Ice shelf fracture parameterization in an ice sheet model

Sun, Sainan; Cornford, Stephen L.; Moore, John C.; Gladstone, Rupert; Zhao, Liyun

doi:https://doi.org/10.5194/tc-11-2543-2017

Articles | Volume 11, issue 6

https://doi.org/10.5194/tc-11-2543-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/tc-11-2543-2017

© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 11, issue 6

Research article

|

09 Nov 2017

Research article |

| 09 Nov 2017

Ice shelf fracture parameterization in an ice sheet model

Sainan Sun, Stephen L. Cornford, John C. Moore, Rupert Gladstone, and Liyun Zhao

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Final revised paper (published on 09 Nov 2017)
Preprint (discussion started on 03 Apr 2017)

Interactive discussion

Status: closed

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

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- Supplement

RC1: 'Review for "Ice shelf fracture parameterisation in an ice sheet model"', Anonymous Referee #1, 03 May 2017
- AC1: 'Response to referee1: 'Ice shelf fracture parameterization in an ice sheet model' by Sainan Sun et al.', Sainan Sun, 18 Jul 2017
RC2: 'Review of manuscript', Jeremy Bassis, 24 May 2017
- AC2: 'Response to referee2 (J. Bassis): 'Ice shelf fracture parameterization in an ice sheet model' by Sainan Sun et al.', Sainan Sun, 18 Jul 2017

Peer-review completion

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

AR by Sainan Sun on behalf of the Authors (18 Jul 2017) Author's response

ED: Referee Nomination & Report Request started (01 Aug 2017) by G. Hilmar Gudmundsson

RR by Anonymous Referee #1 (08 Aug 2017)

RR by Jeremy Bassis (21 Aug 2017)

Suggestions for revision or reasons for rejection

This manuscript presents an updated version of a prior manuscript that sought to include damage in the BISICLES model. The original manuscript was promising, but had some glitches and confusing portions. The authors, however, have done a commendable job of thoroughly addressing reviewer comments. With the exception of one point of minor confusion (which might be my own), I only have nitpicky and minor comments.

The one semi-important point I have is with Equation 11. Here the role of mass balance on damage is still unclear to me. It looks like the authors are assuming that snow deposited to the surface will increase the ice thickness, but will not affect the basal crevasse penetration depth. Geometrically, this makes sense if we imagine a basal crevasse. Snow deposited onto the surface then increases the ice thickness, but leaves the crevasse depth constant. In this case, snow “heals” the crevasse-even if this is a purely geometric effect. This prescription fails, however, if there is a surface crevasse, but this manuscript is mostly concerned with basal crevasses so this is not a significant problem. In contrast, melt around basal crevasses appears to erode the ice around crevasses and also decreases damage. This would seem to assume that there is no melt within the crevasse and all melt instead occurs outside of the crevasse. (Not an unreasonable assumption.) This seems to be contracted, however, when the authors state that melt is assumed to be the same inside and outside of the crevasse. If the melt rate is the same inside and outside the crevasse, then it would appear as though the mass balance term should increase damage and by proportional to total melt rate (surface and bottom) and take the form m * dtr/h. See, for example, Equation 26 in Bassis and Ma (2015, but note the annoying typo where the r is missing from the second term). The reason the term appears this way is that if the melt rate is the same inside and outside the crevasses, the melt rate makes no difference to the crevasse depth. The melt does, however, decrease the ice thickness. Hence, any (positive) melt rate will increase damage. It is possible that I have simply misread the authors statement, but I encourage the authors to check to make sure this statement isn’t a typo and to make sure the equation is consistent with their description.

Some really nitpicky comments:

Near page 2 line 10: “Macro-scale fractures originate from micro-scale cracks, which appear when viscous strain is too high” Is this really what Rist says? Normally we think of micro-cracks forming when *stress* is high. Of course, stress and viscous strain rates are related through the rheology. The technical problem with the statement above is that at first glance, this implies that for a given stress, micro cracks are more likely to form in warm ice than cold ice because the viscous strain rates are larger. This is not well supported by the literature and, in fact, we often see that crevasses form when the stress (after temperature has been accounted for) exceeds a few hundred kPa. More pernicious, large portions of ice sheets have very large viscous **strains** because small strain rates have accumulated over millennia. This does not necessarily lead to micro-fractures because of other processes (like recrystallization). All in all, this is a minor point. If the authors want to be particular about it, I would probably say something along the lines of “Macro-scale fractures originate from micro-scale cracks, which are more likely to form when stresses within the ice become large” or if you want to be more specific “Macro-scale fractures originate from micro-scale cracks, which are more likely to form when stresses within the ice exceed a few hundred kPa”

Near page 2 line 10: “microscopic scales fracturing is a discrete process which operates on time scales determined by the speed of sound in ice” This is a fine statement. The authors might be interested to know that new research is, however, pointing out that slow rupture at speeds that are significantly less than body wave speeds is also possible. This can happen through a variety of processes including void growth and ductile failure. It is, however, unclear that any of these mechanisms are at work in ice.

Results: breaking the results section down into subsections (perhaps identified by the different experiments) would help readers follow the different model results.

Page 11, near line 5. I think there should be a tilde on the D? Also, it is interesting that D~0.5 appears to be an appropriate rule of thumb. This is, of course, the prediction for surface+basal crevasse depth that we would infer based on the Nye zero stress model in an unconfined ice tongue.

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ED: Publish subject to minor revisions (Editor review) (11 Sep 2017) by G. Hilmar Gudmundsson

AR by Sainan Sun on behalf of the Authors (15 Sep 2017) Author's response Manuscript

ED: Publish as is (29 Sep 2017) by G. Hilmar Gudmundsson

AR by Sainan Sun on behalf of the Authors (30 Sep 2017)

Short summary

The buttressing effect of the floating ice shelves is diminished by the fracture process. We developed a continuum damage mechanics model component of the ice sheet model to simulate the process. The model is tested on an ideal marine ice sheet geometry. We find that behavior of the simulated marine ice sheet is sensitive to fracture processes on the ice shelf, and the stiffness of ice around the grounding line is essential to ice sheet evolution.