This paper presents a methodology for parameterizing NOx chemistry to enable the inversion of CO₂, combined with NOx, for constraining fossil fuel CO₂ (ffCO₂) emission estimates at reduced computational cost. The authors employ a machine learning-based random forest regression model to predict the rate of change of NOx, thereby replacing the need for full-chemistry mechanism simulations during inversion. Second model estimates the NO₂:NO ratio to convert satellite-based NO₂ column measurements into total NOx column density. It is trained using GEOS-Chem outputs from a 2019 model run and validated against simulations with randomly perturbed anthropogenic NOx emissions, as well as a 2021 model run. Conceptually, this work on parameterizing NOx chemistry is useful to constrain ffCO2 emissions, but requires more robust model design and validation to be published.

General Comments:

1. Please provide a more detailed explanation of your machine learning model configuration process to ensure that readers who are not familiar with machine learning can follow. For example, include a description of the hyperparameter tuning and the forward feature selection procedures.
2. I believe the current design of the model training and testing has a significant limitation. Validating the model on a simulation with perturbed emissions but under the same atmospheric conditions as the training data may lead to overly optimistic validation results, as it does not sufficiently test the model's generalizability to independent atmospheric states. The authors do evaluate the model on a 2021 simulation; however, I recommend adopting a more rigorous validation approach. Specifically, consider randomly selecting 75% of the full dataset across both grid cells and time steps for training, and using the remaining 25% for evaluation. This would provide a more robust assessment of the model's generalizability across spatial and temporal domains.
3. For model configuration, the authors tested the nine selected features along with pressure, air density, planetary boundary layer height, and the relative mixing ratio of ozone to carbon monoxide. Among these, please explain why the relative mixing ratio of ozone to carbon monoxide is expected to help predict the rate of change of NOx.
4. I would also suggest exploring additional input parameters based on our understanding of NOx chemistry. For example, incorporating time of day could help distinguish between daytime and nighttime chemical processes. Including satellite-derived variables such as O₃ column density and HCHO column density could provide insight into VOC levels, allowing the model to better account for variations in NOx chemistry under different VOC conditions. Variables such as J(O¹D) and H₂O concentrations could help to better represent hydroxyl radical (OH) levels, which play a key role in NOx chemistry.
5. I also recommend providing a more detailed description of the parameter selection criteria, starting with an analysis of the impact of individual parameters on model performance. It would be helpful to show how the inclusion of each parameter incrementally improves the model's accuracy.

Minor Comments:

- Line 35: correct to methodology

- Line 107-108: please use NO2+O2NO+O3

The authors report on a method to derive NOx concentrations and NO2:NO ratios, from a machine-learning method which uses as input variables apart from NOx concentrations the meteorological factors and location, as well as a reaction rate scaling method.

They describe their approach, and validate this against simulations done with the parent CTM (GEOS-Chem), both for the same year but perturbed emissions, and for an alternative year (with alternative meteorology). 

Overall, both methods were shown to sucessfully capture the simulated NOx, as well as simulated NO2 columns when compared to the full-chemistry solution. The errors in NO2 columns were reported typically an order of magnitude smaller than the differences between GEOS-Chem and TROPOMI, and the TROPOMI column precision.

I recommend publication in ACP after addressing the comments given below.

The Introduction could be strengthened, by checking and adding a few more references, as it appears that the authors make quite a few statements that are not well backed up with the given references, and in cases the formulation is a bit sloppy.

In my view a further discussion on the selection of input parameters (Table 1) is welcome. e.g.  What happens if the longitude/latitude is excluded from the parameter list? the thing is that by including this you make implicit assumptions on local conditions in the model, including local emissions, which is actually exactly what you want to derive from the model. This location dependence makes the model implicitly to  account for local conditions, but also suggests that the method cannot directly be adopted for other places in the world, as I understand?

