Dear L. Logan et al,
The revised version of the manuscript was sent to 2 reviewers again (comments further below), and both were positive about the revisions undertaken and indicated that the revised version has strongly improved. However, they both had some remaining points that should be addressed (in particular reviewer 1) but the more substantial issues seem addressable and mainly refer to some further clarifications or discussions. These points should be addressed in some further revisions and In brief concern:
-A clearer discussion of the large differences in effective stresses of brittle versus ductile solutions (reviewer 1)
-some more careful phrasing within the introduction (reviewer 1)
-clarify whether temperature evolution is really used and if not adjust (delete description) in methods. (reviewer 1)
- I leave it up to the authors weather they want to follow the preference of reviewer 2 to cleaerer separate the rheology from the numeric. I think it works ok as it is.
- check and adjust if necessary the exolanation/justification of the ‘dynamic relaxation’ used (reviewer 2)
-in general list all the cited literature in the text in the reference list and check that the references are correct: currently quite a few are missing or not consistent:
not in reference list but in text:
benn 2009, rist et al. 1999lubliner 1990, simo and hughes 2004, Wilkins 1964murray et al 2014, bassis and Jacobs 2013 (there is only Bassis 2013 in list),… , list likely nopt complete

Further address all further rather minor comments of both reviewers (see list below) in a next re-revised version and importantly carefully proofread and re-check the manuscript before resubmission and comment all the changes and revisions undertaken. If the revisions are satisfying, the revised will hopefully not have to be sent to further review.
The editor A. Vieli, 2 Okt 2016

Reviewer comments:

Reviewer 1
I thank the authors for this new version which has clearly been improved since the first one. Nevertheless, I still have one major concern with the results presented in this new version and also many suggestions that could still improve the paper. A large part of the corrections listed below could have been avoided by a careful review of all authors of the paper.

My major concern is about the such large difference in effective stress given by the brittle and ductile solutions, and it would be nice if the paper could discuss more deeply this result. If the inertial term in the momentum equations were neglected, then the static equilibrium implies that the integral of the normal Cauchy stress on the domain boundary equals the integrated gravity acceleration over the domain. With such large differences in the values of the computed effective stress (more than one order of magnitude), I don't see how the integral of the Cauchy stress could be similar for the two methods. I wrote "similar" as I don't expect them to be equal since you are accounting for the inertia terms in the momentum equation, but in the other hand, I don't expect the inertia terms to contribute significantly to the total balance. This result, which is one of the major result of the paper, should be explored in more details, and the reason of such large difference explained by adding supplement information regarding Cauchy stresses and the relative contribution of inertia terms in the momentum equation.

Other remarks (line numbering from the new submitted version) :
- in the introduction, some wording are still a bit naive or too much affirmative, and sometime even not correct. For example, page 2, line 3: "these are often ... full-Stokes (FS) equations" i snot correct. There are much more lower-order models than Stokes models (see the class of models in the papers by Pattyn on ISMIP, MISMIP or MISMIP+ exercices, there is only one or two Stokes model that have applied). An other example: line 7, "most models are designed largely for steady state flow" is just a wrong statement (obviously I missed this in my first review). On what is based this strong statement regarding the fact that most model are diagnostic and not prognostic. At least, all models that performed ISMIP-HOM test F, MISMIP and MISMIP3d are capable to evolve the geometry. All this introductive part regarding ice flow models should be seriously corrected.

- page 3, line 1: A is not a relation, A is a fluidity parameter, which dependency to temperature is given by an Arrhenius relation.

- page 3, line 4: to my point, more than high strain rate, it is high stress or at least you should mention also or high stress

- page 3, line 5: of brittle or ductile deformation -> of ductile and brittle deformation. More logical to invert with the two sentences that follow and also I think it should be and (and not or) as the calving is the result of these two processes.

- page 3, line 17: these models they often -> these models often

- page 4, line 6: magnitude larger -> magnitude much larger

- page 4, line 11: brittle or ductile -> brittle and ductile

- page 4, line 25: finite element method -> finite element model

- page 5, line 4: the system is not complet and cannot be solved with only these equations (4 unknown u, v, w and p for 3 equations). You should add the equation that you solve to close the system to be consistent.

- page 5, line 14: it is a strong assumption, only valid if the base is temperate. Else it should be a heat flux. Anyway, my understanding is that for the test presented the temperature field is imposed (at least for experiment 1, page 13, line 19 and seems not specified for experiment 2)? If this is true, than this part regarding the temperature solution could be removed.

- page 5, line 20: what does it mean to enforce mass conservation via elasticity? Which equation are you solving for? See also the point page 5, line 4.

- page 5, line 22: accounting for accumulation or ablation is not done through a Neumann conditions. Neumann conditions for the Navier-Stokes problem allow to enforce stress type conditions.

- Equation (5): $tr(\epsilon)=\Delta V/ V$ and should be 0 for an incompressible material like ice. Or do you account for the void volume introduced by the opening of cracks?

