Rival framings: A framework for discovering how problem formulation uncertainties shape risk management trade‐offs in water resources systems

Managing water resources systems requires coordinated operation of system infrastructure to mitigate the impacts of hydrologic extremes while balancing conflicting multi-sectoral demands. Traditionally, recommended management strategies are derived by optimizing system operations under a single problem framing that is assumed to accurately represent the system objectives, tacitly ignoring the myriad of effects that could arise from simplifications and mathematical assumptions made when formulating the problem. This study illustrates the benefits of a rival framings framework in which analysts instead interrogate multiple competing hypotheses of how complex water management problems should be formulated. Analyzing rival framings helps discover unintended consequences resulting from inherent biases of alternative problem formulations. We illustrate this on the monsoonal Red River basin in Vietnam by optimizing operations of the system's four largest reservoirs under several different multi-objective problem framings. In each rival framing, we specify different quantitative representations of the system's objectives related to hydropower production, agricultural water supply and flood protection of the capital city of Hanoi. We find that some formulations result in counterintuitive behavior. In particular, policies designed to minimize expected flood damages inadvertently increase the risk of catastrophic flood events in favor of hydropower production, while min-max objectives commonly used in robust optimization provide poor representations of system tradeoffs due to their instability. This study highlights the importance of carefully formulating and evaluating alternative mathematical abstractions of stakeholder objectives describing the multi-sectoral water demands and risks associated with hydrologic extremes.