洪水遭遇概率计算方法比较研究
Comparative Study of Flood Coincidence Probability Calculation Methods
DOI: 10.12677/JWRR.2020.95049, PDF,    国家科技经费支持
作者: 李 娜, 郭生练*, 熊 丰, 王 俊：武汉大学水资源与水电工程科学国家重点实验室，湖北 武汉
关键词: 洪水遭遇概率；Copula函数；联合分布；条件概率；比较研究；Flood Coincidence Probability； Copula Function； Joint Distribution； Conditional Probability； Comparative Study
摘要: 基于Copula函数分别建立金沙江和岷江年最大洪水发生时间和量级的联合分布，推求两江洪水发生时间遭遇的概率，采用联合概率、同现概率和条件概率定量分析两江洪水量级遭遇的风险，并对三种遭遇概率的计算结果进行比较，探讨这三种概率描述洪水遭遇风险的适用性与合理性。结果表明：联合概率的计算结果可能偏大，用来描述洪水遭遇风险并不理想；同现概率和条件概率的计算结果相对合理可靠，符合洪水遭遇的一般规律。
Abstract: The joint distributions of the annual maximum flood occurrence dates and magnitudes of the Jinsha and Min rivers were established based on Copula functions, and the coincidence probabilities of flood occurrence dates were calculated. The joint probability, co-occurrence probability and conditional probability were used to quantitatively analyze the coincidence risk of flood magnitudes, and the results were compared. The applicability and rationality of the three probabilities to describe flood coincidence risk were discussed. It is shown that the results of joint probability may be too large, while the co-occurrence probability and conditional probability are relatively reasonable and reliable, satisfying the natural law of flood coincidence.
文章引用：李娜, 郭生练, 熊丰, 王俊. 洪水遭遇概率计算方法比较研究[J]. 水资源研究, 2020, 9(5): 461-470. https://doi.org/10.12677/JWRR.2020.95049

参考文献

[1] 关帅, 林颖妍, 查悉妮, 等. 基于Copula函数的韩江流域干支流洪水遭遇分析[J]. 中山大学学报(自然科学版), 2015, 54(5): 130-137. GUAN Shuai, LIN Yingyan, ZHA Xini, et al. Copula function-based flood coincidence probability analysis for mainstream and tributary of the Hanjiangriver basin. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2015, 54(5): 130-137. (in Chi-nese)
[2] 郑静, 周鹏飞, 许银山. 金沙江中游与长江中下游洪水遭遇规律分析[J]. 人民长江, 2015, 46(18): 43-47. ZHENG Jing, ZHOU Pengfei and XU Yinshan. Analysis on flood encountering law of middle Jinsha river and mid-lower Yangtze river. Yangtze River, 2015, 46(18): 43-47. (in Chinese)
[3] 熊莹. 长江上游干支流洪水组成与遭遇研究[J]. 人民长江, 2012, 43(10): 42-45. XIONG Ying. Research on flood composition and encounter of main streams and tributaries in upper Yangtze river. Yangtze River, 2012, 43(10): 42-45. (in Chinese)
[4] 戴明龙, 沈燕舟. 长江上游与洞庭湖洪水遭遇规律研究[J]. 水资源与水工程学报, 2010, 21(6): 117-120. DAI Minglong, SHEN Yanzhou. Encountered regulation research on upstream flood of Yangtze River with Dangtinglake flood. Journal of Water Resources and Water Engineering, 2010, 21(6): 117-120. (in Chinese)
[5] 肖天国. 金沙江、岷江洪水遭遇分析[J]. 人民长江, 2001(1): 30-32 + 48. XIAO Tianguo. Analysis on flood encounter of Jinsha river and Minjiang river. Yangtze River, 2001(1): 30-32 + 48. (in Chi-nese)
[6] 陈璐, 郭生练, 张洪刚, 等. 长江上游干支流洪水遭遇分析[J]. 水科学进展, 2011, 22(3): 323-330. CHEN Lu, GUO Shenglian, ZHANG Honggang, et al. Flood coincidence probability analysis for the upstream Yangtze River and its tributaries. Advances in Water Science, 2011, 22(3): 323-330. (in Chinese)
[7] 郭生练, 闫宝伟, 肖义, 等. Copula函数在多变量水文分析计算中的应用及研究进展[J]. 水文, 2008(3): 1-7. GUO Shenglian, YAN Baowei, XIAO Yi, et al. Multivariate hydrological analysis and estimation. Journal of China Hydrology, 2008(3): 1-7. (in Chinese)