- Equation (7): not obvious to derive (7) from (6), may be a reference or more explication could help the reader? Also, the notations are not consistent, with sometime VE and other ve for the viscoelastic indice on stress.

- Equation (8): again, the trace of the strain rate is zero for an incompressible material like ice

- page 7, line 20: I am confused with the sign of the yield surface criteria. The elastic stress is on or within the yield surface if $f \le 0$?

- page 8, line 6: $\sigma_1$ is not used in Equation (9). Should be defined below Equation (10).

- Equation (17): Is $K_s$ different than the $K$ parameter defined above?

- page 13, line 14: boundary conditions in glaciers are often either formulated as a Weertman-style sliding law -> boundary conditions at the base of glaciers are often either formulated as a sliding law

- page 13, lines 17-19: this sentence is not clear. You should insist that you are solving a Lagrangian problem (which is not the classical approach in ice flow modeling, most model being using an Eulerian approach). Suggestion: During the transient simulation, when a basal node reaches the position x=10km, its velocity is tilted to an angle of 3 degrees

- page 15, line 12: the brittle ice remains largely or exactly in its initial configuration? The largely is to said that the deformations are only due to elastic deformation and are small regarding to plastic ones after one year? May be you should be more precise here.

- page 15, line 14: it should ne mentioned that these results are not shown?

- page 15, line 17: the definition of semi-brittle has already be given above. See also the next point.

- page 15, lines 19-26: this text should be in the model presentation

- page 15, line 25: I don't think that strain can be used to estimate when ice should start to accumulate damage. In ice sheet for example, you can find ice that have undergone very large strain that are not damaged at all. On the contrary, the fact that damage should be initiated using strain-rate is still debated in the community, as stress might be a much pertinent variable for that. A lot of the material presented on this paper rely on the work by Duddu et al., 2013, but it was controversial as stated in the comment by Gagliardini et al. (2013).

- page 16, line 10: I am wondering how the stresses (deviatoric and Cauchy) resulting in this procedure looks like. Are they continuous between ductile and brittle area? How large are the discontinuity? How the choice between ductile and brittle distributes over the domain. May some more results on this could be added and useful results on how the model behave might be obtained from this analysis?

- page 16, line 25: 2 difference mesh sizes -> 2 different mesh sizes

- page 17, line 22: would be nice to have also a plot of the stress and velocity for the two different meshes.

- page 18, line 11: we determined an accumulated -> we determined that an accumulated

- page 18, line 12 (and at many other places in the manuscript): .03 should write 0.03

- page 19, line 6: I would said that one hour and even 24 hours is a small computational cost, so the argument of too large computational cost for finer resolution is a bit odd?

- page 19, line 12: is consistent with and predicted by rate-independent. Missing a word at the end of the sentence?

- page 19, line 13: one developed should be suppressed

- page 20, line 13: for a Stokes model, the evolution of the GL is not necesserally based on a criteria on ice thickness but can solve a proper contact problem (so e.g. instead of i.e. would be more appropriate here)

- page 21, line 6: 3 difference stresses -> 3 different stresses; and Figure 10a and b -> Figures 10a and b

- page 21, line 10 (and elsewhere): Fig. 10e and f -> Figs. 10e and f



- Figure 3: two many text in the caption. These comments should be (and are already for some of them) in the main text. The pink vertical line of Fig. 4 should also be added on Figs. 2 and 3 to show where is the GL precisely.

References:

Gagliardini, O., J. Weiss, P. Duval and M. Montagnat, 2013. On Duddu and Waisman (2012a,b) concerning continuum damage mechanics applied to crevassing and icebergs calving, Correspondence to J. Glaciol., 59(216), 797-798, doi:10.3189/2013JoG13J049.

Pattyn, F., L. Perichon, G. Durand, O. Gagliardini, R.C.A. Hindmarsh, T. Zwinger, T. Albrecht, S. Cornford, D. Docquier, J.J. Fürst, D. Golberg, G.H. Gudmundsson, A. Humbert, M. Hütten, P. Huybrechts, G. Jouvet, T. Kleiner, E. Larour, D. Martin, M. Morlighem, A.J. Payne, D. Pollard, M. Rückamp, O. Rybak, H. Seroussi, M. Thoma and N. Wilkens, 2013. Grounding-line migration in plan-view marine ice-sheet models: results of the ice2sea MISMIP3d intercomparison, J. Glaciol., 59(215), doi:10.3189/2013JoG12J129.

Pattyn, F., C. Schoof, L. Perichon, R.C.A. Hindmarsh, E. Bueler, B. de Fleurian, G. Durand, O. Gagliardini, R. Gladstone, D. Goldberg, G.H. Gudmundsson, V. Lee, F.M. Nick, A.J. Payne, D. Pollard, O. Rybak, F. Saito and A. Vieli, 2012. Results of the Marine Ice Sheet Model Intercomparison Project, MISMIP, The Cryosphere, 6, 573-588, doi:10.5194/tc-6-573-2012.

