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Linear Versus Nonlinear (Convex and Concave) Hedging Rules for Reservoir Optimization Operation

Water resources research, 2021-12, Vol.57 (12), p.n/a [Peer Reviewed Journal]

2021. American Geophysical Union. All Rights Reserved. ;ISSN: 0043-1397 ;EISSN: 1944-7973 ;DOI: 10.1029/2020WR029160

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  • Title:
    Linear Versus Nonlinear (Convex and Concave) Hedging Rules for Reservoir Optimization Operation
  • Author: Zeng, Xiang ; Lund, Jay R. ; Cai, Ximing
  • Subjects: Availability ; Aversion ; Carryover storage ; convex and concave ; Criteria ; Decisions ; Economics ; Hydrology ; linear ; marginal value of risk tolerance (MVRT) ; nonlinear ; Optimization ; Reservoir operation ; Reservoir storage ; Reservoir water ; Risk aversion ; Risk levels ; risk premium ; Risk taking ; Tradeoffs ; Uncertainty ; Water availability ; Water conservation ; Water delivery ; Water storage ; Water use
  • Is Part Of: Water resources research, 2021-12, Vol.57 (12), p.n/a
  • Description: Hedging rules of reservoir operations decide the timing and magnitude of current water delivery reduction and consequent carryover water storage conservation based on the tradeoff between the utility of current and future water use. Different forms of hedging can be used for reservoir release decision. This study presents general optimality conditions for hedging with convex, concave, and linear relationships between reservoir water availability and release, using criteria based on the relative value of marginal value of risk tolerance (MVRT) with respect to current reservoir release versus carryover storage. MVRT is quantified to measure reservoir operators' risk tolerance change (sensitivity) to the change of reservoir release or carryover storage, reflecting their attitudes to the risk with current release and that with the carryover storage (i.e., future release), as well as their perception of future water availability uncertainty. Higher, equal, or lower MVRT with current release than that with carryover storage for future release corresponds to convex, linear or concave hedging. Various levels of risk tolerance toward hydrologic uncertainty underlie different hedging types for reservoir release decisions. Specifically, negative, positive, and null risk premiums (or risk seeking, risk aversion, and risk neutrality) result from convex, concave, and linear hedging rules, respectively. In general, high uncertainty will move the convex or concave curve closer to the linear curve. The MVRT‐based criteria for optimal hedging policies are illustrated through a real‐world case study. Plain Language Summary Hedging rules of reservoir operations decide how much water to release for current demand and how much water to carry to the future via storage based on the tradeoff between current and future water use utility. This paper combines hydrology and economics to address general optimality conditions for hedging with convex, concave, and linear relationships between reservoir water availability and release. For the first time, a concept of marginal value of risk tolerance (MVRT) is derived to characterize the hedging rules. MVRT evaluates the magnitude of risk tolerance change due to current release change or carryover storage change. It is found that hydrologic uncertainty underlies different hedging types for reservoir release decisions. The advantages of nonlinear (convex or concave) hedging are shown. This study specifies the various forms of hedging rules by relating hedging to risk premium in resources economics, which can help guide adaptive reservoir operation. Key Points General optimality conditions for linear and nonlinear (convex and concave) hedging are derived Hedging rules are characterized by marginal value of risk tolerance to utility loss with respect to current release and carryover storage Hydrologic uncertainty underlies different hedging types
  • Publisher: Washington: John Wiley & Sons, Inc
  • Language: English
  • Identifier: ISSN: 0043-1397
    EISSN: 1944-7973
    DOI: 10.1029/2020WR029160
  • Source: Wiley Blackwell AGU Digital Archive
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