融合降雨随机变量的洪水频率分布估计方法研究

A derivation method of flood frequency distribution incorporating rainfall stochastic variable

降雨作为一种与洪水存在物理相关性的随机变量,可扩展洪水频率分布估计的信息量。在层次模型的框架下,提出了一种融合降雨随机变量的洪水频率分布推导方法,在构建降雨变量频率分布以及洪水对降雨条件概率分布的基础上,由全概率公式推导出洪水变量的频率分布。选取浙江省兰江流域年最大洪峰流量作为研究实例,引入流域年最大15天前期影响雨量作为洪水变量的相依性变量,结果表明融合降雨变量的洪水频率分布具有较好的拟合效果。通过随机抽样统计实验发现,在降雨样本长于洪水样本的情况下,本文提出的层次模型能够充分利用长系列降雨信息,同时考虑了其他随机因素对洪水频率分布的影响,相较于直接由皮尔逊Ⅲ型分布拟合实测洪水样本的方法以及插补延长法,一定程度上可以提高洪水频率分布的估计精度,减小抽样误差导致的水文设计值不确定性。

As a stochastic variable related to flood,rainfall can be used to expand the information for flood distribution estimation.In this paper,under the framework of hierarchical model,a method for deriving flood frequency distribution derivation is presented with incorporating the rainfall stochastic variables,which derives the flood distribution by using the total probability formula from both the probability distribution of the rainfall variable and the conditional distribution of flood variable given the rainfall.The annual maximum flood peak flow from the Lanjiang River basin in Zhejiang Province was chosen to perform a case study.The results indicate that the flood distribution estimated by the derivation method with incorporating the stochastic variable of annual maximum 15-day antecedent precipitation has a satisfactory performance in fitting the observed flood samples,slightly better than the flood distribution that is obtained by directly fitting the Pearson typeⅢdistribution to the observed flood samples.The results of statistical experiment based on random sampling suggest that the hierarchical model presented in this paper exhibits advantages over traditional methods under the condition that rainfall series are longer than flood series.The hierarchical model,which is able to not only make a full use of the long series of rainfall information but also implicitly consider the influence of other random factors on flood frequency distribution,is of benefit for improving the estimation accuracy of flood distributions as well as declining the uncertainty in hydrological design due to sampling error.