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Bivariate Copulas Functions for Flood Frequency Analysis

机译：双泛频分析的二抗型Copulas功能

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摘要

Bivariate flood frequency analysis offers improved understanding of the complex flood process and useful information in preparing flood mitigation measures. However, difficulties arise from limited bivariate distribution functions to jointly model major flood variables that are inter-correlated and each has different univariate marginal distribution. To overcome these difficulties, a Copula based methodology is presented in this study. Copula is functions that link univariate distribution functions to form bivariate distribution functions. Five Copula families namely Clayton, Gumbel, Frank, Gaussian and t Copulas were evaluated for modeling the joint dependence between peak flow-flood duration. The performance of four parameter estimation methods, namely inversion of Kendall's tau, inversion of Spearman's rho, maximum likelihood approach and inference function for margins for chosen copula's families are investigated. The analysis used 35 years hourly discharge data of Johor River from which the annual maximum were derived. Generalized Pareto and Generalized Extreme Value distribution were found to be the best to fit the flood variables based on the Kolmogorov-Smirnov goodness-of-fit test. Clayton Copula was chosen as the best fitted Copula function based on the Akaike Information Criterion goodness-of-fit test. It is found that, different methods of parameter estimation will give the same result on determining the best fit copula family. On performing a simulation based on a Cramer-von Mises as a test statistics to assess the performance of Copula distributions in modeling joint dependence structure of flood variables, it is found that Clayton Copula are well representing the flood variables. Thus, it is concluded that, the Clayton Copula based joint distribution function was found to be effective in preserving the dependency structure of flood variables. Thus, it is concluded that, the Clayton Copula based joint distribution function was found to be effective in preserving the dependency structure of flood variables.
机译：二元洪水频率分析提供了改进的准备防洪减灾措施的复杂的洪水过程和有用的信息的理解。然而，困难从有限的二元分布函数产生的共同模式发生大洪水的变量是相互关联，每个人都有不同的单变量的边缘分布。为了克服这些困难，基于Copula函数方法介绍了这项研究。系词是链接单变量分布函数，形成二元分布函数的函数。五系词家庭即克莱顿，冈贝尔，弗兰克，高斯和T Copula函数建模洪峰流量，洪水持续时间之间的联合关系进行了评价。四个参数估计方法，即反转Kendall的tau的，Spearman的RHO的反转，极大似然法和推理功能利润率选择系词的家庭性能进行了研究。分析中使用35年从年度最高推导柔佛河每小时排放数据。广义Pareto和广义极值分布被认为是最好的，以适应基于柯尔莫哥洛夫 - 斯米尔诺夫优度拟合检验洪水变量。克莱顿系词被选为基础上，赤池信息量准则拟合优度检验的最佳拟合Copula函数。结果表明，参数估计方法的不同会给出确定最适合系词家庭相同的结果。在执行根据克拉美·冯·米塞斯作为检验统计量来评估Copula函数分布在模拟洪水变量的联合依赖性结构性能仿真，发现克莱顿Copula函数很好代表洪水的变量。因此，得出的结论是，基于克莱顿Copula函数联合分布函数被认为是有效的维护洪水变量的相关性结构。因此，得出的结论是，基于克莱顿Copula函数联合分布函数被认为是有效的维护洪水变量的相关性结构。

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