A review of bivariate hydrological frequency distribution

XIE Hua; HUANG Jie-sheng

Volume 19 Issue 3

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Advances in Water Science > 2008 > 19(3): 443-452.

XIE Hua, HUANG Jie-sheng. A review of bivariate hydrological frequency distribution[J]. Advances in Water Science, 2008, 19(3): 443-452.

Citation:

XIE Hua, HUANG Jie-sheng. A review of bivariate hydrological frequency distribution[J]. Advances in Water Science, 2008, 19(3): 443-452.

Citation:

XIE Hua, HUANG Jie-sheng. A review of bivariate hydrological frequency distribution[J]. Advances in Water Science, 2008, 19(3): 443-452.

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A review of bivariate hydrological frequency distribution

State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China

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Received Date: May 23, 2007

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Abstract

Abstract

Univariate frequency analysis cannot provide a complete description of hydrologic variables with multicharac-teristics,and many hydrological frequency problems should be solved by the bivariate probability distribution model concerning the encounters and joint distributions of different hydrologic events. This article presents a review of various bivariate probability distribution models,and Copulas as a new bivariate probability distribution method are introduced. Advantages and limitations of each of these models are pointed out. Most of the present models are constructed based on the linear correlation of variables,and some of the models usually assume that the variables should have the same marginal distributions or have a strict restriction of correlation between variables. In reality,however,many hydrological events do not have the same type of marginal distributions,and various nonlinear dependence exists among variables. The copula method relaxes the restrictions of traditional bivariate probability models,and no assumption is needed for the variables to be independent or normal or have the same type of marginal distributions. The complex asymmetric and nonlinear correlation among variables can be described using copulas. As a flexible method to construct joint multivariate distribution,the Copula methodology is promising concerning hydrological frequency analysis.
- hydrological frequency,
- bivariate probability distribution model,
- Copula,
- review

