Abstract
Abstract. Multivariate hydrologic design under stationary conditions is traditionally performed through the use of the design criterion of the return period, which is theoretically equal to the average inter-arrival time of flood events divided by the exceedance probability of the design flood event. Under nonstationary conditions, the exceedance probability of a given multivariate flood event varies over time. This suggests that the traditional return-period concept cannot apply to engineering practice under nonstationary conditions, since by such a definition, a given multivariate flood event would correspond to a time-varying return period. In this paper, average annual reliability (AAR) was employed as the criterion for multivariate design rather than the return period to ensure that a given multivariate flood event corresponded to a unique design level under nonstationary conditions. The multivariate hydrologic design conditioned on the given AAR was estimated from the nonstationary multivariate flood distribution constructed by a dynamic C-vine copula, allowing for time-varying marginal distributions and a time-varying dependence structure. Both the most-likely design event and confidence interval for the multivariate hydrologic design conditioned on the given AAR were identified to provide supporting information for designers. The multivariate flood series from the Xijiang River, China, were chosen as a case study. The results indicated that both the marginal distributions and dependence structure of the multivariate flood series were nonstationary due to the driving forces of urbanization and reservoir regulation. The nonstationarities of both the marginal distributions and dependence structure were found to affect the outcome of the multivariate hydrologic design.
Highlights
A complete flood event or a flood hydrograph contains multiple feature variables, such as flood peak and flood volume, which can be associated with the safety of hydraulic structures (Salvadori et al, 2004, 2007, 2011; Xiao et al, 2009; Xiong et al, 2015; Loveridge et al, 2017; Shafaei et al, 2017)
The results indicated that the GEV distribution provided the best fit for the annual maximum daily discharge series Q1, whereas the Gamma distribution was chosen as the theoretical distribution for the flood volume series V3, V7 and V15
The location parameters μ referring to the means of the flood series were generally positively related to the urban population Pop, whereas they were negatively related to the reservoir index RI
Summary
A complete flood event or a flood hydrograph contains multiple feature variables, such as flood peak and flood volume, which can be associated with the safety of hydraulic structures (Salvadori et al, 2004, 2007, 2011; Xiao et al, 2009; Xiong et al, 2015; Loveridge et al, 2017; Shafaei et al, 2017). Multivariate hydrologic design, which takes into account multiple flood characteristics as well as their dependence, provides a more rational design strategy for hydraulic structures compared to univariate hydrologic design (Zheng et al, 2013, 2014; Balistrocchi and Bacchi, 2017). Multivariate hydrologic design under stationary conditions has been widely investigated, and the design criterion is usually quantified by the return period, similar to univariate hydrologic design. Under the definition of the average recurrence interval between flood events equaling or exceeding a given threshold (Chow, 1964), the return period of a given flood event under stationary conditions theoretically equals the average inter-arrival time between flood events divided by the exceedance probability (Salvadori et al, 2011).
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