The present study assesses the potential of the TROPOMI-PAL NO2 observation to derive NOx emissions in France from 2019 to 2021, using prior official emission data from the year 2016 and the Community Inversion Framework coupled to the CHIMERE regional transport model. The study compares the intra-annual relative changes obtained with the satellite-based emissions against the ones reported by the national bottom-up inventory constructed by CITEPA. At the national scale, the top-down estimates fail to reproduce the relative changes reported by CITEPA due to the COVID-19 restrictions, the inconsistencies being attributed by the authors to limitations in the TROPOMI-PAL NO2 observation coverage and the ratio between the current level of errors in the observation and the chemistry-transport model. The authors perform sensitivity runs to assess the impact of the aforementioned limitations. At the urban scale, where anthropogenic NOx emissions dominate, and considering only days during which the TROPOMI coverage is good, the relative changes reported by TROPOMI-based estimates are larger and more in line with national drops reported by CITEPA. The paper is well written and structured, which makes it a good contribution to ACP. However, there are some aspects related to the description of the methods and discussion of the results that should be better clarified before the manuscript is accepted for publication.

Prior estimates of the emission maps: The description of this section is a bit ambiguous and should be clarified. Authors mention that the priors are based on CAMS-REG (year 2016) and the INS inventory (year 2012). However, it is not clear which inventory is being used for which country, pollutant sector and species. From the current text, I assumed INS is being used in France and CAMS-REG in the other countries contained in the CHIMERE working domain. However, later in the presentation and discussion of the results (e.g. section 3.1.2) the authors keep mentioning that 2016 is the reference year of the prior emissions, from which I assume that it is in fact CAMS-REG the inventory used for France. Could you clarify this point in the text?

Also related to this section:

• How is the split of total NOx emissions into NO and NO2 performed?
• Can you provide a reference that describes the spatialization and proxies used for the INS emissions?

Prior uncertainty in the NOx emissions: Could you describe in more detail how prior NOx emission uncertainties are defined and which is the uncertainty range assumed? Are the uncertainties sector-dependent? Do they also include uncertainties in the spatial and temporal distribution, or only in the annual totals? Could it be that part of the mismatch between top-down and bottom-up 2019/2020 emission relative differences are related to an issue with the definition of the prior emission uncertainty?

Role of natural NO emissions: In the present study, soil NOx emissions are estimated using the MEGAN model, which tend to significantly underestimate this natural fluxes according to numerous studies, especially in agricultural areas (e.g., Oikawa et al., 2015; Almaraz et al., 2018; Sha et al., 2021; Zhu et al., 2023). Could it be that the posterior results are not capable of capturing the 2016/2019 or 2019/2020 NOx national emission drops due to the fact that the inversion system is increasing prior soil NOx emissions? Is it possible to split the prior and posterior emission estimates between natural and anthropogenic to see the role of the inversion on each source type?

Oikawa, P. Y. et al. Unusually high soil nitrogen oxide emissions influence air quality in a high-temperature agricultural region. Nat. Commun. 6, 8753 (2015).

Almaraz, M. et al. Agriculture is a major source of NOx pollution in California. Sci. Adv. 4, eaao3477 (2018).

Zhu, Q., Place, B., Pfannerstill, E. Y., Tong, S., Zhang, H., Wang, J., Nussbaumer, C. M., Wooldridge, P., Schulze, B. C., Arata, C., Bucholtz, A., Seinfeld, J. H., Goldstein, A. H., and Cohen, R. C.: Direct observations of NOx emissions over the San Joaquin Valley using airborne flux measurements during RECAP-CA 2021 field campaign, Atmos. Chem. Phys., 23, 9669–9683, https://doi.org/10.5194/acp-23-9669-2023, 2023.

2019/2020 drops in urban areas: The relative 2019/2020 drop in total posterior emissions in urban areas increase (and get closer to national CITEPA estimates) when only considering days during which the TROPOMI coverage is good and assuming no model errors in the covariance matrix. Nevertheless, for some cities the drops of emissions are still quite low, which appears to be inconsistent with the drops in traffic activity reported by CEREMA (https://dataviz.cerema.fr/trafic-routier/) and the drops reported in other studies such as Barré et al. (2021), especially in the cases of Bordeaux, Nice and Toulouse. Can the authors elaborate more on the reasons behind these discrepancies? Could it be, at least partially, related with the city mask considered (using only 1-2 grid cells in some cities may not be representative enough).

Linked to this point, in the abstract authors mention that "these reductions are particularly pronounced for the largest French urban areas (e.g., -26% from April 2019 to April 2020 in the Paris urban area), consistently with the reduction in the intensity of vehicle traffic reported during the lockdown period"

As mentioned before, this is not precise for all cities (e.g., Toulouse and Bordeaux according to CEREMA data).

