of dam overtopping risk based on univariate and bivariate flood frequency analyses. Can J Civil Eng 39(4):374–387

    Article  Google Scholar 

  • Goodarzi E, Shui LT, Ziaei M (2013) Dam overtopping risk using probabilistic concepts—case study: the Meijaran Dam, Iran. Ain Shams Eng J 4(2):185–197

    Article  Google Scholar 

  • Goodarzi E, Shui LT, Ziaei M (2014) Risk and uncertainty analysis for dam overtopping—case study: the Doroudzan Dam, Iran. J Hydro-Environ Res 8(1):50–61

    Article  Google Scholar 

  • Guo SL, Zhang HG, Chen H, Peng DZ, Liu P, Pang B (2004) A reservoir flood forecasting and control system for China. Hydrol Sci J 49(6):959–972

    Article  Google Scholar 

  • Haas CN (1999) On modeling correlated random variables in risk assessment. Risk Anal 19(6):1205–1214

    CAS  Google Scholar 

  • Hosking JR (1990) L-moments: analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc B 52(1):105–124

    Google Scholar 

  • Hsu YC, Tung YK, Kuo JT (2011) Evaluation of dam overtopping probability induced by flood and wind. Stoch Environ Res Risk Assess 25(1):35–49

    Article  Google Scholar 

  • Kuo JT, Yen BC, Hsu YC, Lin HF (2007) Risk analysis for dam overtopping—Feitsui reservoir as a case study. J Hydraul Eng 133(8):955–963

    Article  Google Scholar 

  • Kuo JT, Hsu YC, Tung YK, Yeh KC, Wu JD (2008) Dam overtopping risk assessment considering inspection program. Stoch Environ Res Risk Assess 22(3):303–313

    Article  Google Scholar 

  • Kwon HH, Moon YI (2006) Improvement of overtopping risk evaluations using probabilistic concepts for existing dams. Stoch Environ Res Risk Assess 20(4):223–237

    Article  Google Scholar 

  • Langousis A, Carsteanu AA, Deidda R (2013) A simple approximation to multifractal rainfall maxima using a generalized extreme value distribution model. Stoch Environ Res Risk Assess 27(6):1525–1531

    Article  Google Scholar 

  • Lave LB, Balvanyos T (1998) Risk analysis and management of dam safety. Risk Anal 18(4):455–462

    Article  CAS  Google Scholar 

  • Li N, Liu XQ, Xie W, Wu JD, Zhang P (2013) The return period analysis of natural disasters with statistical modeling of bivariate joint probability distribution. Risk Anal 33(1):134–145

    Article  Google Scholar 

  • Liu ZJ, Guo SL, Zhang HG, Liu DD, Yang G (2016) Comparative study of three updating procedures for real-time flood forecasting. Water Resour Manag 30(7):2111–2126

    Article  Google Scholar 

  • Liu ZJ, Guo SL, Guo JL, Liu P (2017) The impact of Three Gorges Reservoir refill operation on water levels in Poyang Lake, China. Stoch Environ Res Risk Assess 31(4):879–891

    Article  Google Scholar 

  • Liu ZJ, Guo SL, Xiong LH, Xu CY (2018) Hydrological uncertainty processor based on a copula function. Hydrol Sci J 63(1):74–86

    Article  Google Scholar 

  • Mediero L, Jiménez-Álvarez A, Garrote L (2010) Design flood hydrographs from the relationship between flood peak and volume. Hydrol Earth Syst Sc 14(12):2495–2505

    Article  Google Scholar 

  • Mo CX, Liu FG, Yu M, Ma RY, Sun GK (2008) Risk analysis for earth dam overtopping. Water Sci Eng 1(2):76–87

    Google Scholar 

  • Nelsen RB (2006) An introduction to copulas, 2nd edn. Springer, New York

    Google Scholar 

  • Requena AI, Mediero Orduña L, Garrote de Marcos L (2013) A bivariate return period based on copulas for hydrologic dam design: accounting for reservoir routing in risk estimation. Hydrol Earth Syst Sc 17(8):3023–3038

    Article  Google Scholar 

  • Saad C, Adlouni SE, St-Hilaire A, Gachon P (2015) A nested multivariate copula approach to hydrometeorological simulations of spring floods: the case of the richelieu river (québec, canada) record flood. Stoch Environ Res Risk Assess 29(1):275–294

