To the authors,

You have addressed the reviewer comments thoroughly. I would like to invite you to submit a revised manuscript.

Best regards,
Alex

The manuscript is in very good condition, and near-ready for publication, except for potentially one critical point that I believe has been overlooked until now.

I apologize that I didn’t notice it until now, but I am somewhat concerned by the experimental setup described in Section 3.2, in which the initial volume is kept constant by tuning accumulation. This procedure may introduce an unwanted change in the temperature of the ice sheet, since the accumulation rate directly controls the vertical velocity profile, which enters the thermodynamic equation. By e.g., increasing accumulation, one can generally expect a colder ice sheet and a lower rate factor. Accumulation rate differences of between 50% and 300% seem large enough to have a strong impact on internal temperature. Since flow differences due to Q and n are precisely what is studied here, I am worried that the interpretation of the results is contaminated by the systematic changes in accumulation.

The best solution at this stage would be to be able to confirm that this is not the case – i.e., that despite the influence of accumulation on internal temperature, its impact is much smaller than that of the rate factor parameters themselves. Maybe this could be done with a fixed ice thickness profile: then you could diagnose changes in the rate factor and/or ice velocity as a function of the rate-factor parameters and accumulation and see the magnitude of their impacts? If changes in accumulation do play a large role, perhaps you could consider simply allowing the initial volumes to differ – since you report volume losses in percent, the difference in absolute volume should not have a large impact given the idealized configuration of the experiment.

In either case, I think it is important to address this point before moving forward with publication.

Please find additional minor points below:

L42: I suggest separating discussion and references about the parameter n and the parameter Q. Therefore, I would move the sentences of L52-56 concerning the parameter n to just after “which can be between 2 and 4” on L42, to keep the discussion of n together. Then proceed with discussion of Q. Ie, “…, which can be between 2 and 4 [REFS]. [Sentences from L52-56]. The activation energies Q … can also vary by a factor of two [REFS].

L43: 50+ citations to support the statement that n shows a large spread and that the activation energies “can vary by a factor of two” seems a bit excessive. I support the notion of such an extensive review of older and perhaps now forgotten literature, especially if nothing new has been done since beyond it. However, for that I would expect some specific information that came from each paper with separated citations (essentially, a more detailed review paragraph). If you are only interested in supporting the above statement, I would suggest reducing the number of references to the most relevant and ground-breaking ones.

L52: Merge “(Zeitz et al. submitted)” into the other citations here, or specify what is different about the reference, aside from only having been submitted. As it is now, it’s not clear why it stands apart.

L75: It may depend, among others, on => It may depend on water content …, among other things.

L79: temperature difference => temperature relative

L95: independently => independent

L115: the typical standard value => a typical reference value

L116: the standard value => a typical reference value

L118: The standard values serve as a reference point and correspond => The reference values above correspond

L130: warm or cold ice respectively => cold or warm ice, respectively,

L134: in the same order => on the same order

L146: I would expect to see the basal boundary condition here as well, ie, geothermal heat flux.

L196: the volume calculated => the ice profile

L210: , which mathces => that matches

Fig. 6: Remove grey lines connecting the zoom of panel (b) to that of panel (a). They do not help comprehension, and the caption and axes are clear enough.

Fig. 8: Panel (b) should include a y-axis label as well (despite having the same units, I assume), to avoid ambiguity.

L259-261: I’m not able to follow this logic – it sounds like something contradictory is stated. If A_0 reduces with a lower n, or rather if A_0 increases with a higher n, then the rate factor should increase with a higher n. This would lead to faster flow too. Perhaps another sentence or two would help with clarity of the message here. Or simply delete the sentence “This might be linked …”. The last sentence of the paragraph is clear and seems warranted by the results.

L270: shallow ice approximation => shallow shelf approximation [?]

L290: allows to => allows us to

L296: allows to => allows us to

L328: by e.g => by e.g.

L330: to assess => to assessing

L331: allows informed => helps to inform

L332: the Greenland or Antarctic Ice Sheet => continental-scale ice sheets [since these insights could apply to any ice sheet, right?]

To the authors:

I find the revised manuscript to be in excellent condition and almost ready for publication. I only still have one doubt concerning the new sentence “Similar to the MISMIP setup, there is no geothermal heat flux prescribed.” I find this difficult to understand. In the MISMIP experiments, the rate factor was prescribed and thus, there was no temperature dependence, and no geothermal heat flux was needed. However, here you have a fully thermo-mechanical model and basal temperatures near/at the pressure-melting point. With a surface temperature of < -20 degC and Q_geo = 0, what is the heat source warming the base of the ice sheet? I do not believe that internal shearing alone, for example, would be enough in this case. Please check and confirm.

Best regards,
Alex