Dear authors,

Many thanks for the elaborate and clear response to the points raised by the reviewers. I invite you to submit a revised manuscript which includes the modifications you propose int he rebuttal. The referees all provided generally positive feedback on the manuscript, yet, they raised a number of points which require significant modifications of the manuscript. Given this, combined with the changes you suggest to implement, make this a ‘major revision’ of the original manuscript. I will therefore send the revised manuscript back to the referees for a second round of reviews.

Kind regards,
Bert Wouters

Dear authors,

Thank you for the time and effort you put in the revising your manuscript. As you will see in the review reports, the referees were generally pleased by the changes you made to the manuscript. Referee 3 only provided suggestions for technical corrections, and referee 1 has some remaining concerning the robustness of the Phase 2 model (or rather, the way the robustness is presented in the manuscript). I believe the comments of these two referees can be addressed with only a minimal amount of additional work. Referee 2, however, has some more substantial concerns about the manuscript, which I share. These concerns are not so much about the methods or results, but about the format of the paper. the article has now become quite lengthy and a large part consists of comparison of different machine learning techniques and a discussion of the technical details. Whereas the details you provide in the new sections are important for completeness of the article, yet at the same time they make the current manscript a tough read for the wider glaciological community that The Cryosphere aims to reach. To address these concerns, I see two options:

- Referee 2 provided some valuable feedback on how the manuscript can be more accessible for a wider audience. I suggest that you follow the suggestions made in the report and move part of the information to the supplement. I also strongly agree that the advantages to the cryospheric community should receive much more attention in the discussion section, which now is indeed mostly technical. Furthermore, unlike other papers on image classification using machine learning that were published in our journal (https://doi.org/10.5194/tc-13-1729-2019 ; https://doi.org/10.5194/tc-15-1663-2021), no new data set is presented and a physical interpretation of the results is missing in the current manuscript. Although I understand that this is beyond the scope of this manuscript and would only make it longer, I would like to see a short case study which illustrates the benefits of your approach (i.e., what can we do with this method that wasn't possible before).

- Although the above option seems preferable to me, another option that you may consider is to submit the manuscript to the Copernicus journal 'Geoscientific Instrumentation, Methods and Data Systems (GI)’. This journal is more technically oriented and therefore the article in the current form (i.e., without the changes required for option 1) might fit better there. Unfortunately, there is no system to transfer manuscripts from one Copernicus journal to another, but if you would be interested in this option, I'd be happy to assist in transferring all referee reports to the handling editor at GI.

Please let me know which of these two option you'd prefer.

Kind regards,
Bert Wouters

Dear Melanie,

Many thanks for the efforts you and your co-authors took to address the concerns and suggestions from the reviewers and myself. I think the manuscript now reads well for a reader with an interest in ML, and the case study you included are a good showcase of what your method is capable of for the wider audience of the our journal.

It's my pleasure to let you know that your work is now accepted for publication, pending one last modification. The term 'Softmax layer' is mentioned a few times, but it's never really introduced, which I think should be done for those readers with only a basic knowledge of ML. Please add a short description at the first occurrence, which I think is line 216 (e.g. 'converts the scores to a normalized probability distribution', if I interpret your method correctly).

Kind regards
Bert