Dear authors,

thank you for sketching a path by which the comments provided by the three referees will be addressed in your re-submission. In particular, I appreciated the fact that you provided an overarching view for how you intend to address the individual comments, rather than providing one-by-one answers at this stage. Since I herewith invite you to re-submit a suitably revised version of the manuscript, anticipate that you will provide such a point-by-point reply upon resubmission.

In terms of contents of the replies, I would only like to comment on two points:
1) Both Reviewers #1 and #2 take issue with the study’s perceived lack of novelty. Here, I would encourage you to address this point somewhat more vigorously than done in the present replies, especially when replying to Reviewer #1.
2) In my understanding of the comment “Ice thickness vs bedrock topography” by Reviewer #2, the reviewer is only asking to subtract the calculated ice thickness from the used surface DEM, as to obtain a bedrock topography. This is different from the request of investigating the potential differences between bedrock topographies obtained from surveys conducted at different times which, I agree with you, would not be feasible within this study. Since the reviewer’s request seems reasonable to me and since a dataset on bedrock topography would certainly be valuable for future studies, I would support the reviewer’s request.

In terms of further steps, all of the three reviewers recommended the article to be reconsidered after major revisions. In this sense, your revised version of the manuscript – together with your replies to the obtained comments - will be re-sent to review once available. I anticipate that only two (instead of three) referees will be contacted this time.

Best wishes, and thank you for the constructive way by which you have taken up the referees’ comments.
Daniel Farinotti

Editorial comments Vergnano et al. (after 2nd round of reviews)

I have taken over this manuscript from the previous editor because the latter has unexpected urgent work obligations. I have read the manuscript, the two recent reviews and the three initial reviews.
At this point, there are two reviews of which one (#2) recommends minor revision and is generally very positive while the other (#1) is very critical and recommends rejection. I understand the critique raised by #1 and acknowledge that they consider the required revision as too substantial for recommending major revisions. However, I also acknowledge that there are four other reviews who recommend revisions (major or minor). In this challenging situation I take the following decision:
- I ask the authors to revise the manuscript according to both reviews. Review #1 needs to be fully addressed and the authors need to reply to each point raised by the reviewer, explaining how they will address the critique.
- I find the circular reasoning pointed out by #1 particularly concerning. I ask the authors to clearly address this issue. I noticed that Reviewer 3 from the first round of reviews had already commented on that issue (“However, it is important not to turn the logic around [...] reversing the process and leaking the modeling data into the GPR measurements can be delusive. This is the most important comment I have for this work, and I would like to see it discussed further in the manuscript.”) It appears to me that the authors have not answered this critique which has now been repeated by reviewer #1 from the second round of reviews.

Furthermore, a few editorial comments:

Lines 135 to 138: The text gives the impression that the authors are using the original GlabTop2 code. However, this is not the case as the original code was written in IDL. This code has been presented in the study by Frey et al. (2014) and used extensively in e.g. Farinotti et al. (2019). The authors must make clear that here a code is used which is based on the equations presented in Frey et al. (2014), not the original code. The code used here appears to be an incomplete implementation of the equations and description in Frey et al. (2014). The code appears to simulate large ice thickness directly at the glacier margin, as visible in Fig. 4. The original code contains algorithms to avoid such unrealistic sudden transitions from thick ice to no ice. Being the author of the original code, I would be happy to share the original code with the authors, however, its major limitation is that it is written in IDL and I fully understand if the authors prefer using a more modern Python code.
Lines 335 – 336: While I do not know how the original GlabTop2 code would have performed on Rutor glacier, this issue would likely have been reduced.
Lines 376 - 377: This appears to be the only mentioning of circular reasoning, although in a single sentence which is kept vague and whose message on human error is unclear to me. To be clear, any circular reasoning needs to be removed from this study for it to become acceptable.

Dear reviewers and authors

I would like to thank the authors for the revisions and the reviewer for their assessment. The reviewer suggests the manuscript should be accepted, provided minor revisions are made. I would like to ask the authors to implement the suggested changes, or provide clear arguments why they believe certain changes cannot be addressed.

The revised manuscript will be subject to editorial review.

Best wishes, Horst

I thank the reviewer for their comments and the authors for the revisions of the manuscript. I consider the paper now ready for publication.