Abstract
This work proposes a risk analysis model to evaluate the risk of underestimating the predicted peak discharge, i.e. the exceedance of probability due to the uncertainties in rainfall information (rainfall depth, duration, and storm pattern) and the parameters of the rainfall-runoff model (Sacramento Soil Moisture Accounting model, SAC-SMA) during the flooding prevention and warning operation. The proposed risk analysis model is combined with the multivariate Monte Carlo simulation method and the Advance First-Order Second-Moment method (AFOSM). The observed rainfall and discharge measured at Yu-feng Basin study area in Shihmen reservoir watershed is used in the model development and application. The results of the model application indicate that the proposed risk analysis model can analyze the sensitivity of the uncertainty factors for the predicted peak discharge and evaluates the variation of the probability of exceeding the predicted peak discharge with respect to the rainfall depth and storm duration. In addition, the result of risk analysis for a real rainstorm event, Typhoon Morakot, shows that the proposed model successfully explores the risk of underestimating the predicted peak discharge using SAC-SMA and forecasted rainfall information and provides a probabilistic forecast of the peak discharge.
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References
Abdulla F, Al-Bradranih L (2000) Application of a rainfall-runoff model to three catchments in Iraq. Hydrol Sci 45(1):13–25
Ajami NK, Gupta H, Wagener T, Sorooshian S (2004) Calibration of a semi-distributed hydrologic model for streamflow estimation along a river system. J Hydrol 298:112–135
Apel H, Thieken AH, Merz B, Bloschl G (2004) Flood risk assessment and associated uncertainty. Nat Hazards Earth Syst Sci 4:295–308
Apel H, Thieken AH, Merz B, Bloschl G (2006) A probabilistic modeling system for assessing flood risks. Nat Hazards 38:79–100
Beven K, Kirkby MJ (1979) A physically-based, variable contributing area model of basin hydrology. Hydrol Sci Technol 24:43–69
Bring J (1994) How to standardize regression coefficient. Am Stat 48:209–213
Burnash RJC, Ferral RL, McGuire RA (1973) A Generalized streamflow simulation system—conceptual modeling for digital computers. US Department of Commerce, National Weather Service and State of California, Department of Water Resources, Washington
Chang CH, Yang JC, Tung YK (1997) Incorporate marginal distributions in point estimate methods for uncertainty analysis. J Hydraul Eng 123(3):244–251
Cluckie ID, Xuan Y, Wang Y (2006) Uncertainty analysis of hydrological ensemble forecast in a distributed model utilizing short-range rainfall prediction. Hydrol Earth Syst Discuss 3:3211–3237
Collier CG, Kzyzysztofowicz R (2000) Quantitative precipitation forecasting. J Hydrol 239:1–2
De Cesare L, Mayers DE, Posa D (2001) Product-sum covariance for space-time modeling: an environmental application. Environmetrics 12:11–23
De Cesare L, Mayers DE, Posa D (2002) FORTRAN programs or space-time modeling. Comput Geosci 28:205–212
Dimitrakopoulos R, Luo X (1993) Spatiotemporal modeling: covariance and ordinary kriging system. In: Dimitrakopoulos R (ed) Geostatistics for the next century. Kluwer, Dordrecht, pp 88–93
Fang TQ, Tung YK (1996) Analysis of Wyoming extreme precipitation patterns and their uncertainty for safety evaluation of hydraulic structure. Technical report, WWRC-96.5, Wyoming Water Resource Center, University of Wyoming, Laramie, Wyoming
Franchini M (1996) Using a genetic algorithm combined with a local search method for the automatic calibration of conceptual rainfall-runoff models. Hydrol Sci J 41(1):21–40
Gabellani S, Boni G, Ferraris L, Hardenberg J, Provenzale A (2007) Propagation of uncertainty from rainfall to runoff: a case study with a stochastic rainfall generator. Adv Water Resour 30:2061–2071
Ganoulis J (2003) Risk-based floodplain management: a case study from Greece. Int J River Basin Manag 1(1):41–47
Gneiting TM, Genton G, Guttorp P (2005) Geostatistical space-time model, stationarity, separability and full symmetry. University of Washington, Washington
Goldberg DE (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Pub. Co., Reading, MA
Gouldby B, Samuels P, Klijn F, Messner F, van Os A, Sayers P, Schanze J (2005) Language of risk. Project definitions. FLOODSite report, T32‐04‐01, p 56
Grecu M, Krajewski WF (2000) Simulation study of the effects of model uncertainty in variational assimilation of radar data on rainfall forecasting. J Hydrol 239:85–96
