Flood Frequency Analysis Using Archimedean Copula Functions Based on Annual Maximum Series (Case Study:Arazkuseh Hydrometric Station in Golestan Province)

Document Type : Original Article

Authors

1 M.ScGraduated Studentof Water Resources Engineering,Gorgan University ofAgricultural Sciences and Natural Resources., Gorgan., Iran

2 Associate Prof., Dept. of Water Engineering, Gorgan University of Agricultural Sciences and Natural Resources., Gorgan., Iran

3 Assistant professor of Water Engineering Department, water and soil Engineering college, Gorgan Agriculture Science and Natural Resource University., Gorgan., Iran

Abstract

Univariate frequency analysis of hydrological events has some shortcomings caused by the lack of taking into account all characteristics of such events. Therefore, bivariate frequency analysis  of hydrologic events such as flood can be useful in hydraulic design of structures and water resources management. The peak discharge and volume of flood are two important parameters in design of structures, thus, Archimedean copula functions were used for analysis of dependence structure between peak discharges and flood volumes. The time series of discharge for Arazkusehhydrometric station for a period of 40 years was constructed based on annual maximum (AM) discharge in daily scale. This station area is 1678.1 km2.The results showed that Gumbel extreme value copula was the best choice for fitting to data. Beased on design requirements, one can choose joint return period in "and", "or" and "conditional". For example, considering univariate frequency analysis results the return period of peak discharge equal to 50 years, while for a same value of peak discharge and volume in "and", "or" condition, the joint return periods are 72 and 38 respectively.  The return period of "or" case was less than univariateand the highest value was belong to "and" case. This shows that planning or design based on "or" case is more confident, because results to larger values of peak discharge and volume quantile for the same value or univariate return period. 

