Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation
Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation
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DOI：
10.5194/hess-17-1281-2013
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发表时间：
2013-01-01
影响因子：
6.3
通讯作者：
Verhoest, N. E. C.
中科院分区：
文献类型：
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作者：
Graeler, B.;van den Berg, M. J.;Verhoest, N. E. C.
大多数水文学和水力学研究都参考了重现期的概念，以量化设计变量。当处理多个设计变量时，众所周知的单变量统计分析已不再令人满意，几个问题向实践者提出了挑战。我们应该如何结合变量之间的依赖关系呢？应该如何定义和应用多变量回收期，以产生适当的设计事件？在这项研究中，概述了多变量设计事件估计的技术现状，并对不同的方法进行了比较。多变量分布函数的构造是通过使用Copula来完成的，因为它们在多变量频率分析中具有实用性，并且能够以灵活的方式对多种类型的相关性结构进行建模。综合案例研究被用来生成模拟流量的大型数据集，用于说明不同的建模选择对设计事件的影响。基于不同的单变量和多变量方法，推导了由年最大洪峰流量、流量和历时组成的三维现象的设计过程线特征。这些方法基于回归分析、二元条件分布、二元联合分布和肯德尔分布函数，突出了多变量频率分析的理论和实践问题。还提出了一种基于集成的方法。对于给定的设计回收期，所选择的方法显然会影响计算的设计事件，应非常注意所使用的方法的选择，因为这取决于手头的实际问题。
Most of the hydrological and hydraulic studies refer to the notion of a return period to quantify design variables. When dealing with multiple design variables, the well-known univariate statistical analysis is no longer satisfactory, and several issues challenge the practitioner. How should one incorporate the dependence between variables? How should a multivariate return period be defined and applied in order to yield a proper design event? In this study an overview of the state of the art for estimating multivariate design events is given and the different approaches are compared. The construction of multivariate distribution functions is done through the use of copulas, given their practicality in multivariate frequency analyses and their ability to model numerous types of dependence structures in a flexible way. A synthetic case study is used to generate a large data set of simulated discharges that is used for illustrating the effect of different modelling choices on the design events. Based on different uni- and multivariate approaches, the design hydrograph characteristics of a 3-D phenomenon composed of annual maximum peak discharge, its volume, and duration are derived. These approaches are based on regression analysis, bivariate conditional distributions, bivariate joint distributions and Kendall distribution functions, highlighting theoretical and practical issues of multivariate frequency analysis. Also an ensemble-based approach is presented. For a given design return period, the approach chosen clearly affects the calculated design event, and much attention should be given to the choice of the approach used as this depends on the real-world problem at hand.