General comments:

This paper uses firn air measurements from two Greenland sites (NEEM and NGRIP) to investigate the Arctic atmospheric methane history over the 20th century. A firn model is applied first to NEEM to demonstrate model performance, then to NGRIP to try to infer the Arctic methane atmospheric history.

A key assumption of this study is that the Arctic CH4 atmospheric history is uncertain but that the atmospheric histories of the other six gases (CO2, SF6, CFC-11, CFC-12, CFC-113 and CH3CCl3) are known with sufficient accuracy to constrain the firn model. More should be added to justify this assumption - I am not convinced. I do agree that it is a problem that the Arctic methane history is not known as well as has been assumed in previous firn model studies. However, the CO2 atmospheric history from Buizert et al is created in much the same way as CH4 (with an assumed offset from the SH ice core record), but has the added complication that CO2 has the possibility of elevated levels in NH firn due to in situ artefacts (e.g. mentioned in Buizert et al and elsewhere in the literature) - this could affect the ability of CO2 to constrain the firn model. The 14CO2 atmospheric history (relevant for NEEM, but unfortunatly not measured at NGRIP) is probably quite reliable when it is based on atmospheric or tree ring measurements. The halocarbon histories are based on estimates of emissions, but these also have inherent uncertainty (the emissions themselves are due to reported production/sales, assumed emission functions, and atmospheric lifetimes and therefore have uncertainties).  I am not convinced that the atmospheric history of CH4 is significantly more uncertain than these other gases, I think all are known to some extent, but not perfectly.

In addition to the question of how well atmospheric histories are known, it is also relevant to consider how well different gases can constrain firn diffusivity. Halocarbons measured in the deepest few firn samples at both NEEM and NGRIP are very close to zero, so do not provide a strong constraint on diffusivity in that region of the firn. As discussed at line 307, it is the region below about 74m at NGRIP that is used to infer the CH4 atmospheric reconstruction before 1980. The blue, orange and red lines in Figs 5 and 6 have a large spread below 74m for CH4 and CO2, but there is not a very large spread for the other gases, with the spread for some of these gases dropping rapidly to zero as depth increases. This shows that the modeled mole fraction profile for the CFCs, SF6 and CH3CCl3 in the deep firn is not very sensitive to the diffusivity profile, and consequently that the diffusivity profile is not as well constrained by these gases. It has been pointed out in previous studies that methane provides a strong constraint on diffusivity in the deep firn, but, as the authors note, only if the atmospheric history is well known, and unfortunately the authors are correct that it is not well known in the Arctic. CO2 would provide a similarly strong constraint on diffusivity, but I would suggest that the Arctic CO2 atmospheric history is also not well known and has the possibility of in situ artefacts in Arctic firn, as mentioned above. Thus, calibrating the firn model without CH4 for NGRIP, then expecting to reconstruct atmospheric CH4 is risky, and I believe the results show that it has not been successful (the model appears not to have been well constrained by the observations used). 

The most important contribution of this paper is questioning the assumption of a known Arctic atmospheric methane history for constraining firn models for Greenland firn sites. This has consequences both for calibrating firn models and for interpreting the CH4 north-south gradient in terms of emissions, as the authors discuss. However, as I have said, I believe the Arctic atmospheric histories for the other gases should be similarly questioned. I am not convinced that substantial conclusions have been reached in this study. The result that it is difficult to identify the atmospheric CH4 history that consistently reproduces the depth profiles of CH4 in NEEM and NGRIP firn is due to the fact that the firn model has not been adequately constrained by the other gases. The last 2 sentences of the abstract say that a consequence of this result is that the Artic CH4 history should be considered preliminary - it may be true that the methane history is not well known, however is not a consequence of that result. Rather, it is a prior assumption that has not changed as a result of the study.

While this study does highlight the deficiency that we don't know Arctic atmospheric CH4 well, in my opinion it doesn't go any way towards solving it. This makes me question the value of the study as it is currently presented.

Specific comments:

A conclusion in the abstract and at line 374 that "We find that, given the currently available firn air data sets from Greenland, reliable reconstruction of the Arctic CH4 mole fraction is possible only back to the mid 1970s" - atmospheric observations began around 1980, so this isn't much of a result.  The title of the paper is 'Towards reconstructing the Arctic atmospheric methane history ...', but the study doesn't move very far towards that goal.

