Water management performance curves for economic and environmental benefit

Water management usually considers economic and ecological objectives, and involves tradeoffs, conflicts, compromise, and cooperation among objectives. Pareto optimality often is championed in water management, but its relationships with the mathematical representation of objectives, and implications of tradeoffs for Pareto optimal decisions, are rarely examined. We evaluate the mathematical properties of optimized tradeoffs to identify promising regions for compromise, suggest strategies for reducing conflicts, and better understand whether decision-makers are more or less likely to cooperate over environmental water allocations. Cooperation and compromise among objectives can be easier when tradeoff curves are concave and more adversarial when tradeoff curves are convex. “Knees”, or areas with maximum curvature, bulges, or breakpoints in concave Pareto frontiers, suggest more promising areas for compromise. Evaluating the shape of Pareto curves based on each objective’s performance function can screen for the existence of knees amenable to compromise. We explore water management and restorations actions that improve and shift the location and prominence of knees in concave Pareto frontiers. Connecting river habitats and other non-flow management actions may add knees on locally concave regions of Pareto frontiers. Managing multiple streams regionally, rather than individually, can sometimes turn convex local tradeoffs into concave regional tradeoffs more amenable to compromise. Overall, this analysis provides a deep investigation of how the shape of tradeoffs influences the range and promise of decisions to improve performance, and illustrates that management actions may encourage cooperation and reduce conflict.水资源管理通常需兼顾经济与生态双重目标，且涉及多目标间的权衡、冲突、妥协与协作。帕累托最优（Pareto optimality）常为水资源管理领域所推崇，但目标的数学表征与帕累托最优决策的权衡内涵之间的关联，却鲜有研究涉足。本研究通过评估优化后权衡关系的数学特性，旨在识别更具可行性的妥协区间，提出缓解冲突的可行策略，并进一步探析决策者在环境用水配置场景下开展协作的可能性高低。当权衡曲线呈凹性时，目标间的协作与妥协更易达成；反之，当权衡曲线呈凸性时，各方更易产生对抗关系。“膝点（Knees）”，即凹性帕累托前沿（Pareto frontiers）上曲率峰值、存在凸起或断点的区域，被视为更具潜力的妥协区间。基于各目标的性能函数评估帕累托曲线形态，可筛选出适合开展妥协的膝点是否存在。本研究探讨了可优化并调整凹性帕累托前沿膝点位置与显著性的水资源管理与修复措施。连通河流栖息地及其他非流量管理措施，可在帕累托前沿的局部凹性区域新增膝点。相较于单流域独立管理，实施区域多流域统筹管理，有时可将局部凸性权衡转换为更便于妥协的区域凹性权衡。总体而言，本分析深入探究了权衡曲线形态如何影响决策的优化空间与实施潜力，并阐明管理措施可有效促进协作、缓解冲突。