| 05 Aug 2026
Nonlinear and regime-dependent precursor effects shape wintertime PM2.5 formation in Beijing under calm conditions
Abstract. Wintertime PM2.5 pollution in Beijing is increasingly governed by secondary aerosol formation, with sulfate and nitrate constituting the dominant inorganic components. However, quantifying the contribution of ambient SO2 and NO2 to PM2.5 formation from observational data remains challenging because precursor–PM2.5 relationships are confounded by meteorological variability, regional transport, and unmeasured emissions. Using routine monitoring data from Beijing heating seasons during 2016–2023, we develop an episode-based causal framework that restricts the analysis to calm periods to address transport-related confounding, and estimates nonlinear precursor responses using shape-constrained additive models incorporating emission proxies and precursor effect modification.
The proxy-calibrated model shows that combustion-related primary emissions remain the dominant unresolved confounder during calm episodes. Precursor concentrations lagged by 2–3 h explain short-term PM2.5 changes, with faster apparent secondary processing in the pollution-hotspot southeastern urban area. Effect-modification analysis indicates that the SO2 response is primarily regulated by thermal conditions. Annual attribution shows that SO2 reductions dominated precursor-associated PM2.5 improvements in the early years, but their contribution weakened as ambient SO2 declined and its marginal effect diminished at low concentrations. In contrast, NO2 sensitivity increases consistently at higher O3 levels, suggesting that elevated O3 in recent years may have enhanced nitrate-related PM2.5 formation, consistent with the increased benefits associated with NO2 reductions after 2020. These results indicate a transition toward increasingly nitrate-sensitive wintertime PM2.5 formation in Beijing and show that routine monitoring data can provide chemically interpretable precursor sensitivities when transport and emission confounding are explicitly constrained.
Summary
This study investigates the nonlinear and regime-dependent effects of SO2 and NO2 on PM₂.₅ accumulation in Beijing during the winter heating seasons of 2016–2023. The authors develop an episode-based causal inference framework that restricts the analysis to calm episodes, use CO and PM2.5 as proxies for unresolved local emissions, and combine proxy calibration with GAM/SCAM models to characterize precursor responses and effect modification. The study further examines spatial heterogeneity, joint SO2-NO2 response surfaces, and year-to-year precursor-associated PM2.5 changes. The topic is important and potentially suitable for publication. However, there are substantial concerns about whether the current data and assumptions are sufficient to support the causal inferences proposed in this paper. Several substantial issues concerning the credibility of causal identification assumptions, model specification and presentation of results. I recommend major revision before reconsideration for publication.
Major Comments
If some clusters have small sample sizes, their AIC estimates have larger uncertainty, and simple averaging may underweight their influence.
Given the sample size and model complexity, AIC selection may be prone to overfitting. The authors should present the distribution of AIC improvements across candidate pairs, not just mean values, to allow readers to assess selection uncertainty.
Minor Comments