Also can you provide a metric that actually describes the importance of each of the physical input quantities. You briefly describe also other parameters (line 131-133) for the training, but exclude them. I’d be interested in a more detailed description  / quantitative assessment to underline the arguments why the current selection of training parameters was made.

In figure 3 the authors present the skill of the trained model against the actual rates, i.e. from quick reading it appeared that the same data that was used for the training, while in Figure A5 in the Appendix they present the same results, but on more independent data (i.e. data for another year). I would argue to swap the figures, i.e. to show Figure A5 in the main body (which is the more important independent evaluation) while moving the intermediate result, which shows the minimal validity of the regression model to be functional) towards the appendix. Then this allows to report on the correlation performance using the more independent evaluation with a bit more emphasis. This then also allows to trace back the number reported in the Abstract (R2>0.79) in the main body of the text..

Re-reading, I Realize that Figure 3 was created with the perturbed emissions experiments, so there is some modification compared to the training dataset, if I understand well. Please update the figure legend to point this out, for the reader. 

Line 171: ” so, if the concentration doubles then we assume a doubling in the net chemical rate of change”. . Here the authors discuss the characteristics of the lifetime / reaction rate scaling method. I’m a bit puzzled by the use of negative lifetimes. Especially small negative lifetimes, which likely happen to occur now and again in the results,  sounds like a recippee of blowing up the model, in case the rate of change is positive (i.e. a net increase in NOx). Could you please elaborate?

Smaller comments:

Lines 21 - 29: Many statements made by the authors, but I miss proper referencing here, e.g. wrt the availability of bottom-up inventories.

line 21 “reaching net zero” : net zero what? please use more explicit description. 

line 23 “ how does a country know” this is also a bit sloppy formulation of the question, to my taste. please  reformulate

line 25 uncertainty -> “uncertain”

line 29: “subject to uncertainties”: can you add references here of key uncertainties?

line 33: you jump directly to your method, without proper introduction of the link between NOx and CO2. I would expect such a more expicit introduction, + references to past studies who have made attempts in this direction.

line 35 ”methodlogy” 

line 41 , please check sentence.

line 45 “to facilitate the production of NO (..)”, suggest to add the phrase something like “.. which is therefore co-emitted with the CO2 emissions”.

line 47 “parent emissions” please change to “parent NOx emissions”. the linking to CO2 is yet another step that deserves its own discussion, to my taste

line 50 “becomes a widely used approach”, but please also give an overview of the main issues, apart from the computational costs. This is missing so far.

Figure 1 - this figure is introduced at the end of the introduction - but the steps are difficult to follow. Please expand the description of this figure on line 64, or refer more specifically to the various steps in this figure in the consecutive subsections.

line 75 “or a scaling-based method” is this method described further down the text? If not, remove reference to this.. 

line 78 “for data assimilation” : add “on a high horizontal resolution” ? 

line 81: add a reference to a default description of GEOS-Chem (paper? Website? other?)

line 84: “30 models below tropopause” given the importance of near-surface processes, can you specify the depth of the first model layer? I think this is larger than the one used operationally in IFS in its default vertical resolution (10 m, see, .e.g. https://confluence.ecmwf.int/display/UDOC/L137+model+level+definitions) - would that have implications on the accuracy of simulating NOx chemistry, surface fluxes, and dynamics?

line 110: can you discuss, and explain the shape of the diurnal cycle in the NOx tendency over the season? e.g. what explains the large sink in NOx during night-time?

Figure A3: please check the x-axis for the temperature plot. 

Line 156 “the atmospheric lifetime becomes negative”: it is unclear to me what is the physical meaning of a negative lifetime, as well as any possible implications on the model results. Could you please elaborate, especially in the case of small negative lifetimes? 

Figure 2b: as many the points are plotted on top of one another, it might be better to present this information in terms of a scatter density plot. Also, the judgement when delta-NOx changes are considered irrelevant appears a bit ‘ad hoc’ 

line 182 “below” => Above ?