Effect of Uncertainty in Historical Data on Flood Frequency Analysis Using Bayesian Method
Publication: Journal of Hydrologic Engineering
Volume 26, Issue 4
Abstract
The purpose of this paper was to investigate the effect of the uncertainty of historical flood information on flood frequency analyses using a Bayesian approach. The uncertainty of the magnitude was described using variations in lower or upper bound values, but the return period was not changed. Two types of hydrologic data—synthetic data generated from the Pearson type three distribution population and observed peak discharge data from the Yichang hydrologic station located below the Three Gorges Dam on the Yangtze River, China—were used. For the measured and the synthetic data, when the magnitudes were underestimated and the errors increased, the accuracy of the historical flood samples decreased, the estimated values of the parameters and design floods decreased using the Bayesian and probability weighted methods, and the values using the Bayesian method were more sensitive to errors and more quickly decreased relative to the probability weighted method. In contrast, overestimated magnitudes did not improve the representativeness of the historical flood samples but merely appended their values with an increase in errors, and the estimated values were hardly affected by changes in the errors using the Bayesian approach. At the same time, the estimated values continued to increase using the probability weighted method and did not accord with the variations in the errors for the flood frequency analysis. In practice, when the return period could be set with a specific value using several historical or paleoflood events, accurately quantifying the peak values of historical floods with known information was difficult, and we overestimated their magnitudes within a specified interval using the existing approaches and available information to estimate their bounds. The estimated values of the parameters and design floods and their uncertainty were less affected when using the Bayesian approach.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Systematically observed peak discharge values of Yichang station are from Application and Research on Nonparametric Statistics Theory in Flood Frequency Analysis (Dong, doctoral dissertation, Hohai University, 2004) and the Bureau of Hydrology Changjiang Water Resources Commission of China. Some or all of the data, models, or code that support the findings of this study are available from the corresponding author on reasonable request.
Acknowledgments
This study was supported by the Second Tibetan Plateau Scientific Expedition and Research Program (STEP, Grant No. 2019 QZKK0203), the National Natural Science Fund of China (Nos. 41571017, 91647203).
References
Baker, V. R., R. H. Webb, and P. K. House. 2002. “The scientific, and societal value of paleoflood hydrology.” In Vol. 5 of Ancient floods, modern hazards: Principles and applications of paleoflood hydrology. Washington, DC: American Geophysical Union.
Bradley, A. A., and K. W. Potter. 1992. “Flood frequency-analysis of simulated flows.” Water Resour. Res. 28 (9): 2375–2385. https://doi.org/10.1029/92WR01207.
Cameron, D. 2007. “Flow, frequency, and uncertainty estimation for an extreme historical flood event in the Highlands of Scotland, UK.” Hydrol. Processes 21 (11): 1460–1470. https://doi.org/10.1002/hyp.6321.
Cao, G. J., and J. Wang. 2015. Observation and Research on hydrology and sediment of three gorges dam in the Yangtze River, 242. Beijing: Science Press Beijing.
Cohn, T. A., W. L. Lane, and W. G. Baier. 1997. “An algorithm for computing moments-based flood quantile estimates when historical flood information is available.” Water Resour. Res. 33 (9): 2089–2096. https://doi.org/10.1029/97WR01640.
Cong, S. Z., and Y. B. Xu. 1987. “The effect of discharge measurement error in flood frequency-analysis.” J. Hydrol. 96 (1–4): 237–254. https://doi.org/10.1016/0022-1694(87)90156-9.
Dong, J. 2004. “Application and research on nonparametric statistics theory in flood frequency analysis.” Ph.D. dissertation, College of Hydrology and Water Resources, Hohai Univ.
England, J. F., J. D. Salas, and R. D. Jarrett. 2003. “Comparisons of two moments-based estimators that utilize historical and paleoflood data for the log Pearson type III distribution.” Water Resour. Res. 39 (9): 1243. https://doi.org/10.1029/2002wr001791.
Fei, Y. F. 1999. “The effect of historical flood events on design flood.” [In Chinese.] J. Hydroelectric Eng. 67 (4): 45–50.
