RESOURCES AND ENVIRONMENT IN THE YANGTZE BASIN >> 2015, Vol. 24 >> Issue (08): 1425-1433.doi: 10.11870/cjlyzyyhj201508023

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JOINT DISTRIBUTION OF THE EXTREME RAINFALL AND FLOOD FOR THE UPPER-MIDDLE REACHES OF THE HANJIANG RIVER BASED ON COPULA FUNCTION

CHEN Xin-chi1,2, ZHANG Li-ping1,2, SHAN Li-jie1, YANG Wei1, XU Xia3   

  1. 1. State KeyLaboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China;
    2. Hubei Collaborative Innovation Center for Water Resources Security, Wuhan 430072, China;
    3. Changjiang water resources protection institute, Wuhan 430051, China
  • Received:2014-08-06 Revised:2014-12-29 Online:2015-08-20

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Abstract: The upper-middle reaches of Hanjiang River is chosen to be the research object in this paper, based on the daily precipitation data of 9 meteorological stations in River and the daily runoff data of Danjiangkou reservoir from 1969 to 2008. The maximum 1 day extreme samples and 3 days extreme samples of rainfall and flood were selected by the Annual Maximum (AM) and percentile method. Then these samples are marginal distribution fitted for the single variable to extreme value statistical models respectively, which are named as Generalized Extreme Value (GEV), Generalized Pareto Distribution (GPD) and Gamma distribution. After this, the most suitable distribution model for specific sampling method can be found out from the comparison results of model testing, and it will be a priority selection and verification for the corresponding sampling method in the later work. After the above process, the samples are joint distribution fitted for multivariate to Gumbel Copula function model, Clayton Copula function model and Frank Copula function model, respectively. It contains two-dimensional conjoint distribution and three-dimensional conjoint distribution, finally the optimal probability model which describes joint distribution of rainfall and flood in the basin will be selected. After calculation and analysis, the result showed that: for AM samples, no matter two-dimensional or three-dimensional Copula conjoint distribution, Frank Copula function gives the best fitting result for rainfall and flood when using GEV distribution as marginal distribution; for percentile samples, Gumbel Copula function gives the best fitting results for two-dimension joint distribution and Frank Copula function gives the best for three-dimension joint distribution, both are used the GPD distribution as the marginal distribution. What's more, the design value which is estimated by three-dimensional Copula function is greater than that is from two-dimensional Copula function after comparison of their simulation results. It means that three-dimensional joint distribution takes more variable and extreme information into account, and it can reflect the true feature of extreme rainfall and flood more accurate and more comprehensive, so choosing the three-dimensional joint distribution will be more suitable and safer for engineering design.

Key words: extreme rainfall, extreme flood, generalized extreme value distribution, generalized Parato distribution, Copula function

CLC Number: 

  • P333
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