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References

[1]	郑红星,刘昌明.南水北调东、中两线不同水文区降水丰枯遭遇性分析[J].地理学报,2000,55(5):523-532.(ZHENG Hong-xing,LIU Chang-ming.Analysis on asynchronism-synchronism of regional precipitation in planned South-to-North Water Transfer areas[J].Acta Geographica Sinca,2000,55(5):523-532.(in Chinese))
[2]	赵英林.洞庭湖洪水地区组成及遭遇分析[J].武汉水利电力大学学报,1997,30(1):36-39.(ZHAO Ying-lin.Analysis of flood region composition and encounter in Dongting lake[J].Journal of WuHan University of Hydraulic and Electric Engineering,1997,30(1):36-39.(in Chinese))
[3]	林荣,李国芳.黄浦江风暴潮位、区间降雨量和上游来水量遭遇分析[J].水文,2000,20(3):1-5.(LIN Rong,LI Guo-fang.Occurrence of storm tide level,regional rainfall and upstream inflow of the Huangpujiang river[J].Hydrology,2000,20(3):1-5.(in Chinese))
[4]	戴昌军,粱忠民.多维联合分布计算方法及其在水文中的应用[J].水利学报,2006,37(2):160-165.(DAI Chang-jun,LIANG Zhong-min.Computation methods of multivariate joint probability distribution and their applications in hydrology[J].Journal of Hydraulic Engineering,2006,37(2):160-165.(in Chinese))
[5]	刘德辅,施建刚,王铮.海洋环境条件联合设计标准[J].海洋学报,1994,16(2):116-123.(LIU De-fu,SHI Jian-gang,WANG Zhen.Joint design criteria of ocean engineering[J].Acta Oceanologica Sinica,1994,16(2):116-123.(in Chinese))
[6]	SACKL B,BERGMANN H.A bivariate flood model and its application[A].Singh V P.Hydrologic Frequency Modeling[C].Dordrecht:Reidel Publishing Company,1987.571-582.
[7]	GOEL N K,SETH S M,CHANDRA S.Multivariate modeling of flood flows[J].Journal of Hydraulic Engineering,ASCE,1998,124 (2):146-155.
[8]	YUE S.Applying the bivariate normal distribution to flood frequency analysis[J].Water International,1999,24(3):248-252.
[9]	YUE S.Joint probability distribution of annual maximum storm peaks and amounts as represented by daily rainfalls[J].Hydrological Sciences Journal,2000,45(2):315-326.
[10]	CORREIA F N.Multivariate partial duration series in flood risk analysis[A].SINGH V P.Hydrologic Frequency Modeling[C].Dordrecht:Reidel Publishing Company,1987.541-554.
[11]	郭生练.设计洪水研究进展与评价[M].北京:中国水利水电出版社,2005.(GUO Sheng-lian.Progress and evaluation of design flood[M].Beingjing:China WaterPower Press,2005.(in Chinese))
[12]	YUE S.The bivariate lognormal distribution to model a multivariate flood episode[J].Hydrological Processes,2000,14:2 575-2 588.
[13]	YUE Sheng.The bivariate lognormal distribution for describing joint statistical properties of a multivariate storm event[J].Envirometrics,2002,13:811-819.
[14]	GUMBEL E J.Multivariate extreme distributions[J].Bulletin of the International Statistical Institute,1960,39 (2):471-475.
[15]	YUE S,OUARDA T B M J,BOBEE B,et al.The Gumbel mixed model for flood frequency analysis[J].Journal of Hydrology,1999,226:88-100.
[16]	YUE Sheng.The Gumbel mixed model applied to storm frequency analysis[J].Water Resources Management,2000,14:377-389.
[17]	GUMBEL E J,MUSTAFI C K.Some analytical properties of bivariate extreme distributions[J].Journal of the American Statistical Association,1967,62:569-588.
[18]	OLIVERIA J T D.Bivariate extremes:Extensions[J] Bull of International Statistical Institute,1975,46(2):241-251.
[19]	YUE Sheng.The Gumbel logistic model for representing a multivariate storm event[J].Advances in Water Resources,2001,24:179-185.
[20]	周道成,段忠东.耿贝尔逻辑模型在极值风速和有效波高联合概率分布中的应用[J].海洋工程,2003,21(2):45-51.(ZHOU Dao-cheng,DUAN Zhong-dong.The Gumbel-logistic model for joint probability distribution of extreme-value wind speeds and effective wave heights[J].Ocean Engineering,2003,21(2):45-51.(in Chinese))
[21]	FREUND J E.A bivariate extension of the exponential distribution[J].Journal of the American Statistical Association,1961,56:971-977.
[22]	GUMBEL E J.Bivariate exponential distributions[J].Journal of the American Statistical Association,1960,55(292):698-707.
[23]	MARSHALL A W,INGRAM O.A multivariate exponential distribution[J].Journal of the American Statistical Association,1967,62(317):30-44.
[24]	BACCHI B,BECCIU G,KOTTEGOA N T.Bivariate exponential model applied to intensities and durations of extreme rainfall[J].Journal of Hydrology,1994,155:225-236.
[25]	DOWNTON F.Bivariate exponential distributions in reliability theory[J].Journal of the Royal Statistical Society.Series B (Methodological),1970,32(3):408-417.
[26]	NAGAO M,KADOYA M.Two-variate exponential distribution and its numerical table for engineering application[J].Bulletin of the Disaster Prevention Research Institute,1971,20(3):183-215.
[27]	CHOULAKIAN V,EL-JABI N,MOUSSI J.On the distribution of flood volume in partial duration series analysis of flood phenomena[J].Stochastic Enviromental Research and Risk Assessment,1990,4:217-226.
[28]	YUE S.Applicability of the Nagao-Kadoya bivariate exponential distribution for modeling two correlated exponentially distributed variates[J].Stochastic Enviromental Research and Risk Assessment,2001,15:244-260.
[29]	ASHKAR F,EL-JABI N,ISSA M.A bivariate analysis of the volume and duration of low-flow events[J].Stochastic Hydrology and Hydraulics,1998,12:97-116.