Frances, F., J. D. Salas, and D. C. Boes. 1994. “Flood frequency-analysis with systematic and historical or paleoflood data-based on the 2-parameter general extreme-value models.” Water Resour. Res. 30 (6): 1653–1664. https://doi.org/10.1029/94WR00154.
Haario, H., E. Saksman, and J. Tamminen. 2001. “An adaptive Metropolis algorithm.” Bernoulli 7 (2): 223–242. https://doi.org/10.2307/3318737.
Herget, J., T. Roggenkamp, and M. Krell. 2014. “Estimation of peak discharges of historical floods.” Hydrol. Earth Syst. Sci. 18 (10): 4029–4037. https://doi.org/10.5194/hess-18-4029-2014.
Hosking, J. R. M., and J. R. Wallis. 1986a. “Paleoflood hydrology and flood frequency-analysis.” Water Resour. Res. 22 (4): 543–550. https://doi.org/10.1029/WR022i004p00543.
Hosking, J. R. M., and J. R. Wallis. 1986b. “The value of historical data in flood frequency-analysis.” Water Resour. Res. 22 (11): 1606–1612. https://doi.org/10.1029/WR022i011p01606.
Huang, W. J., W. S. Wang, J. L. Jin, and J. Fu. 2006. “Influence of uncertainty from large historical flood upon frequency analysis.” J. Sichuan Univ. Eng. Sci. Educ. 38 (3): 13–16.
Jin, M. H., and J. R. Stedinger. 1989. “Flood frequency-analysis with regional and historical information.” Water Resour. Res. 25 (5): 925–936. https://doi.org/10.1029/WR025i005p00925.
Kuczera, G. 1992. “Uncorrelated measurement error in flood frequency inference.” Water Resour. Res. 28 (1): 183–188. https://doi.org/10.1029/91WR02269.
Kuczera, G. 1996. “Correlated rating curve error in flood frequency inference.” Water Resour. Res. 32 (7): 2119–2127. https://doi.org/10.1029/96WR00804.
Kuczera, G. 1999. “Comprehensive at-site flood frequency analysis using Monte Carlo Bayesian inference.” Water Resour. Res. 35 (5): 1551–1557. https://doi.org/10.1029/1999WR900012.
Lam, D., C. Thompson, J. Croke, A. Sharma, and M. Macklin. 2017. “Reducing uncertainty with flood frequency analysis: The contribution of paleoflood and historical flood information.” Water Resour. Res. 53 (3): 2312–2327. https://doi.org/10.1002/2016WR019959.
Lee, K. S., and S. U. Kim. 2008. “Identification of uncertainty in low flow frequency analysis using Bayesian MCMC method.” Hydrol. Processes 22 (12): 1949–1964. https://doi.org/10.1002/hyp.6778.
Li, T., S. Guo, L. Chen, and J. Guo. 2013. “Bivariate flood frequency analysis with historical information based on copula.” J. Hydrol. Eng. 18 (8): 1018–1030. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000684.
Liang, Z. M., W. J. Chang, and B. Q. Li. 2012. “Bayesian flood frequency analysis in the light of model and parameter uncertainties.” Stochastic Environ. Res. Risk Assess. 26 (5): 721–730. https://doi.org/10.1007/s00477-011-0552-y.
Liang, Z. M., B. Q. Li, Z. B. Yu, and W. J. Chang. 2011. “Application of Bayesian approach to hydrological frequency analysis.” Sci. China-Technol. Sci. 54 (5): 1183–1192. https://doi.org/10.1007/s11431-010-4229-4.
Ministry of Water Resources of the People’s Republic of China. 2006. Regulation for calculating design flood of water resources and hydropower projects. SL 44-2006. Beijing: China Water & Power Press.
Montanari, A., and G. Di Baldassarre. 2013. “Data errors and hydrological modelling: The role of model structure to propagate observation uncertainty.” Adv. Water Resour. 51 (Jan): 498–504. https://doi.org/10.1016/j.advwatres.2012.09.007.
