基于广义第二类beta分布的洪水频率分析

Application of Generalized Beta Distribution of Second Kind for Flood Frequency Analysis

精确计算设计洪水值对水利水电工程规划设计至关重要,其关键问题之一是选择合适的分布函数。目前多数研究仅选取单一的频率分布线型进行洪水频率分析,其设计洪水结果具有较大的不确定性。研究引入一种新的广义分布函数,即第二类beta分布(Generalized beta distribution of the second kind,GB2),进行洪水频率分析。该四参数分布具有较好的灵活性,基本可拟合任何偏度和峰度的曲线。采用最大熵原理推求分布函数的参数。研究利用科罗拉多河流域数据检验广义第二类beta分布函数的拟合效果,并将所提分布与水文中的其它传统分布进行比较分析。结果表明:四参数的广义第二类beta分布非常适于水文频率分析,其拟合效果基本优于水文中的其它传统分布。

T-year flood estimation at a given location in mountainous areas is a crucial task for design of hydraulic and civil in-frastructure facilities. One of the key steps in flood frequency analysis（FFA） is the selection of a suitable distribution. More than one distribution is often found to be adequate for FFA, and choosing the best one is often less than objective. In order to over-come this difficulty, generalized beta distribution of the second kind（GB2 distribution） was introduced in this study. And the prin ciple of maximum entropy method（POME） was employed to derive this distribution with its parameters to be estimated. The Col-orado River was selected as a case study. The maximum stream flow data from the sites, Steamboat Springs, Near Colorado-Utah and Hoover Dam, were considered to test the perfor mances of GB2 distribution. Finally, the fitting results of GB2 distribution at Hoover Dam were compared with those of common used distributions in hydrology. The results indicate that GB2 distribution is an appealing option for FFA, since it has four parameters and include some well-known distributions. Compared with the widely used distribution in hydrology, the performances of Gb2 distribution is comparable.