Abstract
Flood forecasting plays an essential role in enhancing the safety of residents downstream and preventing or reducing economic losses. One critical issue in flood risk assessment is the determination of the probability distribution of forecast errors. Several investigations, which have been carried out to analyze the influence of the uncertainty in real-time operation or water resources management, assumed that the relative forecast error was approximately normally distributed. This study investigates whether the flood forecast error follows the normal distribution. Several distributions were fitted to the flood error series, and their performances were analyzed using the data from Three Gorges Reservoir (TGR) and Muma River. Then, the most appropriate distribution was selected. Results show that the assumption of normal distribution is not justified for the flood forecast error series of TGR and Muma River. The use of normal distribution for estimating flood risk may lead to incorrect results.
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References
Alemu ET, Palmer RN, Polebitski A, Meaker B (2011) Decision support system for optimizing reservoir operations using ensemble streamflow predictions. J Water Res PL-ASCE 137(1):72–82
Bergström S (1992) The HBV model—its structure and applications. SMHI Reports RH No. 4, Norrköping
Boucher MA, Tremblay D, Delorme L, Perreault L, Anctil F (2012) Hydro-economic assessment of hydrological forecasting systems. J Hydrol 416:133–144
Chen H, Guo SL, Xu CY, Singh VP (2007) Historical temporal trends of hydro-climatic variables and runoff response to climate variability and their relevance in water resource management in the Hanjiang basin. J Hydrol 334:171–184
Chen L, Guo SL, Yan BW, Liu P, Fang B (2010) A new seasonal design flood method based on bivariate joint distribution of flood magnitude and date of occurrence. Hydrol Sci J 55(8):1264–1280
Chen L, Singh VP, Guo S, Hao Z, Li T (2012) Flood coincidence risk analysis using multivariate copula functions. J Hydrol Eng 17(6):742–755
Chen L, Singh VP, Guo S, Ashok KM, Guo J (2013) Drought analysis based on copulas. J Hydrol Eng 18(7):797–808
Christensen S (2003) A synthetic ground water modelling study of the accuracy of GLUE uncertainty intervals. Nord Hydrol 35(1):45–59
Diao YF, Wang BD, Liu J (2007) Study on distribution of flood forecasting errors by the method based on maximum entropy. J Hydraul Eng 38(5):591–595
Griffiths GA (1989) A theoretically based Wakeby distribution for annual flood series. Hydrol Sci J 34:231–248
Grillakis MG, Tsanis IK, Koutroulis AG (2010) Application of the HBV hydrological model in a flash flood case in Slovenia. Nat Hazards Earth Syst Sci 10:2713–2725
Harlin J, Kung CS (1992) Parameter uncertainty and simulation of design floods in Sweden. J Hydrol 137:209–230
Li X, Guo S, Liu P, Chen G (2010) Dynamic control of flood limited water level for reservoir operation by considering inflow uncertainty. J Hydrol 391:124–132
Lindström G (1997) A simple automatic calibration routine for the HBV model. Nord Hydrol 28(3):153–168
Ministry of Water Resources (MWR) (2006) Regulation for calculating design flood of water resources and hydropower projects. Chinese ShuiliShuidian Press, Beijing (in Chinese)
Ngoc T, Hiramatsu K, Harada M (2013) Optimizing parameters for two conceptual hydrological models using a genetic algorithm: a case study in the DauTieng River Watershed. Vietnam. Jpn Agric Res Q 47(1):85–96
Stedinger JR, Vogel RM, Lee SU, Batchelder R (2008) Appraisal of the generalized likelihood uncertainty estimation (GLUE) method. Water Resour Res 44:W00B06
Xu D, Wang W, Chau K, Cheng C, Chen S (2013) Comparison of three global optimization algorithms for calibration of the Xinanjiang model parameters. J Hydroinf 15:174–191
Yan B, Guo S, Chen L (2013) Estimation of reservoir flood control operation risks with considering inflow forecasting errors. Stoch Environ Res Risk Assess. doi:10.1007/s00477-013-0756-4
Yin HF, Li CA (2001) Human impact on floods and flood disasters on the Yangtze River. Geomorphology 41:105–109
Zelenhastic E, Salvai A (1987) A method of streamflow drought analysis. Water Resour Res 23(1):156–168
Zhao RJ (1992) The Xinanjiang model applied in China. J Hydrol 135:371–381
Zhao RJ, Zhang YL, Fang LR (1980) The Xinanjiang model. Paper presented at Hydrological Forecasting Proceeding Oxford Symposium, IASH-AISH Publ. no. 129, Washington, pp. 351–356
Zhao TTG, Cai XM, Yang DW (2011) Effect of streamflow forecast uncertainty on real-time reservoir operation. Adv Water Resour 34(4):495–504
Zhao T, Zhao J, Yang D, Wang H (2013) Generalized martingale model of the uncertainty evolution of streamflow forecasts. Adv Water Resour 57:41–51
Acknowledgments
The project was financially supported by the National Natural Science Foundation of China (NSFC Grant 51309104, 51209221), Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research (IWHR-SKL-201408), Natural Science Foundation of Hubei Province (No. 2013CFB184) and Wuhan Planning Project of Science and Technology (2014060101010064).
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Zhang, J., Chen, L., Singh, V.P. et al. Determination of the distribution of flood forecasting error. Nat Hazards 75, 1389–1402 (2015). https://doi.org/10.1007/s11069-014-1385-z
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DOI: https://doi.org/10.1007/s11069-014-1385-z