A full Stokes subgrid scheme in two dimensions for simulation of grounding line migration in ice sheets using Elmer/ICE (v8.3)

Cheng, Gong; Lötstedt, Per; von Sydow, Lina

doi:https://doi.org/10.5194/gmd-13-2245-2020

Articles | Volume 13, issue 5

https://doi.org/10.5194/gmd-13-2245-2020

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

https://doi.org/10.5194/gmd-13-2245-2020

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

Articles | Volume 13, issue 5

Development and technical paper

|

13 May 2020

Development and technical paper |

| 13 May 2020

A full Stokes subgrid scheme in two dimensions for simulation of grounding line migration in ice sheets using Elmer/ICE (v8.3)

Gong Cheng, Per Lötstedt, and Lina von Sydow

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Final revised paper (published on 13 May 2020)
Preprint (discussion started on 16 Sep 2019)

Interactive discussion

Status: closed

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

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- Supplement

RC1: 'Review – Cheng, et al., A full Stokes subgrid model for simulation of grounding line migration in ice sheets using Elmer/ICE (v8.3)', Anonymous Referee #1, 19 Oct 2019
- AC1: 'Response to reviewer 1', Gong Cheng, 10 Dec 2019
  - AC4: 'The changes are marked in the supplement.', Gong Cheng, 10 Dec 2019
RC2: 'A review of “A full Stokes subgrid model for simulation of grounding line migration in ice sheets using Elmer/ICE (v8.3)” by Cheng et al.', Anonymous Referee #2, 29 Oct 2019
- AC2: 'Response to reviewer 2', Gong Cheng, 10 Dec 2019
RC3: 'Review of “A full Stokes subgrid model for simulation of grounding line migration in ice sheets using Elmer/ICE” by Gong Cheng et al.', Anonymous Referee #3, 04 Nov 2019
- AC3: 'Response to reviewer 3', Gong Cheng, 10 Dec 2019

Peer-review completion

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

AR by Gong Cheng on behalf of the Authors (10 Dec 2019) Manuscript

ED: Referee Nomination & Report Request started (06 Jan 2020) by Alexander Robel

RR by Anonymous Referee #1 (21 Jan 2020)

RR by Anonymous Referee #2 (27 Jan 2020)

Suggestions for revision or reasons for rejection

Major concerns:
1. As clearly illustrated in the paper (Section 2.4, and many other places), the authors are using a first-order approximation to determine the location of the grounding line. Thus, I don’t quite understand why they call it a “full Stokes subgrid scheme”?
2. In Elmer/Ice, originally, the location of the grounding line is decided by comparing the water pressure (Pw) and the normal stress (Tau; which can be determined from the Stokes solution) at each node (N = Pw - Tau). We can tell which node is floating or grounded by looking at the sign of N. Note that Elmer/Ice uses nodal force and contact force, instead of the actual water pressure and normal stress. Therefore, if we consider a 2D case, I guess it would still be possible to estimate the exact grounding line location by simply interpolating the N values at two neighboring nodes. Did the authors test it and then decide to go for their first-order method? If yes, what is the difference between these two methods?
3. If the author cannot provide the sub-grid results of 3D experiments (i.e., MISMIP3d), I would question the applicability of this 2D scheme in 3D cases. I agree the 2D results are still valuable in some senses, but for a complete and thorough evaluation of this first-order sub-grid scheme, I would suggest the authors do the MISMIP3d tests before its final publication. However, if the editor and other reviewers feel the 2D experiments are sufficient to prove its applicability, I would strongly suggest they remove all 3D discussions in the paper, and explicitly demonstrate that it is a 2D scheme in the title and elsewhere in the manuscript. A possible title would be “A two-dimensional first-order subgrid scheme for simulation of grounding line migration in ice sheets using Elmer/ICE (v8.3)”. By that it is safe to limit this paper in 2D discussion.
4. I am confused about the subgrid scheme, i.e., Eq (29). According to Line 267-268, the GL element is referred to the element that is partially grounded and partially floating. If it is true, then the Nitsche step function in Eq (29) should be 0, according to Line 301-302, “it is only imposed on the element which is fully on the ground” (I interpret it as “fully grounded”), and the lower panels in Fig. 2 and 3. Then, the right hand side of Eq. (29) is

\int_{\varepsilon_i}

\mathcal{H}_\beta \beta \mathbf{u}\cdot\mathbf{v} + p_w\mathbf{n}\cdot\mathbf{v}

ds

This is different from Eq. (15) where the water pressure term is integrated partially from xGL to xi, instead of over the whole GL element. Also, I still don’t follow where the friction step function of 1 / 2 is from. In the previous first round of the review, there was already a question about this, as it looks like a smoothing function than a partial integration using JUST the integration points in the grounded portion of the GL element. I don’t get useful answers from the authors’ response to this point.