Neppel, L., B. Renard, M. Lang, P.-A. Ayral, D. Coeur, E. Gaume, N. Jacob, O. Payrastre, K. Pobanz, and F. Vinet. 2010. “Flood frequency analysis using historical data: Accounting for random and systematic errors.” Hydrol. Sci. J. 55 (2): 192–208. https://doi.org/10.1080/02626660903546092.
O’Connell, D. R. H., D. A. Ostenaa, D. R. Levish, and R. E. Klinger. 2002. “Bayesian flood frequency analysis with paleohydrologic bound data.” Water Resour. Res. 38 (5): 13. https://doi.org/10.1029/2000wr000028.
Parent, E., and J. Bernier. 2003. “Bayesian POT modeling for historical data.” J. Hydrol. 274 (1–4): 95–108. https://doi.org/10.1016/S0022-1694(02)00396-7.
Parkes, B., and D. Demeritt. 2016. “Defining the hundred year flood: A Bayesian approach for using historic data to reduce uncertainty in flood frequency estimates.” J. Hydrol. 540 (Sep): 1189–1208. https://doi.org/10.1016/j.jhydrol.2016.07.025.
Payrastre, O., E. Gaume, and H. Andrieu. 2011. “Usefulness of historical information for flood frequency analyses: Developments based on a case study.” Water Resour. Res. 47 (8). https://doi.org/10.1029/2010wr009812.
Reis, D. S., and J. R. Stedinger. 2005. “Bayesian MCMC flood frequency analysis with historical information.” J. Hydrol. 313 (1–2): 97–116. https://doi.org/10.1016/j.jhydrol.2005.02.028.
Schendel, T., and R. Thongwichian. 2017. “Considering historical flood events in flood frequency analysis: Is it worth the effort?” Adv. Water Resour. 105 (Jul): 144–153. https://doi.org/10.1016/j.advwatres.2017.05.002.
Shang, X., Z. Wang, and D. Wang. 2011. “Uncertainty analysis of parameters estimation in hydrologic frequency analysis based on Bayesian method: A case study of P-III distribution.” [In Chinese.] J. Basic Sci. Eng. 19 (4): 554–564.
Song, D. 1989. “New method for calculating parameter estimation with discrete series 644: Probability-weighted moment.” [In Chinese.] J. Hydraul. Eng. 9: 25–32.
Stedinger, J. R., and T. A. Cohn. 1986. “Flood frequency-analysis with historical and paleoflood information.” Water Resour. Res. 22 (5): 785–793. https://doi.org/10.1029/WR022i005p00785.
Strupczewski, W. G., K. Kochanek, and E. Bogdanowicz. 2014. “Flood frequency analysis supported by the largest historical flood.” Nat. Hazards Earth Syst. Sci. 14 (6): 1543–1551. https://doi.org/10.5194/nhess-14-1543-2014.
Strupczewski, W. G., K. Kochanek, and E. Bogdanowicz. 2017. “Historical floods in flood frequency analysis: Is this game worth the candle?” J. Hydrol. 554 (Nov): 800–816. https://doi.org/10.1016/j.jhydrol.2017.09.034.
Viglione, A., R. Merz, J. L. Salinas, and G. Bloeschl. 2013. “Flood frequency hydrology: 3. A Bayesian analysis.” Water Resour. Res. 49 (2): 675–692. https://doi.org/10.1029/2011WR010782.
Zhan, D. J., and S. Z. Ye. 2000. Engineering hydrology. 3rd ed., 189–190. Beijing: China Water Power Press.
Zhang, J. Y., and M. J. Hall. 2004. “Regional flood frequency analysis for the Gan-Ming River basin in China.” J. Hydrol. 296 (1–4): 98–117. https://doi.org/10.1016/j.jhydrol.2004.03.018.
Information & Authors
Information
Published In
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jan 20, 2020
Accepted: Dec 10, 2020
Published online: Feb 15, 2021
Published in print: Apr 1, 2021
Discussion open until: Jul 15, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.