Overall, it is clear that a large amount of work was done by the authors. However, in its current state, I cannot recommend publication. I do encourage the authors to carefully consider my comments and resubmit the revised manuscript.

A major concern of mine is that this article doesn’t present new science, so it may be better suited to another journal, such as Earth System Science Data (ESSD). The title and introduction actually sound somewhat appropriate for ACP, but the manuscript content is really not appropriate for ACP.

Another issue is that the manuscript is poorly organized and, therefore, difficult to read. ACP gives handy recommendations on the structure of a manuscript: https://www.atmospheric-chemistry-and-physics.net/policies/guidelines_for_authors.html. I highly suggest that the authors review these recommendations. Here are two examples of what I mean:

• The title doesn’t reflect what the paper is about. The paper title indicates that the paper is focused on discussing the causes of trends in European NOx emissions. At least, that’s what I thought when reading the title. This isn’t the case. Please revise the title to reflect the actual manuscript content.
• The paper is wordy (by 30-50%); the introduction is particularly wordy and needs paragraph indents for clarity. Note that a goal of technical writing is to clearly and concisely convey a particular message. As an example, the purpose of your paper should be given in one sentence, such as in the abstract and as a topic sentence of a paragraph in the introduction. I had to piece it together over a very long paragraph, but I still don’t know the overall goal of the paper given the vague title, vague abstract, and vague conclusions. An overview diagram of the steps in your work would be helpful.

Another major concern is the lack of validation of the data products and emission estimates. Why don’t you compare results with independent in situ observations, such as from the Pandora network? That would certainly strengthen your conclusions about how your method impacts the emissions estimates. In fact, you say in the last sentence of the abstract “…our results —with OMI and TROPOMI data leading to different magnitudes of corrections on NOx anthropogenic emissions—suggest that more observational constraints would be required to sharpen the European emission estimates.” You haven’t even used the existing observational constraints!

Section 2.1: What are the strengths and limitations of this inversion system for your work? Has it been applied and validated with independent observations (e.g., Pandora)? Why are you using it relative to other inversion systems?

This manuscript presents NO_x emission inversion experiments driven by two different satellite NO₂ column observational data sets. By performing inversions for 2019 using prior emissions for 2005, this study addresses the question to what extent bottom-up reported NO_x emission reductions can be reconciled using satellite NO₂ observations in an emission inversion. This study is an important contribution to the literature and is well within the scope of ACP, with the community increasingly focusing on reconciling top-down and bottom-up emission estimates. The methodology is mostly scientifically sound, but the presentation of the methodology and results in the manuscript is unclear. This paper can be considered for publication in ACP after a revision focused primarily on restructuring the manuscript and improving the clarity of writing. Please find below the specific issues to be addressed in a revised manuscript.

Methodological issues:

• While I agree with the authors that soil emissions are a relatively minor term on annual time scales, this is not the case for the spring and summer months when biogenic and agricultural emissions peak and anthropogenic emissions are lowest. Previous studies (e.g., Silvern et al. 2019) found that accounting for soil emissions is important to reconcile simulated and observed NO₂ column trends. Please discuss the effect of omitting agricultural soil emissions on the estimated NO_x emission reduction trends.
• In my view, this study is missing a section on the performance of the CIF-CHIMERE system using the two assimilated datasets. Please include this, e.g. by presenting error reductions or a comparison with independent (surface) observations.

Writing issues:

• The title does not reflect the contents of the paper: TROPOMI observations were not available in 2005, and the paper does not focus on detecting NO_x emission decreases but rather on reconciling top-down- and bottom-up-derived emission trends. Please revise.
• The introduction is too lengthy. Please formulate in a more concise manner (in my view, this section can be shortened by roughly 50%) and rethink the presentation of the research questions towards the end of the section.
• Methodology: there is little coherence between these subsections. Please consider giving more descriptive names to your inversion experiments and including a conceptual diagram summarizing your methods.

Minor issues:

Introduction: please introduce non-anthropogenic NO_x emissions before the first use of biogenic emissions in line 55.

Section 2.1: please add more detail on the CIF-CHIMERE setup. Since NO_x chemistry is non-linear, how do NO_x emission changes impact NO₂ columns via the chemistry scheme?

L217-218: what is the goal of reprocessing the NO₂ column observations using meteorological data?

L350-351: wouldn’t OMI also underestimate columns in polluted areas, due to the coarse-resolution a priori NO₂ profiles? Why is this problem larger for TROPOMI?

L355-360: please explain better what is meant with ‘an indirect comparison of OMI and TROPOMI using the CHIMERE CTM as an intermediate’. I am also missing this paragraph’s key message and contribution to the subsection.

L394-395: this seems specific to the experiment setup with a missing agricultural soil emission term.

References

Silvern, R. F., Jacob, D. J., Mickley, L. J., Sulprizio, M. P., Travis, K. R., Marais, E. A., Cohen, R. C., Laughner, J. L., Choi, S., Joiner, J., and Lamsal, L. N.: Using satellite observations of tropospheric NO₂ columns to infer long-term trends in US NO_xemissions: the importance of accounting for the free tropospheric NO₂ background, Atmos. Chem. Phys., 19, 8863–8878, https://doi.org/10.5194/acp-19-8863-2019, 2019.