Ice shelf rift propagation: stability, three-dimensional effects, and the role of marginal weakening

Lipovsky, Bradley Paul

doi:https://doi.org/10.5194/tc-14-1673-2020

Articles | Volume 14, issue 5

https://doi.org/10.5194/tc-14-1673-2020

© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/tc-14-1673-2020

© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 14, issue 5

Research article

|

27 May 2020

Research article |

| 27 May 2020

Ice shelf rift propagation: stability, three-dimensional effects, and the role of marginal weakening

Bradley Paul Lipovsky

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Final revised paper (published on 27 May 2020)
Preprint (discussion started on 22 Oct 2019)

Interactive discussion

Status: closed

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

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RC1: 'Review', Anonymous Referee #1, 25 Nov 2019
- AC1: 'Response to Reviewers', Bradley Lipovsky, 28 Jan 2020
RC2: 'Fracture Mechanics of ice and rift propagation', Anonymous Referee #2, 17 Jan 2020
- AC1: 'Response to Reviewers', Bradley Lipovsky, 28 Jan 2020

Peer-review completion

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

ED: Publish subject to revisions (further review by editor and referees) (07 Feb 2020) by Olivier Gagliardini

AR by Bradley Lipovsky on behalf of the Authors (07 Feb 2020) Author's response Manuscript

ED: Referee Nomination & Report Request started (18 Feb 2020) by Olivier Gagliardini

RR by Anonymous Referee #3 (23 Apr 2020)

Suggestions for revision or reasons for rejection

Review of the paper: ‘Ice shelf rift propagation: stability, three-dimensional effects, and the role of marginal weakening’ by B. Lipovsky.
The paper deals with an important problem in ice sheet dynamics understanding: ice shelf stability. The approach proposed here is to couple 3D and 2D numerical analysis of schematic ice-shelfs, focusing in particular on the role of the margins. The approach is interesting in itself and the results highlight possible simple effects of the rift localization and of the margins in schematic configuration. The paper suffers however, to my point of view, of a lack of accuracy in the presentation of the model used and on the assumptions that are made. A mixture of too complicated vocabulary (and to my point of view not necessary) and not enough explanation of simple notions make the paper very difficult to follow and read. Furthermore, the paper would be very much improved by adding more detailed comparison with rift propagation and ice-shelf stability in the field where I expect measurements have been made. I detail below the points that have to be clarified:
0 - Abstract:
L4-5: The sentence is not clear: ‘… near-tip rift walls’.
L6-7: It is not obvious by reading just the abstract to understand ‘….advection of rifts … may trigger rift propagation’. In particular what does mean ‘advection of rift’ ? How is it different from rift propagation? This has to be more clearly stated for readers that are not exactly in the field.
More generally, when reading the last sentence, it seems that there is no other studies on the description of calving physics based on fracture mechanics. It seems however to me that other studies have been done in this direction.
1- Introduction

In the introduction, discussion and conclusion, there is a lack of detailed description of what is observed on the field related to the study performed in this paper. Furthermore, there is a lot of work based on fracture mechanics that have been done in rock mechanics and also in rupture propagation for earthquakes. Because no references related to this work are present in this paper, it seems that the author is not aware of it, making it difficult to situate his work compared to the state of the art in the domain.
2 – Background
One of the main problem of this paper is that the equations and hypothesis used are not clearly presented. At the beginning of the background section, simple equations described by complicated words are presented. First, equation (1) is related to the hydrostatic approximation for the pressure taking into account buoyancy but is referred to as ‘in-plane horizontal membrane stress’. While I assume that the author refer to the shallow ice approximation, the use of such words do not provide clear description of the approximation made at least for researchers that are not specialists of the ice-shelf and rift problem.
To make the considered forces clear, I suggest to draw the forces involved in Figure 1 or Figure 2. Because the cryosphere readers are not all aware of the way you calculate the balance of forces, this should be clearly recalled as it is the basis of this paper.
I don’t understand why the author used the symbol  that he refers to ‘a definition’. Equation (1) is not a definition, it represents the normal stress under some approximations. Again, this kind of things complicate the problem for nothing (at least I don’t see what information it provides to the reader) and is very strange when put in regards to the very simple approximations, equations, and approach used here (with no demonstration, etc.).
L 58: Demonstrate how to you express the bending moment leading to equation (3) (use a figure if necessary).
L66: show in the figure 1b what you state in the text.
L72: There should be studies on 3D effects on rupture propagation in Earthquake or rock mechanics that should be recalled here.
Figure 1 : It is difficult to make the link between Figure 1A and Figure 1B. To avoid getting lost, the author could draw the flow direction in each sub-figures of Figure 1 and 2. The orange arrow associated to ‘Top-out rotation’ correspond to me to ‘Bottom-out’ rotation for calving. What is the point here ? Represent the rift tip on the figure.
Legend of Figure 1B: I don’t see on the figure what is stated in the legend ‘Zoomed in view of an ice shelf rift tip showing how buoyancy driven rotation of the rift walls results in partial contact of the rift walls near the rift tip’. Define in the text or in the legend how the flexural gravity wavelength is calculated.

3 – Mechanical model
What is the link between the background section and the model used here ? Why two different L are chosen for the marginal and central rifts. It makes the message unclear as the role of L may be important in the different behavior of the marginal and central rifts. Could you explain your choice and could you do the analysis by comparing marginal and central rifts for the same L ?

L 97-101 : This is not clear, illustrate on a figure.
L 100: Show in the appendix the sensitivity to the choice of the width because it is not obvious how much its influence is negligible.
L 100-101: Give more details about what you do when you refer to ‘tapering’.

Equation (5): You forget the Identity tensor. Same L 116.
Equation (6): What is H ? Is it h in Figure 1 ? Then the same notation should be used. H is not constant when there is a rift so that the horizontal pressure gradient could not be neglected when replacing T’ by T ? As a result, equation (7) is not obtained. Maybe I missed something but all this should be made clearer.

Equation (10): As you makes a variable change and use T instead of T’, the boundary conditions should be expressed in terms of T too.
L 135: relate the displacement vector to u_i, u_j, …
Figure 2: The flow direction should be added here too.
L 145-146: What are the boundary conditions used in the 3D calculations then ?
L 150 : recall what is ‘free’ (triangular mesh)

Equations (12)-(14) Recall the hypothesis made to obtain these equations
L 200: It is not clear how do you calculate them.
L 260: It could be good to show it on a figure.

5 - Discussion:
The main problem of the discussion is that the results are not enough compared with field observation.
L 299-301: Put marks on Figure 6 to show what is stated in the text.
L 304-305 and L 308-309 are not clear.

6 - Conclusion: This should recall the assumptions made in the model and summarize the results, the limitation of the approach and the comparison with field observation.

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ED: Publish subject to minor revisions (review by editor) (24 Apr 2020) by Olivier Gagliardini

AR by Bradley Lipovsky on behalf of the Authors (27 Apr 2020) Author's response Manuscript

ED: Publish subject to technical corrections (28 Apr 2020) by Olivier Gagliardini

AR by Bradley Lipovsky on behalf of the Authors (28 Apr 2020) Manuscript

Short summary

Ice shelves promote the stability of marine ice sheets and therefore reduce the ice sheet contribution to sea level rise. Ice shelf rifts are through-cutting fractures that jeopardize this stabilizing tendency. Here, I carry out the first-ever 3D modeling of ice shelf rifts. I find that the overall ice shelf geometry – particularly the ice shelf margins – alters rift stability. This work paves the way to a more realistic depiction of rifting in ice sheet models.