Results of the work to support the development of bottom-up inventories: In the introduction, the authors emphasize the large uncertainty associated with bottom-up inventories, which come from several elements, including emission factors and spatial and temporal proxies, among others. The authors indicate that the use of observations can complement and support the development of such inventories. I completely agree with this statement. However, in this study I fail to see in which aspects the obtained top-down results are helping to improve or complement the prior estimates, considering that they are not capable of capturing the relative drop in emissions occurred between 2016/2019 and 2019/2020. I think that the limitations encountered in this work and uncertainties associated to the estimation of satellite-based emissions should be better reflected in the abstract and conclusions, as they can be used as a guideline for others. Based on the results of this exercises, what elements are the top-down emission estimation community currently missing to effectively being capable of accurately accounting NOx emissions in space and time and assess the effectiveness of emission abatement policies?

Other comments:

Abstract: "The inversions lead to a decrease of the average emissions over 2019-2021 compared to 2016 of -3% at national scale"

I recommend putting "compared to the 2016 prior emission estimates of..."

Table 3 and Table B3: error in columns names (some of the should be “Apr” instead of “Mar”)

Table B1: If no data available for CITEPA, perhaps better to remove the corresponding columns.

Data availability: please include the CAMS-REG, CITEPA and INS emission datasets

Lines 38-40: "For example, at national and annual scales, these uncertainties reach 50-200% depending on the activity sector in the European Monitoring and Evaluation Programme (EMEP) inventory (Kuenen and Dore, 2019)"

According to the Informative Inventory Reports provided by Member States, uncertainties in total national NOx emissions are lower than what is reported by the authors. More specifically, and according to Schindlbacher et al. (2021), in most EU countries the uncertainty estimate for total anthropogenic NOx emissions is below 30% (19% in the case of France).

Schindlbacher, S., Matthews, B., Ullrich, B.: Uncertainties and recalculations of emission inventories submitted under CLRTAP. Technical report CEIP 01/2021. Available at: https://www.ceip.at/fileadmin/inhalte/ceip/00_pdf_other/2021/uncertainties_and_recalculations_of_emission_inventories_submitted_under_clrtap.pdf

The paper by Plauchu et al. entitled ‘NOx emissions in France in 2019-2021 as estimated by the high spatial resolution assimilation of TROPOMI NO2 observations’ explores the use of TROPOMI NO2 data in combination with an inversion framework to estimate the reduction of NOx emissions due to COVID-19 lockdowns in France in 2020, with a focus on several large urban centres. The paper is very comprehensive and well-structured throughout. As the authors note, the initial results show a somewhat limited correction of the posterior by the observations due to several possible reasons. The authors then try two alternative setups that allow for a larger influence of the observations on the posterior emissions. The authors highlight further data needs and developments that could help improve the use of inversions for case studies such as these.

General comments:

• Interesting and relevant addition to existing literature.
• Comprehensive description of the methodology
• Overall, the paper is well written.

Specific comments:

• 281-284: Can you comment on the expected influence of using 2016 prior emissions for this inversion study? If prior emissions (for 2016) are systematically higher (~13% based on CITEPA) compared to 2019 or 2020, could this have an effect on the posterior emissions? What if you would have used 2019 prior emissions?
• 369-372: Could the differences between cities also be partly due to different contributions of (heavy) industry to NOx emissions in or around these urban centres?
• 422: “yielding a more accurate estimate of the COVID-19 delta”. The qualification of the alternative method using filtered observations being more accurate has not been made before in the paper. Can you comment on why you conclude that it is more accurate than the initial estimate? Could this lesson be generalized to other studies looking at emission variations at such high spatial and temporal resolution?

 Technical corrections:

• 10: Consider replacing “The inversions lead to a decrease…” by “The inversions suggest a decrease…”.
• 18: “consistently” should be “consistent”
• 20-22: Consider splitting up the first sentence of the introduction, as it is rather long, e.g., “Nitrogen dioxide (NO2) is of great interest due to its important role in many atmospheric processes with strong implications for air quality, health, climate change and ecosystems. NO2 is emitted mainly by road traffic, thermal power plants and industrial activities and produced in the atmosphere by the oxidation of nitric oxide (NO), which is emitted by the same activities.”
• 27: “UE” should be “EU”
• 32: “reached with since” should be “reached by”
• 167: “Gloabl" should be “Global”
• 279: “with emissions higher than 72 kteqNO2 during winter” either add “per month”, or “monthly emissions”.
• Figure 5: Would it be possible to show the country borders a bit more clearly in these maps?
• 404: “are about 800 kteqNO2.” In lines 280-281 an average of 850 kteqNO2 is mentioned.
• 430: “randome” should be “random”