The authors present a study to solve the mixed pixel problem in the remote sensing of ice surface temperature and ice leads by using convolutional neural network. Then the finer resolution data facilitate the further lead heat flux estimation at a more detailed level. The proposed deep learning-based method outperforms other methods mainly due to its capability of capturing complex nonlinear spatial pattern/relationship between images on different scales.  Overall, the study provides a new prospects of lead mapping, but the manuscript in its current state does not meet the standard of the TC. I suggest major revision and the language needs further improvements.

General Comments：

1. Most of the study area cover the ice zones, having temperature lower than -2℃ (Fig.2 and Fig.12). This might not be appropriate to use the term “sea surface temperature”. I suggest to use “Ice surface temperature”.
2. This experiment was conducted on the Beaufort Sea. Would the model be suitable for other Arctic sea ice regions such as the central Arctic Ocean where the Landsat imagery is lacking? Although the reconstructed SR IST is hard to validated there, it is possible to assess the accuracy of leads map through other source of high resolution dataset such as SAR image.
3. In the introduction, has CNN-based SR method ever been used in downscaling thermal infrared images in other regions, for example, in middle latitude areas? I suggest adding some background about it.
4. The wind and air temperature are referred at different altitude, any measure on solving the inconsistence? on which height is the turbulent heat flux calculated? Also, the hourly air temperature from ERA5 reanalysis is provided on 0.25°grid (which is not mention in the manuscript). The scale of air temperature data doesn’t match with those of MODIS or Landsat images, therefore potential influence of warm lead surface on the bottom air might be neglected. Uncertainty in this case should be noted.
5. Please rewrite the conclusion section, it looks to me that it is more like a discussion.
6. I found some long sentences such as Line 60-62, Line 519-520, hard to understand. Suggest authors do professional English editing.

Specific Comments:

1. Figure 1: The light color rather than black area represents leads.
2. Line 92~94: could the authors elaborate on their decision to not use the NSIDC MOD29 sea-ice surface temperature product directly but instead calculate it themselves?
3. The document “Hall and Riggs, 2001” is not cited properly. “Algorithm Theoretical Basis Document (ATBD) for the MODIS Snow and Sea Ice-Mapping Algorithms” has three main contributors and another seven co-authors, thus you should cite this paper as following: Hall, D.K.; Riggs, G.A.; Salomonson, V.V.; Barton, J.; Casey, K.; Chien, J.; DiGirolamo, N.; Klein, A.; Powell, H.; Tait, A. Algorithm Theoretical Basis Document (ATBD) for the MODIS Snow and Sea Ice-Mapping Algorithms; NASA GSFC: Greenbelt, MD, USA, 2001.

Or Hall D.K., Riggs G.A. and Salomonson V.V., 2001. Algorithm Theoretical Basis Document (ATBD) for the MODIS Snow and Sea Ice-Mapping Algorithms. NASA's Goddard Space Flight Center, Greenbelt, MD.,1-45.

4. Line 105: As for choosing the retrieval algorithm for sea ice, I recommend to cite a related publication:

Fan, P., Pang, X., Zhao, X., Shokr, M., Lei, R., Qu, M., Ji Q, Ding, M. (2020). Sea ice surface temperature retrieval from Landsat 8/TIRS: Evaluation of five methods against in situ temperature records and MODIS IST in Arctic region. Remote Sensing of Environment, 248(January), 111975. https://doi.org/10.1016/j.rse.2020.111975.

5. Line112: “manually drawn”, what is the criteria in producing the reference lead maps? Is there any physical threshold used here, like that in Lindsay et al. (1995)?
6. Line115: why don’t you use the 100 m raw data instead of relying on the up-sampled 30 m product?
7. Line 174: Is the layer number of very deep residual CNN model a prescriptive constant, or we can adjust them?
8. Line 211~213: Does the lead map show consistency with the assumption that the surface temperature all above the freezing point?
9. Line 239: The Pearson coefficient is generally represented as “r” instead of “R”.
10. 6: Suggest to mark the name of corresponding methods in the sub-images or sub-titles.
11. Line 284~286: the subsentence after “because” is not the cause, please rephrase this sentence.
12. 7: In this figure the labels of both X and Y-axis are not appropriate. As the scatter plots represents the IST between Landsat and SR images, the X and Y-label can be “Reference IST” and “IST from xxx”.
13. Line309: what about the surface temperature distribution of the lead in the map? Are they all above the freezing point? Same question for the Fig 13.
14. Line 397: What is “at a step size of 40”? please clarify.
15. 12: Note that Landsat images acquired on 25 April 2018 is partly contaminated by cloud. You also mentioned the red dashed ellipse in Fig. 13c.Could you discuss the impact of the cloud on your method?
16. 13: It seems the sub-plots m to x do not maintain the same sizes with the black rectangle r1 to r3. Please make sure they have same size and do not stretch them.

