Uncertainty assessment of estimation of hydrological design values
Hydrological frequency analysis is the foundation for hydraulic engineering design and water resources management. However, the existence of uncertainty in sample representation usually causes the uncertainty in quantile or design value estimation. Standard deviation (SD) of the design value with a given non-exceedance probability, as an extremely valuable indicator, is suggested to quantify the uncertainties of hydrological frequency analysis. In order to assess the impact of the sampling uncertainty on design value, in China’s national standard for design flood calculation, an empirical formula for estimating SD of the design value was suggested; however, it is applicable only to the case that Pearson type three probability distribution function (PE3) and method of moment are used to analyze the hydrological samples. In principle, for other types of probability distribution functions and parameter estimation methods, the suggested empirical formula is not suitable. The aim of this article is to propose a general approach to estimate the SD of a design value by using the Bootstrap resampling technique. In order to testify the applicability of the approach, under the condition of PE3 distribution, three kinds of schemes were designed to calculate SD, i.e. the suggested empirical formula in China’s national standard for design flood calculation (SEF), Bootstrap technique with method of moment for parameter estimation and Bootstrap with linear moment for parameter estimation. The annual precipitation observations from 50 gauges around China were analyzed using these three approaches. Results show that the SD values of quantile estimates are significantly different among these three approaches, which means that when parameter estimation methods rather than method of moment are employed, the SD provided by SEF is inapplicable. It also indicates that, in terms of modified design value, i.e., original design value adding security correction value, the proposed method using the Bootstrap method, as a general method for SD estimation, is effective and feasible.
KeywordsHydrological frequency analysis Hydrological design value or quantile Standard deviation Security correction value Bootstrap method Uncertainty analysis
This study was supported by the Major Program of National Natural Science Foundation of China (Grant no. 51190095), the National Natural Science Foundation of China (Grant nos. 51079039, 51309105), and Graduate Research and Innovation Program for Ordinary University of Jiangsu Province (1043-B1305324). We wish to thank the reviewers and editors, whose suggestions have helped us to improve the quality of the paper.
- Changjiang Water Resources Commission (CWRC), Nanjing Institute of Hydrology and Water Resources (1995) Handbook for calculating design flood of water resources and hydropower projects. China Water Power Press, Beijing, pp 34–86Google Scholar
- Ding J, Yang R (1988) The determination of probability weighted moments with the incorporation of extraordinary values into sample data and their application to estimating parameters for the pearson type three distribution. J Hydrol 101(1):63–81Google Scholar
- Hosking JRM (1990) L-moments: analysis and estimation of distribution using linear combinations of order statistics. J R Stat Soc B 52:105–124Google Scholar
- Hu Yiming, Liang Zhongmin, Li Binquan, Yu Zhongbo (2013) Uncertainty assessment of hydrological frequency analysis using Bootstrap method. Math Probl Eng. doi: 10.1155/2013/724632
- Kendall MG (1975) Rank Correlation Methods, 4th edn. Charles Griffin, LondonGoogle Scholar
- Mann HB (1945) Non-parametric tests against trend. Econometrica 13:163–171Google Scholar
- Tang WH (1980) Bayesian frequency analysis. J Hydraul Div 106(7):1203–1218Google Scholar