|I thanks 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.
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.