Minor points:
The abstract needs improvements. The abstract should cover the key points of the paper and the current version is still a bit ambiguous. My suggestion is it should at least cover the details of the improvements of the sub-grid method, compared to old model results.
The flow of the introduction section needs further care. For example, in the paragraph Line 28-34, the authors discussed a bit of different “model equations” (which looks a bit odd), and then in the paragraph Line 46-54, the authors discussed about different lower order models again. Would be nice to put them together so that the readers can easily follow the authors’ logic here? Another example is that, in the paragraph Line 46-54, the authors discussed the sub-grid scheme and said “the purpose of a subgrid scheme is to avoid such fine meshes”, and then in the next paragraph there is a similar sentence “Our subgrid scheme is aiming at improving the accuracy in GL simulations for a static mesh”. It would be great if the authors make further organization for the introduction section.
I don’t think the citation style is correct. For example, Line 14, “It is shown in (Kingslake et al., 2018)” should be “It is shown in Kingslake et al. (2018)”. Similar mistakes should be corrected all over the whole paper.
Line 12: remove “be able”
Line 13: change “sea” to “ocean”
Line 15: “km” -> “kilometers”
Line 18: The ice flow is dominated by vertical shear only when the basal friction is large.
Line 20: Any references for “gradual change of the stress field”?
Line 23: “interaction” -> “coupling”
Line 28: this sentence is unclear to me. I guess the authors try to say that different ice sheet models can generate different GL locations, which also depends on basal friction and some other numerical parameters. But it reads awkward.
Line 31-32: “ice equations such as FS and SSA” is right. We can’t say “equations such as Full Stokes and Shallow Shelf Approximation”.
Line 51-52: Need details of the subgrid modeling in Cornford et al., 2016
Line 53-54: I suggest to remove the sentence “The purpose of ...”
Line 56: the sentence “Since the GL moves” duplicates with a similar sentence above
Line 77: I would suggest use “2D ice domain” to replace “2D vertical ice”
Line 86: in Eq (1), g is a vector, not its z component.
Line 87： Change the sentence “The rate factor...” to “The viscosity (\eta) is a function of the rate factor A(T). T is the ice temperature.”
Line 91: “vector t, see Fig. 1” -> “vector t (see Fig. 1)”
Line 91: “In the 2D vertical case” -> “For the 2D ice domain”, and similarly in the following
Line 106: GL is the boundary (xGL, yGL) between …
Line 108: “and g is ...” is a repeat of the description of g in Eq (1).
Line 128: “as observed also” -> “as also observed”
Line 136: On the grounded ice domain, we have …
Line 152, switch the order of references according to the year.
Line 261-262: “by” -> “as”
Line 264-265: at the node xi
Figure 2: in the lower panel, why is the beta 1 / 2 at [xGL, xi] where the ice is floating?
Line 292-294: The sentence “Moreover, this correction … as discussed in Sect 3.3” is hard to understand. Can the authors provide more details/explanations? From my understanding, if we don’t use a sub-grid scheme, wouldn’t it be a slower advance?
Line 298: “slip boundary” -> “grounded boundary”
Line 302: add comma after “On the contrary”

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ED: Reconsider after major revisions (29 Jan 2020) by Alexander Robel

AR by Gong Cheng on behalf of the Authors (11 Mar 2020) Author's response Manuscript

ED: Publish subject to minor revisions (review by editor) (25 Mar 2020) by Alexander Robel

Dr. Dr. Cheng and co-authors,
Your revised manuscript is greatly improved, and I find that you have made satisfactory responses to the latest comments of the reviewers. I do have some minor concerns regarding readability, and the error analysis that I discuss below. However, pending these modifications and additions, I don’t see too much barrier to publishing this paper, pending my final review.

The only substantive concern I have regards the error analysis, which one of the reviewers also brought up. I see that you have added a high resolution run, but the main way in which you address the error is by pointing out that you get similar results to previous papers with much lower resolution. While this is certainly impressive, it does not constitute an error analysis per se. For one, it does not preclude the possibility that you get these results “by accident”, and also does not explain why your results don’t appear to converge monotonically (i.e. there’s some oscillation in the solution). It may be that you have converged already at these resolutions, and perhaps doing some coarser runs would show the convergence. The main point here is that I would like to see more discussion of the error and how it is changes with resolution.

The rest of my suggested edits are primarily cosmetic and primarily to enhance readability. To cut down on the turn-around time for my decision, I have made these edits directly on the PDF, which is attached here. If you have any questions or do not understand these, do not hesitate to e-mail me.

Best,
Alex Robel
Topical Editor, GMD
robel@eas.gatech.edu

Comments to the Author: PDF

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AR by Gong Cheng on behalf of the Authors (01 Apr 2020) Author's response Manuscript

ED: Publish as is (18 Apr 2020) by Alexander Robel

AR by Gong Cheng on behalf of the Authors (20 Apr 2020) Manuscript

Short summary

A full Stokes subgrid scheme in two dimensions for the grounding line migration problem is presented in the open-source finite-element framework Elmer/ICE. This method can achieve comparable results to previous research using a more than 20 times larger mesh size, which can be used to improve the efficiency in marine ice sheet simulations.