An improved Bayesian inversion to estimate daily NO_x emissions of Paris from TROPOMI NO₂ observations between 2018–2023

We present a comprehensive quantification of daily NO_x emissions from Paris using an inverse analysis of tropospheric NO₂ columns measured by the Tropospheric Monitoring Instrument (TROPOMI) over a 5-year period (May 2018–August 2023). Our analysis leverages a superposition column model that captures the relationship between the increase in NO₂ with distance over an urban source region to underlying NO_x emissions, accounting for chemical transformations and wind in the urban boundary layer. To evaluate the robustness of the superposition column model, we tested it against high-resolution (300 m) Large Eddy Simulations (LES) using MicroHH, a computational fluid dynamics model, with atmospheric chemistry, confirming that the model’s simplifying assumptions introduce uncertainties below 10 %. Building on this foundation, we develop a new Bayesian inversion method that incorporates prior knowledge on NO_x emissions and lifetimes and accounts for model and prior uncertainties. Compared to a previous look-up table approach, which relied on least-squares minimization without prior constraints, the Bayesian method demonstrated superior performance. In controlled tests, it reproduced known NO_x emissions within 5 %. Applying Bayesian inversion to TROPOMI data in Paris, we observed a significant reduction in NO_x emissions from 44 mol s⁻¹ in 2018 to 32 mol s⁻¹ in 2023, representing a 27 % decrease. This decline exceeds the 12 % reduction predicted by the TNO-MACC-III bottom-up inventory, indicating limited accuracy of current inventories. Seasonal analysis revealed higher posterior emissions in winter, possibly highlighting the role of residential heating or vehicle cold starts, which may be underrepresented in bottom-up estimates. Our improved Bayesian framework delivers accurate NO_x emission estimates that align well with independent data sets. This approach provides a valuable tool for monitoring urban NO_x emissions and assessing the efficacy of air quality policies.