The authors present a study on estimating methane emissions in Finland from both bottom-up and top-down approaches. In particular, the focus lies on the comparison of an ensemble of different bottom-up estimates and, subsequently, optimizing both anthropogenic and natural CH₄ emissions simultaneously using different set-ups of prior estimates and uncertainties. This study shows a relevant example of estimating CH₄ emissions from different sources at country scale. Additionally, since the study encompasses a study period of more than 20 years, it gives a valuable insight in long-term CH₄ emission trends in a northern European country.

In my opinion, this study is well prepared and carefully reflected upon. However, I see a major weakness in the presented manuscript, namely the description and documentation.

I can see that the authors have put a lot of thought and effort into this study and have come to valuable and conclusive results, but the current presentation does not do justice to the work. I would strongly recommend revising the manuscript keeping in mind the following advices, which will help the reader to follow the presented work and understand the underlying train of thoughts:

• Provide reasons and constraints for the choices of the set-up

• Provide equations to explain the calculations

• When describing figures, start with the general findings and end with more detailed ones (e.g. first describe the whole period of time and then individual years)

• Be more generous with putting cross-references to other sections of the paper, where details of a topic have been discussed or will be discussed, so the reader knows where to find the corresponding information

More specifically, in my view, there are four relevant points which should be addressed in the revision of the manuscript:

1. I would strongly suggest to extend Section 2.2 (“Atmospheric inversion model CTE-CH₄”) where the details of the inverse modeling set-up is explained. I assume this paragraph was kept short since the CTE-CH₄ model has been explained in detail in in a different paper, but nevertheless crucial information are missing.

   First of all, the equation of the ensemble Kalman filter that was used in the study should be included and the different components explained. Otherwise, explanations like “The size of the ensemble is 500 with a time lag of 5 week” are incomprehensible. Additionally, some basic information on the TM5 atmospheric chemistry model (e.g. is it Eulerian or Lagrangian, is it used in forward or backward mode, was a spin-up period or additional input-data for the initial conditions used etc.) should be given. The model and inversion domain is also not very clear: first it is written that optimized CH₄ estimates are provided over “high northern latitudes”. Later it is written that the fluxes are also optimized at 1°x1° in Canada, the USA, Europe and Russia. So not only in high northern latitudes or just in the northern parts of these countries? Also, the transport model has a global resolution of 4°x6° with a zoomed grid over Europe at 1°x1° with a 2°x3° around it, but how large is this ”around zone” and what area (longitude and latitude) is defined as Europe? I think it would be very helpful to illustrate this by having a map showing the different zones of the transport model and/or the inverted domain. For the observations in Finland, the author’s should provide a table with the sites including their full name, exact locations and altitudes, either in the main text or the supplements, as an addition to Figure 1.

   Moreover, I think the authors should consider splitting this section (2.2) in three different subsections: one for the transport model, one for the inversion set-up and one for the observations. If the authors prefer to keep the inversion setup and transport model together, that would also be appropriate, but in particular the section on observations (P5, L140-151) should, in my opinion, be a separate subsection.

2. The authors have clearly put a lot of thought into estimating the prior uncertainties, which is excellent, but the explanation in Section 2.2.2 is sometimes difficult to follow.

   First of all, which uncertainties are used for the anthropogenic fluxes, is it also 80% and 20%? Also, the calculation that are described from P6, L179 is only used for one of the inversion set-ups, which should already be highlighted in the description, otherwise it is unclear why there is a default uncertainty in the first place. It is written: “We made the test for the post-2010 period, so we calculated monthly averages for the 2010–2017 period” – which test and why only until 2017 and not 2021? I would highly recommend explaining this calculation with the help of an equation, it will be much easier to follow your description.

3. It would be interesting if the authors could provide some additional information on how the area of Finland is “defined”. In Figure 1 on page 8, defined areas of northern and southern Finland corresponding to Figure S1 and Figure 7 are shown. However, these areas exclude small parts of Finland and include larger parts of Sweden and Russia. Later in Section 3, the prior and posterior CH₄ emissions in Finland are shown. Since the optimization was at 1°x1°, these estimates probably also include emissions outside the Finish borders, which is evident from the Figures S3-S6. I think it would be nice to add a clarification of the area and/or a small discussion on the share of emissions, that actually lie outside of Finland.

4. Throughout the paper I noticed numerous grammatical errors. I have pointed out some of these in the technical comments, but to correct them all would be beyond the scope of this review. The authors should also pay some attention to tenses: sometimes the authors switch between past and present tense for no apparent reason. The grammar of the manuscript should be checked thoroughly before resubmitting the paper (I would suggest using a grammar checker for the whole text).