Keywords


اسلامیان،س،س و سلطانی کوپایی،س.1381. در ترجمه تحلیل فراوانی سیل، رائو، ا.ر.، و حامد، ح.خ. (مؤلفان). انتشارات ارکان، اصفهان، ایران.
امیدی،م.، محمدزاده،م.، مرید،س. 1389. تحلیل احتمالاتی شدت- مدت خشکسالی در استان تهران با استفاده از توابع مفصل. مجله تحقیقات آب و خاک ایران. 41(1): 95-102
تمسکنی،ا. 1392. مقایسه روش‌های جداسازی دبی پایه از هیدروگراف روزانه جریان(مطالعه موردی حوضه بالادست سد بوستان در استان گلستان) .نشریه پژوهش‌های حفاظت آب و خاک. 20(6):127- 145.
فرخ‌نیا،ا و مرید،س. 1387. تحلیل شدت و مدت خشکسالی با استفاده از توابع مفصل. چهارمین کنگره ملی مهندسی عمران.
عباسیان،م،ص.، موسوی ندوشنی،س،س. 1392. تحلیل توأم دبی اوج و حجم رواناب سیلاب با استفاده از تابع مفصل فرانک (پوستر). هفتمین گنگره ملی مهندسی عمران. دانشگاه سیستان و بلوچستان.
عبدالحسینی،م. 1391. کاربرد کوپلا در تحلیل فراوانی چند متغیره‌ی جریان‌های کم و ارزیابی رگرسیون کوپلایی به منظور استفاده در تحلیل متغیرهای غیرمستقل. رساله دکتری. دانشگاه صنعتی اصفهان. دانشکده کشاورزی. 232 ص.
Ahmad,U.N and Shabri,A.2011. Flood frequency analysis of annual maximum stream flows using L-moment and TL-moment approach. J. Applied Mathematical Sciences. 5(5):243-253.
B´ardossy,A and Pegram,G.G.S. 2009. Copula based multisite model for daily precipitation simulation. J. Hydrol. Earth Syst. Sci. 13:2299–2314.
Cherubini,U., Luciano,E and Vecchito,W. 2004. Copula methods in finance.Wiley. 310p.
De Michele,C and Salvadori,G.2003.A Generalized Pareto intensity-duration model of storm rainfall exploiting 2-Copulas. J. Geophys. Res. 108(D2):1-11.
Favre,A-C., Adlouni,S.E., Perreault,L., Thiémonge, N and Bobée,B. 2004. Multivariate hydrological frequency analysis using copulas.Water Resources Research.40, W01101.doi:10.1029/2003WR002456.
Fermanian,J.-D. 2005. Goodness-of-fit tests for copulas. Journal of Multivariate Analysis 95:119–152.
Genest,C., Ghoudi,K and Rivest,L.P. 1995. A semiparametric estimation procedure of dependence parameters in multivariate families of distributions. J. Biometrika. 82(3): 543-552.
Genest,C and Werker,B.J.M. 2002. Conditions for asymptotic semiparametric efficiency of an omnibus estimator of dependence parameters in Copula models. In: Cuadras, C., Fortiana, J., and Lallena, J.R. (eds) Distributions with given marginals and statistical modeling, Kluwer, pp 103-112.
Genest,C., R´emillard,B and Beaudoin,D. 2009. Goodness-of-fit tests for copulas: A review and a power study. J. Mathematics and Economics.44: 199–213.
Grimaldi,S and Serinaldi,F. 2006. Asymmetric copula in multivariate flood frequency analysis. J. Advanc Water Resour. 29:1155-1167.
Grimaldi,S., Kao.S.C., Castellarin,A., Papalexiou,S.M., Viglione,A., Laio,F., Aksoy,H and Gedikli,A. 2011. 2.18-Statistical Hydrology. In : P. Wilderer(ed.) Treatise on Water Science, Elsivier, Oxford, pp. 479-517.
Poulin, A., Huard, D., Favre, A.C and Pugin, S .2007. Importance of tail dependence in bivariate frequency analysis J. Hydrol.Eng.12(4):394-403.
Karmakar,S and Simonovic,S.P. 2009. Bivariate flood frequency analysis. Part 2: a copula-based approach with mixed marginal distributions. J. Flood Risk Management. 2:32–44.
Lee,T and Salas,J.D. 2011. Copula-based stochastic simulation of hydrological data applied to Nile river flows. J. Hydrol. Research. 42(4):318-330.
Ma,M.W., Ren,L.L., Song,S.B., Song,J.L and JI Ang,S.H. 2013. Goodness-of-fit tests for multi-dimensional copulas: expanding application to historical drought data. J. Water Science and Engineering.6 (1):18-30.
Madadgar,Sand Moradkhani,H. 2013. Drought Analysis under Climate Change Using Copula. J. Hydrol. Eng., 18(7):746–759.
Nelsen,R.B. 2006. An Introduction to Copulas. New York, Springer. 269p.
Requena,A.I., Mediero,L and Garrote,L.2013. A bivariate return period based on copulas for hydrologic dam design: accounting for reservoir routing in risk estimation. J. Hydrol. Earth Syst. Sci. 17: 3023–3038.
Reddy,M.J and Ganguli,P. 2012. Bivariate flood frequency analysis of upper Godavari river flows using Archimedean Copulas. J. Water Resource Management. 26(14): 3995-4018.
Rachev,S.T. 2003. Handbook of heavy tailed distributions in finance.Amsterdam ; Boston : Elsevier. 662p.
Salvadori,G., De Michele,C., Kottegoda,N.T and Rosso,R. 2007. Extremes in nature: An approach using Copulas. Water Science and Technology Library.56. Netherland, Springer. 292p.
Sklar,A. 1959. Fonctions de repartition à n dimensions etleursmarges. Publ. Inst. Statist. Univ. Paris, 8: 229-231.
Serinaldi,F and Grimaldi,S.2007. Fully Nested 3-Copula: Procedure and Application on Hydrological Data. J. Hydrol. Eng..12(4):420-430.
Shiau,J.T., Feng,S and Nadarajah,S. 2007. Assessment of hydrological droughts for the Yellow River, China, using copulas.Hydrological Processes. 21(16): 2157–2163.
Shiau,J.T and Modarres,R. 2009. Copula-based drought severity-duration-frequency analysis in Iran. J. Meteorol. Appl. 16: 481–489.
Shih,J.H and Louis,T.A.1995. Inferences on the association parameter in copula  models for bivariate survival data. J. Biometrics. 51(4): 1384-1399.
Yue,S., Ouarda,T.B.M.J and Bobée,B. 2001. A review of bivariate gamma distribution for hydrological application.J.Hydro.246(1-4):1-18.
Yue,S and Rasmussen,P. 2002. Bivariate frequency analysis: discussion of some useful concepts in hydrological application. J. Hydrolgy Process. 16:2881-2898.
Zhang,L and Singh,V.P. 2006. Bivariate flood frequency analysis using the copula method. J. Hydrol. Eng. ASCE. 11(2):150-164.
Zhang,L., Singh,V.P and ASCE,F. 2007. Gumbel–Hougaard Copula for trivariate rainfall frequency analysis. J. Hydrol. Eng.12(4):409-419.
Zhang,Q., Chen,Y., Chen,X and Li,J. 2011. Copula-based analysis of hydrological extremes andimplications of hydrological behaviors in the Pearl river basin, China. J. Hydrol. Eng. 16(7): 598–607.
Volume 8, Issue 2 - Serial Number 46
November and December 2014
Pages 353-365
  • Receive Date: 03 December 2013
  • Revise Date: 09 April 2014
  • Accept Date: 07 May 2014
  • First Publish Date: 22 May 2014