1) General comments

Methane is second most important greenhouse gas in Earth's atmosphere,

and the Arctic region is a potential large source of CH4 emission.

Emission detection and monitoring is therefore an interesting and

relevant research question. The authors compare emission estimates

based on surface-only and TROPOMI based inversions using two different

retrieval products. A sensitivity study is conducted to asses the

robustness of the results. Since the article adresses a relevant

sicientific topic from an inversion modelling perspective, it

should be published after consideration of the specific comments

given below.

2) Specific comments

*) page 4, line 99: the inversion method used in this study is the same

   as in Ward (2024). A few lines about the general setup of this method

   would make the rest of the section easier to follow for those readers

   who are not familiar with this method and don't have the time to read

   the referenced paper (e.g. what is the "tuning phase" (line 115) or

   "MCMC sample" (line 119), or how is the uncertainty interval (line 118)

   calculated?).

*) page 5, line 108: in some models negative emissions are interpreted

   as uptake instead. Why is that not considered here?

*) page 6, lines 156-158: I interpret regridding as calculating the

   average of all observations falling into the gridcell of the

   mentioned dimensions. This already reduces the data density of the

   observations, so why is additional reduction step necessary? Would

   using larger regridded "observations" without the additional

   reduction step have the same effect as the current approach?

*) page 9 line 203-205: the XCH4^{model}_{pert} is apparently valid

   from surface to maxlev (right-hand side of supplement eq 4 =

   left-hand side of supplement eq. 7). That should be made clear in the

   text as well, since now it's just "we have equation 2 and subtract

   two other terms".

      So these lines could be clarified by first stating why you would

   need XCH4^{model}_{pert}, and then how you calculate it.

*) page 9, equation 4: if the first summation is from "1 till maxlev",

   shouldn't the second one be from "maxlev+1 till n"? In other words,

   which of the two summations includes maxlev? Related to that is

   equation 3 and the rest of the derivation in the Supplement.

*) page 9, line 220: please clarify the CAMS dataset that you're using

   and why you use an outdated version (based on the "data availability"

   section, you could have downloaded one in 2023).

   The problem with a "CAMS dataset" is that there are multiple datasets

   providing methane estimates, see

      https://ads.atmosphere.copernicus.eu/datasets?q=methane&limit=30

   Neither of the datasets listed here is from 2019. The only dataset

   that I found using a "v19r1" or similar versioning scheme is called

   "CAMS global inversion-optimised greenhouse gas fluxes and concentrations"

   for which the "Evaluation and quality assurance (EQA) reports" on the

   documentation tab point to a report by Segers, not to Inness.

*) page 10, line 229: why use EDGAR v6? As you mention in section 4.1

   (line 492-494), emission totals over Alaska may vary significantly

   according to the version of the database being used.

3) Technical corrections

*) page 1, line 80: Since the acronym HBMCMC is used here, I would

   capitalise the word "hierarchical" as well.

*) page 5, line 125: the 78W should be 78N?

*) page 6, line 156: please clarify if the regridding resolution is

   latitude x longitude or the other way around? The same holds for

   the other spatial resolutions mentioned hereafter.

*) Supplement page 1, eq. 6: the second summation term should have

   n instead of 1 as it's upper level

*) page 19, line 387-388: there is no figure 9A or 9B.

Overall, the study appears to be well justified. The research gap is clearly articulated, as is the importance of investigating this topic and the substantial challenges associated with it. The use of recent observations positions the study as a meaningful and timely contribution, particularly in regions known to contain significant gaps in observational coverage and monitoring infrastructure, and which represent an important source of methane emissions.

I think it is a great contribution that the study examines uncertainty through the sensitivity of inversions to various configurations. However, I believe that these results could have been given greater prominence, especially considering that one of the stated objectives of the manuscript is precisely the quantification of uncertainty. The analysis places more emphasis on RMSE reduction than on RMSE spread, which is the quantity that more directly reflects uncertainty. I expected the manuscript to be more tightly centered on uncertainty quantification, in alignment with what the title suggests.