Line 61 - "The NEEM-S1 data are notably higher than the ice core data after ~1850." The NEEM-S1 data after 1850 are fairly consistent with the Blunier et al 1993 data in Fig 1. The NEEM-S1 data are definitely higher than the Nakazawa data, but some of the Nakazawa data are lower than the SH Law Dome data which is unrealistic. Rhodes et al note that the uncertainty in absolute mole fraction of the NEEM-S1 data is about 6-9 ppb, and that that is a limitation to deducing the interpolar gradient, but perhaps the NEEM-S1 are our best chance at the moment to reconstruct NH methane between 1850 and 1945, seemingly better than the firn reconstruction presented here. The NEEM-S1 data were mentioned once in this study but otherwise dismissed (unfairly, in my opinion). 

The strategy with prior and calibrated diffusivity profiles is not clear to me. For example:

Line 177 - "The diffusivity profile optimised for the CIC model was tuned for our model" - what does this mean? Was the CIC profile used as a prior then improved by comparing to observations?

Line 182 - What diffusivity profile gave the RMSD value for NEEM of 0.83? Is this the same as the case shown in Fig 2?

Line 197 - was that the initial diffusivity from equation 4 or Ishijima et al (2007)?

Lines 198-203 - This paragraph is a little hard to follow, it became clearer as you read further, but could be improved. For example, line 198 "We examined the different sets of profiles" .. which different sets? (It becomes clearer, but is confusing at this point). Line 201 - "We prepared 100 different sets" - at this point the reader wonders how they are prepared, this also becomes clearer (page 12), but if this information was given when the steps are first discussed, it would improve readability.

Line 222 - which diffusivity profile was used in Fig 3? Eqn 4, Ishijima or a tuned profile?

Why aren't the NGRIP results corresponding to the diffisivity profile giving RMSD=0.51 shown as a case (e.g. dashed black line) in Figs 4, 5, 6, 7 and 8? This would be good to see.  

Fig 2 - It is difficult to see some of the observations, particularly CH4 in the deep firn. Could the observations be shown more clearly?

line 212 - the atmospheric history is not quite monotonic, so there could be more than one time with atmospheric mole fraction matching the mole fraction at the firn depth - how is that handled? Was the atmospheric history smoothed?

Line 230 - at this point I'm already wondering what the modeled CH4 depth profile at NGRIP looks like with the Buizert et al atmospheric scenario in the model, but I need to wait.... 

The colored lines (red, orange, blue) cover many different diffisivity profiles, some of which don't fit the firn data well at all, particularly the blue cases. Is it worth showing the blue cases at all? At line 293, they are described as "less likely", but many of them simply do not fit the observations. Could the red group be split into two to highlight the really good cases? Do the better diffusivity profiles tend to fit all gases well, or do some profiles fit some of the gases well and others not so well, and vice versa (for groups of gases)? 

line 297 "suggesting that the CH4 mole fraction may have been lower than the initial modeling scenario" - I am not convinced that this is a robust result. I am not convinced that the atmospheric scenarios are known more accurately for the other gases, or that they provide sufficient constraint on the model so that it can be used to infer the CH4 history, as discussed above. 

Line 309 - "The differences between the initial and corrected atmospheric CH4 scenario from these three deepest data are up to ~ 100ppb" - because the model is not well constrained by the other gases.

Line 313 - "NGRIP firn data suggests decreased CH4 mole fraction from the 1950s to 1970s in any case, albeit with large uncertainty" - I do not believe this is a robust result, for reasons given above.

Line 320-322 - if I understand this correctly, the CH4 history reconstructed from NGRIP gives a larger model-data difference at NEEM than the original history, is that not indicating an inconsistency?

Umezawa et al. used a suite of gas measurements from NGRIP firn air (CO2, CH4, SF6, CH3CCl3, CFC-11, CFC-113, and CFC12) in combination with a firn model to reconstruct the atmospheric history of CH4 in the northern hemisphere (NH). Although the firn air samples were collected close to 20 years ago (in 2001), a great care has been taken to use state-of-the-art (or close to state-of-the-art) measurement techniques to achieve analytical precisions that are comparable or better than present-day modern atmospheric measurements. This is not a trivial merit and I think the authors should be commended. Following precedents set by previous studies of firn air (e.g., Rommelaere et al., 1997; Trudinger et al., 2002; Witrant et al., 2012; Buizert et al., 2012), Umezawa et al. used a forward gas transport firn model that takes in a “known” atmospheric history of a certain gas as an input and produce the expected mole fraction of that gas vs. depth profile in the open porosity of the firn. The difference between the expected mole fraction depth profile vs. measurements is then used to tune the “effective diffusivity” for this particular firn air sampling borehole (which is the Japanese firn sampling borehole at NGRIP).