Specific comments

P1, L19:

For people studying CH₄ it may be obvious what is meant by "renewed growth rate in 2007". However, I think it would be beneficial if you could add, for example, "renewed growth rate in 2007, after a significant decline in growth at the beginning of the millennium" for further specification.

P2, L20:

When you say "record growth rates", are you referring only to 2020 and 2021? That is a bit unclear. You could put the years in brackets for clarification.

P2, L22:

Please add the atmospheric lifetime and GWP of CH₄ in numbers for completeness.

P2, L27:

The “(UNFCCC)” is a bit confusing. Is it for clarification of the abbreviation and if so, why at this place? Or do you want to say “by the UNFCCC”?

P3, L67:

Another strategy for constraining the sources in inverse modeling approaches is to use co-emitted gases such as Ethane, e.g. Thompson et al., 2018; Rice et al., 2016 (see references). It is not necessary to mention it, but you can consider including it for completeness.

P3, L74:

You mention that the CH₄ estimates vary considerably in Finland. It would be nice if you could already include a range of annual CH₄ emissions in numbers to show how large the the discrepancies are with the corresponding sources. Alternatively, you could make a cross-reference to section 3.1, where the issue is discussed.

P4, L95-L96:

I think it would be good to add the explanation for the abbreviation “NGHGI Fi”. Even though it may be obvious that you mean the NGHGI of Finland, it is the first time you use it in this abbreviation and should therefore be explained.

P4, L97:

Would it be possible to add an explanation of “Tiers 1, 2 and 3”? Personally, I’m not familiar with this term and I don’t think it is common knowledge.

P4: L109-L111:

The first sentence of this paragraph is confusing. Was CAMS-REG created in 2020? Or are the emissions from 2005-2018 based on the numbers from 2020? Or are the reports from 2020 used to create the emissions from 2005-2018 but based on the corresponding years? Please reformulate this sentence and if possible, also explain the abbreviation “LRTAP” and “NEC”.

P5, L144:

I would suggest including a map and/or a table with the 175 global stations in the supplements for completeness.

P5, L148-150:

Could you provide one or two examples of which “site-specific characteristics” were taken into account and how they influenced the error estimation?

P6, L63:

With “natural prior from Saunois et al.”, do you refer to wetland fluxes only or is it really all natural fluxes combined? It is a bit unclear because fire, termites, geological fluxes etc. are also natural CH₄ sources.

P6, L66:

In section 2.2, you have described well the atmospheric sinks that you have considered for the inversion. However, if I understand correctly, you do not include the CH₄ soil sink as negative prior emissions. Is that correct, and if so, could you explain why you have excluded them?

P6, L175-L176:

It would be nice if you could add an example of the range of annual wetland emissions in numbers to make this more illustrative.

P7, L198:

I think it would be good to also explain the reason for the different time periods (shown in Table 1) in this paragraph.

P8, L211- P9, L29:

It would be helpful if you could give a little outlook, for what the different data types described in the subsections of 2.4 will be used for. Otherwise it is a bit incomprehensible, why you suddenly start writing about flux measurements, global freshwater emissions and fire inventories. The subsections are also so short that I would suggest combining them.

P11, L268:

With “Finland’s annual total emission estimates” you are referring to the bottom-up/prior emissions I assume? If so, please add it for clarification.

P11, L269-L270:

Please re-write this sentence. I would suggest: “As discussed in section 3.1, the range of total prior emissions was large. The range of optimized emissions was smaller, especially between 2009 and 2020 with an average range of 0.57 Tg yr^-1, while the range of prior emissions was 0.69 Tg yr^-1 in the same period.”

P12, L283-L286:

Please also re-write this sentence. I would suggest: “The order of the emission estimates was also maintained after optimization: the posterior emissions of Inv_{JSBACH_CAMSREG} were the highest and Inv_{GCP_EDGAR} the lowest. The three posterior emissions using LPX-Bern DYPTOP as prior lay between these two estimates, with the inversion using the varying uncertainty estimates (Inv_{LPX_EDGAR_UNC}) showing the lowest estimates of the three.”

P12, L288 – P14, L297:

I assume you forgot to put a references for Table 2 in this paragraph?

P13, L306:

I would add “In 2021, there were only three posterior emission estimates” to make it clearer that there is a difference to 2020.

