IDEAS home Printed from https://ideas.repec.org/a/spr/waterr/v26y2012i14p3995-4018.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11269-012-0124-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11269-012-0124-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. B. Parida & R. Kachroo & D. Shrestha, 1998. "Regional Flood Frequency Analysis of Mahi-Sabarmati Basin (Subzone 3-a) using Index Flood Procedure with L-Moments," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 12(1), pages 1-12, February.
    2. S. Nadarajah & J. Shiau, 2005. "Analysis of Extreme Flood Events for the Pachang River, Taiwan," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 19(4), pages 363-374, August.
    3. Rakesh Kumar & C. Chatterjee & Sanjay Kumar & A. Lohani & R. Singh, 2003. "Development of Regional Flood Frequency Relationships Using L-moments for Middle Ganga Plains Subzone 1(f) of India," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 17(4), pages 243-257, August.
    4. Genest, Christian & Rémillard, Bruno & Beaudoin, David, 2009. "Goodness-of-fit tests for copulas: A review and a power study," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 199-213, April.
    5. repec:dau:papers:123456789/2332 is not listed on IDEAS
    6. Thierry Ane & Cecile Kharoubi, 2003. "Dependence Structure and Risk Measure," The Journal of Business, University of Chicago Press, vol. 76(3), pages 411-438, July.
    7. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    8. Kojadinovic, Ivan & Yan, Jun, 2010. "Comparison of three semiparametric methods for estimating dependence parameters in copula models," Insurance: Mathematics and Economics, Elsevier, vol. 47(1), pages 52-63, August.
    9. Abhijit Bhuyan & Munindra Borah & Rakesh Kumar, 2010. "Regional Flood Frequency Analysis of North-Bank of the River Brahmaputra by Using LH-Moments," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(9), pages 1779-1790, July.
    10. Robert T. Clemen & Terence Reilly, 1999. "Correlations and Copulas for Decision and Risk Analysis," Management Science, INFORMS, vol. 45(2), pages 208-224, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Sajjad Abdollahi & Ali Mohammad Akhoond-Ali & Rasoul Mirabbasi & Jan Franklin Adamowski, 2019. "Probabilistic Event Based Rainfall-Runoff Modeling Using Copula Functions," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 33(11), pages 3799-3814, September.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    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. 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.
    15. 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.
    16. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Penikas, H., 2010. "Financial Applications of Copula-Models," Journal of the New Economic Association, New Economic Association, issue 7, pages 24-44.
    2. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
    3. Zhichao Zhang & Li Ding & Fan Zhang & Zhuang Zhang, 2015. "Optimal Currency Composition for China's Foreign Reserves: A Copula Approach," The World Economy, Wiley Blackwell, vol. 38(12), pages 1947-1965, December.
    4. Mikhail Semenov & Daulet Smagulov, 2017. "Portfolio Risk Assessment using Copula Models," Papers 1707.03516, arXiv.org.
    5. Benoumechiara Nazih & Bousquet Nicolas & Michel Bertrand & Saint-Pierre Philippe, 2020. "Detecting and modeling critical dependence structures between random inputs of computer models," Dependence Modeling, De Gruyter, vol. 8(1), pages 263-297, January.
    6. Hobæk Haff, Ingrid, 2012. "Comparison of estimators for pair-copula constructions," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 91-105.
    7. Benoumechiara Nazih & Bousquet Nicolas & Michel Bertrand & Saint-Pierre Philippe, 2020. "Detecting and modeling critical dependence structures between random inputs of computer models," Dependence Modeling, De Gruyter, vol. 8(1), pages 263-297, January.
    8. Penikas, Henry & Simakova, Varvara, 2009. "Interest Rate Risk Management Based on Copula-GARCH Models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 13(1), pages 3-36.
    9. Ostap Okhrin & Martin Odening & Wei Xu, 2013. "Systemic Weather Risk and Crop Insurance: The Case of China," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(2), pages 351-372, June.
    10. Zhang, Shulin & Okhrin, Ostap & Zhou, Qian M. & Song, Peter X.-K., 2016. "Goodness-of-fit test for specification of semiparametric copula dependence models," Journal of Econometrics, Elsevier, vol. 193(1), pages 215-233.
    11. Emura, Takeshi & Lin, Chien-Wei & Wang, Weijing, 2010. "A goodness-of-fit test for Archimedean copula models in the presence of right censoring," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3033-3043, December.
    12. Durante Fabrizio & Puccetti Giovanni & Scherer Matthias & Vanduffel Steven, 2016. "Stat Trek. An interview with Christian Genest," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-14, May.
    13. Nguyen, Tristan & Molinari, Robert Danilo, 2009. "Quantifizierung von Abhängigkeitsstrukturen zwischen Risiken in Versicherungsunternehmen," German Risk and Insurance Review (GRIR), University of Cologne, Department of Risk Management and Insurance, vol. 5(2), pages 28-52.
    14. Grundke, Peter & Polle, Simone, 2012. "Crisis and risk dependencies," European Journal of Operational Research, Elsevier, vol. 223(2), pages 518-528.
    15. E. Petrova A. & Е. Петрова А., 2014. "Оценка Риска Остаточной Стоимости Секьюритизированного Пула Активов Оперативного Лизинга // A Securitized Pool Of Operating Lease Assets And Its Residual Value Risk Evaluation," Финансы: теория и практика/Finance: Theory and Practice // Finance: Theory and Practice, ФГОБУВО Финансовый университет при Правительстве Российской Федерации // Financial University under The Government of Russian Federation, issue 3, pages 127-138.
    16. Петрова Екатерина Александровна, 2014. "Оценка Риска Остаточной Стоимости Секьюритизированного Пула Активов Оперативного Лизинга," Вестник Финансового университета, CyberLeninka;Федеральное государственное образовательное бюджетное учреждение высшего профессионального образования «Финансовый университет при Правительстве Российской Федерации» (Финансовый университет), issue 3, pages 127-138.
    17. Liang Zhu & Christine Lim & Wenjun Xie & Yuan Wu, 2017. "Analysis of tourism demand serial dependence structure for forecasting," Tourism Economics, , vol. 23(7), pages 1419-1436, November.
    18. MICHIELS, Frederik & DE SCHEPPER, Ann, 2007. "A copula test space model: How to avoid the wrong copula choice," Working Papers 2007027, University of Antwerp, Faculty of Business and Economics.
    19. Gregor Weiß, 2011. "Copula parameter estimation by maximum-likelihood and minimum-distance estimators: a simulation study," Computational Statistics, Springer, vol. 26(1), pages 31-54, March.
    20. Roman Matkovskyy, 2019. "Extremal Economic (Inter)Dependence Studies: A Case of the Eastern European Countries," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 17(3), pages 667-698, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:waterr:v:26:y:2012:i:14:p:3995-4018. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.