Dear Lea-Sophie and co-authors,

Thank you for your thorough responses to the reviewer comments. I now invite you to submit a revised manuscript, addressing the reviewer comments, along with a tracked changes version of the manuscript.

There are a couple of points in the reviewers’ comments that would be good to see addressed in a bit more detail, as follows:
- R1 makes a good point about the balance between the details of the L-curves (i.e., specifics relevant to ISSM) and those of the effect of different regularisation values on the outputs of the inversion (basal traction fields). The latter is also very relevant as we’re starting to see more outputs from advances in automatic differentiation, where small differences in basal traction can make a large difference in the evolution of the system over time, and particularly in response to climate change. It would be good to make sure that aspects of the work that have broad applicability for ice sheet modelling studies is addressed in the discussion. I also agree with the reviewer that the point about potentially needing different λbest values for different basal friction regimes is a key result – one of the most significant and compelling results – and one that deserves a more detailed discussion. How do you envisage such an analysis could be undertaken? Can you make recommendations about an approach that could be suitable here, particularly given what is known about the ice-bed interface zone (e.g., from geology and subglacial hydrology)?
- Both R1 and R2 comment on structure and conciseness for improved readability. It would be good to please point out where edits in the tracked changes document pertain to this request.

Best regards,
Felicity McCormack

Dear Lea-Sophie and co-authors,

Thank you for your detailed responses and the considerable edits made to address the reviewers' comments. In general, I am happy with the originality, scientific quality, significance, and presentation quality -- reviewed as per the TC/TCD requirements. However, I will send this out for a further review by the referees.

Thanks again very much for your submission to TC/TCD.

Best regards,
Felicity McCormack

Dear Lea-Sophie and co-authors,

I've now received the reviewers' latest round of comments. Based on the comments and your subsequent revisions, I suspect that your manuscript will be acceptable for publication in TC.

In your preparation of a revised version of the manuscript, please take into account the recommendations from referee #1, along with the following minor comments of my own:

- L8: “... optimal trade-off between the cost function terms, resulting in smooth L-curves.” → ““... optimal trade-off between the cost function terms that result in smooth L-curves.”
- L10: “curves” → “L-curves”
- L44: I’m not sure what “... in the most realistic sense” means here? Do you mean “... in realistic settings”?
- L49: “It is therefore desirable to resemble the subglacial water pressure on a more realistic and physical basis…”. Consider citing papers by Dow, Flowers, Werner, etc. here, who have made substantive contributions to the development of subglacial hydrology models towards this aim. Also Ehrenfeucht et al. (2024; https://doi.org/10.1029/2024GL111386), which describes whole-Antarctic subglacial hydrology model outputs using GlaDS.
- L79: numerical instability?
- L93: “physical-based” → “physically-based”
- L230: Could you add a sentence describing why you don’t use a logarithmic misfit term in the cost function equation (5), as per other studies (e.g., Morlighem et al., 2013)? This could be helpful for other modellers.
- Figure 7: update the font size of axis labels in panels b-i to be approximately the same as that of the main text
- L625: “...a reduced skin drag. Indicating, that…” → “...a reduced skin drag, indicating that…”
- A general revision of the Conclusion section for improved clarity would be good. E.g., L659-660: “The L-curve analysis taught us…” → “We find that ill-shaped L-curves with many outliers are most likely the result of inconsistencies in the model setup that should be addressed.” There are also some incomplete sentences to reword (e.g., L663 starting with “Overall, …”)

General things to check:
- An overall check for grammar throughout the manuscript would be good. E.g., checking commas to delete (e.g., end of L63; L70 “examine both,”; L82 “point out,”; L86 “invert for both,”; etc.); prepositions (L119: “...on a manageable” → “...to a manageable”); and conjugations (e.g., L201-202 30% of the domain is frozen to the bed)
- Check parentheses in citations. E.g., L95 should be (CUAS-MPI; Beyer et al., 2018; Fischler et al., 2023). Similar elsewhere.

Thanks once again for your submission to TCD.

Best regards,
Felicity McCormack

Dear Lea-Sophie and co-authors,

Thanks very much for your edits. I am happy to recommend publication of the updated manuscript.

Thanks again for considering publishing with TC.

Best regards,
Felicity McCormack