Publisher’s note: a supplement was added to this comment on 10 October 2023.

Please see the attached file for a PDF of the review.

Review of “Historical snow and ice temperature observations document the recent warming of the Greenland ice sheet” by Vandecrux et al.

I found this an interesting paper to read, and it is well suited for The Cryosphere. The authors compiled an extensive dataset of firn temperatures at 10m below the surface. Using machine learning, they created a unified time series on which trend analysis can be performed. The trends are compared with contemporary, widely used regional climate models and highlight agreements and discrepancies between models and observations. I think this makes it relevant for a broad range of scientists. I think only minor revisions are necessary before publication. Even though I list some major comments, I think that they must be relatively easy to resolve by the authors. Writing style and figure quality are good. I have some comments that I think will make the paper stronger, more understandable, and better accessible for a broader audience, as detailed below. I am not very familiar with machine learning techniques, so it is difficult for me to fully judge this aspect of the work.

Major comments

• I think the Introduction should provide more context to the reader of the relevance of the 10m firn temperature. Why not surface temperature, or 20m temperature? It’s not that I question it, but I think it needs to be discussed in the introduction. I assume that it is related to the fact that it sometimes is considered the bottom of the near surface layer, where seasonal variations are more or less fully dissipated (see for example Fig. 1.3 in Ligtenberg, 2014). Keenan et al. (2021) also simulates only the uppermost 10m of firn, arguing that at depth, the firn temperature equilibrates with annual average air temperature (in the absence of melt), seasonal fluctuations in temperature have dissipated and that seasonal variability in accumulation (for example density fluctuations) also has been diffused over the firn layer when it reaches 10m depth. I assume that authors have this kind of reasoning in mind when deciding to focus on 10m temperatures, but maybe data availability also plays a role. In any case, I think this should be briefly discussed in the introduction.
• I do get the impression that the trends in the machine learning model might be overestimated. This is hard to really conclude from the presented material, but looking in Fig. 3e for example, the trend between 1998 and 2009 seems stronger in the ANN than in the observations. Generally, the seasonal fluctuations seem to be stronger in the ANN, for example in Fig. 3g. So could it be that the ANN is a little bit oversensitive to warming and cooling, whether it is seasonal, or a long term trend? Is it possible to construct a figure with the trend in observations vs the trend in the ANN reconstructed temperature for time periods where there is overlap? I’m curious to see if such a scatter plot would confirm my impression of an overestimation of the trends in the ANN. Note that depending on the outcome of the correlation between observed and ANN temperature trends, the statements in the Conclusions may be weakened a bit by adding that the reported temperature trends were derived from the ANN. The statements currently are formulated in a rather absolute sense.
• I’m not very familiar with machine learning techniques, but I’m wondering if more substantiation of the chosen features can be provided. Often, it is reported on the relative feature importance after training the ANN, such that it can be identified if the chosen features contributed significantly to the ANN. This seems to be missing a bit in the manuscript.

Minor comments

• The title could be considered slightly misleading, suggesting that the trend is derived from the observations only. I think the title should reflect that the trends were derived from machine learning on historical data.
• Abstract, L25: here, I also recommend to briefly mention in one sentence why T_10m is relevant
• Abstract, L27: here, briefly introduce why you want to train the ANN. I understood that it is because the measurements vary in spatial and temporal coverage, and in order to create a unified dataset, you constructed the ANN?

• L76: Note that the abstract mentions 4500 measurements, L63 mentions 4600, and here 4615 is mentioned.
• L77: Just for completeness, I would add both unpublished datasets to the table, listing them as “Unpublished” in the first column, or by making a data citation for these two unpublished datasets and cite those, after putting them on a repository, if that’s allowed.
• L81: What does UUB stand for?
• L106: As I read “the latter”, it only concerns the two measurements from Benson. But I assume that also the aforementioned 5 measurements from Koch also couldn’t be used, since they are outside the current ice sheet extent? If not, then I don’t understand this sentence.
• Table 1, I think table caption should specify what non-bold numbers indicate.
• Section 2.2: I would recommend starting this section with a motivation for what the goal of the ANN is. See my similar comment for the Abstract.
• L131: How deep is “subsurface” in this case? As far as I know, 10m temperature seems to be considered to equilibrate with annual average air or surface temperature pretty well (see major comment). In that case, this argument won’t really hold? Obviously, the results presented do show that seasonal temperature fluctuations are still present, but just strongly dampened.
• L131: Also provide an example of snowfall and its impact on firn temperature (contrasting high vs low accumulation areas for example).
• Section 2.2.1: I think this section should provide a reference or other argumentation that ERA5 is reliable for Greenland.
• L151: “changes in long term changes” I guess this must be simply: “long term changes”, since otherwise it would be acceleration or deceleration of temperature trends, and that’s not what’s meant here I think.
• Section 2.2.2: So were the weights determined time-dependently? With the temporal variability of the availability of the observations, as indicated by the histogram in Fig. 1, it may have been necessary, since during different climatological periods, the spatial coverage also varied. Was it actually necessary to apply the weights? Would the ANN have performed much worse without them?
• L256: Would the validation dataset also not be important to discuss to provide uncertainty bounds on the ANN?
• L282: “HIRHAM, the use” is grammatically not a correct sentence.
• L307: Note that the referenced figure (Fig. 3), but also Fig. 4 separate “All sites” vs “Ablation sites”, while text mentions “Dry sites” vs “Ablation sites”. I guess it makes more sense to separate dry vs ablation, so I assume this is what has been done in the figures? Please make consistent.
• L393: I suggest writing: “that occurred here”.
• Fig. 7: Why is the dotted area only in panel (a) and (c)? Does this mean that all other trends shown in all other subpanels of fig. 7 are significant? Maybe mention then in the caption that all modeled trends test significant.
• L418: What is meant by “upper percolation area”? According to Table 2, the trend from ANN over 1985-2022 for the full percolation area is +0.9, while here, it is stated that the trend in the upper percolation area is +0.9. I’m not really sure I comprehend this. Is “upper” like high in elevation, or rather the northern parts on the ice sheet? I find it all a bit confusing. Similarly, the phrasing “this localized warming” is confusing, because the full percolation area warms with the same rate as this "upper percolation area", so is the warming then really “localized”?

References used in the review

• Ligtenberg, S.R.M. (2014) The present and future state of the Antarctic Firn layer. PhD Thesis https://dspace.library.uu.nl/bitstream/handle/1874/291634/Ligtenberg.pdf?sequence=1&isAllowed=y 
• Keenan, E., Wever, N., Dattler, M., Lenaerts, J. T. M., Medley, B., Kuipers Munneke, P., and Reijmer, C.: Physics-based SNOWPACK model improves representation of near-surface Antarctic snow and firn density, The Cryosphere, 15, 1065–1085, https://doi.org/10.5194/tc-15-1065-2021, 2021.