Deriving Design Flood Hydrograph Based on Conditional Distribution: A Case Study of Danjiangkou Reservoir in Hanjiang Basin

Abstract

Design flood hydrograph (DFH) for a dam is the flood of suitable probability and magnitude adopted to ensure safety of the dam in accordance with appropriate design standards. Estimated quantiles of peak discharge and flood volumes are necessary for deriving the DFH, which are mutually correlated and need to be described by multivariate analysis methods. The joint probability distributions of peak discharge and flood volumes were established using copula functions. Then the general formulae of conditional most likely composition (CMLC) and conditional expectation composition (CEC) methods that consider the inherent relationship between flood peak and volumes were derived for estimating DFH. The Danjiangkou reservoir in Hanjiang basin was selected as a case study. The design values of flood volumes and 90% confidence intervals with different peak discharges were estimated by the proposed methods. The performance of CMLC and CEC methods was also compared with conventional flood frequency analysis, and the results show that CMLC method performs best for both bivariate and trivariate distributions which has the smallest relative error and root mean square error. The proposed CMLC method has strong statistical basis with unique design flood composition scheme and provides an alternative way for deriving DFH.

Joint probability analysis of flood hazard at river confluences using bivariate copulas

“…(3) = Furthermore, the conditional distribution function of U 1 given U 2 < u 2 can be expressed as: (4) Furthermore, the probability density function of a copula function can be expressed a: (5) A copula C is called an extreme value copula if there exists a copula C F such that: (6) for all (u 1…”

“…The copula function selection has been in the focus of numerous studies and different families of copulas have been proposed for hydraulic models, as described in relevant literature. Volpi and Fiori [2] used Gumbel-Hougaard copulas to model dependency between peak and volume in flood analysis; Gräler et al [1] used synthetic dataset to show difference in performance of 2D and 3D copulas for various combinations of hydrologic variables; Xu et al [5] compared four Archimedean family copulas for derivation of a design flood hydrograph; Bender et al [14] used Gumbel copula for bivariate analysis of concurrent flows at a river confluence, and Bender et al [15] continued to investigate bivariate analysis of discharges on confluences, investigating sites where floods do not occur simultaneously. Szolgay et al [16] evaluated applicability of different copula types to a peakvolume flood relationship over a large region in Austria and its sub-catchments, and also studied the influence of the data series length on bivariate copula performance.…”

“…For the Gumbel-Hougaard copulas, the relationship between the Kendall's coefficient and the generating function shows that only the positive dependence structure of the bivariate data can be analysed, i.e. the flood peak and volume, and the flood duration and volume are positively correlated, and their bivariate distributions can be derived using this copula [5,19]. On the other hand, the flood duration and flood peak are usually negatively correlated and therefore the Gumbel-GRAĐEVINAR 70 (2018) 4, 267-275 Gordon Gilja, Eva Ocvirk, Neven Kuspilić Hougaard copula is not suitable for deriving their joint distribution.…”

“…The identification of marginal distributions of the correlated variables Is the initial task in constructing the bivariate copula model. The distribution of population of maximum annual discharges can be compared with a parametric distribution using the so called Chi-square test [5] or the Anderson-Darling test [14]. After estimation of marginal distributions, the joint distribution function can be calculated using one of the copula functions evaluated by, for instance, goodness of fit test based on the Cramér-von-Mises statistics [15].…”

“…It was established that, during occurrence of a flood wave, a correlation can be made between its maximum flow rate (flood peak discharge), volume and duration, which may affect design requirements in a number of way, depending on the planned use of a particular hydraulic structure [4]. Joint probability distributions of flood peak discharge and volume have been used for the design of flood control reservoirs [2], for estimating parameters for a synthetic design hydrograph [1,5], for the design of flood control systems [6,7], and for dam design [8].…”