|The revised manuscript is now better organized and clearer. I think it provides an interesting discussion of the problems of sliding and basal ice in the context of ice sheet motion on hard beds. Although conceptual, it has the potential to stir debate and promote further research on sliding, one of the greatest uncertainty in modeling glaciers and ice-sheets. The revision takes into account comments by reviewers. One point, however, still requires some further clarification in my opinion. This and some minor points are detailed below.|
Major point: The meaning of power-law creep is confusing and this has generated a heated discussion during the review. Probably the confusion arose because of the unclear and undefined meaning of "standard" or "normal" power law or "Glen's flow law". Mathematically the meaning of power-law for ice is clear: strain rate depends on stress to some power. This is what glaciologists usually refer to as Glen's flow law (see Cuffey and Paterson, 4th edition, p. 55). The deformation mechanism, the value of the exponent n in the power-law (whether it is 1.8 or 3 or 4.2), and the Arrhenius function are irrelevant: Glen's flow law is a power-law equation and the value of n is not implicitly fixed when one mentions Glen's flow law (n could be 3.2 as suggested by Glen, 1955, or it could take some other value). If n=1, then it's a linear law. Usually numerical ice flow models use n=3 with some specific values for the prefactor and the activation energy in the Arrhenius relationship and this may be what the author refers to as "standard" or "normal" power law or "Glen's flow law" but the meaning of such qualifier or the definition is not clear in the text (it's clear in the response to reviewer though).
There is no discussion that basal ice at or near the melting temperature behaves differently than cold clean bulk ice. Ice near the melting temperature or ice at low stress may also well have different power-law exponents (closer to 1) and different Arrhenius parameters but they still both behave as power-law materials. If the exponent is exactly one then one can argue that it is not a power-law but a linear material.
Following that strict mathematical definition, Weertman's sliding model (and that of others) is valid for power-law creep regardless of the values of n, the prefactor or the activation energy used. Weertman's specifically chose some particular values for n and A (n=3) but his theory is valid for any combination of n and A.
The data near the melting point in Fig. 5 do not suggest that power-law creep is not dominant (page 7 line 15) because that plot does not show the dependence of strain rate on stress. The exponent of power-law creep could have a different value near the melting temperature depending on the deformation mechanism but the data of Morgan (1991) has no bearing on this as stated by reviewer Montagnat and discussed by the anonymous reviewer. It only indicates a changing Arrhenius parameterization.
To clarify the manuscript, I suggest defining early on the meaning of "standard" power-law as Glen's flow law with n=3 and with parameters for the Arrhenius equation that are commonly used for cold to near-temperate ice (could cite values in Cuffey and Paterson 4th edition). Then the author can argue that this "standard" power-law (used by many including Weertman) is not valid for temperate ice because n=3 does not represent deformation mechanisms operating near the melting temperature and the values of the Arrhenius constants are not appropriate as shown by Morgan 1991. Remove references to Glen's flow law that assume n=3. Call this the "standard" power-law model instead as done almost everywhere in the paper.
- Thermal equilibrium: An argument has appeared between the anonymous reviewer and the author because of the use of this term. The author and the reviewer are not using this term in the same sense hence the discord. From a purely thermodynamics point of view, the author is correct, thermal equilibrium means that the temperature is everywhere the same. The reviewer, however, is using a more conventional meaning in glaciological modeling: equilibrium means steady state conditions, i.e., nothing changes in time but there can spatial variations of the temperature field (or any other fields). In that sense there is equilibrium in Weertman's model but it is not thermodynamic equilibrium. To make the sense clear and avoid confusion because of use of different jargon, may be the first mention of "thermal equilibrium" should indicate that it means a uniform temperature everywhere with no thermal gradient. Related to that I don't see why ice and brine can't be in thermal equilibrium (page 8 line 31).
- Write paleo or palaeo but be consistent
- p2, line 19, comma after "warm-based"
- p3 item 2) The question is awkward because it seems to imply that classic sliding models don't assume temperate ice. But they all do.
- p3 line 14 "thermal different controls" -> "different thermal controls"
- Fig 1. h_ice = 800 m (small m for meter)
- p4 line 9. The work of Emerson and Rempel "the sliding resistance of simulated basal ice", TC, 1, 11-19, 2007, should also be cited.
- p4 Equation 2 would be better rewritten as a conventional melt rate, i.e. with units of length over time (so by dividing everywhere by density). See response to anonymous reviewer
- p5 line 2 Change "Any thermal gradient at" to "Any thermal gradient along" to make clear that this refers to the longitudinal direction, not the vertical.
- p6 Fig 5 is cited before Figs 3 and 4. Change figure order
- p 11 line 6 Influx is singular so "represents"
- p13 line 3 The last "transport" is not necessary