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The proposed bivariate EFC and CEC methods were used to estimate flood peak and 7-day flood volume quantiles with return periods of T = 1,000 and T = 200 years, respectively. For the purpose of comparison, the univariate flood quantiles (called marginal quantiles by Chebana & Ouarda (2011)) were estimated by marginal distributions, assuming that the univariate return periods (TQ and TW) were equal to the bivariate return period (i.e., TQ = TW = T). The univariate flood quantiles can be obtained from the equations and . The results of the component-wise excess realization and the most likely realization proposed by Salvadori et al. (2011) were also estimated. The estimation results of bivariate and univariate quantiles were listed in Table 6. It is shown that the design values of bivariate quantiles are larger than those of univariate quantiles. The quantiles estimated by the four bivariate event selection methods are also shown in Figure 7, and the estimation points of the EFC method are denoted as point E, while the quantiles estimated by the CEC method are denoted as point F. For the results of selection approaches proposed by Salvadori et al. (2011), the events of component-wise excess realization are denoted as point W, and the events of most likely realization are denoted as point L. From Figure 7, we find that the joint design values estimated by the four event selection methods are within the feasible regions. Consequently, the two proposed methods and selection approaches proposed by Salvadori et al. (2011) could be selected as an option of deriving unique flood quantiles, and they could satisfy the inherent law of hydrologic events and have statistical basis to some degree. It can be seen from Table 6 and Figure 7 that the estimated events of the EFC method and that of the most likely realization are similar. The bivariate EFC results have larger flood volume and smaller flood peak than bivariate CEC results. As well, the results estimated by the component-wise excess realization have larger flood peak and smaller flood volume than the other three methods.

Table 6

Design flood values and corresponding highest water levels estimated by bivariate quantile combinations and univariate distribution

TMethodQp (m3/s)W7 (×108 m3)Zmax (m)
1,000 EFC 23,390 63.09 202.97 
CEC 23,420 62.98 202.92 
Component-wise excess realization 23,510 62.78 202.90 
Most-likely realization 23,400 63.05 202.95 
Univariate distribution 22,800 61.49 202.58 
200 EFC 19,800 51.87 198.10 
CEC 20,130 51.11 197.79 
Component-wise excess realization 20,200 51.03 197.59 
Most-likely realization 19,940 51.50 197.82 
Univariate distribution 19,300 50.23 197.30 
TMethodQp (m3/s)W7 (×108 m3)Zmax (m)
1,000 EFC 23,390 63.09 202.97 
CEC 23,420 62.98 202.92 
Component-wise excess realization 23,510 62.78 202.90 
Most-likely realization 23,400 63.05 202.95 
Univariate distribution 22,800 61.49 202.58 
200 EFC 19,800 51.87 198.10 
CEC 20,130 51.11 197.79 
Component-wise excess realization 20,200 51.03 197.59 
Most-likely realization 19,940 51.50 197.82 
Univariate distribution 19,300 50.23 197.30 

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