Dear Felicity,

I have now received two new reviews of your paper and both consider that the revised manuscript doesn't take enough into consideration the recommendations made in the two first reviews. Even if it has not been mentioned by reviewers during the reviewing process of your two previous papers focussing only on the law itself and its validation against lab experiments, I think that the current reviews clearly raised two important points that must be clarified and discussed in this new paper. A clear discussion stating the limit of the law in term of anisotropy and applicability to polar ice must be added to the manuscript before it can be published in TC. Reviewer #1 gave a lot of references and definitions to modify the manuscript accordingly. You might also consider renaming your law without the qualification of anisotropy.

Best regards,
Olivier Gagliardini

Dear Felicity,

Thanks for this new version of the paper and your careful reply to both reviewers. I now think that the two main points discussed by both reviewers are appropriately addressed in this new version of the manuscript, but as you will see below, there is a problem with our description of the ISMIP-HOM experiments and few other remarks that has to be corrected/specified. They are also listed below by order of appearance in the text.
Regards,
Olivier Gagliardini

* ISMIP-HOM experiments:
- I am confused by the presentation of these experiments as you are speaking of "steady-state", "timestep", "initial surface", etc... whereas these experiments are diagnostic and should not imply time and surface evolution: the velocity field should be computed for given (fixed) geometry and boundary condition. If you are solving a modified version of these tests, which I don't believe is the case, it should be mentioned. Else, why do you need a time step to solve these diagnostic experiments? This should be corrected in many places (text and figure captions), the terms "steady-state", "timestep", "initial surface", "prognostic", etc... should be removed/replaced.

- Also, as I understand, you have modified the Glen's flow law parameter such that the new value (:8) times the Glen's enhancement factor (=8) is equal to the ISMIP-HOM one (8:8=1). If this is correct, then I would expect that your results for the Glen's law are comparable with the ISMIP full-Stokes results, which seems not to be the case, especially for experiments B. This should be commented and discussed. On the same line, the sentence "to ensure our results are as close as possible to the original ISMIP-HOM experiments." page 17, line 3 should write "to ensure the solution with the Glen law does correspond to the original ISMIP-HOM experiments."

- Sections 6.2 and 6.3 are quite long and could be shortened by discussing in parallel the two cases for L.

* Other remarks:

-page 1, line 4: scalar, constitutive or flow relation -> scalar, constitutive relation (specified below, not necessary here)

- page 5, 2: (Fig. 3a Budd and Jacka, 1989) -> (Fig. 3a in Budd and Jacka, 1989)

- page 8, line 21: in Eq. 2, Eq. 3 differs -> in Eq. (2), Eq. (3) (and everywhere in the manuscript, refer to https://www.the-cryosphere.net/for_authors/manuscript_preparation.html)

- Eq. (8): what is w_D, a vector ? Not clear from above where it is said it is the deformation (tensor). Its expression should be given.

- page 12, line 6: define what is v.

- page 13, line 8: stress (bridging effects van der Veen and Whillans, 1989) -> (bridging effects, van der Veen and Whillans, 1989)

- page 15, line 14: about the boundary condition below the ice-shelf, it is not mentioned if you are prescribing a normal friction accounting for change in water pressure when the basal surface elevation changes (see Durand et al 2009). If not, it might explain why you need such small timestep (< 1 day) to have a stable ice-shelf. This should be discussed.

- page 19, line 23: the free surface. in the next section -> the free surface. In the next section

- page 19, line 24: flow relation . Shear dominates -> flow relation. Shear dominates

- page 19, line 33: The results of a full-Stokes prognostic run to steady-state for the ISMIPD -> ISMIPD is not a prognostic simulation so that there is no steady state to look at.

- page 21, line 32: Accordingly, in the flow regime of these prognostic experiments -> again, ISMIP B and D experiments are diagnostic, not prognostic

- Figure 8: the size of the subplots should be similar than in the previous figures

- Table 1: It is not clear from the text that you are also increasing the number of CPUs used to run this comparison between Glen and ESTAR walltime. Are you doing parallel simulations? Then you should also discuss this results in term of scalability? Why do you need the CPUs to increase much faster than the DOFs? I don't also understand why the number of DOFs is smaller than the Vertices. With the FEM, for 3D Stokes, the DOF per node is 4, so that I would expect that the total number of DOFs is ~4 x the Vertices.

References:
Durand G., O. Gagliardini, B. de Fleurian, T. Zwinger and E. Le Meur. 2009. Marine Ice-Sheet Dynamics: Hysteresis and Neutral Equilibrium, J. of Geophys. Res., Earth Surface, 114, F03009, doi:10.1029/2008JF001170.

Dear Felicity,

Thanks for this new version of the manuscript.

The fact that you were performing prognostic simulations adapted from the ISMIP-HOM experiments was indeed not clear. I am still a bit confuse about this choice as it doesn't allow any comparison with previously published ISMIP-HOM results. Also, if you keep this choice, I would suggest to make clearer in the manuscript that your results should not be compared to the ISMIP-HOM ones and clearly justify the choice of running these initially diagnostic tests in transient. I think the paper can now be accepted in TC, but I let you decide if you want to keep the prognostic experiments from ISMIP-HOM (and therefore justify why and make more clear this choice) or change to the initial ones. There are few more points listed below that should be corrected before publication.

Regards,
Olivier Gagliardini

- As you are running the ISMIP-HOM tests in transient, you should specify which accumulation/ablation function is applied to solve the free surface evolution. I guess it is null, but any other function fulfilling periodicity and having a null integral over the domain should work? For the results, the comparison should not only be done on the velocity but also on the surface elevation, which should be different from Glen and ESTAR? These surface elevation differences should be quantified.

- Figures 8 and 9 should be merged and made similar to Fig. 10 as it seems that the 5+3 panels are identical to the 8 panels of Fig. 10. Also, you should avoid to repeat the caption of a figure when it is similar to a previous one. For example, caption of Fig. 7 should simply writes: "Same as Fig. 6 but for L=5 km".

- For all figures of modified ISMIP-HOM results, the surface elevation should clearly be shown by increasing the maximal elevation on the vertical axis. For ISMIPDp, it seems from Fig. 10 that the surface is everywhere higher than the 2000m, which should not be possible if the mass conservation is correctly fulfilled (and assuming a null surface accumulation/ablation, which still as to be specified).

Dear Felicity,

Thanks for this new version of your manuscript and your reply to my last questions. I am happy to now accept your paper as it is in The Cryosphere.

Thanks for having choosing The Crysophere to publish your work.

Best regards,
Olivier Gagliardini