Review of the paper "Towards monitoring CO2 source-sink distribution over India via inverse modelling: Quantifying the fine-scale spatiotemporal variability of atmospheric CO2 mole fraction" by Thilakan et al. The authors have tried to estimate representation errors (REs) for model resolution, using a 10x10 km simulation by WRF-VPRM simulations. They also briefly discuss CO2 concentrations from global models.

I have found this version of the ms reads better than the previous version. The paper still lacks clear direction. Impacts of nversion results are less than expected at the end. At the minimum the paper require major revisions before consideraion for publication in Atmos. Chem. Phys.

Specific comments: 

Line 145ff : I feel you do not need this paragraph, the introduction have talked about the rationale well. Go straight to model description

Line 214-2015: this is very strange, why cannot you do continuous simulation?

you are loosing some 20% of computing time and may be some inconsistency in simulation with repeated initialisation + plus may be some discontinuity in transport. 

Line 284: India specific study: Kulchala et al., Spatio-temporal variability of XCO2 over Indian region inferred from Orbiting Carbon Observatory (OCO-2) satellite and Chemistry Transport Model, Atmospehric Research, 269, 106044, 2022. 

Line 299: there is a paper discussing these statements here (Patra et al., ACP, 2011)

Line 387ff: I still don’t know what this means or if it is needed here? If true, why are you doing this exercise anyways? What are the relevance to your WRF simulation analysis? Any comparison or cross checking?

I am still not convinced what the authors are aiming at with this analysis (Figs. 2 & 3). there are measurements from CONTRAIL if you want to get a true picture of the global model uncertainties using model-observation comparison please check Patra et al. (2011) for a methodology. i think the readers need a bit more clarification about this analysis

Line 417: is this a novel finding of this study for the this study area ??

Line 422: what is the basis of plausibility ?

Line 440: Why gap filling is needed ? You cannot replace measurement by model, if you believe the satellites are doing something right!

Line 475ff: When you say representation error in CO2, I assume fossil-fuel component is also included in the analysis. I wonder why the cities or power plants hotspots are not revealed as the areas of high representation error ?

Line 481 : I was expecting about an order of magnitude lower representation error for XCO2, compared to REs in CO2 at 200 m. Can you give an equation how you calculated XCO2 ? also could you please show the REs in CO2 in the supplement, say at 2 km and 5 km altitude ? That will give an idea to the readers how REs propagate upwards 

Line 510ff: I like fig. 7. I think this is the most novel result of this study. But i am curious if you can quantify the REs arising from flux smoothing or transport error ? In TransCom continuous experiment Patra et al. (GBC, 2008) ran two sets of experiment to make such separation (please ref to their Fig. 8 associated discussion). Of course their method of estimation of REs is different from yours, but nevertheless the flux vs transport REs is an important information to derive from such OSSEs 

Line 534: Again I would like to draw your attention to one paper here by Chandra et al. (ACP, 2017). Think there is not too much scopes or need for speculations. The Indian monsoon domain is well studied for dynamic and now for chemical species

Line 559ff: Not sure how you get these numbers for RE fractions. I am a bit concerned about the low contrast in REs with latitude or longitude over India, there are forest ecosystems, agricultural land, semi-arid land and deserts. I cannot explain the distributions of REs I see in Fig. 4 or Fig. 5. How good is the VPRM ? Any testing has been done? At the very least can you compare your results with global model results for seasonal cycles, e.g., in Fig. 2b ??

Line 596 : how can you explain higher CO2 sink in Nov compared to July over India (Fig. S2b suggest otherwise). also other published literature suggests higher uptake in July than November (Patra et a., ACP, 2011)

The study by Thilakan et al. can be understood as a preparatory study for future inverse modelling of CO2 fluxes over India once an in-situ observation network with sufficient coverage is established. As a starting point, it investigates the spread in CO2 concentrations simulated by current state-of-the-art global CO2 data assimilation systems and then analyzes the impact of spatial representation errors in global models on the ability to inversely estimate CO2 fluxes over India. These representation errors are caused by the inability of coarse global models to resolve small-scale variations in CO2 due to variations in topography and biospheric and anthropogenic surface fluxes.

The present manuscript is much improved compared to an earlier version and is acceptable with minor revisions. In particular, the motivation of the work is much clearer now, although the individual elements still do not perfectly fit together. The analysis of differences in CO2 concentrations simulated by different global models is interesting (and in fact alarming), but this part is still only loosely connected to the core of the study, which is the analysis of representation errors. The conclusions section is much more compelling now than in previous versions.

