Dear authors,

thank you for sketching a path by which the comments provided by the two referees will be addressed in your re-submission. Albeit implementing the changes as you suggest is likely to require some time, I am very confident that the effort will result in a manuscript that the two referees will deem as being worth publication. Indeed, I found all your answers pertinent and your argument understandable.

One minor thought from my side: although I understand that including an additional test case is likely to be linked to some effort, I was wondering whether you would not want to consider including an ITMIX test case after all. Including such a “standard case” would facilitate the comparison to other, already-existing methods, which might be insightful for you and the readers alike. I am not going to insist on this point but wanted to at leas point out that the ITMIX dataset does also include some ice-caps, i.e. is not fully focused on valley glaciers (as one of your answers suggests).

Independently of your final decision on the point above, I would invite you to submit a revised version of your manuscript. This version will then be re-seen by the two referees, as they had indicated their willingness to do so. I expect this new round of reviews to either lead to a final acceptance, or to a further request for minor adjustments.

Best wishes
Daniel Farinotti

Dear authors,

Your revised manuscript has now been re-seen by the two reviewers that had already commented on your initial submission. I am happy to see that both reviewers found very positive words for how you dealt with their feedback. While one reviewer now suggests for the work to be accepted upon technical corrections, one reviewer is left with some minor comments. My appreciation is that these can be accommodated by slightly amending the discussion. In particular, this seems true for the request of presenting more than one metric for quantifying the model’s performance, and the requests put forward in terms of discussing the model’s sensitivity and parameter equifinality. As for the request of comparing your approach to a standardized test case from the ITMIX suite, it seems that this request is too demanding. Here, it would be useful if the discussion section could at least provide a hint for why such a comparison is not included, as it is likely that other readers might have the same question.

I am looking forward to see your manuscript finalized.

Best wishes
Daniel Farinotti

Dear authors,

Thank you very much for your additional work on the manuscript. I am happy to see that the remaining reviewer comments were taken on board, notably including the comparison with the established benchmark cases.

At this stage, the manuscript seems ready to be accepted without further delay. Let me thus take the opportunity to congratulate you for the successful completion of this valuable contribution.

Best regards
Daniel Farinotti