A two-stage distributionally robust optimization framework for water quality management in uncertain reservoirs network

Water pollution management in reservoirs network involves complex interactions among strategic investments, operational decisions, and multidimensional uncertainties. This study develops a two-stage distributionally robust optimization (DRO) framework that integrates proactive investment planning with adaptive operational controls under Wasserstein ambiguity sets. The framework systematically captures multi-dimensional uncertainty spaces encompassing pollution loads, treatment efficiencies, monitoring inaccuracies, and spatiotemporal correlation structures. To address complex structure of the problem, a knowledge-enhanced adaptive column-and-constraint generation (KACCG) algorithm is developed, incorporating mass-balance intelligent initialization, expert-derived valid inequalities, adaptive trust region mechanisms, and quadratic regularization. Comprehensive validation on 28-node reservoirs network demonstrates the effectiveness and efficiency of the proposed framework. The framework provides quantitative foundations for ecological compensation mechanism design, quantifying 8.6M annual cooperation benefits across jurisdictions, and demonstrating that coordinated upstream investments amplify downstream pollution reduction by 80% relative to independent management approaches.