A copula-based chance-constrained programming framework for BMPs spatial configuration planning

Spatial allocation of best management practices (BMPs) is crucial for reducing non-point source pollution at the watershed scale. However, uncertainty in BMP effectiveness caused by varying hydro-meteorological conditions can pose challenges to achieving water quality management goals, emphasizing the need to incorporate these uncertainties into decision-making. Here we develop a credibility-based chance-constrained programming (CCP) framework to explicitly embed uncertainty into BMP planning and to support reliable multiobjective decisions. We model the dependence in BMP effectiveness with vine copulas and assess its implications for outlet loads via a Markov-based surrogate that approximates the relationship between BMP spatial configurations and outlet load responses. We couple this stochastic simulation–optimization workflow with NSGA-II to search Pareto-optimal trade-offs between implementation cost and nutrient-load reduction while explicitly estimating the reliability (credibility) of candidate solutions. To support actionable choices, the resulting solution set is further condensed via clustering and fuzzy-set ranking to identify representative best-compromise solutions. The results show that the system cost increased by up to 3.4 times with the increase of reduction goal (30–60%). Notably, higher credibility levels allow for slight increases in pollution loads (1.48%-5.67%) without significantly raising costs. Overall, the proposed uncertainty-aware CCP framework enables decisionmakers to balance costs and environmental benefits while ensuring robust and reliable decisions. This approach is highly adaptable to BMP planning in complex environmental systems, enhancing its practicality for multiobjective watershed management.