基于二维Gumbel分布的降雨径流频率分析模型及其应用

本文探讨了二维Gumbel分布模型,给出了其经验频率和理论频率的计算方法,并建立了其联合重现期和条件重现期的分布模型。它可以给出不同程度暴雨和径流遭遇组合的频率,也可以在一定的降雨量条件下给出不同径流量的发生频率,或一定的径流量条件下给出不同降雨量的发生频率。这对于解决与风险有关的多因素影响下的水文计算问题是非常有用的。并以滹沱河流域岗南水库的入库年径流和年降雨量为例,分析了该模型的实用性,结果表明采用二维Gumbel分布模型来描述水文随机变量的联合分布是有效的。

The Two-dimension Gumbel Model for Runoff and Rainfall Frequency Analysis and Application

The two-dimension Gumbel mixed model was proposed,the bivariate extreme value distribution model with Gumbel marginals was given to analyze the joint probability distribution of correlated rainfall and reservoir inflow.Based on the marginal distributions of these random variables,the joint distributions,the conditional probability functions,and the associated return periods were derived.The joint and conditional frequency of rainfall with different runoffs and runoff with different rainfalls were figured out with this model. It was helpful to solve the multi-variations hydrology problem.The model was tested and validated using observed data of Gangnan reservoir in the Hutuohe River Basin.Results indicated that the model was suitable for representing the joint distributions of rainfall and reservoir inflow.