Water Resources Management

, Volume 32, Issue 5, pp 1795–1809 | Cite as

Uncertainty Analysis of Bivariate Design Flood Estimation and its Impacts on Reservoir Routing

  • Jiabo Yin
  • Shenglian Guo
  • Zhangjun Liu
  • Guang Yang
  • Yixuan Zhong
  • Dedi Liu


The bivariate hydrological quantile estimation may inevitably induce large sampling uncertainty due to short sample size. It is crucial to quantify such uncertainty and its impacts on reservoir routing. In this study, a copula-based parametric bootstrapping uncertainty (C-PBU) method is proposed to characterize the bivariate quantile estimation uncertainty and the impact of such uncertainty on the highest reservoir water level is also investigated. The Geheyan reservoir in China is selected as a case study. Four evaluation indexes, i.e. area of confidence region, mean horizontal deviation, mean vertical deviation and average Euclidean distance, are adopted to quantify the quantile estimation uncertainty. The results indicate that the uncertainty of quantile estimation and the highest reservoir water level increases with larger return period. The 90% confidence interval (CI) of highest reservoir water level reaches 1.56 m and 2.52 m under 20-year and 50-year JRP respectively for the sample size of 100. It is also indicated that the peak over threshold (POT) sampling method contribute to uncertainty reduction comparing with the annual maximum (AM) method. This study could provide not only the point estimator of design floods and corresponding design water level, but also the rich uncertainty information (e.g. 90% confidence interval) for the references of reservoir flood risk assessment, scheduling and management.


Design flood Bivariate quantile Uncertainty analysis Reservoir routing Copula functions 



This study was financially supported by the National Key Research and Development Plan of China (2016YFC0402206) and the National Natural Science Foundation of China (51539009; 51579183). We are very grateful to the editor and three anonymous reviewers for their valuable comments and constructive suggestions that helped us to greatly improve the manuscript.


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Jiabo Yin
    • 1
  • Shenglian Guo
    • 1
  • Zhangjun Liu
    • 1
  • Guang Yang
    • 1
  • Yixuan Zhong
    • 1
  • Dedi Liu
    • 1
  1. 1.State Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanChina

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