Pattyn, F., Perichon, L., Aschwanden, A., Breuer, B., de Smedt, B., Gagliardini, O., Gudmundsson, G. H., Hindmarsh, R. C. A., Hubbard, A., Johnson, J. V., Kleiner, T., Konovalov, Y., Martin, C., Payne, A. J., Pollard, D., Price, S., Rückamp, M., Saito, F., Soucek, O., Sugiyama, S., and Zwinger, T., 2008. Benchmark experiments for higher-order and full-Stokes ice sheet models (ISMIP–HOM), The Cryosphere, 2, p. 95-108.


Reviewer 2:
The semi-brittle rheology employed by the authors of this study is novel and has the potential for significant improvement of our understanding of glacier failure. I think the authors have done an excellent job responding to reviewer comments and I generally prefer to avoid torturing authors with a second round of changes. I still, however, I have a small number of minor comments, described below, that the authors may consider addressing.

Comment 1: I am satisfied by the updated description of the rheology. I would prefer to see the rheology cleanly separately from the numerics because the rheology defines the “physics” and is at the heart of the model while the numerics consists of a set of choices made to solve the physical equations, but I leave this at the description of the authors. The one question I have is whether the Lagrangian scheme is valid for large strains, which is important for the deformation of ice over long periods of time. This should be clarified.


Comment 2: I still object to the term “dynamic relaxation” being described as a means of accurately solving the dynamic (i.e., with inertial terms) equations. In the original experiments by Cundall and others, dynamic relaxation was clearly introduced as an approximation. In fact, it is straight forward to prove that the mass weighting approximation can be arbitrarily incorrect when applied to the full dynamic problem and only approximates the inertia-less solution in the limit of long time scales. To sketch out the proof for the first case, we note that a solution to the short-time scale elastic behavior consists of an elastic wave traveling at the p-wave velocity, which we call c. In the mass weighted method, the p-wave velocity is c’, where c’ is less than c. After some time t, using d’Alembert’s solution, an arbitrary perturbation will have travelled a distance d=c*t. In the mass weighted system, the perturbation will have only travelled a distance d’=c’*t< c*t. Given the fact that the perturbation is arbitrary, the mass weighted solution can be arbitrarily incorrect unless c’ approaches c. This completes the proof that dynamic relaxation cannot provide an accurate solution of the full dynamic equations. We next turn to the limitations of applying dynamic relaxation to the quasi-static analogue (i.e., when inertia is omitted). The quasi-static limit corresponds to solving an elliptic equation in which velocity is non-local. In the dynamic, mass weighted approximation, one still solves a hyperbolic or diffusive set of equations in which information propagates locally. Let us again consider a perturbation, but this time to the ice thickness. In the quasi-static limit, a point a distance “x” away from the location of the perturbation feels the effect of the perturbation instantaneously. However, in the dynamic limit with mass weighting, information still only propagates at a speed of c’. Hence, for sufficiently small time “t”, c’*t<

Minor comments:
Page 20: Matching the limited laboratory data to simulate ductile failure is a process fraught with error. First, the laboratory data are generally obtained using laboratory grown samples of ice and these samples do not necessarily reflect “actual” ice. Second, the studies seem to lump many different crystal deformation processes into a “damage” parameter and this is not always robust. However, given the limited laboratory and field data available, this is probably the best that can be done. This limit afflicts previous studies, like those of Duddu and others that were also limited by the lousy quality of laboratory studies.

Page 31: the lack of numerical convergence in Experiment 2 is worrisome. Is the spacing of basal crevasses a function of grid spacing does the model simply require a much greater resolution than the authors are capable of providing to numerically converge? This is something that the authors should comment on.

References cited are not all in the reference list. This should be carefully checked.

Page 16, line 9: sigma_e is the effective stress, not the effective pressure. Effective pressure is usually defined as the pressure minus pore pressure. The effective stress is the 2nd stress invariant

Page 16, line 23: Grammar problems—>“When simulating ice rupture however these models they often employ failure criteria developed with elastic underpinnings.”
-missing commas before and after however
-extra “they”

Additional minor comments by editor:
p. 2, Line 8: I agree with reviewer 1 that probably ‘most’ models have prognostic capabilities by now (although they may not all have been used for this)
Fig 11 (appendix): clarify the legend in the figure, I assume ‘FS’ in the legend stands for ‘Full Stokes’.

P. 26 line 16: it should be Murray T. (surname is Murray)

The authors adressed the remaining issues raised by the two reviewers in detail and satisfactorily and only very few writing issues remain which are listed below.
After addressing these issues i can accept this publication for publication in TC.
The editor A. Vieli

Keywords: i suggest to add the keywords glacier and ice sheet
p. 2 line 12: should there not be a comma after Thus?
p. 13 line 24: should it not be ‚...prescribed at an angle...’ (istead of prescribed angle)?
p. 17 line 9: should there not be an ‚at’ before ‚and other places’?
p. 19 lines 3 and 5: at least one if not both ‚truly’ should be deleted.
p. 20 line 10: should it not be ‚occuring’ instead of ‚occurs’?
p. 21 line 19: move bracket (with content) to AFTER ‚plastic strain’.