This paper uses an improved flux divergence algorithm to estimate sources of CH4 in the middle east. The results are compared with different emission inventories, and discrepancies are noted with both over and under estimations of emissions. Overall the paper is well written and informative, the method seems sound and the results are interesting, timely and relevant. I am happy to recommend publication.

One weakness was some missing citations of recent work that is relevant. You cite Beirle et al., 2019, but should really also consider Beirle et al., 2022 which contains version 2 of the flux divergence method. Sun, 2022, provide further developments to the method. Although both of these are for NO2, they are for the same sensor and there is sufficient overlap with CH4 that merits their mention. De Foy and Schauer, 2023 estimate CH4 emissions in urban areas, including Tehran. It would be interesting to see the difference in estimates. Finally, Roberts et al., 2023 specifically look into the impact of missing data on CH4 flux retrievals. There may be further papers – it would be good to compare this paper with the latest publications.

Line 167 to 187: I was a bit skeptical of the boundary layer treatment: fixing PBLH at 500m seems rather crude. However, I notice that you published this already in your previous paper. I do wonder what would happen if you used actual PBLH from ERA5, or at a minimum if it would be worth plotting average PBLH over your domain.

Coastal regions present a particular challenge in terms of data filtering. Some of your figures do seem to suggest that there are anomalous retrievals near coastlines. It might be that more careful filtering of boundary retrievals is necessary compared with the default land/water mask used. This could be discussed for future reference.

Line 325: Is it really feasible that a farm in the desert would produce a detectable amount of CH4? I think that this should be backed up with a bit more information if it is to stay here – information about the agricultural emissions, comparisons with farms with known CH4 emissions, threshold values for TROPOMI.

Minor points:

Fig. 5g&h: “Mehttane”

Line 137: despite *the fact* that the three

Line 449: 3 kg/m2 (remove extra /)

References:

Beirle, S., Borger, C., Jost, A. and Wagner, T., 2023. Improved catalog of NOx point source emissions (version 2). Earth System Science Data Discussions, 2023, pp.1-37.

de Foy, B., Schauer, J.J., Lorente, A. and Borsdorff, T., 2023. Investigating high methane emissions from urban areas detected by TROPOMI and their association with untreated wastewater. Environmental Research Letters, 18(4), p.044004.

Sun, K., 2022. Derivation of Emissions From Satellite‐Observed Column Amounts and Its Application to TROPOMI NO2 and CO Observations. Geophysical Research Letters, 49(23), p.e2022GL101102.

Roberts, C., IJzermans, R., Randell, D., Jones, M., Jonathan, P., Mandel, K., Hirst, B. and Shorttle, O., 2023. Avoiding methane emission rate underestimates when using the divergence method. Environmental Research Letters, 18(11), p.114033.

This study presents an interesting attempt to further improve the divergence method for estimating methane fluxes, by correcting for divergence in the dynamical flow and temporal filtering of retrieval artefacts. The divergence concept is interesting, but can be puzzling in its implementation also. It is important that this is done well, and doesn't overlook anything important (such as the assumption of stationary state, which is probably satisfied reasonably well but still a simplifying  assumption). Promising results are obtained suggesting that the method works, and yields useful additional information about the intermittency of emissions. However, as explained further below, the proof that emissions that look better are indeed better is missing. This makes the validation of the proposed inprovements currently too weak in my judgment. Besides this most important point of my review there are a few other issues to clarify, including the deriviation of estimation uncertainties. With those issues solved I do not see a reason to uphold publication, but it is important that it is carefully done.

GENERAL COMMENTS

In Liu 2021 a great job was done validating the divergence implementation to methane using GeosChem. Those results looked promising, but also suggested room for improvement. It would be interesting to know if the improvements that are proposed here improve the comparison presented there (which has the same issues with elevation, surface albedo influences could easily be mimiced). This raises the question why it was not done. This concerns not only the estimation of emissions, but also the corresponding emission uncertainties. It is not obvious to me that altering the wind field to make it divergence free improves the comparison between this simplified 'model' of the atmosphere and the TROPOMI observations, unless the observations themselves are corrected  for the influence of dynamical divergence influences.

SPECIFIC COMMENTS

l170: The treatment of methane in EAC4 is not explained in Inness et al (2019), but from what I understand it uses a mass balance method to maintain the observed zonal mean background concentration. This means that there are "emissions" in the surface layer of the model to prevent the concentration from going down due to the atmospheric sink. Then what is mentioned here about only transport driven methane is incorrect. Even worse, the distribution of these emissions (or concentration corrections if you wish) does not resemble reality, which questions the realism of the simulated subcolumn above the PBL. But if the EAC4 column above PBL does not vary a lot on the spatial scales of interest this may not be much of an issue. The question then is if the method really benefits from turning total column into PBL columns. Wouldn't the method perform as well without subtracting EAC4 columns?

l192: Besides divergence, orographic changes also influence XCH4 because they influence the weight of the stratospheric subcolumn - where methane mixing ratios are significantly lower. I do not see how this effect is accounted for in the method that it used. For a fixed PBL height above the surface, the EAC4 methane column should correlate with origraphy. I wonder if the variation in EAC4 is taken into account, and can actually be at the required spatial scale.

l198: The benefit of correcting w for divergence is not clear to me. The TROPOMI data have the imprint of the wind divergence, which the flux divergence method allows to elegantly account for. However, if you tweak the wind fields to remove divergence then I expect you end up projecting the TROPOMI observed immpact of wind divergence on the surface fluxes. Or do you correct the TROPOMI data for this divergence component? If so, that should be explained better.

l285: I understand that by randomly selecting 80% of a time series a standard deviation can be computed, and that this standard deviation is larger when the time series is noisier. But what justifies using 80% to derive a presumably 1 sigma uncertainty range? Wouldn't it be better to take the standard deviation for individual days and divide by the square root of N or something like that? The errors in figure 5 look very optimistic to me, given the scatter plots in Liu et al, 2021 (for perfect winds and without measurement errors).

l318: But under low wind speed the XCH4 enhancement is much larger, and therefore easier detectable than at high wind speed. Then how do you relate a threshold XCH4 enhancement to a threshold emission enhancement?

Figure 5, caption: Averaged or total emissions?

Figure 5b: Is the arc above Riyadh real, or a remnant of the surface albedo related feature in figure 3?

Figure 7: The information about EMIT was in the caption of Figure 6 also. I advise to mention it once in the main text and remove it from the captions.

l408: How do you know that the 5 selected regions are hardly influenced by retrieval issues?

l422-423: Why not use the same filtering of 3km/km2/h for the inventory to quantify this difference?

Figure 8: this figure would be easier to read if TROPOMI is one one side of the bars and the inventories on the other side. Right now they are mixed. According to the color legend the pink bar is 'CEDS energy related CH4 emission' while according to the caption it is the total emission of sources > 3kg/km2/h.

l428: more constant than what?

l450: How do you know that if the emissions are constant the have a constant emission factor? I do not see how your method can separate between the emission factor and activity (wich are multiplied in inventories to obtain the emission).

TECHNICAL CORRECTIONS

l145: asses io access

l198: proposed io imposed?

l252: or caused

l327: we found sources

l340: is aim?

l360: 'mentel'?

l370: remove 'the area'

l317: 'explanation' io 'explanations'

l317: 'for the emissions' io 'about emissions'

Figure 6, caption: 'observations in 2019', 'the EMIT instrument', 'the VIRRS instrument'

Figure 7, caption: see my comments about figure 6

l506: 'a temporal filter' io 'the temporal filter'