Dear authors

I now collected two reviews of your revised manuscript.

In general, both reviewers are rather positive about your revision, both acknowledge your efforts and agree that the manuscript has been improved compared to the initial submission.

However, both reviewers still expressed some reserved for several aspects of the study and ask for clarifications. I myself provided several (rather minor) suggestions in an annotated version of your manuscript.

Regarding the reviewer comments about the need to clarify (or modify) the iterative calibration procedure. What about a small flowchart showing the steps of the iteration? Good help the readers.

With the help of the referees, I will carefully checked that you reply to all comments and modify the manuscript in an adequate way.

Best regards,

Etienne Berthier

Dear Authors,

Both referees now agree with the publication of your study pending some technical corrections that are listed below or attached (let me know if they were not transfer automatically along this decision). If you reply carefully to these final comments and modify the text accordingly where necessary, I do not expect another round of review (but I will check thoroughly and transfer your response to the referees as they are interested).

Do not hesitate to contact me if you have some further questions.

Best regards,

Etienne Berthier

Dear Authors,

Thanks for taking into account the final comments by both referees.

I have the pleasure to accept your paper for publication in our journal.

I detected several remaining typos listed below. Can you double-check carefully your manuscript (MS) a last time?

This decision is also the opportunity for me to acknowledge both referees for the time they dedicated to successive versions of the MS.

Do not hesitate to contact me if you have some further questions.

Best regards,

Etienne Berthier

8.20. (track-change version of the MS
“(for the elevation of the ocean surface zw , we assume that it is 0 m a.s.l.). For this reason, most of our experiments and results focus on marine-terminating glaciers only, with the exception of the experiment presented in section 4.2.” could be simply changed to “For this reason, most of our experiments and results focus on marine-terminating glaciers only (Zws is set of 0 m a.s.l.), with the exception of the experiment presented in section 4.2.”

11.29. I am not sure it is obvious what “this” stands for

13.1 “long term average”

14.30. “m a.s.l.”

15.3 “the the”

15.6 “A wrong elevation” rather than “the wrong”, I think.

16.10. I think “large” is better than “big” here.

16.20. “independent of” (I think, check also elsewhere in the MS)

16.31. ‘an realistic estimate’ -> “a realistic estimate”

Figure 3a and 3b. “km3.yr-1” → “km3 yr-1” [no dot]

Figure 6. “km.yr-1” -> “km yr-1” [no dot]

Figure 7. Same comment as for Figure 3

Figure 8. “the grey bar represents”. I would write “for these glaciers” rather than “these types of glaciers”

Figure 9. “if no correction is applied”