This study evaluates the use of "convolutional neural networks" (CNN) to improve calculations of turbulent heat flux (THF) in Arctic leads from 1km resolution MODIS Terra infrared satellite imagery. It represents a novel application of machine learning to both MODIS imagery, which is widely used and invaluable in studies of polar regions, and THF in leads, which is an important parameter in our understanding of climate change in Arctic regions. Though the discussion section is lacking and editing is needed with regards to the English language, this is a exciting paper that should be published following revision.

Overall comments

• I agree with the first reviewer in that "Ice Surface Temperature (IST)" would be a more appropriate term than SST. "IST" is used in studies of polynyas using MODIS data, even when describing open water pixels. One of many literature examples is: https://www.mdpi.com/2072-4292/10/3/366. It is also the term used by NASA for their level-2 product.
• The discussion section would be suitable if this were submitted to a journal purely focused on machine learning techniques, but because this is The Cryosphere and readers will be interested in the DeepSTHF methodology in the context of polar science, this section should be expanded to include discussion of:
  • The significance of the improvement in calculated THF using the DeepSTHF vs other methods, eg. is the magnitude of improvement in W/m^2 significant relative to the overall heat budget in the Beaufort Sea or similar study area? Is it worth the additional computing resources to utilize DeepSTHF over CubicSTHF?
  • How applicable do the authors think DeepSTHF would be to other areas outside the Beaufort Sea in the Arctic, or even the Antarctic?Does the fact that DeepSTHF was unable to capture very narrow leads mean it may be less applicable in certain areas or times of year, when narrow leads are more common? A discussion of the nature of leads in the study area/broader Arctic would add some helpful context
  • DeepSTHF is promising, but exactly how far is it, or neural networks in general, from being widely implemented in studies of THF in leads? What are the next steps?
• Also agreed with the first reveiwer in that the paper would benefit from professional English editing

Line/Section/Figure Notes

Line 50: Would be helpful to list out specific (satellite-related?) examples instead of just citing the papers

Line 53: Is there a way to explain how CNN is used to produce super-resolution imagery to those of us without a extensive technical understanding of its mechanics or machine learning in general? 

Line 60: It would be nice to explain these names so they are easier to remember- eg. DeepSTHF is based on deep learning and THF, but I am unsure what the S is for. Likewise, does the "Ori" in OriSTHF stand for "original" image?

Line 93: Why is SST calculated manually instead of using the Level 2 MODIS IST product with the same 1km resolution?

Line 93: Should also cite original work of Key et al. (1994, 1997), which Hall and Riggs (2001) followed for IST calculations

 

Line 95: Because clear sky is so important to the split-window algorithm, can you explain how you chose the 10% cloud cutoff?

Line 120: You introduce these formulae here but don't show them until lines 221-222. To avoid confusion, perhaps just describe the meterological variables collected and don't describe the formulae yet. 

Line 167-168: Move to beginning of section

Line 169: Move "The following subsection explains the two CNNs fmore fully) to Line 162, after the sentence "Therefore, we used two CNNs... to achieve generation of a fine-resolution SST image and lead map."

Line 225: Though the Goosse paper does describe everything in detail, because the latent and sensible flux calculations are so essential to this study, it would be good to write out more detail in this section, especially regarding the calculation of transfer coefficients, which can be parameterized many ways.

Line 342: DeepSTHF method achieved the most accurate THF, but there still appears to be a considerable amount of scatter in Figure 10c. Related to my overall comment regarding the discussion section, further discussion of the magnitude of the descrepency between reference and estimated THF and what the nature of this descrepency means for a potential broader application of DeepSTHF is important

Line 400: Why were these specific dates chosen?

Line 408: Please describe this additional layer of error caused by temporal correction

Section 3.3: I don't think the second paragraph (Lines 237-243) is necessary, as you describe these statistics in the results section. Instead, it would be more helpful for the reader if, after describing the three methods DeepSTHF, CubicSTHF, and OriSTHF in Lines 230-236, you explain that you will run two experiments: One with simulated MODIS imagery and one without, and why you do this. I was unaware at start that there are two separate experiments, which led to confusion while reading the long results section.

Section 4.2.2: Why are the THF algorithms compared to Landsat for the lead maps but not the overall THF calculation as they are in Section 4.1.2 with the simulated MODIS imagery? Quantifying how well DeepSTHF performs relative to the reference is important, especially when applied to real MODIS imagery.

Figure 6: The caption suggests it is a simulated super resolution image when it is instead a coarse resolution MODIS image simulated from Landsat imagery (I think). Please clarify this

Figure 14 - Why is THF calculated from the reference Landsat imagery not shown as well?