|This manuscript presents a revised version of a manuscript that I reviewed earlier. The authors main conclusion is that ungrounding of a portion of the glacier associated with block detachment can increase longitudinal stresses and promote iceberg detachment. In general, I have no objections to publication. I do, however, have a couple of minor comments|
The Durand et al., (2009) method to solve the contact problem involves introducing a vertical damping force to balance buoyant uplift in portions of the glacier. The reason why a buoyant damping force is needed is to keep the problem well posed and allow closure in the vertical force balance without needing to resolve the inertial terms. However, the method proposed by Durand et al., (2009) usually results in a time step dependent velocity field. This suggests two concerns:
1. The authors should state what time step was used in solving the contact problem. I apologize if this was included and I missed it or this is not actually what the authors are going;
2. The authors should characterize the time-step sensitivity of the strain rate and stress field. In my experience, for relatively small changes between time steps, the strain rate field, which is related to the symmetric gradient of the velocity field is only weakly time step independent. However, the strong change in geometry associated with the block removal is larger than anything that I have examined. If there is no time step sensitivity, then the authors can merely state this quickly to avoid any future confusion. I don’t anticipate that this will be a problem, but even if there is some time step sensitivity, then simply documenting it would be sufficient from my perspective. It isn’t my goal to act as some kind of gatekeeper and the idea that the decrease in longitudinal stress could promote calving still merits consideration in the literature.
I also have a question about the mechanism resulting in large basal stress concentrations in the Weertman sliding law. The transition from no-slip to slip is known to result in a singularity in the stress field at the slip/no-slip transition. Including a sliding law, like the Weertman sliding law, allows a smooth transition from slowly slipping to freely slipping and this removes the singularity in the stress field. The introduction of the Weertman sliding law essentially regularizes the singularity in the crack problem, but large values of stress are still expected near the transition to free-slip and these values of stress should increase with the sliding law coefficient. This looks like what is shown in Figure 5. However, it is often necessary to increase the resolution of a model near the slip transition to fully capture the peak in stress. Is it the slow slip/free slip transition that is generating the large stress concentrations> Are these numerically resolved? Does the magnitude of the stress concentration increase with increasing friction coefficient?
This also seems inconsistent with Figure 6, which I really don't understand. For small friction coefficients, the ice is essentially freely-slipping so I don’t quite understand why the transition to buoyancy decreasing the shear stresses matters in this regime. Shear stress are already negligible and decreasing them further seems like it shouldn’t make a difference after a point. Clearly, large basal friction coefficients are more stable and this makes me wonder how much the sensitivity depends on the baseline longitudinal stresses (smaller for high friction and larger for low friction).
Page 4, near line 15. The discussion of observations of fracture strength mixes quite different loading regimes. The yield criterion that Vaughan (1993) deduced was based on the Von Mises stress criterion. This is only equal to the tensile stress used by the authors in purely tensile loading. An appropriate comparison would plot the Von Mises stress. Or stick to the Schulson experiments. The experiments in Schulson (2001), specifically include tensile failure experiments, which seem more in line with largest principle stress criterion that the authors prefer for failure.
Equation (9) doesn’t provide a sign. I assume that the actual implementation includes multiplying by the sign of the basal velocity or some such additional implementation decision to ensure that friction opposes flow. Mentioning how this is implemented in Elmer/Ice would be nice.
How were the constants in the Coulomb-limited sliding law chosen? Are these determined so that they roughly correspond to the same basal shear stress as the Weertman sliding law?
Page 4 near Line 25, It says the vertical velocity is set to zero when the ice is grounded, but for the contact problem, isn’t it the velocity normal to the bed zero?