A previous study by Buizert et al. (2012) set a precedent by including CH4 as part of the suite of gases used to tune the effective diffusivity at the NEEM ice core site. Buizert et al. (2012) achieved this by first making an educated guess about the “known” atmospheric history of CH4 in the NH. However, in this study Umezawa et al. challenge this assumption, treat the NH atmospheric history of CH4 as an unknown, and only used the other six gas measurements (CO2, SF6, CH3CCl3, CFC-11, CFC-113, and CFC12) to tune the effective diffusivity profile for NGRIP. As a result, the atmospheric CH4 history reconstructed by Umezawa et al. has larger uncertainties; from this, Umezawa et al. argue that we cannot take the NH CH4 history for granted as a known variable to tune effective diffusivity profile for ice cores collected in the northern hemisphere and to certain extent, we also do not know the true atmospheric history of NH CH4 before the 1970s.

The main conclusion from of Umezawa et al. study (to which precision do we know the NH atmospheric history of CH4) is potentially an important one, so I would recommmend the manuscript for publication if the following comments are sufficiently addressed.

Major comments:

1. As reviewer #1 pointed out, it is not immediately clear whether the atmospheric histories for the other six gases outside of CH4 (CO2, SF6, CH3CCl3, CFC-11, CFC-113, and CFC12) used to tune the effective diffusivity profile are sufficiently known as well. Why focus on CH4 and not say, the uncertainty on NH CO2 history? I think a discussion or even a specific section addressing this question is warranted. Fortunately, given the current state-of-science knowledge, I think Umezawa et al. should be able justify their assumption in using CO2, SF6, CH3CCl3, and CFCs to tune effective diffusivity profile. Meinshausen et al. (2017) took a great care in synthesizing all available data from historical atmospheric measurements, firn and ice cores from several sites to best reconstruct the GHGs (including CO2, CH4, SF6, CH3CCl3 and the CFCs measured by Umezawa et al.) mole fraction, interhemispheric gradient, and seasonal variabilities for the purpose of CMIP6 model runs. This would be a great starting point. The justification for treating the NH histories of CO2, SF6, and the CFCs as “known” parameters, or at least better known parameters than NH CH4 history in my opinion should revolve around a discussion about the interpolar gradients of these gases (which are relatively small owing to their long atmospheric lifetimes), but I will leave the exact formulation of this argument to Umezawa et al.

I think a sensitivity analysis comparing what mole fraction should we expect in the open porosity of NGRIP firn if we put in NH vs. SH history from Meinshausen et al. (2017) for CO2, SF6, and the halocarbons is warranted to further drive the point home. I might be wrong, but I would expect the mole fraction vs. depth profiles for these suite of gases in the firn open porosity would not be as sensitive to NH vs. SH difference, at least relative to their respective measurement precisions compared to CH4 given their long atmospheric lifetimes and relatively low interhermispheric gradient. Given Umezawa et al. already had their forward firn model setup, hopefuly this does not require a lot of additional work. Furthermore, as a more general comment, I would also recommend Umezawa et al. to use gas histories from Meinshausen et al. (2017) for their overall firn gas transport and effective diffusivity tuning because the GHGs histories proposed by Meinshausen et al. (2017) represent more updated, better-educated “guesses” than the gas histories previously used by Buizert et al. (2012).

2. The suite of CFCs measurements (CFC-11, CFC-113, and CFC12), CH3CCl3 and SF6 do not provide good constraints for reconstructing effective diffusivity for the deep firn just because the concentration of these gases are all very low and close to zero. Usually, the gases that are most useful to reconstruct the effective diffusivity in this firn region are CH4, CO2, and 14CO2 due to their respective unique atmospheric histories. 14CO2 is especially useful as its atmospheric history can be validated from tree rings and historical atmospheric measurements. Furthermore, 14CO2 has a unique profile from the “bomb pulse” in the 1950s that provides a strong and unique constraint on the effective diffusivity. Unfortunately, 14CO2 measurements for NGRIP are not available. Because the CH4 history in this study is treated as unknown, the effective diffusivity in the lower part of the NGRIP Japanese borehole presented by Umezawa et al. is almost solely constrained by CO2 data. This made me question whether the conclusion obtained by Umezawa et al. regarding how we cannot accurately reconstruct NH CH4 history from firn air samples is a unique problem pertaining to NGRIP (and its suite of gas measurements) or is it more general problem to other Greenland ice core sites as well. I don’t think the current version of the manuscript sufficiently answer this question and additional work might be warranted to justify the conclusion put forward by Umezawa et al.

