Deriving Design Flood Hydrograph Based on Conditional Distribution: A Case Study of Danjiangkou Reservoir in Hanjiang BasinReport as inadecuate

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Mathematical Problems in Engineering - Volume 2016 2016, Article ID 4319646, 16 pages -

Research Article

State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, Wuhan 430072, China

Bureau of Hydrology, Changjiang Water Resources Commission, Wuhan 430010, China

Received 18 October 2015; Revised 19 January 2016; Accepted 14 February 2016

Academic Editor: Renata Archetti

Copyright © 2016 Changjiang Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Design flood hydrograph DFH for a dam is the flood of suitable probability and magnitude adopted to ensure safety of the dam in accordance with appropriate design standards. Estimated quantiles of peak discharge and flood volumes are necessary for deriving the DFH, which are mutually correlated and need to be described by multivariate analysis methods. The joint probability distributions of peak discharge and flood volumes were established using copula functions. Then the general formulae of conditional most likely composition CMLC and conditional expectation composition CEC methods that consider the inherent relationship between flood peak and volumes were derived for estimating DFH. The Danjiangkou reservoir in Hanjiang basin was selected as a case study. The design values of flood volumes and 90% confidence intervals with different peak discharges were estimated by the proposed methods. The performance of CMLC and CEC methods was also compared with conventional flood frequency analysis, and the results show that CMLC method performs best for both bivariate and trivariate distributions which has the smallest relative error and root mean square error. The proposed CMLC method has strong statistical basis with unique design flood composition scheme and provides an alternative way for deriving DFH.

Author: Changjiang Xu, Jiabo Yin, Shenglian Guo, Zhangjun Liu, and Xingjun Hong



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