Overall, the study provides a number of interesting analyses that will be valuable for future inversion studies over India and therefore deserves being published. These aspects include

• analysis of the factors contributing to small-scale CO2 variability
• quantification of corresponding representation errors in global models
• quantification of the impact of these representation errors on inverse estimation of CO2 fluxes
• presentation of an approach to reduce representation errors in global models, which accounts for the impact of sub-grid scale variability in orography and surface fluxes

I only have a number of minor comments that should be addressed before publication. I trust that other issues in terms of language and grammar will be corrected during the copy-editing phase.

• Line 57: It is true that the predictability of CO2 concentrations is better for windy situations, but in these situations CO2 will be dominated by the large background while the sensitivity to regional CO2 fluxes will be small
• L67: Replace "Further" by "Furthermore"
• L73: Change "over the regions" to "over other regions"
• L94: Replace "availability of radiation" simply by "radiation"
• L126-127: The sentence could be simplified to "The month of July represents a monsoon period when both biospheric and convective activity are strong".
• L129: "In contrast" would probably fit better than "On the other hand"
• Replace "the ways" by "possible ways"
• L206: I was unable to find information on this CAMS product (version 2.2.4). Is this a reanalysis product (like EGG4)? What is the original resolution of this product?
• L207-208: I doubt that the product has a 6-hour temporal and 0.5° spatial resolution. This is probably only the resolution at which the data was obtained, not the resolution of the original product.
• L221: Replace "during the year" by "for the year"
• L223: Delete "for the optimization" because it appears twice in the sentence.
• L238: Simply write "scales not captured" instead of "scales which could not be captured"
• L257-258: Change to "As space-borne instruments measure total columns rather than near-surface concentrations, we extend .."
• L261: Here and at several other places: It would be better to write "errors" rather than "error"
• L266: Change "difference in the sub-grid scale process" to "difference in sub-grid scale processes"
• L272-273: This could be written more elegantly as ".. which describes the systematic component of the representation error and provides important constraints for inversions .."
• L295: Replace "seasonal changes" by "seasonal differences" as you have only analyzed two different months but not the whole year.
• L298: Instead of "associated mesoscale activity." I suggest to write "associated convective activity that is only parameterized in global models".
• L372: Here and later in the same sentence: Replace "grids" by "grid cells"
• L382: Replace "using this approach can be inferred as the lower bound" by "using this approach may be considered as a lower bound"
• L389: Replace "is not sufficient to justify the model's performance" by "does not guarantee a good model performance"
• L404: Here and at a few other places "while" should be replaced by "when" (i.e. "when analyzing")
• L436: The formulation "seasonally varying observations" makes no sense. An observation does not vary seasonally unless e.g. different instruments are used in different seasons.
• L441: Why should the satellite community gap-fill the observations? Standard satellite products do not provide gap-filled data.
• L449: You should also cite Zellweger et al. (2016). https://amt.copernicus.org/articles/9/4737/2016/, which shows that the compatibility goal of WMO of 0.1 ppm is achievable with current instruments but is still quite challenging. You should also replace "less than 0.1 ppm" by "of the order of 0.1 ppm".
• L460: Replace "over the land and ocean boundary" by "at the boundary between land and ocean"
• L486: The statement "The estimated column representation error is thus capable of causing significant biases in the satellite inferred CO2 fluxes over these regions" should be better backed up. How do these errors compare, for example, with the impact of XCO2 retrieval biases on regional CO2 fluxes discussed in Chevallier et al. (2007)? https://doi.org/10.1029/2006JD007375
• L570: It should be "the dependence of the representation error on sigma_bio" rather than the other way round.
• L568: It is not quite clear whether the numbers presented here are based on an analysis of the variance or only of the standard deviations. This is important because only variances (and covariances) explained by different factors can be added up to explain the total variance. Standard deviations cannot be added up in this way.
• L588: It is only the resolution of an atmospheric transport model that is a limitation, not the accuracy of the digital elevation model used to generate the model orography. Differences between different DEMs are typically very small.
• L597 and following: How does the fact that only 35% of the area of India is covered by the 9 stations affect these results? This should be discussed in this paragraph.
• L617: How good is the performance in terms of R-square? It would be good to add this information to be consistent with the statement on L613.
• L624: Again, the accuracy of the DEM is not a limitation.
• L655: Comparing Figures 4 and 5 or looking at Figure 6, I don't see an order of magnitude difference in representation errors between surface and column CO2. The representation errors in column CO2 are in fact surprisingly large.