Hill ID, Hill R, Holder RL (1976) Algorithm AS 99 Fitting Johnson curves by moments. Appl Stat 25:180–189
Jain A, Srinivasulu S (2004) Development of effective and efficient rainfall-runoff using integration of deterministic, real-coded genetic algorithms and artificial neural network techniques. Water Resour Res 40(W04302):1–12
Johnson NL (1949) System of frequency curves generated z i = γ + δ ln [y i α/(1 − y i α)] by method of translation. Biometrika 36:149–176
Kelly KS, Krzysztofowicz R (1994) Probability distribution for flood warning systems. Water Resour Res 30(4):1145–1152
Koren VI, Smith M, Wang D, Zhang Z (2000) Use of soil property data in the derivation of conceptual rainfall-runoff model parameters. In: 15th conference on hydrology, Long Beach, CA, pp 103–106
Krzysztofowicz R (1999) Bayesian theory of probabilistic forecasting via deterministic hydrologic model. Water Resour Res 35(9):2739–2750
Krzysztofowicz R (2001) The case for probabilistic forecasting in hydrology. J Hydrol 249:2–9
Kwon HH, Moon YI (2006) Improvement of overtopping risk evaluations using probabilistic concept for existing dams. Stoch Environ Res Risk Assess 20(4):223–237
Liu PL, Der Kiureghian A (1986) Multivariate distribution models with prescribed marginals covariances. Probab Eng Mech 1(2):105–112
Madsen H (2000) Automatic calibration of a conceptual rainfall-runoff model using multiple objectives. J Hydrol 235:276–288
Madsen H, Wilson G, Ammentorp HC (2002) Comparison of different automated strategies for calibration of rainfall-runoff models. J Hydrol 261:48–59
Mays LW (2001) Stormwater collection system design handbook. McGraw-Hill, New York
Medieroa L, Garroteb L, Martin-Carrascob F (2010) A probabilistic model to support reservoir operation decisions during flash floods. J Hydrol Sci 52(3):523–537
Montanari A, Brath A (2004) A stochastic approach for assess the uncertainty of rainfall-runoff simulations. Water Resour Res 40(W001106):1–11
Moore RJ (2002) Aspects of uncertainty, reliability and risk in flood forecasting systems incorporating weather radar. In: Bogardi JJ, Kundzewicz ZW (eds) Risk, reliability and uncertainty and robustness of water resources system. Cambridge University Press, New York
Nataf A (1962) Determination des distributions don’t les marges sont donnees. C R Acad Sci Paris 225:42–43
Paik Y (2008) Analytical derivation of reservoir routing and hydrological risk evaluation of detention basins. J Hydrol 352:191–201
Plate EJ (2002) Flood risk and flood management. J Hydrol 267:2–11
Rodriguez-Iturbe I, Mejia IM (1974) The design of rainfall networks in time and space. Water Resour Res 10:713–728
Shafii M, De Smedt F (2009) Multi-objective calibration of a distributed hydrological model (WetSpa) using a genetic algorithm. Hydrol Earth Sys Sci 13:2137–2149
Smith PJ, Kojiri T, Sekii K (2006) Risk-based flood evacuation decision using a distributed rainfall-runoff model. Annu Rep Disaster Prev Res Inst Kyoto Univ 49(B):717–732
Subret B (2008) Global sensitivity analysis using polynomial chaos expansions. Reliab Eng Syst Saf 93(7):964–979
Tang Y, Reed P, Wagener T, Werkhoven KV (2007) Comparing sensitivity analysis method to advance lumped watershed model identification and evaluation. Hydrol Earth Syst Sci 11:793–817
Todini E (1999) An operational decision support system for flood risk mapping, forecasting and management. Urb Water 1:131–143
Tung YK, Mays LW (1981) Risk model for flood levee design. Water Resour Res 17(4):833–841
Tung YK, Yen BC (2005) Hydrosystems engineering uncertainty analysis. MCGraw Hill Construction. ASCE Press, New York
Wang QJ (1991) The genetic algorithm and its application to calibrating conceptual rainfall-runoff models. Water Resour Res 27(9):2467–2471
Wang QJ (1997) Using genetic algorithm to optimize model parameters. Environ Model Softw 12(1):27–34
Wu SJ, Tung YK, Yang JC (2006) Stochastic generation of hourly rainstorm events. Stoch Environ Res Risk Assess 21(2):1436–3240
Yu PS, Tseng TY (1996) A model to forecast flow with uncertainty analysis. Hydrol Sci J 41(3):327–344
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Wu, SJ., Lien, HC. & Chang, CH. Modeling risk analysis for forecasting peak discharge during flooding prevention and warning operation. Stoch Environ Res Risk Assess 24, 1175–1191 (2010). https://doi.org/10.1007/s00477-010-0436-6
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DOI: https://doi.org/10.1007/s00477-010-0436-6