    Article  Google Scholar 

  • Salvadori G, De Michele C (2007) On the use of copulas in hydrology: theory and practice. J Hydrol Eng 12(4):369–380

    Article  Google Scholar 

  • Sraj M, Bezak N, Brilly M (2015) Bivariate flood frequency analysis using the copula function: a case study of the litija station on the sava river. Hydrol Process 29(2):225–238

    Article  Google Scholar 

  • Sun YF, Chang HT, Miao ZJ, Zhong DH (2012) Solution method of overtopping risk model for earth dams. Safety Sci 50(9):1906–1912

    Article  Google Scholar 

  • Tung YK, Mays LW (1981) Risk models for flood levee design. Water Resour Res 17(4):833–841

    Article  Google Scholar 

  • Volpi E, Fiori A (2014) Hydraulic structures subject to bivariate hydrological loads: return period, design, and risk assessment. Water Resour Res 50(2):885–897

    Article  Google Scholar 

  • Xiao Y, Guo SL, Liu P, Yan BW, Chen L (2009) Design flood hydrograph based on multicharacteristic synthesis index method. J Hydrol Eng 14(12):1359–1364

    Article  Google Scholar 

  • Yan BW, Guo SL, Chen L (2014) Estimation of reservoir flood control operation risks with considering inflow forecasting errors. Stoch Environ Res Risk Assess 28(2):359–368

    Article  Google Scholar 

  • Yin JB, Guo SL, Liu ZJ, Yang G, Zhong YX, Liu DD (2018) Uncertainty analysis of bivariate design flood estimation and its impacts on reservoir routing. Water Resour Manag 32(5):1795–1809

    Article  Google Scholar 

  • Yue S, Ouarda TB, Bobée B, Legendre P, Bruneau P (2002) Approach for describing statistical properties of flood hydrograph. J Hydrol Eng 7(2):147–153

    Article  Google Scholar 

  • Zhang L, Singh VP (2006) Bivariate flood frequency analysis using the copula method. J Hydrol Eng 11(2):150–164

    Article  Google Scholar 

  • Zhang SR, Tan YS (2014) Risk assessment of earth dam overtopping and its application research. Nat Hazards 74(2):717–736

    Article  Google Scholar 

  • Zhong YX, Guo SL, Liu ZJ, Wang Y, Yin JB (2018) Quantifying differences between reservoir inflows and dam site floods using frequency and risk analysis methods. Stoch Environ Res Risk Assess 32(2):419–433

    Article  Google Scholar 

  • Zhou YL, Guo SL (2014) Risk analysis for flood control operation of seasonal flood-limited water level incorporating inflow forecasting error. Hydrol Sci J 59(5):1006–1019

    Article  Google Scholar 

Download references

Acknowledgements

This study is financially supported by the Water Resources Science and Technology Project of Jiangxi, China (KT201601) and Provincial Natural Science Foundation of Jiangxi, China (2015ZBBF60006). The authors would like to thank the editor and anonymous reviewers whose comments and suggestions help to improve the manuscript.

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Authors and Affiliations

  1. Jiangxi Provincial Institute of Water Sciences, Nanchang, 330029, China

    Zhangjun Liu, Xinfa Xu, Jingqing Cheng, Tianfu Wen & Jiao Niu

  2. Research Center of Water Resources and Ecological Environment of Poyang Lake, The Ministry of Water Resources P.R.C, Nanchang, 330029, China

    Zhangjun Liu

  3. Jiangxi Provincial Key Laboratory of Water Resources and Environment of Poyang Lake, Nanchang, 330029, China

    Zhangjun Liu

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  1. Zhangjun Liu
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  2. Xinfa Xu
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  3. Jingqing Cheng
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  4. Tianfu Wen
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  5. Jiao Niu
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Correspondence to Zhangjun Liu.

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Liu, Z., Xu, X., Cheng, J. et al. Hydrological risk analysis of dam overtopping using bivariate statistical approach: a case study from Geheyan Reservoir, China. Stoch Environ Res Risk Assess 32, 2515–2525 (2018). https://doi.org/10.1007/s00477-018-1550-0

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