地理科学 ›› 2015, Vol. 35 ›› Issue (11): 1460-1467.doi: 10.13249/j.cnki.sgs.2015.011.1460

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不同概率分布函数降雨极值的适用性分析

张玉虎1(), 王琛茜1,2, 刘凯利3, 陈秋华3   

  1. 1.首都师范大学资源环境与旅游学院, 北京 100048
    2. 北京建筑大学测绘与城市空间信息学院, 北京 100044
    3. 首都师范大学数学科学学院, 北京 100048
  • 收稿日期:2014-09-17 修回日期:2014-11-20 出版日期:2015-11-20 发布日期:2015-11-20
  • 作者简介:

    作者简介:张玉虎(1975-),男,江苏省徐州市人,博士,讲师,主要从事水资源、水环境分析评价与灾害风险应对研究。E-mail:zhang_yuhu@163.com

  • 基金资助:
    国家十二五科技支撑计划课题 (No.2013BAC10B01、2012BAC19B03-05)资助

Applicability of Different Probability Distributions to Estimated Extreme Rainfall

Yu-hu ZHANG1(), Chen-xi WANG1,2, Kai-li LIU3, Qiu-hua CHEN3   

  1. 1. College of Resources Environment and Tourism, Capital Normal University, Beijing, 100048, China
    2. Institute of Surveying and City Spatial Information, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
    3. Institute of Math Science, Beijing University of Civil Engineering and Architecture, Beijing 100044, China
  • Received:2014-09-17 Revised:2014-11-20 Online:2015-11-20 Published:2015-11-20

摘要:

极端降雨极值发生的重现期是流域与城市防洪设施规划设计标准需要参考的最重要参数之一。利用常用的5种水文统计学分布函数,选取中国十大流域内10个站点不同时段的最大降雨极值序列进行拟合,并检验筛选不同站点的适用性分布函数。结果表明:10个站点拟合优度检验拟合效果较好,曲线差异度较小的分布依次为广义极值分布、对数正态分布、皮尔逊III分布;不同站点适宜性曲线的差异程度不同。研究结果可为区域降雨极值序列的拟合提供参考,即不同的区域、不同的季节、不同时长的降雨极值序列都应寻找其较适宜的分布函数并采用多种检验方法来拟合,以降低不确定性。

关键词: 极端降雨, 概率分布, 重现期, K-S检验, A-D检验

Abstract:

Heavy precipitation is a crucial nature factor of flood. The return period of the extreme value of precipitation depth is the most significant reference of the design standard of flood prevention facilities in an urban or a basin. In this article, the series of annual, summer and winter maxima of precipitation depths for 1-day, 2-day and 3-day durations measured at ten selected stations in China are analyzed, using five commonly used hydrological statistical distribution functions. The distribution functions applicable for these stations were measured using the Kolmogorov Smirnov (K-S) and the Anderson Darling (A-D) tests. The results show that: 1) The summer maxima series shows higher standard deviation and larger differences between distributions than other maxima series and the annual maxima occur mostly in summer; 2) The Generalized Extreme Value (GEV) distribution, the lognormal (LN) distribution and the Pearson III distribution perform were better in the imitative effect test of goodness of fit, and the degree of curve difference is smaller; 3) Differences between estimates of rainfall with return periods were shorter than 25 years are smaller; 4) Estimates of precipitation can change significantly depending on the probability distribution being used, particularly for the summer series; 5) Suitability curves present seasonal difference. By statistical analysis of precipitation maxima, the precipitation is concentrated in summer; due to the disperse and skewness of precipitation series, and the appropriate distribution functions are quite different in different season periods; 6) In some extreme rainfall sequences, two curves of linear fitting are almost the same. Even if the return period extending to 100 years, the difference quantity of two curves is only a few millimeters. In this situation, the results of small probability rainfall events are more reliable; 7) There are differences among 1-day, 2-day and 3-day durations of precipitation depths, the probability distribution of 1-day maximum precipitation fits better. When carrying out statistical analysis of hydro-meteorological extremes, various probability distribution function and test methods should be taken for calculating, to reduce the uncertainty of single calculation. In this study, experimental analysis of 10 sites demonstrated that the Pearson III is not suitable for all sites. It is suggested here that the estimation of extreme precipitation should take into consideration the range of extreme values estimated by the best-fit distributions identified by more than one test as an approach to assess uncertainties related to extreme rainfall analysis.

Key words: extreme precipitation, probability distribution, return periods, Kolmogorov-Smirnov test, Anderson-Darling test

中图分类号: 

  • P426.615