Dear Ronja,

Thanks for this new version of your manuscript and your reply to both reviews, which have been checked again by reviewer #1.

I think that the current version of your paper can be accepted in The Cryosphere. Nevertheless, after this last careful reading I found some typos and have one suggestion that you might want to include to improve the final version of the paper. See below.

Best regards,
Olivier Gagliardini

Main suggestion:
In the discussion, the sensitivity of the results are studied as a function of different parameters (sliding exponent, regularisation, mesh), but the fact that the model is not relaxed after inversion might have much more influence on your results? It is well know that flux divergence are very often not realistic from the inversion (even if the horizontal velocity are close to the observed ones, vertical ones might be far from observations at some place, inducing potentially large surface adjustment), such that a short relaxation period of the free surface is required before running any transient simulations. How much your results would be influenced by such a relaxation procedure could be discussed, at the same level than the parameter sensitivity experiments.

Typos:
- page 1, line 9: complexed-valued -> complex-valued ?
- page 2, line 31: no capital letter after ":"
- Figure 1 could be improved: reduce the space between the different panel, the size of label should be similar to the main text size and homogeneous for all panels
- page 6, line 27: can you name tau_f?
- page 9, line 12: theta must be negative -> a negative value for theta is obtained (?)
- In Figs. B3 and B5, it is not clearly mentioned that it is theta_1 that is plotted. Also, in the legend of Figs. B4 and B5, extended is used instead of analytical.

Dear Ronja,

Thanks for this new version of you paper. I am very happy to accept it for publication in The Cryosphere.

Thanks for having choosing TC to publish this piece of work.

Regards,
Olivier Gagliardini