It is also noteworthy that the study demonstrates that, although TROPOMI observations provide a significant advancement, important observational gaps persist. The period from October to March remains essentially unobserved, suggesting that future missions could meaningfully support Arctic monitoring. Presenting the progress that can be achieved with the current observational record—while also highlighting the remaining potential—is highly valuable.

Below, I provide my comments section by section, indicating numbering at both general and detailed levels, and referring to specific lines when applicable:

0. Abstract: The abstract is concise and clearly presents the study. It effectively communicates the context, objectives, and main findings.

1. Introduction: The introduction appropriately presents the key elements that frame the research, identifies the gaps and challenges, and convincingly justifies the importance of studying the Arctic. Given that a substantial portion of the analysis focuses on tundra regions, I suggest including a land-cover map of the study domain, or alternatively a map distinguishing tundra and anthropogenic emission sources.

2.1 The work of Ward et al. (2024) is cited frequently throughout the manuscript. In several instances, the manuscript is not sufficiently self-contained, and the citation alone does not provide enough context for the reader to fully understand the methodological or conceptual point being referenced. While it is reasonable to avoid restating the entire content of Ward et al. (2024), the manuscript should nonetheless include the essential information needed for it to be understandable on its own.

Line 99: The methods section begins by citing Ward et al. (2024), followed by an explanation of the method. It is unclear whether the description corresponds directly to Ward et al. or whether it represents an adaptation or extension. A brief summary would help clarify this, as well as an explicit statement that further methodological details can be found in Ward et al. (2024).

2.4 Figure 3, which presents the average footprints, is not referenced in the discussion. It would be valuable to connect the inversion results to the sensitivity patterns shown in this figure, particularly to assess how the inversions based on each product relate to sensitivities over tundra and anthropogenic regions. It would also be helpful to include the sensitivity of the BRW station in the figure.

2.6 The domain used for the inversions—particularly in the sensitivity tests—was not entirely clear. Figure 1 defines domain, region, and measurement sites; however, since multiple configurations are tested, it is important to explicitly clarify whether the same domain is consistently applied (if that is the case). It would also be helpful to explicitly state that the analysis focuses on the NSA region, even if this seems implied. Furthermore, to more directly assess uncertainty, it would have been interesting to include an experiment involving, for example, 10 perturbed prior ensembles and to evaluate the resulting spread.

In Figure 4b, the color scheme overlaps with that of Figure 1, which generated confusion. For instance, the Ward domain appears in orange in Figure 4a but in black in Figure 1.

I recommend relocating Figure 4 to the Results section, as it corresponds to the first point addressed there.

3.2.1 In this subsection, the inversions correspond to the NSA, but Alaska is used as the domain—is this correct?

3.2.2 – Figure 6 The shift between TROPOMI-OPER and BRW-based inversions is not addressed in either the results or the discussion. Although the manuscript comments on monthly matches, the phase differences are particularly striking and, in my view, merit discussion. This may even be connected to the sensitivity analysis previously conducted for TROPOMI.

3.3 – Figure 7 The legend lists “Uniform prior” twice. I assume that the solid line corresponds to the posterior of the Uniform-prior experiment and the dashed line to the prior.

3.3.4 – Lines 387–388 No Figures 9A or 9B are present.

3.6 To address uncertainty more directly, I recommend evaluating the spread of RMSE values for each TROPOMI product—that is, assessing how wide the RMSE range is across the experiments. The discussion currently emphasizes the RMSE magnitude for individual experiments and highlights improvements, but the variability among experiments is not addressed.

3.7 Tables S1 and S2 should be included in the main manuscript.

Line 435: The reference does not correspond to Figure S15; I understand that Figure S16 is intended instead.

6. Conclusions Line 684: The recommendations from Tsuruta should be briefly summarized; including new citations in the conclusions is not advisable. The same applies to line 695.