Table 4

Results of the two time-varying marginal distributions with the precipitation and the RI as the covariates of flood-generating mechanism and reservoir regulation in the distribution parameters under non-stationary assumption

SeriesDistributionDistribution parameters
K–S statistic indicatoraAIC value
Qa Gaussian 11,595 exp(−721+1.08Pa−14.59RIa– 0.132 459 
Gamma 11,418 exp(−522+0.94Pa−10.33RIa– 0.134 448 
Gumbel 10,107 exp(−339+1.11Pa−15.23RIa– 0.111 355 
GEV 9,817 exp(−283+0.76Pa−16.05RIa0.22 0.130 460 
Person type III 11,507 exp(−610+1.25Pa−16.58RIa0.35 0.146 502 
Log-Weibull 183 exp(−138+2.09Pa−10.24RIa0.30 0.195 531 
Qh Gaussian exp(−303+0.75Ph−10.01RIh0.35 – 0.148 743 
Gamma exp(−219+1.02Ph−8.40RIh0.33 – 0.153 807 
Gumbel exp(−412+0.91Ph−9.05RIhexp(−650+1.19Pa−16.61RIa– 0.131 726 
GEV exp(−406+1.09Ph−15.84RIh0.38 0.27 0.115 618 
Person type III exp(−452+0.78Ph−11.10RIh0.32 0.48 0.144 765 
Log-Weibull exp(−229+0.84Ph−14.23RIh3.11 0.35 0.173 794 
SeriesDistributionDistribution parameters
K–S statistic indicatoraAIC value
Qa Gaussian 11,595 exp(−721+1.08Pa−14.59RIa– 0.132 459 
Gamma 11,418 exp(−522+0.94Pa−10.33RIa– 0.134 448 
Gumbel 10,107 exp(−339+1.11Pa−15.23RIa– 0.111 355 
GEV 9,817 exp(−283+0.76Pa−16.05RIa0.22 0.130 460 
Person type III 11,507 exp(−610+1.25Pa−16.58RIa0.35 0.146 502 
Log-Weibull 183 exp(−138+2.09Pa−10.24RIa0.30 0.195 531 
Qh Gaussian exp(−303+0.75Ph−10.01RIh0.35 – 0.148 743 
Gamma exp(−219+1.02Ph−8.40RIh0.33 – 0.153 807 
Gumbel exp(−412+0.91Ph−9.05RIhexp(−650+1.19Pa−16.61RIa– 0.131 726 
GEV exp(−406+1.09Ph−15.84RIh0.38 0.27 0.115 618 
Person type III exp(−452+0.78Ph−11.10RIh0.32 0.48 0.144 765 
Log-Weibull exp(−229+0.84Ph−14.23RIh3.11 0.35 0.173 794 

aThe K–S test is performed at a significance level of 0.05. The null hypothesis states that the empirical distribution fits the theoretical distribution. If the value of the K–S test indicator is smaller than the value of D(65, 0.05) , the null hypothesis would not be rejected. The variables Pa, Ph, RIa and RIh are the precipitation and the RI corresponding to the Ankang and Huangzhuang stations, respectively.

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