General Comments

Overall, this interesting and valuable paper is generally well written. There is some additional discussion needed in places and some tightening of prose, particularly in the second half of the introduction and in the discussion/conclusion. Yet the research itself is comprehensive and the science is good.

Specific Comments

• After Page 2 Line 30 the introduction needs a bit of attention to retain the good quality of previous paragraphs. It felt like the flow of the narrative was lost around here and there is a bit of repetition.
• For the satellite data please give an explanation for the choice of a 0.25 by 0.25 degrees regular geographical grid. This seems quite a coarse resolution given the input data, is this to correspond to T2m datasets from other sources or model grids?
• Page 7 Lines 5-7:
  • It took a couple of reads to figure out that the ISTskin_L3 is the daily version of the L3 not the 3 hourly (assuming I understand correctly). I think changing the text to something like “Here, we have aggregated the AASTI ISTskin_L2 observations into 3 hourly and daily, gridded 5 Level 3 (L3) averages of ISTskin_L2 on a fixed 0.25 by 0.25 degrees regular geographical grid. The daily gridded averages (ISTskin_L3) are calculated by averaging” might make this clearer.
• Page 8 Line 26:
  • You mention the distances but not temporal matching. I guess from the data this is a daily average comparison, but this might be worth mentioning explicitly here.
• Page 14 28-29:
  • This sentence reads as though only the random uncertainties are provided for each pixel and the others are provided as one value for the whole dataset. Is this correct?
  • Surely given the inclusion of a sampling uncertainty in the synoptic component and separate equations for land ice and sea ice there should be a value for each pixel? This is the case for synoptic uncertainties for similar satellite products such as from e.g. Ghent et al (2017).
• Page 15 Line 1-4:
  • This sentence makes it sound like only ice over sea is included; ice shelf (land ice) and sea ice. But Figure 6 and previous figures show data over the Greenland ice sheet. Is the Greenland ice sheet included in the dataset?
• Results:
  • I would like to see a few more citations and additional discussion of the results here as I was often left wondering how the results compared with previous research or observations that might back up your results. For example:
    • “The monthly mean air temperature typically reaches 20 a maximum of -4°C during July and a minimum of about -28°C during winter.” Does this correspond to previous research and/or observations? Perhaps the GrIS in situ observations could be added to Figure 12 to show how close the T2m_sat is?
    • It seems that the results from comparisons of ERA-Interim (and ERA-5) suggest that the long standing warm bias in these reanalyses for the Arctic still exists, which deserves some comment here and perhaps citation of previous studies on this. I also don’t know if ERA-5 has been compared to in situ T2m over the Arctic in other research yet so this could be an interesting result given the warm bias may still be a feature of this dataset series. Again, if so this is worth noting.
    • Page 17 Lines 5-9, I believe your statements about Arctic cloud cover are correct, but I think a citation would be useful to back this statement up.
  • Discussion:
    • This section was more like a list of additional things to note that did not fit in the rest of the paper rather than a coherent discussion. I felt it didn’t really tell the story of the research in the way it deserves.
    • I think this needs a bit of work to restructure and possibly a short summary of results relevant to each point made. For example:
      • Page 22 Lines 11-18 seem to refer to the fact that “The satellite 10 derived air temperatures are about 0.3°C warmer than measured in situ air temperature for both land ice and sea ice.” which is probably due to the influence of the linear regression? It would be nice to include the context for these sorts of statements in the discussion.
    • Will the surface temperature dataset be extended to seasonal snow and ice?

Technical Corrections

• Page 2 Line 19: Satellite not Satellites
• Page 2 Line 23: Either un-capitalise The or remove
• Figure 3, 4: might be a big ask depending on the software used, but is there any chance of removing the sliver of white from the plots?
• Page 8 Line 22: I think a subheading for this validation section would be useful to the reader.
• Page 16 Line 8: there is not there are
• Page 23 Line 17: MODIS not Modis (acronym of sensor)
• Page 15 Line 2: could you expand the acronym ETOPO1 or provide a very brief indication in text of what this is? Perhaps “ETOPO1 global relief model” or similar?
• Conclusion section: a bit long and should be distilled down to the major points.

General Comments

This is an exceptionally well-written contribution; if only all papers were so clear. The datasets collected seem very comprehensive, and the careful attention to uncertainties in satellite estimates is a strength, as is the good practice of independent validation of both the data and the data uncertainties. The value of this observational effort (compared to just taking re-analysis outputs) is demonstrated. The conclusions are well supported by the discussion.

Specific Issues

8.5 - Why should surface melting situations necessarily be excluded? How common is the situation of the (wet) skin temperature being > 5 deg compared to it being a wrong observation? I guess this is explained more in the reference, but perhaps a little more comment here would be justified.

Figure 4 includes open ocean areas, so this presumably is the SD of any surface present not of specifically ice surfaces, despite the wording of 8.12? 

