Flood is becoming an intensive hydro-climatic issue at the Kelantan River basin in Malaysia. Univariate frequency analysis would be unreliable due to multidimensional behaviour of flood, which often demands multivariate flow exceedance probabilities. The joint distribution analysis of multiple interacting flood characteristics, i.e. flood peak, volume and duration, is very useful for understanding critical hydrologic behaviour at a river basin scale. In this paper, a copula-based methodology is incorporated for multivariate flood frequency analysis for the 50-year annual basis flood characteristics of Kelantan River basin at Guillemard bridge station in Malaysia. Investigation reveals that the Lognormal (2P), Johnson SB-4P and Gamma-3P are selected as marginal distributions for the flood peak flow, volume and duration series. Several bivariate families such as mono-parametric, bi-parametric (i.e. mixed version) and rotated version of Archimedean copulas and also the elliptical copula are introduced to cover a large dependence pattern of flood characteristics. The dependence parameter of bivariate copulas is estimated by the method of moments (MOM) based on the inversion of Kendall’s tau and maximum pseudo-likelihood estimator. To analytically validate and recognize most parsimonious copulas, GOF test and Cramer–von Mises distance statistics (S_n) with the parametric bootstrap method are employed. The Gaussian copula is identified as the most justifiable model for joint modelling of the flood peak–volume and peak–duration combination for MOM-based parameter estimation procedure. Similarly, the Frank copula is selected as the best-fitted structure for modelling peak–duration combination based on MPL estimators, but the MOM estimator recognized Gaussian copula as most suitable for peak–volume pair. Furthermore, the best-fitted copulas are used for obtaining the joint and conditional return periods of the flood characteristics.

中文翻译：

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参数copula框架下的双变量洪水分布分析-以马来西亚吉兰丹河流域为例

在马来西亚吉兰丹河流域，洪水正成为一个严重的水文气候问题。由于洪水的多维行为，单变量频率分析将是不可靠的，而洪水的多维行为常常需要多变量流量超出概率。对洪水的峰值，流量和持续时间等多个相互作用的洪水特征进行联合分布分析，对于了解流域尺度上的关键水文行为非常有用。本文采用基于copula的方法对马来西亚吉列马德大桥站吉兰丹河流域50年年洪水特征进行多变量洪水频率分析。调查表明，对数正态（2P），Johnson SB-4P和Gamma-3P被选为洪水峰值流量，流量和持续时间序列的边际分布。引入了几个双变量族，例如单参数，双参数（即混合版本）和旋转版本的阿基米德copulas，以及椭圆copula，以涵盖洪水特征的较大依赖性模式。基于Kendall tau倒数和最大伪似然估计器，通过矩量法（MOM）估计了双变量系动词的依赖参数。为了分析验证和识别大多数简约系，GOF检验和Cramer-von Mises距离统计（基于Kendall tau倒数和最大伪似然估计器，通过矩量法（MOM）估计了双变量系动词的依赖参数。为了分析验证和识别大多数简约系，GOF检验和Cramer-von Mises距离统计（基于Kendall tau倒数和最大伪似然估计器，通过矩量法（MOM）估计了双变量系动词的依赖参数。为了分析验证和识别大多数简约系，GOF检验和Cramer-von Mises距离统计（小号_Ñ）与参数引导方法被采用。对于基于MOM的参数估计程序，洪峰峰量和峰时组合的联合建模被认为是最合理的模型。同样，Frank copula被选为最适合基于MPL估计器建模峰期组合的结构，但MOM估计器认为高斯copula最适合峰量对。此外，使用最合适的系索来获得洪水特征的联合和有条件返回期。