[8] 闫宝伟, 郭生练, 郭靖, 等. 多变量水文分析计算方法的比较[J]. 武汉大学学报(工学版), 2009, 42(1): 10-15. YAN Baowei, GUO Shenglian, GUO Jing, et al. Comparative study of multivariate hydrological frequency analysis methods. Engineering Journal of Wuhan University, 2009, 42(1): 10-15. (in Chinese)
[9] 仇红亚, 李妍清, 陈璐, 等. 洞庭湖流域洪水遭遇规律研究[J]. 水力发电学报, 2020, 39: 1-13. QIU Hongya, LI Yangqing, CHEN Lu, et al. Study on the law of flood coincidence in the Dongting Lake basin. Journal of Hy-droelectric Engineering, 2020, 39: 1-13. (in Chinese)
[10] 王占海, 陈元芳, 黄琴, 等. M-Copula函数在洪水遭遇中的应用研究[J]. 水电能源科学, 2009, 27(1): 69-73. WANG Zhanhai, CHEN Yuanfang, HUANG Qin, et al. Application study on M-Copula function in flood encounter. Water Re-sources and Power, 2009, 27(1): 69-73. (in Chinese)
[11] 甘富万, 韦吉华, 刘欣, 等. 基于Copula函数的郁江与西江干流洪水遭遇概率[J]. 武汉大学学报(工学版), 2016, 49(3): 341-346. GAN Fuwan, WEI Jihua, LIU Xin, et al. Flood encounter probability of Yujiang River and main stream of Xijiang river based on copula function. Engineering Journal of Wuhan University, 2016, 49(3): 341-346. (in Chinese)
[12] 张新田, 邵骏, 邴建平, 等. 金沙江干流与雅砻江洪水遭遇规律研究[J]. 水文, 2018, 38(4): 29-34. ZHANG Xintian, SHAO Jun, BING Jianping, et al. Flood coincidence probability analysis for Jinshajiang River and Yalongjiang River. Journal of China Hydrology, 2018, 38(4): 29-34. (in Chinese)
[13] 蒋楠, 高成, 夏欢. 基于Copula函数的锦河与连锦河洪水遭遇分析[J]. 水资源与水工程学报, 2019, 30(3): 85-91. JIANG Nan, GAO Cheng and XIA Huan. Analysis of flood encounters in Jin River and Lianjin River based on Copula function. Journal of Water Resources and Water Engineering, 2019, 30(3): 85-91. (in Chinese)
[14] 闫宝伟, 郭生练, 陈璐, 等. 长江和清江洪水遭遇风险分析[J]. 水利学报, 2010, 41(5): 553-559. YAN Baowei, GUO Shenglian, CHEN Lu, et al. Flood encountering risk analysis for the Yangtze River and Qingjiang River. Journal of Hydraulic Engineering, 2010, 41(5): 553-559. (in Chinese)
[15] 张超, 彭杨, 纪昌明, 等. 长江上游与洞庭湖洪水遭遇风险分析[J]. 水力发电学报, 2020, 39(8): 55-68. ZHANG Chao, PENG Yang, JI Changming, et al. Floods encountering risk analysis of the upper Yangtze River and Dongting Lake. Journal of Hydroelectric Engineering, 2020, 39(8): 55-68. (in Chinese)
[16] NELSEN, R. B. An introduction to copulas. New York: Springer Science & Business Media, 2007.
[17] 方彬, 郭生练, 肖义, 等. 年最大洪水两变量联合分布研究[J]. 水科学进展, 2008(4): 505-511. FANG Bin, GUO Shenglian, XIAO Yi, et al. Annual maximum flood occurrence dates and magnitudes frequency analysis based on bivariate joint distribution. Advances in Water Science, 2008(4): 505-511. (in Chinese)
[18] CARTA, J. A., BUENO, C. and RAMÍREZ, P. Statistical modelling of directional wind speeds using mixtures of von Mises distributions: Case study. Energy Conversion and Management, 2007, 49(5): 897-907. [Google Scholar] [CrossRef] 
[19] 中华人民共和国水利部. SL44-2006 水利水电工程设计洪水计算规范[S]. 北京: 中国水利水电出版社, 2006. Ministry of Water Resources of the People's Republic of China. SL44-2006 regulation for calculating design flood of water re-sources and hydropower projects. Beijing: China Water Power Press, 2006. (in Chinese)