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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 724632, 7 pages
Research Article

Uncertainty Assessment of Hydrological Frequency Analysis Using Bootstrap Method

1State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China
2College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China
3Department of Geoscience, University of Nevada Las Vegas, Las Vegas, NV 89154, USA

Received 29 December 2012; Accepted 8 May 2013

Academic Editor: Yongping Li

Copyright © 2013 Yi-Ming Hu 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.


The hydrological frequency analysis (HFA) is the foundation for the hydraulic engineering design and water resources management. Hydrological extreme observations or samples are the basis for HFA; the representativeness of a sample series to the population distribution is extremely important for the estimation reliability of the hydrological design value or quantile. However, for most of hydrological extreme data obtained in practical application, the size of the samples is usually small, for example, in China about 40 50 years. Generally, samples with small size cannot completely display the statistical properties of the population distribution, thus leading to uncertainties in the estimation of hydrological design values. In this paper, a new method based on bootstrap is put forward to analyze the impact of sampling uncertainty on the design value. By bootstrap resampling technique, a large number of bootstrap samples are constructed from the original flood extreme observations; the corresponding design value or quantile is estimated for each bootstrap sample, so that the sampling distribution of design value is constructed; based on the sampling distribution, the uncertainty of quantile estimation can be quantified. Compared with the conventional approach, this method provides not only the point estimation of a design value but also quantitative evaluation on uncertainties of the estimation.