Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the full Stokes and shallow-shelf approximation frameworks using adjoint equations

Cheng, Gong; Kirchner, Nina; Lötstedt, Per

doi:https://doi.org/10.5194/tc-15-715-2021

Articles | Volume 15, issue 2

https://doi.org/10.5194/tc-15-715-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/tc-15-715-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 15, issue 2

Research article

|

15 Feb 2021

Research article |

| 15 Feb 2021

Sensitivity of ice sheet surface velocity and elevation to variations in basal friction and topography in the full Stokes and shallow-shelf approximation frameworks using adjoint equations

Gong Cheng, Nina Kirchner, and Per Lötstedt

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Final revised paper (published on 15 Feb 2021)
Preprint (discussion started on 13 May 2020)

Interactive discussion

Status: closed

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

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- Supplement

RC1: 'Review', Anonymous Referee #1, 17 Jul 2020
- AC1: 'Response to reviewer 1', Gong Cheng, 17 Aug 2020
RC2: 'review of tc-2020-108', Anonymous Referee #2, 22 Jul 2020
- AC2: 'response to reviewer 2', Gong Cheng, 17 Aug 2020

Peer-review completion

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

ED: Reconsider after major revisions (further review by editor and referees) (21 Aug 2020) by Olivier Gagliardini

AR by Gong Cheng on behalf of the Authors (29 Sep 2020) Author's response Manuscript

ED: Referee Nomination & Report Request started (04 Oct 2020) by Olivier Gagliardini

RR by Anonymous Referee #1 (24 Oct 2020)

RR by Anonymous Referee #2 (10 Nov 2020)

Suggestions for revision or reasons for rejection

I still feel the authors are presenting number of results as new, that really are not. Let me put this in a positive way. By repeating well-know aspect of glacier flow in, for example, the last three sentences of the abstract, they are underselling their work by suggesting they merely rediscovered old facts rather than stressing the methodological advances that this work. What they do provide is a general numerical framework for studying the relationship between bed and surface properties.

The emphasis on the finite-time it takes for a perturbation to be expressed at the surface appears misplaced to me. There is a direct and instantaneous effect. This of course is well known and does not need to be stressed.
What the manuscript is missing is an introduction over previous work. Either such section must be included, or the authors change the focus of the work to the methodological advances they make. This focus of the current introduction on global warming and RCPs’ etc, is too general and does not really introduce the subject of the paper.

This is clearly a very good piece of science and it deserves to be published. The authors have mostly avoided/refused to address my previous statements and continue to sell this as a new study on the relationships between bed and surface. While this is partly true, the real strength of the work is the development of the numerical adjoint approach. I feel that a title such as ‘A general numerical framework for studying the relationship between bed and surface properties on glaciers’, is much truer to the actual focus of this study.

The manuscript is somewhat unevenly written. Have the co-authors spent enough time in helping with the formulation? It feels the manuscript needs some fresh eyes to go over it in detail and streamline it.

-I feel the citation of SSA should be to the original work by Morland, or alternatively to the first paper by MacAyeal (this is cited.) No need to attribute this idea to any later authors that then used this idea in later studies.

-SSA in two dimensions might be misunderstood. I think you are referring to a flowline situation, ie to one horizontal dimension.

-Not sure Weertman included longitudinal stresses in his 1961 solution as stated in the manuscript. Is this correct? Do check this, not sure it is.

-L14 p 8 :‘calibrated’ ->scaled or normalized

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ED: Publish subject to minor revisions (review by editor) (17 Nov 2020) by Olivier Gagliardini

AR by Gong Cheng on behalf of the Authors (27 Nov 2020) Author's response Manuscript

ED: Publish subject to minor revisions (review by editor) (09 Dec 2020) by Olivier Gagliardini

Dear Gong,

After a careful read of the last version of your manuscript, based on the two last reviews, I think there is still room for improvements. I have one main remark (which was already a point in my first review) as well as few minors points that should be accounted for before the final decision for publication is taken.

The main point concern the traitement of the grounding line dynamics for the transient cases (both FS and SSA). Indeed, solving for the GL dynamics in FS would require to solve the evolution equation for the bottom boundary z_b, in a similar form of (4a) for h. But this equation is missing in (4)? And one should also take care to enforce that h > z_b >= b. For the SSA equations (8), equation (8a), using h_t, implicitly assume that all changes in H impacts the upper surface elevation h, which is certainly true for grounded ice (where z_b=b), but doesn’t hold anymore for floating shelves (where z_b>b), and where floatation criteria gives h and z_b as a function of H. So I think that h_t should write H_t in (8a) and that the flotation criteria should be given to determine h from zb in the grounded and floating cases. On the same lines, how is determined x_{GL} in the analytical solution (12)? The proposed solution depends on the value of x_{GL} but nothing is said on how it is obtained.

Best regards,
Olivier Gagliardini

Minors remarks:
- page 4, line 12: not sure that ISCAL needs to be mentioned here as it is specific to the Elmer/Ice context
- page 5, lie 17: In a two dimensional vertical ice -> For a two dimensional flow line geometry?
- Eq. (2): I don't think that \nu is used further in the manuscript so may be not necessary to define it?
- page 6, line 1: the equation for the friction law should be given
- page 9, line 7: MISMIP is already used above. The acronym should be define at its first use.
- Eq. (12): how do you explain that your analytical solution (starting from the same set of equations) is different than the one of Greve and Blatter (2019). Especially the uniform ice shelf thickness looks like a strange solution?
- Eq. (14): should it be b or z_b for the integral born?
- page 17, line 21: same questioning as above. You are mentioning a change in the bottom topography by delta b, whereas it should be delta z_b?
- page 25, line 12: how the GL will move should be given in the initial set of equations.

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AR by Gong Cheng on behalf of the Authors (15 Dec 2020) Author's response Author's tracked changes Manuscript

ED: Publish as is (15 Dec 2020) by Olivier Gagliardini

Short summary

We present an inverse modeling approach to improve the understanding of spatiotemporally variable processes at the inaccessible base of an ice sheet by determining the sensitivity of direct surface observations to perturbations of basal conditions. Time dependency is proved to be important in these types of problems. The effect of perturbations is analyzed based on analytical and numerical solutions.