Dear authors,

I thank you for your detailed and constructive answers in the interactive discussion. Based on the very positive feedback of the reviewers, and the amendments announded in your responses, you can regard your paper as provisionally accepted for publication. Please submit a suitably revised manuscript, effectively addressing all reviewers' comments, along with a tracked-change version.

Best regards,
Guillaume Chambon / TC Topical Editor.

Dear authors,
I am pleased to announce that your paper is now accepted for publication in The Cryosphere.

There remains several typos in the manuscript (notably in the newly-introduced parts), and you may want to carefully proof-check the text at the copy-editing step to make sure that they have been corrected. The following clarifications could also been added prior to submitting your final version:
-p. 5, line 20: this (ratio) ...
-p.8, line 15: "the following section" - don't you rather mean section 2.4?
-Table 1 and Fig. 2: I could not find the definition of parameter $\tau_0$ in the text.

Best regards,
Guillaume Chambon / TC Topical Editor