"Daily mean" surface air temperature data from weather stations are often actually the mean of the daily max and daily min reported. Is that the definition applied to the in situ data in section 3.1 here?

Technical / editorial

1.10 - unnecessary hyphen after weather

1.11 - meter -> metre and also throughout eg 8.25 etc; reserve "meter" for an instrument

2.23 - micron -> micrometre

Figure 4 caption: not totally unambiguous what calculation this is, but I think it is the SD for the named month of each year, then averaged over years?

12.3 -- explain "theoretical shortwave radiation" -- is this top of atmosphere to give seasonality?

The manuscript addresses estimation of 2-m air temperature (T2m) over the Greenland Ice sheet and the Arctic Ocean sea ice. The work is based on satellite remote sensing data on clear-sky ice/snow surface temperatures and their comparison with in-situ observations on T2m. I am impressed by the amount of data analysed, originating from different sources, and by the carefulness and detail of the analyses made. Among others, a lot of attention is paid on uncertainty analyses. The manuscript is well organized, the text is well written, and the illustrations are of high quality. The results are important, convincingly demonstrating that T2m estimates based on satellite remote sensing data are useful and reasonably accurate. Hence, they can supplement reanalysis products and rare in-situ observations on T2m. I suggest accepting the manuscript subject to minor revisions.

Specific comments

I wish to see more attention to the seasonal distribution and accuracy of the satellite-based T2m estimates. The quantitative results are given for the entire data set (e.g. page 22, lines 26-28), but it is well known that over the Arctic sea ice clouds are more common in summer than other seasons. Figure 8 demonstrates that there are less data from summers, but Figure 7 suggests that the estimates are better in summer than in winter, which must be related to smaller thermal differences between the ice and air in summer. Detailed comparison of skill scores (bias and rmse) between different seasons is, however, missing, and it remains unclear how useful the satellite-based T2m product is over sea ice in summer. This could be easily improved by presenting quantitative results for different seasons.

It would be good to make it clear already in the Abstract that the study addresses the Arctic Ocean and Greenland Ice Sheet, but not other land ice in the Arctic. Related to this, in Table 1 land snow must refer to seasonal snow. However, in the Discussion, Conclusions, and Abstract, there is nothing mentioned about results for seasonal snow. Were the results similar to those for land ice?

Page 1, last sentence: Could the information be updated (2010s vs. 2000s) and extended to also address the strong winter warming over the Arctic sea ice? The latter is evident on the basis of reanalyses.

Page 2, lines 7-8: “In particular” is questionable. It is even more difficult to achieve climate-quality precipitation and air humidity records from the region.

Page 3, lines 4-5: Make it clear that the zones refer to the Greenland ice sheet.

Table 1: Use of Polarstern data as a proxy for 2-m air temperature sounds surprising. According to my knowledge, in the Polarstern weather station the air temperature sensors are located 29 m above the sea surface. In Figure 11, however, the rms-errors are small for Polarstern. Could it be because the data are mostly from summer, when the vertical temperature gradients in the boundary layer are mostly small?

Page 20, line 21: The temporal variability of air temperature is largest in winter because the meridional temperature gradient is largest, the atmospheric circulation is vigorous, and the cloud radiative effect is large (compared to near-zero in summer).

Page 22, lines 1-10: As new results are presented here, consider moving this paragraph to the Results section.

End of page 22 – beginning of page 23: I am surprised that the use of wind speed did not improve the results over sea ice (over Greenland Ice Sheet, the reanalysis errors for near-surface winds may be so large that it is not so surprising there). Also, it looks strange that the correlation coefficients and RMS-errors are exactly the same for the four regressions presented for sea ice in Table 3. I suggest double-checking the calculations.

Page 23, line 30: In summer, the air temperature over sea ice in not so good indicator for Arctic climate change. Ice and snow are rapidly declining, but T2m remains the same, close to 0 deg C, as long as there is sea ice left.  See e.g. Figure 2g in Vihma et al. (2008) (just for information, no reason to cite).

Page 24, last paragraph: The independence of the satellite-based T2m product and reanalyses is stressed here but, as mentioned earlier, reanalyses actively assimilate available in-situ observations. In particular, the ECMWF has had a pioneering role in assimilation of T2m data, which was done also in the Arctic already in the old ERA-40 reanalysis. However, I fully agree that the satellite-based T2m product is very valuable, and may indeed yield even better results than assimilation of (rare) observations into a reanalysis system. T2m is a diagnostic product in reanalyses, calculated on the basis of surface temperature and air temperature at the lowest model level, and liable to uncertainties in the parameterization of turbulence in the stably stratified atmospheric boundary layer. Note, however, that the NCEP-CFSR reanalysis, which is based on a coupled atmosphere – sea ice – ocean model, has performed better for near-surface atmospheric variables over sea ice.

Figure 6: In the legend, replace “air surface temperature” by “near-surface air temperature” or “2-m air temperature”.