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      基于Copula函数的洪水量级与发生时间联合分布研究

      Research on the Joint Distribution of Flood Magnitude and Occurrence Time Based on Copula Function

      • 摘要: 为了克服传统分期设计洪水计算中仅考虑量级而忽视发生时间概率的局限性,本研究以龙滩水库1951-2022年实测数据及历史调查洪水为样本,构建了洪水量级年最大15日洪量与发生时间的联合分布模型。首先,采用具有良好的拟合效果的P-III分布和Von Mises分布分别作为洪水量级和发生时间的边缘分布。随后引入Copula函数理论,选取Clayton Copula函数最适合描述年最大15日洪量与时间的联合分布。结果表明龙滩水库年最大15日洪量与发生时间存在强正相依性,Kendall秩相关系数达0.7918;年最大洪水事件高度集中于5-8月主汛期,洪量级越大,发生时间越集中于主汛期核心时段,非汛期发生特大洪水的概率几乎为0。该模型突破了传统分期洪水计算的独立假设,可为龙滩水库分期设计洪水推求、汛期防洪调度方案优化提供更为全面、可靠的概率依据。

         

        Abstract:  To overcome the limitation of traditional staged design flood calculation that only considers the magnitude but neglects the probability of occurrence time, this study takes the measured data from 1951 to 2022 and historical surveyed floods of Longtan Reservoir as samples, and constructs a joint distribution model of the annual maximum 15-day flood volume and occurrence time. Firstly, the P-III distribution and Von Mises distribution with good fitting effects are adopted as the marginal distributions of flood magnitude and occurrence time respectively. Then, the Copula function theory is introduced, and the Clayton Copula function is selected as the most suitable one to describe the joint distribution of the annual maximum 15-day flood volume and time. The results show that there is a strong positive dependence between the annual maximum 15-day flood volume and occurrence time of Longtan Reservoir, with a Kendall rank correlation coefficient of 0.7918; the annual maximum flood events are highly concentrated in the main flood season from May to August, and the larger the flood volume, the more concentrated the occurrence time is in the core period of the main flood season, and the probability of extremely large floods occurring in the non-flood season is almost zero. This model breaks through the independent assumption of traditional staged flood calculation and can provide a more comprehensive and reliable probabilistic basis for the staged design flood calculation and flood control dispatching scheme optimization of Longtan Reservoir.

         

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