多变量情况下的水文频率分析方法及其应用

本文探讨了以Gumbel分布为边际分布的二维联合分布模型，给出了其经验频率和理论频率的计算方法，建立并探讨了联合重现期和条件重现期分布模型的实用功能。由此，可以计算不同程度降雨和入境水遭遇组合的频率，也可以在一定的降雨量条件下计算不同年入境水的发生频率，或特定的年入境水条件下计算不同降雨量的发生频率，还可以给出某一重现期对应的某一安全指标下的风险区间，方便于解决与风险有关的多因素影响下的水文计算问题。以天津市北三河系的降雨和入境水为例，分析了该模型的实用性，结果表明，采用Clayton作为联结函数来描述水文随机变量的联合分布是有效的。

Method for hydrological reoccurrence frequency analysis under the condition of multivariate

The two dimension associate models with Gumbel marginal distribution are proposed and the methods for calculating the empirical frequency and theoretical frequency of hydrological reoccurrence are given to investigate the practical functions of the distribution models for calculating united reoccurrence interval and conditional reoccurrence interval. On this basis the joint distribution, the conditional probability functions and the associated reoccurrence periods are derived. The joint and conditional frequency of rainfall with different runoffs and runoff with different rainfalls as well as the risk interval of a certain reoccurrence period for a certain safety target can be figured out with this model, which is helpful to solve the multivariate hydrological problems. The validity of the model is verified by observation data obtained from the Beisan River Baisn.