Sliding of temperate basal ice on a rough, hard bed:
creep mechanisms, pressure melting, and implications for ice streaming

Krabbendam, Maarten

doi:https://doi.org/10.5194/tc-10-1915-2016

Articles | Volume 10, issue 5

https://doi.org/10.5194/tc-10-1915-2016

© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/tc-10-1915-2016

© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 10, issue 5

Research article

|

05 Sep 2016

Research article |

| 05 Sep 2016

Sliding of temperate basal ice on a rough, hard bed: creep mechanisms, pressure melting, and implications for ice streaming

Maarten Krabbendam

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Final revised paper (published on 05 Sep 2016)
Preprint (discussion started on 01 Apr 2016)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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- Supplement

SC1: 'Ice facies evidence of grain boundary melting', Doug Benn, 06 Apr 2016
- AC1: 'reply to Doug Benn: ‘Ice facies evidence of grain boundary melting’', Maarten Krabbendam, 05 May 2016
RC1: 'Comments on the paper “Basal sliding of temperate basal ice on a rough, hard bed: pressure melting, creep mechanisms and implication of ice streaming” by M. Krabbendam', Maurine Montagnat, 28 Apr 2016
- AC3: 'reply to comments by M Montagnat (referee)', Maarten Krabbendam, 05 May 2016
  - RC3: 'Reply to reply to comments...', Maurine Montagnat, 09 May 2016
RC2: 'Review', D. Cohen, 29 Apr 2016
- AC4: 'Reply to interactive comment by D Cohen (referee)', Maarten Krabbendam, 17 May 2016
SC2: 'Update of literature and discussion needed', Olaf Eisen, 02 May 2016
- AC2: 'reply to O Eiden: 'Update of literature and discussion needed'', Maarten Krabbendam, 05 May 2016
RC4: 'Full paper', Anonymous Referee #3, 18 May 2016
- AC5: 'Reply to Referee #3', Maarten Krabbendam, 26 May 2016

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

AR by Maarten Krabbendam on behalf of the Authors (20 Jun 2016) Author's response Manuscript

ED: Referee Nomination & Report Request started (21 Jun 2016) by Olivier Gagliardini

RR by Maurine Montagnat (13 Jul 2016)

RR by Denis Cohen (18 Jul 2016)

Suggestions for revision or reasons for rejection

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.

Minor comments:
- 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

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ED: Publish subject to minor revisions (Editor review) (21 Jul 2016) by Olivier Gagliardini

Dear Maarten,

I have now received two new reviews on the revised version of you manuscript. Both referees have noticed the improvement of this new version and that most of the initial comments were taken into account in the new version. Nevertheless, as mentioned by referee 0000002, the manuscript still need some corrections, especially regarding the definition of what is called "Glen's law" or "Weertman friction law". From my point of view, the manuscript could also be improved by adding a strongest discussion on the form of the friction law that should be used in ice flow models. As a modeler, I found the discussion/conclusion a bit weak in term of suggestion of what should be done to improve current parametrization used in ice flow model. What should be the form of such law? What would be the typical range of the parameters entering such friction law? This would be very helpful for the modeling community. I have also noticed few minor typos that are listed below.

On the basis of these two new reviews, I think that your paper can be accepted after these minor revisions have been accounted for. From a revised version with changes highlighted as well as a point to point reply to referee 0000002 and my comments, I will take the final decision.

Best regards,
Olivier Gagliardini

Minor corrections:
- Abstract: is the power-law creep behaviour not applicable for temperate ice is not clear for me. It will be a different exponent and different parameters than the ones used in the classical Glen's law, but it will remain a power-law creep law?
- page 4, line 6: avoid a complete sentence in bracket, or insert it before the point of the first sentence.
- Figure 1: it should be h_ice = 800 m and not 800 M. In this figure, it is assumed that Q_geo = 50?
- page 6, line 25: no space between \epslion and ","
- page 9, line 7: ice(Tison -> ice (Tison
- page 12, line 24: temperature. the rheology -> temperature. The rheology
- Appendix: equations that are already written in the main text should not be rewritten here but cited with their number.
- page 30, line 1: give directly the value of \tau in kPa

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AR by Maarten Krabbendam on behalf of the Authors (05 Aug 2016) Author's response Manuscript

ED: Publish subject to technical corrections (18 Aug 2016) by Olivier Gagliardini

AR by Maarten Krabbendam on behalf of the Authors (22 Aug 2016) Author's response Manuscript

Short summary

The way that ice moves over rough ground at the base of an ice sheet is important to understand and predict the behaviour of ice sheets. Here, I argue that if basal ice is at the melting temperature, as is locally the case below the Greenland Ice Sheet, this basal motion is easier and faster than hitherto thought. A thick (tens of metres) layer of ice at the melting temperature may better explain some ice streams and needs to be taken into account when modelling future ice sheet behaviour.