In particular, I think it would be especially useful to revisit the NEEM data from Buizert et al. (2012) with the same firn model and iterative dating algorithm presented in this study, but also excluding CH4 as part of the suite of gases to tune the effective diffusivity of the NEEM site. This would provide a more fair comparison rather than putting in the atmospheric history reconstruction from likely underconstrained NGRIP site into NEEM with a forward firn model. It would be interesting to see whether additional constraints from 14CO2 data at NEEM will allow for reconstruction of NH CH4 history with a better uncertainty and to what extent the uncertainty is better. For this experiment, I would recommend using the updated “known” 14CO2 history from Graven et al. (2017). Given Umezawa et al. already had their firn model tuned for the NEEM EU borehole as part of their model validation, I don’t think this extra calculation would require significant amount of additional work.

3. I think the uncertainty analysis/discussion regarding the conclusion is a bit lacking. It is not immediately clear to me whether conclusion reached by Umezawa et al., that NH CH4 history in general should be considered preliminary and should not be used to tune effective diffusivity is sufficiently justified. From the study, it is clear that reconstructing NH CH4 history from NGRIP firn air samples, when CH4 is excluded from the suite of gases used to tune the effective diffusivity result in large uncertainties. But I think we know the NH CH4 history slightly better than just the reconstructed history from NGRIP firn air presented in this study.

Meinshausen et al. (2017) decided against providing uncertainties to the reconstruction of GHG histories that they did, arguing that the CMIP6 models would not have the computational resources to run multiple scenarios and sensitivity analysis from multiple GHG histories on top of the envisaged SSPs. I think an assessment about the uncertainty of historical CH4 reconstruction is very valuable and Umezawa et al. is in a unique position to take a first attempt at this. How about reconstructing NH CH4 history from NEEM (with its additional 14CO2 constraint) like discussed above, how about combining NGRIP, NEEM history inversion results to make a best-estimate of NH CH4 history and its uncertainties, and how about including CH4 in the suite of gases used for effective diffusivity tuning, but through iterative method starting first with larger uncertainty for the RMSD calculation to account for uncertainty in the CH4 history? There are still many avenues to explore beyond the reconstructed NH CH4 history from NGRIP firn samples before one can conclusively claim that we don’t know the NH CH4 history to such a degree that it should not be included in the suite of gases used to tune effective diffusivity in firn profiles. I don’t demand Umezawa et al. to do all of the above, as it might constitute a whole different study entirely, but a preliminary exploration on this and an honest assessment about how well can we reconstruct the NH CH4 history would significantly strenghten the manuscript and provide very valuable insights to the community.

Minor comments:

I find that in general, the description about the firn gas transport models and the iterative method is very brief and might be bit hard to follow. The brevity is fine for the main manuscript, but the authors might want to consider a supplementary material where they will have more room to describe the gas transport model, iterative methods, and especially additional data treatments. For example

Line 212 “Effective age at each sampling depth was calculated...” Several steps are clearly skipped here. It is not immediately clear to me, from the description of the model and equations above how one can determine the effective age at each sampling depth, as all the description before this line only pertains to the forward firn model. Did Umezawa et al. calculated a depth-age transfer function similar to Rommelaere et al. (1997) or through other means? Either way this needs to be elaborated.

Fig.3. From the text it says “Figure 3 presents the initial simulations …” Does this mean this is the initial effective diffusivity profile? It might also be beneficial to have the other effective diffusivity profiles like Fig.5 shown in Fig. 3.

There are several data treatment steps that is missing/the authors did not explain in sufficient details, or if the authors didn’t do it, it is not well justified why they choose not to. For example, in their supplementary material Buizert et al. (2012) discussed how they added additional uncertainties for CO2 to account for possible in situ production and bubble close-off fractionation. In Buizert et al. (2012), uncertainty in atmospheric histories is accounted during the tuning of effective diffusivity by running the uncertainties through the forward model when the tuning of effective diffusivity is near complete to transfer the uncertainties from time domain to depth domain. I might miss it somewhere, but I think it is not immediately clear to me how the uncertainties of “known” atmospheric gases used to tune the effective diffusivity is treated in this study.

References

Buizert, C., Martinerie, P., Petrenko, V. V., Severinghaus, J. P., Trudinger, C. M., Witrant, E., Rosen, J. L., Orsi, A. J., Rubino, M., Etheridge, D. M., Steele, L. P., Hogan, C., Laube, J. C., Sturges, W. T., Levchenko, V. A., Smith, A. M., Levin, I., Conway, T. J., Dlugokencky, E. J., Lang, P. M., Kawamura, K., Jenk, T. M., White, J. W. C., Sowers, T., Schwander, J., and Blunier, T.: Gas transport in firn: multiple-tracer characterisation and model intercomparison for NEEM, Northern Greenland, 12, 4259–4277, https://doi.org/10.5194/acp-12-4259-2012, 2012.