Water Resources Management

, Volume 32, Issue 13, pp 4239–4252 | Cite as

Nonstationary Flood Frequency Analysis for Annual Flood Peak and Volume Series in Both Univariate and Bivariate Domain

  • Jianzhu LiEmail author
  • Yuming Lei
  • Senming Tan
  • Colin D. Bell
  • Bernard A. Engel
  • Yixuan Wang


Flood frequency analysis for practical application is traditionally based on the assumption of stationarity, but this assumption has been open to doubt in recent years. A number of studies have focused on the nonstationary flood frequency analysis, and the associated causes of nonstationarity. In this study, the annual maximum flood peak and flood volume of Wangkuai reservoir watershed were used, and several univariate and bivariate models were established to investigate the nonstationary flood frequency, with the distribution parameters changing over the climate indices (NPO, Niño3) and the check dam indices (CDIp, CDIv). In the univariate models, the Weibull distribution performed best and exhibited an undulate behavior for both flood peak and volume, which tended to describe the nonstationarity reasonably well. The bivariate models were constructed using copulas, of which the optimal Weibull distribution in the univariate flood frequency analysis was considered as marginal distributions within the joint distribution. The results showed that the Gumbel-Hougaard copula offered the best joint distribution, and most of the probability isolines crossed each other, which demonstrated the possibility that the occurrence of combinations of the flood peak and volume may be the same under multiple effects of phase changes in the climate patterns and certain human activities (i.e. soil and water conservation). The most likely events were elaborated in diagrams, and the associated combinations of the flood peak and volume were smaller than that estimated by the fixed parameters (i.e. stationary condition) during most of the study period, while it was the opposite in 1956, 1959 and 1963. The results highlight the necessity of nonstationary flood frequency analysis under various conditions in both univariate and multivariate domains.


Nonstationarity Univariate model GAMLSS Bivariate model Copulas 



This work was supported by National Natural Science Foundation of China (No. 51209157). We are also grateful to Hydrology and Water Resource Survey Bureau of Hebei Province for providing the hydrometeorological data.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Hydraulic Engineering Simulation and SafetyTianjin UniversityTianjinChina
  2. 2.Pearl River Comprehensive Technology Center (Information Center) of Pearl River Water Resources Commission of the Ministry of Water ResourcesGuangzhouChina
  3. 3.Department of Agricultural and Biological EngineeringPurdue UniversityWest LafayetteUSA

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