[30]	SINGH K,SINGH V P.Derivation of bivariate probability density functions with exponential marginals[J].Stochastic Hydrology and Hydraulics,1991(5):55-68.
[31]	SL278-2002.水利水电工程水文计算规范[S].(SL278-2002.Regulation for hydrologic computation of water resources and hydropower projects[S].(in Chinese))
[32]	SL44-93.水利水电工程设计洪水计算规范[S].(SL44-93.Regulation for calculating design flood of water resources and hydropower projects[S].(in Chinese))
[33]	KIBBLE W F.A two-variate Gamma type distribution[J].Sankhya,1941,5:137-150.
[34]	CHERIAN K C.A bi-variate correlated Gamma-type distribution function[J].Journal of Indian Mathematical Society,1941,5:133-144.
[35]	YUE S,OUARDA T B M J,BOBEE B.A review of bivariate gamma distribution for hydrological application[J].Journal of Hydrology,2001,246:1-18.
[36]	MORAN P A P.Statistical inference with bivariate gamma distributions[J].Biometrika,1969,56:627-634.
[37]	YUE Sheng.A bivariate gamma distribution for use in multivariate flood frequency analysis[J].Hydrological Processes,2001,15:1 033-1 045.
[38]	KELLY K S,KRZYSZTOFOWICZ R.A bivariate meta-Gaussian density for use in hydrology[J].Stochastic Hydrology and Hydraulics,1997,11:17-31.
[39]	FARLIE D J G.The performance of some correlation coefficients for a general bivariate distribution[J].Biometrika,1960,47(3):307-323.
[40]	戴昌军.多维联合分布计算理论在南水北调东线丰枯遭遇分析中的应用研究[D].南京:河海大学,2005.(DAI Chang-jun.Multivariate joint probability distribution and its' application to analysis of plentiful or scanty runoff encountering in South-to-North Water Transfer Project (East Areas)[D].Nanjing:Hohai University,2005.(in Chinese))
[41]	LONG D,KRZYSZTOFOWICZ R.Farlie-Gumbel-Morgenstern bivariate densities:are they applicable in hydrology?[J].Stochastic Hydrology and Hydraulics,1992(6):47-54.
[42]	JAIN D,SINGH V P.A comparison of transformation methods for flood frequency analysis[J].AWRA,Water Resource Bulletin,1986,22 (6):903-912.
[43]	GENEST C,MACKAY J.The Joy of Copulas:Bivariate distributions with uniform marginals[J].American Statistician,1986(40):280-283.
[44]	JOE H.Parametric families of multivariate distributions with given marginals[J].Journal of Multivariate Analysis,1993,46:262-282.
[45]	JOE H.Multivariate Models and Dependence Concepts[M].New York:Chapman and Hall,1997.
[46]	FREES E W,VALDEZ E A.Understanding relationships using copulas[J].North American Actuarial Journal,1998,2(1):1-25.
[47]	ROGER B Nelson.An Introduction to copulas[M].New York:Springer,1999.
[48]	EMBRECHTS P F,LIDSKOG,MCNEAL A J.Modeling Dependence with Copulas and Applications to Risk Management[A].Handbook of Heavy Tailed Distributions in Finance[C].Amsterdam:North-Holland Publishing Compang,2003.329-384.
[49]	EMBRECHTS P.Correlation and Dependence in Risk Management:Properties and Pitfalls,ETH Zurich[EB/OL]. http://www.ccfz.ch/files/Embrechtspitfalls.pdf,1999.
[50]	FREES E W,WANG P.Credibility using copulas[J].North American Actuarial Journal,2005,9(2):31-48.
[51]	FRESS E W,CARRIERE J,VALDEZ E A.Annuity valuation with dependent mortality[J].Journal of Risk and Insurance,1996,63:229-261.
[52]	DE MICHELE C,SALVADORI G.A generalized pareto intensityduration model of storm rainfall exploiting 2-copulas[J].Journal of Geophysical Research,2003,108(D2):4067.
[53]	SALBADORI G,MICHELE C De.Analytical calculation of storm volume statistics involving Pareto-like intensity-duration marginals[J].Geophysical Research Letters,2004,31(4):L04502.
[54]	SERINALDI F,GRIMALDI S,NAPOLITANO F,et al.A 3-copula function application to flood frequency analysis[A].Environmental Modelling and Simulation[C].US Virgin Islands:ACTA Press,2004.200-206.
[55]	FAVRE A C,EL ADLOUNI S,PERREAULT L,et al.Multivariate hydrological frequency analysis using copulas[J].Water Resources Research,2004,40(1):1-12.
[56]	SALVADORI G.Bivariate return periods via 2-copulas[J].Statistical Methodology,2004,12(1):129-144.
[57]	SALVADORI G,MICHELE C De.Frequency analysis via copulas:Theoretical aspects and applications to hydrological events[J].Water Resources Research,2004,40(12):W12511.
[58]	DE MICHELE C,SALVADORI G,CANOSSI M,et al.Bivariate statistical approach to check adequacy of dam spillway[J].Journal Hydrologic Engineering,2005,10(1):50-57.
[59]	JENQ T S,HSIN Y W,CHANG T T.Bivariate frequency analysis of floods using copulas[J].Journal of the American Water Resources Association,2006,42(6):1 549-1 564.
[60]	SALVATORE G,FRANCESCO S.Design hyetograph analysis with 3-copula function[J].Hydrological Sciences Journal,2006,51(2):223-238.
[61]	SALVATORE G,FRANCESCO S.Asymmetric copula in multivariate flood frequency analysis[J].Advances in Water Resources,2006,29:1 155-1 167.
[62]	李隆章.实用非参数统计方法[M].北京:中国财政经济出版社,1989.119-180.(LI Long-zhang.Practical nonparametric statistics method[M].Beijing:China Financial & Economic Press,1989.119-180.(in Chinese))

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