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Conventional reservoir operation rule curves are based on the assumption of hydrological stationarity. The aggravating non-stationarity under the changing environment rocked this foundation. The hedging theory is one of the options for adaptive operation based on hydrological forecasts, which can provide a practical tool for optimal reservoir operation under a changing environment. However, the connections between hedging theory and rule curves are not clear. This paper establishes the linkage of rule curves and hedging theory by analyzing three fundamental problems surrounding the design of conventional rule curves, namely the law and design of water supply rule curves, the determination of flood control storage, and the division of refill and drawdown circle. The general interpretation of the conventional water supply rule curves with hedging theory is conducted. Both the theoretical analyses and the Danjiangkou Reservoir case study reveal that, based on the historical records, the rule curves can be interpreted as a specific expression of hedging theory. This intrinsic linkage allows us to propose a more general and scientific method of updating rule curves in the context of non-stationarity. On this basis, the rule-curve-based climate adaptation strategies are figured out using hedging theory. This research is helpful for practical adaptive operation of reservoirs in the changing environment.