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Bivariate Flood Frequency Analysis of Upper Godavari River Flows Using Archimedean Copulas

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  • M. Reddy
  • Poulomi Ganguli

Abstract

In this paper, a copula based methodology is presented for flood frequency analysis of Upper Godavari River flows in India. By using the specific advantages of copula method in modeling the joint dependence structure of uncertain variables, this study applies Archimedean copulas for frequency analysis of flood characteristics annual peak flow, flood volume and flood duration. To determine the best fit marginal distributions for flood variables, few parametric and nonparametric probability distributions are examined and the best fit model is adopted for copula modeling. Four Archimedean family of copulas, namely Ali-Mikhail-Haq, Clayton, Gumbel-Hougaard and Frank copulas are evaluated for modeling the joint dependence of annual peak flow-volume, and flood volume-duration pairs. The performance of two parameter estimation methods, namely method-of-moments-like estimator based on inversion of Kendall’s tau and maximum pseudo-likelihood estimator for copulas are investigated. On performing Monte Carlo simulation to assess the performance of copula distributions in modeling the joint dependence structure of flood variables, it is found that the developed copula models are well representing the observed flood characteristics. From standard statistical tests, Frank copula has been identified as the best fitted copula for both bivariate models. The Frank copula function is used for obtaining joint and conditional return periods of flood characteristics, which can be useful for risk based design of water resources projects. Copyright Springer Science+Business Media B.V. 2012

Suggested Citation

  • M. Reddy & Poulomi Ganguli, 2012. "Bivariate Flood Frequency Analysis of Upper Godavari River Flows Using Archimedean Copulas," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(14), pages 3995-4018, November.
    • Handle: RePEc:spr:waterr:v:26:y:2012:i:14:p:3995-4018
    DOI: 10.1007/s11269-012-0124-z
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    2. James Charalambous & Ataur Rahman & Don Carroll, 2013. "Application of Monte Carlo Simulation Technique to Design Flood Estimation: A Case Study for North Johnstone River in Queensland, Australia," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(11), pages 4099-4111, September.
    3. Ummul Abdul Rauf & Panlop Zeephongsekul, 2014. "Analysis of Rainfall Severity and Duration in Victoria, Australia using Non-parametric Copulas and Marginal Distributions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(13), pages 4835-4856, October.
    4. Qiao-feng Tan & Xu Wang & Pan Liu & Xiao-hui Lei & Si-yu Cai & Hao Wang & Yi Ji, 2017. "The Dynamic Control Bound of Flood Limited Water Level Considering Capacity Compensation Regulation and Flood Spatial Pattern Uncertainty," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(1), pages 143-158, January.
    5. Dayang Wang & Dagang Wang & Chongxun Mo & Yi Du, 2021. "Risk variation of reservoir regulation during flood season based on bivariate statistical approach under climate change: a case study in the Chengbihe reservoir, China," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 108(2), pages 1585-1608, September.
    6. Ziqiang Xing & Denghua Yan & Cheng Zhang & Gang Wang & Dongdong Zhang, 2015. "Spatial Characterization and Bivariate Frequency Analysis of Precipitation and Runoff in the Upper Huai River Basin, China," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(9), pages 3291-3304, July.
    7. Shahid Latif & Slobodan P. Simonovic, 2023. "Trivariate Probabilistic Assessments of the Compound Flooding Events Using the 3-D Fully Nested Archimedean (FNA) Copula in the Semiparametric Distribution Setting," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(4), pages 1641-1693, March.
    8. Chao Zhang & Changming Ji & Yi Wang & Qian Xiao, 2022. "Flood hydrograph coincidence analysis of the upper Yangtze River and Dongting Lake, China," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 110(2), pages 1339-1360, January.
    9. Nejc Bezak & Matjaž Mikoš & Mojca Šraj, 2014. "Trivariate Frequency Analyses of Peak Discharge, Hydrograph Volume and Suspended Sediment Concentration Data Using Copulas," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(8), pages 2195-2212, June.
    10. Guilherme Armando Almeida Pereira & Álvaro Veiga, 2019. "Periodic Copula Autoregressive Model Designed to Multivariate Streamflow Time Series Modelling," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(10), pages 3417-3431, August.
    11. Shahid Latif & Slobodan P. Simonovic, 2022. "Nonparametric Approach to Copula Estimation in Compounding The Joint Impact of Storm Surge and Rainfall Events in Coastal Flood Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(14), pages 5599-5632, November.
    12. Wenzhuo Wang & Zengchuan Dong & Wei Si & Yu Zhang & Wei Xu, 2018. "Two-Dimension Monthly River Flow Simulation Using Hierarchical Network-Copula Conditional Models," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(12), pages 3801-3820, September.
    13. Xiang Fu & An-Qiang Li & Hui Wang, 2014. "Allocation of Flood Control Capacity for a Multireservoir System Located at the Yangtze River Basin," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(13), pages 4823-4834, October.
    14. Jiawei Zhou & Xiaohong Chen & Chuang Xu & Pan Wu, 2022. "Assessing Socioeconomic Drought Based on a Standardized Supply and Demand Water Index," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(6), pages 1937-1953, April.
    15. Milan Cisty & Anna Becova & Lubomir Celar, 2016. "Analysis of Irrigation Needs Using an Approach Based on a Bivariate Copula Methodology," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(1), pages 167-182, January.
    16. Homa Razmkhah & Alireza Fararouie & Amin Rostami Ravari, 2022. "Multivariate Flood Frequency Analysis Using Bivariate Copula Functions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(2), pages 729-743, January.

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