Inverse Modeling Identifies Efficient Emission Control Strategy for Mitigating PM2.5 Pollution.

Air-quality standards are the backbone of air pollution regulation, yet they create an underdetermined planning problem: many emissions pathways can satisfy the same concentration target. The traditional approach to emissions mitigation design ("forward" scenario testing) evaluates candidate emissions-control strategies but does not directly determine the smallest set of emissions reductions sufficient to bring modeled concentrations below a standard. Here, we invert the planning task and solve a constrained Bayesian inverse problem to estimate the minimum, spatially explicit emissions changes required to meet a fine particulate matter (PM2.5) concentration target, while determining the distance to compliance across space, precursors, and sectors. We demonstrate the method with a case study of meeting the recently adopted annual primary National Ambient Air Quality Standard across the contiguous United States. Aggregate emissions reductions alone prove insufficient to predict attainment. Modeled strategies with similar total reductions range from perfect compliance to minimal progress, depending on which source locations, sectors, and precursors are controlled. Conversely, other plausible strategies increase the standard-compliant population fraction modestly but require substantially larger emission reductions. Our inverse method provides a benchmark for designing and evaluating air-quality attainment, while clarifying how spatial and sectoral levers drive progress toward a given concentration standard.