Abstract
Hydrologic engineering designs and analyses often require the specification of design storm which involves rainfall amount, duration and hyetograph. In practice, the determination of design rainfall in hydrologic engineering applications involves the frequency analysis of extreme rainfalls of different durations and the establishment of rainfall hyetograph for the design event under consideration. Sampling errors exist in the estimation of rainfall depth (or intensity) quantiles from frequency analysis, which will be transmitted in the process of determining the design rainfall hyetograph. This paper presents a practical methodological framework based on the bootstrap resampling scheme to assess the uncertainty features associated with the magnitude of estimated rainfall depth/intensity quantiles and the corresponding design hyetographs. The procedure is implemented to quantify uncertainty of design rainfall hyetograph following the Stormwater Drainage Manual of Hong Kong involving the use of rainfall intensity–duration–frequency (IDF) model. Of particular interesting is that the bootstrap resampling scheme implemented herein is modified to handle unequal record period of annual maximum rainfall data series of different durations and to account for their intrinsic correlations. According to the adopted rainfall IDF model, the design rainfall hyetograph is a function of the IDF model coefficients. Due to the correlation among rainfall quantiles of different durations, the IDF coefficients are found to be strongly related in a nonlinear fashion which should not be ignored in the establishment of the design hyetographs.
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References
Chen CL (1976) Urban rainfall runoff inlet hydrograph study, vol 4. Synthetic rainfalls for design of urban highway drainage facilities. Report FHWA-RD-76-119. Federal Highway Administration, US Department of Transportation, Washington, DC
Diaconis P, Efron B (1983) Computer-intensive methods in statistics. Sci Am Mag 248:116–131
Drainage Services Department (2000) Stormwater drainage manual. Hong Kong Special Administrative Region, Hong Kong
Efron B (1979a) Bootstrap methods: another look at the jackknife. Ann Stat 3:1189–1242
Efron B (1979b) Computers and theory of statistics: thinking the unthinkable. SIAM Rev 21:460–480
Efron B (1982) The jackknife, the bootstrap, and other resampling plans. In: CBMS-NSF regional conference series in applied mathematics, vol 38. SIAM, Philadelphia
Efron B, Tibshirani RJ (1993) An introduction to the bootstrap. Chapman and Hall, New York
Lam CC, Leung YK (1994) Extreme rainfall statistics and design rainstorm profiles at selected locations in Hong Kong. Technical Note No. 86
Huff FA (1967) Time distribution of rainfall in heavy rainfalls. Water Resour Res 3(4):1007–1019
Keifer CJ, Chu HH (1957) Synthetic rainfall pattern for drainage design. ASCE J Hydraul Div 83(HY4):1–25
Kite GW (1988) Frequency and risk analyses in hydrology. Water Resources Publications, Littleton
Mooney CZ, Duval R (1993) Bootstrapping: A nonparametric approach to statistical inference. Sage Publications, Newbury Park, CA
Rao AR, Hamed KH (2000) Flood frequency analysis. CRC Press, New York
Stedinger JR, Vogel RM, Foufoula-Georgiou E (1993) Frequency analysis of extreme events. In: Maidment DR (ed) Handbook of hydrology. McGraw-Hill, New York
Tung Y (1987) Uncertainty analysis of national weather service rainfall frequency atlas. J Hydraul Eng ASCE 113(2):179–189
Tung YK, Mays, LW (1981) Generalized skew coefficients for flood frequency analysis. J Am Water Resour Assoc 17(2):262–269
Tung YK, Yen BC (2005) Hydrosystems engineering uncertainty analysis. McGraw-Hill, New York
Wang DB, Hagen SC, Alizad K (2012) Climate change impact and uncertainty analysis of extreme rainfall events in the Apalachicola River basin, Florida. J Hydrol 480:125–135
Wu SJ, Yang JC, Tung YK (2006) Identification and stochastic generation of representative rainstorm temporal patterns in Hong Kong Territory. J Stoch Environ Res Risk Assess 20(3):171–183
Wu SJ, Yang JC, Tung YK (2011) Risk analysis for flood control structure under consideration of uncertainties in design flood. Nat Hazards 58(1):117–140
Yen BC, Chow VT (1980) Design hyetographs for small drainage structures. J Hydraul Eng ASCE 106(HY6):1055–1076
Yen BC, Chow VT (1983) Local design rainfall, methodology and analysis, vol II. Report, FHWA/RD-82/064. Federal Highway Administration, US Department of Transportation, Washington DC
Yen BC, Tang WH (1976) Risk–safety factor relation for storm sewer design. J Environ Eng ASCE 102:509–516
Yu PS, Cheng CJ (1998) Incorporating uncertainty analysis into a regional IDF formula. Hydrol Process 12(5):713–726
Acknowledgments
Materials presented in this paper are parts of the study on “Uncertainty and Sensitivity Analysis of Mike-11 Model for Shenzhen River Basin” sponsored by the Drainage Services Department of Hong Kong Special Administrative Region. Gratitude is extended to the two anonymous reviewers for their constructive comments.
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Tung, Yk., Wong, Cl. Assessment of design rainfall uncertainty for hydrologic engineering applications in Hong Kong. Stoch Environ Res Risk Assess 28, 583–592 (2014). https://doi.org/10.1007/s00477-013-0774-2
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DOI: https://doi.org/10.1007/s00477-013-0774-2