SCIENTIA GEOGRAPHICA SINICA ›› 2015, Vol. 35 ›› Issue (11): 1460-1467.doi: 10.13249/j.cnki.sgs.2015.011.1460

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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


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

CLC Number: 

  • P426.615