P14, L307:

Could you clarify how the differences diverged between 2020 and 2021? And did you only use the EDGAR set-ups for comparison the two years?

P17, L351-L352:

Are the small uncertainties in the winter months a result of the low natural emissions during those months? And could you clarify “In February and March, both the natural CH₄ emissions and the uncertainties were small regardless of the uncertainty estimates used” please? Do you mean “both the posterior natural CH₄ emissions and the uncertainties regardless of the prior uncertainty estimates used“?

P19, L385 – P20, L424:

In section 3.4, you use the full names of the observation sites multiple times. However, the only reference that you provide for the sites is Figure 1, where only the abbreviations of the sites are given. As mentioned in my first general comment, a proper documentation of these observation sites would be very helpful and I would suggest to use the abbreviations of the sites in this section, so that they are easy to find on Figures 1 and 11.

P24, L499:

I assume the “CH₄ emissions” from Feng et al. refer to global CH₄ emission? I would suggest to add this information at the beginning of the sentence.

Technical corrections

E.g. P1, L18-L19, P2, L34-L35:

To make the paper more pleasant to read, I would suggest to avoid double brackets like “(15.15 ppb in 2020 and 17.97 ppb in 2021) (Lan et al., 2024)” and brackets inside brackets like “(CAMS-REG,(Kuenen et al., 2022))” or “ (GAINS, Höglund-Isaksson et al. (2020))”.

You could instead just put a comma: “(15.15 ppb in 2020 and 17.97 ppb in 2021, Lan et al., 2024)”, “CAMS-REG, Kuenen et al., 2022)” and “(GAINS, Höglund-Isaksson et al., 2020)”

P2, L22:

I don’t think “CH₄’s” is technically incorrect, but it looks a bit unusual. Maybe write “short atmospheric lifetime of CH₄” instead.

P2, L28-L29:

Please check the sentence structure. I would suggest to write “They are based on a bottom-up approach that starts at the sources and estimates how much GHGs is emitted by each source.”

P2, L48:

“All countries” → “All these countries” makes it clearer

P4, L89:

“agrees the best with observations” → “ agrees best with the observations.”

P4, L95:

Why do you write “(Intergovernmental Panel on Climate Change, 2019)” instead of just “(IPCC, 2019)”?

P4, L97:

“category, (LULUCF), are” → either write “category (LULUCF) are” or “category, LULUCF, are”.

P7, L207:

“total CH₄ emission” → “total CH₄ emissions”

P8, Figure 1:

I’m a bit confused by the caption “black and old”. The color of the circles looks rather gray and I assume you mean “bold”?

P12, P13 & P16, Fig. 5, 6 & 7:

I would suggest to also put “prior” and “posterior” in the legends as was the case in Fig. 3.

P12, L285:

(Inv_{LPX_EDGAR_UNC})) → (Inv_{LPX_EDGAR_UNC})

P16, L324:

“posterior emission” → “posterior emissions”

P16, L125:

I’m not sure if “with the VERIFY ensemble” is correct. Do you mean “in the VERIFY ensemble”?

P16, Fig 7:

Maybe you could use a different color for the freshwater emissions? Despite the different line style, they are a bit hard to spot.

E.g. P26, L552 and 555:

When talking about emissions, use “high” and “low” instead of “large” and “small”.

References

Thompson, R. L., Nisbet, E., Pisso, I., Stohl, A., Blake, D., Dlugokencky, E., Helmig, D., and White, J.: Variability in atmospheric methane from fossil fuel and microbial sources over the last three decades, Geophysical Research Letters, 45, 11–499, 2018

Rice, A. L., Butenhoff, C. L., Teama, D. G., Röger, F. H., Khalil, M. A. K., and Rasmussen, R. A.: Atmospheric methane isotopic record favors fossil sources flat in 1980s and 1990s with recent increase, Proceedings of the National Academy of Sciences, 113, 10 791–10 796, 2016.

The study presents the estimation of methane emissions in Finland from bottom-up and top-down approaches using different model ensemble methods and optimizing natural and anthropogenic CH₄ emissions using different prior estimates and uncertainties. The long-term study of more than 20 years strengthens the long-term CH₄ emission trends in Finland.

Though the authors have done good research on the methodologies and resources, in my opinion, the presentation of the manuscript needs careful assessment and major improvements to showcase the efforts that have gone into the study.

The methodology session needs more clarity and descriptions with respect to the model set-up and calculations that have been specifically used to carry out the study. 

There are also many technical and grammatical corrections that need to be accounted for thoroughly.