两变量极值分布在洪水频率分析中的应用研究

Application study of a bivariate extremal distribution in flood frequency analysis

采用了一种两变量极值分布来研究长江流域上某个站点的洪峰流量Q和洪水总量V之间的联合分布。该联合分布由实测资料来进行率定。率定结果表明,观测值(Q,V)联合分布的理论概率和经验概率基本上相符。在洪峰流量Q和洪水总量V联合分布函数的基础上,就可以很方便地推求洪峰流量和洪水总量同时发生的概率,或者在给定一个变量(比如洪水总量)的发生概率的条件下推求另外一个变量(比如洪峰流量)发生的概率,从而能对水文事件的统计规律有更加全面的认识。

A bivariate extremal distribution is adopted to analyze the joint distribution between the annual flood peak Q and flood volume V observed at a hydrological station of the Yangtze River. The parameters of this joint probability distribution are calibrated by using the observed data. The results display that the calibrated bivariate extremal distribution of (Q,V) fits the empirical distribution quite well. With the joint distribution of (Q,V) , it will be easy to derive the probability of the co-occurrences of flood peaks and flood volumes, or to find the occurring probability of either of two events (e.g., a flood peak), if the probability of another event (e.g., a flood vlume) is given. The application of the bivariate extremal distribution in flood frequency analysis will enhance our understanding of statistical properties of the extreme hydrological events.