3维Copula函数在降雨特征多变量频率分析中的应用

Research of methodology of multivariate analysis of design storm based on 3-copula function

摘要:

鉴于径流数据缺乏且难以长期监测而降雨数据相对完整,通常假定降雨和径流同频率,采用设计降雨进行水文分析计算,但此方法很难真实全面地反映降雨变化特征. 为此,提出一种基于3维Copula函数的降雨特征多变量频率分析方法. 首先利用降雨强度法将连续的降雨时间序列分割成若干个降雨事件,采用年最大值法取样,统计出表征雨量的特征变量,然后引入3维Copula 函数构建降雨特征3变量联合概率模型,并以广州1961~2012年历史降雨数据为例进行分析. 结果表明,基于3维Copula函数的多变量分析方法计算简单、可靠性高,可以进行3种不同降雨特征变量的组合分析,得到各种不同量级变量的遭遇概率和条件概率,能够更全面地反映降雨特征并更好地满足水文分析计算需求.

Abstract:

There is an underlying assumption that run-off and rainfall in a given urban catchment are equivalent and, further, to use design rainfall depth as a proxy for run-off in hydrological analyses and calculations. However, when employing this approach, it is difficult to accurately and fully reflect the variability in rainfall characteristics. To address this issue, a method for the copula-based multivariate frequency analysis of rainfall characteristics was proposed by using historical rainfall data (1961-2012) from Guangzhou city. First, continuous rainfall time series were divided into individual rainfall events using the rainfall intensity method. Then the characteristic variables of rainfall were calculated by sampling using the annual maximum method. Finally, a three-dimensional copula was introduced to build a multivariate joint probability distribution model of rainfall characteristics. The results show that the copula-based multivariate analysis is easy to implement and provides reliable results. This approach can be used to analyse the conditional probabilities of variables for different orders of magnitude. It can fully reflect rainfall characteristics, which serve an important reference for urban flood control and drainage planning.