Abstract
Flood hedging reservoir operation is when a pre-storm release creates a small flood downstream to reduce the likelihood of a more damaging but uncertain larger flood in the future. Such pre-storm releases before a flood can increase reservoir storage capacity available to capture more severe flood flows, but also can immediately increase downstream flood damage and reduce stored water supply. This study develops an optimization model for pre-storm flood hedging releases and examines some necessary theoretical conditions for optimality, considering hydrologic uncertainty from flood forecasts and engineering uncertainty from flood failures. Theoretically, the ideal optimality condition for pre-storm flood hedging releases is where the current marginal damage from the hedging release equals the future expected marginal damage from storm releases. Additional water supply losses due to pre-storm releases tend to reduce pre-storm flood hedging releases. The overall flood damage cost to be minimized must be a convex function of pre-storm hedging releases for flood hedging to be optimal. Such convexity is determined by the overall flood risk together with the probability distribution of storm forecasts. Increasing the convexity of the failure probability function can induce more pre-storm hedging release. Categorized by flood risk likelihood downstream, forecasted storms that are large, but not yet overwhelming flood management systems, drive optimal flood hedging operation. A wide range of near-optimal hedging releases is observed in numerical examples, providing options for more rational water resources management decisions.
Similar content being viewed by others
References
Bower BT, Hufschmidt MM & Reedy WW (1962) Operating procedures: their role in the design of water-resource systems by simulation analyses. Des Water Resour Syst 443–458
Camacho EF & Alba CB (2013) Model predictive control. Springer Science & Business Media
Connaughton J, King N, Dong L, Ji P, Lund J (2014) Comparing simple flood reservoir operation rules. Water 6(9):2717–2731
Ding W, Zhang C, Peng Y, Zeng R, Zhou H & Cai X (2015) An analytical framework for flood water conservation considering forecast uncertainty and acceptable risk. Water Resour Res
Draper AJ, Lund JR (2004) Optimal hedging and carryover storage value. J Water Resour Plan Manag 130(1):83–87
Feller W (2008) An introduction to probability theory and its applications (Vol. 2). John Wiley & Sons
Galelli S, Goedbloed A, Schwanenberg D, van Overloop PJ (2012) Optimal real-time operation of multipurpose urban reservoirs: case study in Singapore. J Water Resour Plan Manag 140(4):511–523
Hsu NS, Wei CC (2007) A multipurpose reservoir real-time operation model for flood control during typhoon invasion. J Hydrol 336(3):282–293
Hufschmidt MM, Dorfman R, Thomas HA Jr, Marglin SA, Fair GM (1962) Design of water-resource systems (pp. 443–458). Harvard University Press, Cambridge, MA
Hui R, Lund J (2015) Optimal flood pre-releases—flood hedging for a single reservoir. World Environ Water Resour Congr 2015:2192–2201. doi:10.1061/9780784479162.215
Hui R, Jachens E, Lund J (2016) Risk‐based planning analysis for a single levee. Water Resour Res 52(4):2513–2528
Labadie JW (2004) Optimal operation of multireservoir systems: state-of-the-art review. J Water Resour Plan Manag 130(2):93–111
Loucks DP & Sigvaldason OT (1981) Multiple reservoir operation in North America. In Surface Water Impoundments (pp. 711–728). ASCE
Loucks DP, Stedinger JR & Haith DA (1981) Water resource systems planning and analysis. Prentice-Hall
Lund JR (1996) Developing seasonal and long-term reservoir system operation plans using HEC-PRM (No. HEC-RD-40). Hydrologic Engineering Center Davis CA
Lund JR (2002) Floodplain planning with risk-based optimization. J Water Resour Plan Manag 128(3):202–207
Lund JR, Guzman J (1999) Derived operating rules for reservoirs in series or in parallel. J Water Resour Plan Manag 125(3):143–153
Neelakantan TR, Pundarikanthan NV (1999) Hedging rule optimisation for water supply reservoirs system. Water Resour Manag 13(6):409–426
Perlea M & Ketchum E (2011) Impact of non-analytical factors in geotechnical risk assessment of levees. Reston, VA: ASCE copyright Proceedings of Georisk 2011, June 26. 28, 2011, Atlanta, Georgia| d 20110000
Rayner S, Lach D, Ingram H (2005) Weather forecasts are for wimps: why water resource managers do not use climate forecasts. Clim Chang 69(2–3):197–227
Shiau JT (2011) Analytical optimal hedging with explicit incorporation of reservoir release and carryover storage targets. Water Resour Res 47(1)
Shiau JT, Lee HC (2005) Derivation of optimal hedging rules for a water-supply reservoir through compromise programming. Water Resour Manag 19(2):111–132
Shih JS, ReVelle C (1995) Water supply operations during drought: a discrete hedging rule. Eur J Oper Res 82(1):163–175
Srinivasan K, Philipose MC (1998) Effect of hedging on over-year reservoir performance. Water Resour Manag 12(2):95–120
Stedinger JR (1997) Expected probability and annual damage estimators. J Water Resour Plan Manag 123(2):125–135
Thomas F, Knüppe K (2016) From flood protection to flood risk management: insights from the Rhine River in North Rhine-Westphalia, Germany. Water Resour Manag 30(8):2785–2800
USACE (2011) Cranford levee reliability project for flood risk management Rahway, Cranford, NJ
Wan W, Zhao J, Lund JR, Zhao T, Lei X & Wang H (2016) Optimal Hedging Rule for Reservoir Refill. J Water Resour Plan Manag 04016051
Wang H, Liu J (2013) Reservoir operation incorporating hedging rules and operational inflow forecasts. Water Resour Manag 27(5):1427–1438
Wolff TF (1997) Geotechnical reliability of levees. In Proc of a Hydrology and Hydraulics Workshop on Risk-Based Analysis for Flood Damage Reduction Studies, USACE, Hydrologic Engineering Center
Wurbs RA (1993) Reservoir-system simulation and optimization models. J Water Resour Plan Manag 119(4):455–472
Xu W, Zhang C, Peng Y, Fu G & Zhou H (2014) A two stage Bayesian stochastic optimization model for cascaded hydropower systems considering varying uncertainty of flow forecasts. Water Resour Res
You JY, Cai X (2008a) Hedging rule for reservoir operations: 1. A theoretical analysis. Water Resour Res 44(1):W01415
You JY, Cai X (2008b) Hedging rule for reservoir operations: 2. A numerical model. Water Resour Res 44(1):W01416
Zhang C, Zhu X, Fu G, Zhou H, Wang H (2014) The impacts of climate change on water diversion strategies for a water deficit reservoir. J Hydroinf 16(4):872–889
Zhao J, Cai X, Wang Z (2011) Optimality conditions for a two‐stage reservoir operation problem. Water Resour Res 47(8):W08503
Zhao T, Yang D, Cai X, Zhao J, Wang H (2012) Identifying effective forecast horizon for real-time reservoir operation under a limited inflow forecast. Water Resour Res 48(1):W01540
Zhao T, Zhao J, Lund JR & Yang D (2014) Optimal hedging rules for reservoir flood operation from forecast uncertainties. J Water Resour Plan Manag
Zhu X, Zhang C, Yin J, Zhou H, Jiang Y (2013) Optimization of water diversion based on reservoir operating rules: analysis of the Biliu river reservoir, China. J Hydrol Eng 19(2):411–421
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hui, R., Lund, J., Zhao, J. et al. Optimal Pre-storm Flood Hedging Releases for a Single Reservoir. Water Resour Manage 30, 5113–5129 (2016). https://doi.org/10.1007/s11269-016-1472-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11269-016-1472-x