枯水流量频率分析方法研究

发布时间：2018-04-10 10:41

本文选题：枯水流量频率分析　+ 年最小值取样　；参考：《武汉大学》2014年博士论文

【摘要】：枯水流量频率分析是水文学在工程设计领域应用的一个重要组成方面,但是在气候变化和人类活动影响日益显著的背景下,传统的枯水流量频率分析中的“一致性”和“代表性”假设通常不能满足。因此本文试图构建一个枯水流量频率分析框架,包括了年最小值取样枯水流量频率分析和低定量取样(Pit under Threshold, PUT)枯水流量频率分析,单站枯水流量频率分析和区域枯水流量频率分析,基于枯水流量观测资料的频率分析和基于退水模型的枯水流量频率分析,单变量频率分析和多变量频率分析。论文的主要研究内容和结果如下： (1)介绍了年最小值取样的极值理论,并指出三种极值分布中仅含有下边界的Weibull分布可以用来模拟年最小流量的频率分布。法国摩泽尔河流域的35个测站的年最小流量样本表明Weibull分布能够很好的模拟绝大多数子流域的年最小流量分布。 (2)建立了模拟年最小流量频率分布的Weibull分布的参数和日流量的变差系数之间的函数关系,并进一步推导了年最小流量的均值和标准差与日流量的变差系数之间的函数关系,其中分别假设日流量服从Gamma分布、Lognormal分布和Power law分布。通过对法国摩泽尔河流域的资料分析,表明Weibull分布的参数与日流量的变差系数相关,年最小流量的矩和日流量的变差系数存在函数关系这些假设在该流域不能被拒绝。在此基础上提出了基于日流量统计特征的年最小流量频率分析方法,该频率分析方法在摩泽尔河大多数子流域能够取得比较满意的模拟精度。最后将此基于日流量统计特征的年最小流量频率分析方法用于年最小流量区域频率分析中,与传统的区域频率分析方法相比,该区域频率分析方法能够考虑到每个测站不同的日径流统计特征。 (3)根据极值理论推导了PUT枯水流量的Generalized Pareto分布,该分布存在上下边界,可以用于PUT枯水流量样本频率分析中。将该Generalized Pareto分布用于模拟渭河流域、清江流域和北江流域的PUT枯水流量样本的频率分布,结果显示此分布在清江流域和北江流域取得了令人满意的模拟精度。 (4)根据公式推导法,分别基于描述枯水形成的水文过程的线性退水模型和非线性退水模型,以退水模型中的参数干旱天数为随机变量,由干旱天数的分布推导了PUT枯水流量的分布,分别称为LLF分布和NLLF分布。LLF分布和NLLF分布均存在上下边界,可以用于PUT枯水流量样本频率分析中。LLF分布和NLLF分布的参数既可以采用传统的适线法估计,还可以根据推导法估计,即通过退水参数和干旱天数的统计特征推求。在渭河流域、清江流域和北江流域的应用显示：虽然基于推导法的LLF分布和NLLF分布的整体模拟精度低于基于适线法的整体模拟精度,但是枯水流量年频率分析表明基于推导法的NLLF分布的枯水流量设计值与实测枯水流量值很接近,特别是针对较长的重现期,其模拟结果更为理想。 (5)提出了结合Copula函数的公式推导法来推求PUT枯水流量分布。该方法在推求枯水流量分布时,不仅考虑了形成枯水的水文过程,还将枯水事件的内部相关性考虑在内。本文在应用该方法时,采用线性退水模型描述形成枯水的退水过程,以退水模型中的参数干旱天数和退水参数为随机变量,由它们的联合分布推求PUT枯水流量的分布,其中采用Copula函数构建联合分布。渭河流域、清江流域和北江流域的应用表明基于Copula函数的枯水流量分布的模拟精度与边缘分布的选择紧密相关,Copula函数的选取对枯水流量分布尾部的模拟精度有一定的影响。当边缘分布和Copula函数的选择适合时,基于Copula函数的枯水流量分布与经验点距的拟合度很高。
[Abstract]:The frequency analysis of low water flow rate is an important component of the application of hydrology in the field of engineering design , but in the background of climate change and human activities , the " consistency " and " representative " assumption in traditional low - water flow frequency analysis are usually not satisfied . Therefore , this paper attempts to construct a low - water flow frequency analysis framework , including the annual minimum sampling dead - water flow frequency analysis and low - quantitative sampling ( Pit under Threshold ) frequency analysis , the frequency analysis of single - station dry - water flow rate and the analysis of the frequency of dry - water flow based on the water - return model , the single - variable frequency analysis and the multivariate frequency analysis . The main research contents and results are as follows :

( 1 ) The extreme value theory of the annual minimum sampling is introduced , and it is pointed out that the Weibull distribution of only the lower boundary in the three extreme distributions can be used to simulate the frequency distribution of the annual minimum flow . The annual minimum flow samples from 35 stations in the Morazel River Basin show that the Weibull distribution can simulate the annual minimum flow distribution of most sub - basins .

( 2 ) The function relation between the parameter of the Weibull distribution of the minimum flow frequency distribution and the variation coefficient of daily flow is established , and the function relation between the mean value and the standard deviation of the annual minimum flow and the variation coefficient of daily flow is further derived .

( 3 ) According to the extreme value theory , the generalized Pareto distribution of the flow of the dry water is derived . The distribution of the distribution has the upper and lower boundaries , which can be used in the analysis of the frequency of the flow samples in the low water flow . The distribution of the generalized Pareto distribution is used to simulate the frequency distribution of the samples of the low water flow in the Weihe river basin , the Qingjiang river basin and the Beijiang river basin . The results show that the distribution has achieved satisfactory simulation accuracy in the Qingjiang river basin and the Beijiang river basin .

( 4 ) According to the formula derivation method , based on the linear regression model and non - linear regression model describing the hydrological process of dry water formation , the distribution of dry water flow is derived from the distribution of LLF and NLLF .

( 5 ) A formula derivation method combining Copula function is proposed to calculate the flow distribution of dry water .

【学位授予单位】：武汉大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：TV12

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