The manuscript presents an inversion of methane emissions over India using TROPOMI satellite observations in conjunction with the WRF-GHG model. Due to the lack of in situ measurements in India, the inversion relies entirely on TROPOMI observations.

India is a highly relevant methane emitter due to its large cattle population, rice cultivation, and fossil fuel use. Quantifying Indian CH₄ emissions and verifying reported or bottom-up estimated values is of great importance. Given the current scarcity of inverse studies focused on India, this regional inversion study has the potential to make a valuable contribution to the field.

The manuscript provides helpful background on Indian CH₄ emissions and their spatial, temporal, and sectoral characteristics. The simulation setup is described in a generally clear way and appears to be well-designed, with appropriate model resolution. The model has been evaluated against TROPOMI data and observations from the Thumba station. The results are broadly consistent with previous top-down estimates of Indian CH₄ emissions. However, I find that several aspects of the WRF-GHG model configuration and the inversion setup are insufficiently explained, and in some cases may require revision. In addition, the presented inversion results should be substantially expanded to fully support the study’s conclusions. Furthermore, I recommend a careful linguistic revision of the manuscript to improve clarity and readability.

General Comments

• Choice of inversion method: Why was an analytical inversion chosen instead of an ensemble Kalman filter, which would allow for a much finer resolution of the state vector? India's political states are quite large, and it would be valuable to assess the redistribution of emissions relative to the prior also at a sub-state scale.
• Use of observations: It is unclear how exactly the observations are used in the inversion. On page 9, line 164, the authors write that the measurement vector y contains m elements, representing the total column observations where m represents the total number of observations in each political state. Does this imply that only observations at a given state are used to constrain emissions within that same state? Ideally, all observations should be used in the inversion. If this is only a wording issue, the sentence should be rephrased to avoid confusion.
• Presentation of results: The inversion results are currently presented only as total national emissions. This is insufficient. The changes in emissions at the state level should be shown. A map illustrating the posterior emissions by state would be very helpful. Could the state vector also be resolved temporally to illustrate seasonal adjustments? This would be particularly interesting given the strong seasonality of emission sectors in some states. Moreover, the comparison of model results to TROPOMI data is limited to monthly means. A more detailed comparison is needed: how well does the model reproduce individual observations? Much of the variability may already be explained by seasonal changes in concentrations, meaning that comparisons of total CH₄ concentrations are more indicative of agreement in the CAMS product than of the model performance. What do the statistics look like for enhancements only? Summary statistics such as bias, RMSE, and correlation before and after the inversion would add substantial value.
• Use of additional TROPOMI products: It would be highly desirable to include the other two TROPOMI XCH₄ products: the operational and the GOSAT-blended product. These can differ considerably. Since the authors employ an analytical inversion (which requires only a single forward model run), incorporating these additional datasets seems feasible. This could also help better assess the posterior uncertainty, which currently appears rather low in this study.

Technical Comments

• Page 2, Line 18: nearly --> more than
• Page 2, Line 28: OH^- --> OH
• Page 2, Line 36: "largest" in the world?
• Page 3, Line 49: Jones et al. (2021) and Cusworth et al. (2022) are not really appropriate references at this point
• Page 3, Line 64: "more advanced" is disputable. It's certainly different than GOSAT.
• Page 4, Line 74: Is there really no other in-situ site available in India to validate the simulation?
• Page 4, Line 87: "single-pass" --> "single overpass"
• Page 5, Line 104: This likely refers to the temporal resolution of the output, not of the model itself.
• Page 5, Line 108: Does this mean that the simulated concentrations are only affected by emissions up to 18:00 the previous day? Or are the tracer concentrations (from emissions) propagated to the following day? And is also the background/CAMS tracer re-initialized every day?
• Page 5, Line 110: Have the authors considered using a different CAMS product, such as one that is fully inversion-optimized? This might have substantially lower biases than the GQIQ product which is crucial when subtracting the background concentrations from the observations for assimilation.
• Page 5, Line 111: Only initial fields? Is the CAMS product not used to also provide the boundary condition of the background tracer?
• Figure 1: The state boundaries are very difficult to distinguish. Since these abbreviations are used numerous times, clearer boundary delineation is important.
• Table 7: The table formatting needs to be revised! Column titles must be visually separated.
• Page 8, Line 137: "Calibration was performed periodically": How often was the calibration performed? This type of instrument is known to be temperature-sensitive, hence frequent calibration is important.
• Equation 1: The summation sign is missing.
• Equation 9: Why does "TR" appear in the equation? Should the expression not just be "Φ perturbed – Φ" ?
• Page 9, Line 182: Does the optimization of anthropogenic emissions alone not lead to potential systematic errors in regions with very high wetland emissions in the northeast of the country? Have the authors considered optimizing these as well?
• Page 10, Line 184: "biomass emissions" --> "biomass burning emissions"?
• Page 10, Line 187: Are these background mixing ratios simulated by the model or derived from observations?
• Page 10, Line 193: Is also S_a a diagonal matrix?
• Page 10, Line 199: Do the authors mean that the emissions are indeed "spatially averaged" or are they saying that one parameter per state represents the total emissions for that state?
• Equation 9: The summation signs are missing. Also, what unit does x have?
• Page 11, Line 211: "Regional distribution" --> "Regional and sectorial distribution"
• Section 4.1: This section presents interesting content, but it is quite lengthy and somewhat tedious to read. A more concise and focused text would greatly enhance readability.
• Page 11, Line 213: Why is EDGARv8 used here when the inversion was performed using EDGARv7?
• Figure 2: Subfigures c–f are too small to discern meaningful details in the emission maps.
• Page 12, Line 240: Please add a reference to Fig. 3 when discussing the GFAS emissions.
• Page 14, Line 260: Both links are invalid.
• Page 15, Line 295: Vertical mixing does not reduce column mean concentrations. Could this be due to the seasonality of OH instead? Or does this seasonality really result from the combination of increased mixing and the higher sensitivity towards near-surface concentrations of TROPOMI?
• Figure 4: The upper end of the color scale is too low. Seasonal patterns described in the text (p.15, line 294) are not visible in the current plot.
• Page 20, Line 339: How do the authors derive the values of 75 (72) ppb? These are not clearly traceable from the table.
• Page 20, Line 349: The fact that the model explains 56% and 79% of the observed variability is largely due to the seasonality already captured in the CAMS product. What do these statistics look like for the enhancements only?
• Page 20, Line 350: This sentence does not make sense.
• Section 4.4: This section would make more sense if it came right after Section 4.1. This would mean that the analysis of the enhancements and the comparison with the satellite data would come before the inversion results.
• Figure 9: It is difficult to reconcile Fig. 7b with Fig. S7b. They do not seem consistent. In the supplementary figure, the comparison appears much better.
• Page 21, Line 376: How do the authors arrive at the uncertainty range of 14 to 23%? Based on the total a posteriori emissions and uncertainty, I calculate a reduction of 3.8 to 26.8%.
• Page 23, Line 429: The study’s estimate is 24% higher than the IPCC value. This means the IPCC estimate is 19% lower than the study’s result, not the other way around.
• Page 23, Line 422: Would this large effect of wetlands on XCH₄ not suggest that these emissions should be optimised?

Overall, this manuscript addresses a highly relevant topic and contributes important knowledge ond Indian CH₄ emissions. However, several methodological clarifications and improvements to the result presentation are needed before the manuscript can be recommended for publication.