Planning-Oriented Receptor Modeling: Apportioning Emissions Reductions Required for PM2.5 Attainment

Air-quality concentration standards inherently do not specify which emissions controls are necessary to achieve them. Such standards set up a planning challenge that is fundamentally underdetermined, since many distinct emissions pathways can achieve the standard. Forward scenario testing rarely reveals which control levers are truly required versus merely sufficient, and does not necessarily identify optimal approaches. Here, we present a planning-oriented receptor modeling framework that inverts the traditional source apportionment approach. Instead of attributing observed concentrations to sources, we apportion the emissions reductions required for attainment to specific locations, precursors, and sectors, conditional on receptor-based concentration constraints.

We couple a source–receptor sensitivity matrix (mapping emissions changes to downwind concentration  responses at receptors) with a constrained Bayesian inverse problem that infers the minimal, spatially explicit emissions changes needed to meet a fine particulate matter (PM_2.5) concentration target everywhere (or within a specified attainment definition). An emissions prior regularizes solutions toward a baseline inventory, while constraints enforce physical and policy realism (e.g., non-negativity, sectoral controllability, optional caps/targets by precursor or region). This yields a transparent “control apportionment” output dictating how much each source category must change and where, in order to satisfy receptor targets. In addition, the model estimates uncertainty-aware diagnostics of which receptors bind and which sources dominate the required controls.

In application across the contiguous United States, we show that strategies with comparable economy-wide reductions (~10%) can produce dramatically different attainment outcomes depending on spatial allocation, ranging from near-universal compliance to minimal improvements in population exposure. By systematically exploring the feasible solution space, we quantify a compliance penalty for misallocation: the additional emissions reductions required when controls are applied non-optimally. Together, the framework bridges receptor modeling and attainment planning by producing source-resolved, defensible control requirements and actionable diagnostics that help agencies benchmark, compare, and stress-test attainment strategies.