基于Copula函数的汉江中上游流域极端降雨洪水联合分布特征

doi:10.11870/cjlyzyyhj201508023

长江流域资源与环境 >> 2015, Vol. 24 >> Issue (08): 1425-1433.doi: 10.11870/cjlyzyyhj201508023

基于Copula函数的汉江中上游流域极端降雨洪水联合分布特征

陈心池^1,2, 张利平^1,2, 闪丽洁¹, 杨卫¹, 徐霞³

1. 武汉大学水资源与水电工程国家重点实验室, 湖北武汉 430072;
2. 水资源安全保障湖北省协同创新中心, 湖北武汉 430072;
3. 长江水利委员会水资源保护科研所, 湖北武汉 430051

收稿日期:2014-08-06 修回日期:2014-12-29 出版日期:2015-08-20
作者简介:陈心池(1989~),男,硕士研究生,主要研究方向为水文水资源.E-mail:stephencug@outlook.com
基金资助:
国家自然科学基金(51339004、51279139);中央高校基本科研业务费专项资金(2042014kf1012、2042014kf0033)

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

CHEN Xin-chi^1,2, ZHANG Li-ping^1,2, SHAN Li-jie¹, YANG Wei¹, XU Xia³

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

摘要/Abstract

摘要： 选取汉江中上游流域作为研究对象,根据流域九个气象站点1969~2008年逐日降雨资料以及丹江口水库同时期日入库流量资料,采用年最大值法(AM)和百分位法两种选样方式选取1 d、3 d降雨和1 d、3 d洪量极值样本,分别运用广义极值分布(GEV)、广义帕累托分布(GPD)、伽玛分布(Gamma)3种极值统计模型对样本进行单变量边缘分布拟合,运用Gumbel、Clayton以及Frank Copula函数模型对样本进行多变量联合分布拟合,遴选出描述流域降雨和洪水联合分布规律的最优概率模型。结果显示:对于AM选样样本,边缘分布为GEV时降雨洪量的二维和三维联合分布Frank Copula函数拟合效果最优;对于百分位选样样本,边缘分布为GPD时降雨洪量的二维联合分布Gumbel Copula函数拟合效果最优,三维联合分布则是Frank Copula函数拟合效果最优;比较二维和三维Copula函数模拟结果,三维联合Copula函数推求的设计值更大,说明三维联合分布考虑了更多的变量和极值信息,能更全面地反映极端降雨洪水事件的真实特征,对工程设计更显安全。

关键词: 极端降雨, 极端洪水, 广义极值分布, 广义帕累托分布, Copula函数

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

中图分类号:

P333

陈心池, 张利平, 闪丽洁, 杨卫, 徐霞. 基于Copula函数的汉江中上游流域极端降雨洪水联合分布特征[J]. 长江流域资源与环境, 2015, 24(08): 1425-1433.

CHEN Xin-chi, ZHANG Li-ping, SHAN Li-jie, YANG Wei, XU Xia. JOINT DISTRIBUTION OF THE EXTREME RAINFALL AND FLOOD FOR THE UPPER-MIDDLE REACHES OF THE HANJIANG RIVER BASED ON COPULA FUNCTION[J]. RESOURCES AND ENVIRONMENT IN THE YANGTZE BASIN, 2015, 24(08): 1425-1433.

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