This manuscript performed NOx emission inversions using finite difference mass balance and OMI and TROPOMI data. The authors found systematic low biases in the estimates from TROPOMI due to the biases in the retrievals. They also found improvement in the posterior simulation of ozone with measurements. The topic fits the readership of ACP. However, several clarifications and more detailed discussions are needed, see details below.

Specific Comments

Abstract, please include what is the period and spatial scale for this work.

L15-16, Please explain how 3D-Var plays a role in the inversion.

L73-74, it is not clear to me how this work is different from previous assimilations in addressing near-surface NO2 just based on this statement. Please elaborate more.

L197, “assimilating” causes some confusion here. A more proper word here might be “performing an inversion”?

L224, please clarify whether you are using the total NO2 column to adjust lightning NOx or only NO2 observation in the upper atmosphere. It makes more sense to me if it is the latter.

L255, again, I think most previous emission inversions did the same. It is not clear to me how the method used in this work differs from previous work.

Figure 6, for the emission adjustments, could you discuss a bit more on how you determine whether it is due to emissions or chemistry in the model? Over those regions that have different seasonal adjustments in emissions, would that be due to different beta under different chemistry regimes? Otherwise, would the activity or emission factor of anthropogenic emissions have seasonal variations that are not well-captured?

Figure 7, are the differences in emission adjustments proportional to the differences in the NO2 column from OMI and TROPOMI?

L475, did you see better agreement in upper tropospheric NO2 between the simulation and observations after adjusting lightning NOx?

Section 4, I presume the motivation to use this FDMB is to reduce computational cost. Please discuss how the computational cost of this work is compared to other methods.

The authors developed an inverse modeling framework to infer NOx emissions by assimilating satellite observations. The highlight of the method is to separate the surface and lightning emissions contributions. However, I don’t fully understand how the separation has been achieved by reading section 2.5. Additionally, the writing may need improvement. I recommend careful copy editing of the manuscript.

General comments:

1. CMAQ model does not include stratosphere simulations. Will this contribute to uncertainties in the inferred emissions? I recommend adding some discussion about this.
2. Section 2.1. Fig 2. The OMI/TROPOMI ratio is larger than 2 for large areas. I fully understand that it is time-consuming to integrate the TROPOMI data into the system and thus the authors did not update it. But the tremendous differences between those two datasets as shown in Fig 2 make me worried about the uncertainties associated with the usage of the early version of TROPOMI data. I suggest at least running the system with updated TROPOMI data for a short period, like a month, to have an understanding of the uncertainties.
3. Section 2.4. Lamsal et al use OMI NO2 to calculate delta omega and omega. In this work, the authors propose to use CMAQ simulations for the calculation alternatively. What is the advantage of using CMAQ simulations compared to satellite NO2 observations?
4. Section 2.5. Do the authors treat all changes in NO2 as lightning emissions changes for non-populated areas? Do anthropogenic emissions only cover populated areas? If so, I would recommend clarifying and pointing this out in the abstract and conclusion.
5. Is there any specific reason to use both OMI and TROPOMI? It seems the system works well by using a single instrument. I recommend clarifying the pro of using two instruments.

Specific comments:

1. line 20. Inferred from?
2. Line 22. Smaller bias?
3. Line 24. Improve performance or reduce bias?
4. line 25. This sentence is the conclusion sentence of the abstract, but it looks lengthy and unclear to me. I recommend rephasing this sentence substantially.
5. Line 33. It is more common to use “global inventory”.
6. Line 42. Why is the bottom-up inventory incomplete?
7. Line 42-43. Are you indicating that large uncertainties in emissions estimates for developing countries will propagate into that for developed countries? Please try to rephrase the sentence here. The current meaning is unclear to me.
8. Line 48. What is the definition of detailed emissions updates?
9. Line 57. What is the emissions smearing effect?
10. Line 59. Do the authors indicate that averaging a few observations will reduce the biases significantly? I assume the averaging will help to reduce noise, but not systematic bias.
11. Line 73. Please try to briefly explain the reason why assimilation allows for minimizing influence from the upper troposphere before claiming it. It is also not clear to me how it will be an extension of the work of Lamsal et al.
12. Line 83. I rarely see the term "surface-based observations". I suggest a more common-used term of ground observations.
13. Fig 1. Caption. I don’t quite get the meaning of “the boundary of the inversion algorithm”.
14. Line 118. Improvement of the bias?
15. Line 122. Results should not be capitalized.
16. Line 138. What is representative-day?
17. Sect 2.2. What is the spatial resolution of the CMAQ simulation?