Satellite based inversion with NOx derived priors uncovers underestimated SO2 emissions over coal-based regions of China

The relocation of coal production has driven the expansion of the coal chemical industry and associated pollutant emissions in northwestern China, a region with sparse ground-based monitoring. Although data assimilation frameworks combining TROPOMI observations and chemical transport models are widely applied to infer NO_x and SO₂ emissions, their ability to resolve spatiotemporal variability is limited by smoothed priors and parameterized uncertainties, particularly where prior emissions are weak. Divergence-based approaches are computationally efficient but typically assume fixed lifetimes, failing to capture the pronounced variability of SO₂ lifetimes under changing atmospheric conditions. In this study, we employ a light weight method based on a model free mass conserving estimates (MCMFE) framework to quantify co-emitted NO_x and SO₂ emissions from four coal-based regions in northwest China for the period 2019 to 2020. The MCMFE-NO_x emission estimates including inclusion of explicit observational uncertainty, have been extensively evaluated and demonstrated to be robust in previous studies. Building upon this foundation, the present study improves the framework by introducing an iterative training strategy (IT-NO_x). IT-NO_x increases the number of valid grids by approximately 13.5%, corrects about 4.2% of grids with more physically reasonable estimates, and resolves severe underestimation in roughly 0.23% of grids. For SO₂, the approach is newly formulated around a five-term equation that integrates TROPOMI SO₂ observations with ERA5 wind fields, allowing the derivation of dynamic driving factors of SO₂ emissions, including lifetimes, transport distances, and diffusion rates. Rather than relying solely on “bottom-up” inventories to provide the SO₂ a priori, pseudo-priors for SO₂ used in this study are constructed by multiplying MEIC-derived SO₂/NO_x ratios with IT-NO_x emissions. Compared with directly using inventories as a priori, the daily pseudo-SO₂ framework based on IT-NO_x better captures realistic spatial variability of key driving factors and reduce the occurrence of extreme diffusion rates. The 20^th to 80^th percentile ranges of inferred lifetimes span from 5.2 hours to 14.8 hours, revealing seasonal region-specific energy-use patterns. Distinct weekday/weekend contrasts linked to two different emission sectors (transportation with residential activities, and coal plants) are also exhibited. Approximately half of coal-plant-dominated grids show modest lifetime differences, consistent with continuous operations, while transportation and residential dominated grids generally decline during weekends, due to increased private travel and tourism. Compared with the MEIC inventory, 84% of NO_x grids and 92% of SO₂ grids show higher emissions, with regional means of 0.82 ± 0.02 µg/m²/s and 0.52 ± 0.15 µg/m²/s, respectively. It is hoped that these findings will drive a new approach to SO₂ emissions estimation, one in which emissions are based consistently on remotely sensed measurements and associated uncertainties, especially in rapidly developing coal-based regions in northwest China.