Dear Authors
Thank you for your extensively revised version of the paper. This improved version is essentially acceptable for publication in The Cryosphere. However, I would like to recommend many minor (in substance) but in my view important revisions before publication. I am including an annotated manuscript detailing the recommended changes. These suggestions are intended to improve the readability and attractiveness of your paper for a wider audience. Please go over each comment and consider making the recommended changes. Please note that I have also made a number of suggestions to improve the readability of the figures.
Furthermore, you may consider mentioning briefly hydrological applications, for which accurate SWE determination is important, but accurate density profile data are not critical. This is optional and the decision is yours.
Please upload a manuscript in track changes mode in your response. You only need to comment briefly on the suggestions that you have chosen not to follow. Please also make sure not just one author proof-reads the final version before submission. This seriously limits errors, improves clarity and significantly reduces delays by avoiding further modifications.
I thank you in advance for your final version, and for submitting your work to The Cryosphere.
Florent Domine

Dear Authors,

Thank you for your revised version and your careful attention to the points I raised earlier. I am now happy to accept your paper for publication in The Cryosphere. Thank you for submitting your work to our journal.

Best regards,

Florent Domine