Brief communication: Time step dependence (and fixes) in Stokes simulations of calving ice shelves

Berg, Brandon; Bassis, Jeremy

doi:https://doi.org/10.5194/tc-14-3209-2020

Articles | Volume 14, issue 9

https://doi.org/10.5194/tc-14-3209-2020

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

https://doi.org/10.5194/tc-14-3209-2020

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

Articles | Volume 14, issue 9

Brief communication

|

22 Sep 2020

Brief communication |

| 22 Sep 2020

Brief communication: Time step dependence (and fixes) in Stokes simulations of calving ice shelves

Brandon Berg and Jeremy Bassis

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Final revised paper (published on 22 Sep 2020)
Preprint (discussion started on 21 Jan 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, 02 Mar 2020
- AC1: 'Responses to Referee comments by Anonymous Referee #1', Brandon Berg, 29 May 2020
RC2: 'Berg and Bassis, 2020', Christian Schoof, 25 Apr 2020
- AC2: 'Responses to Referee comments by Christian Schoof', Brandon Berg, 29 May 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 Jun 2020) by Valentina Radic

AR by Brandon Berg on behalf of the Authors (08 Jun 2020) Author's response Manuscript

ED: Referee Nomination & Report Request started (19 Jun 2020) by Valentina Radic

RR by Christian Schoof (26 Jul 2020)

Suggestions for revision or reasons for rejection

The revised paper is very well written and addresses the points that I raised. There are a few points of clarification that I would like to see, but i don't need to re-review the paper.

1. In stating the boundary conditions, I think it's important to state the second boundary condition on Gamma_1. I think this must be vanishing shear stress sigma_zx; if the left-hand end of the domain was clamped in the sense of horizontal *and* vertical velocity being fixed, the solution would be unique and force balance would be ensured

2. In the plots in figure 2, it is still ambiguous what is being plotted. I can compute maximum principal stresses, L2 norms of stress etc *instantaneously* after the removal of the chunk of ice that causes the readjustment of the orientation of the ice block in the water, (or at any other fixed point in time after that removal), I can average over a given period of time, or I can take the maximum of the quantities indicated over a given period of time (like (0,infty)). The last of these would make the most sense as otherwise it's a bit of a case of comparing apples and oranges. Please be specific.

3. The manuscript still dances around the fact that there is a true solution and a fake solution. The "fake" solution is the sea spring without the intertial terms, which can never be meaningful since it relies on a numerical stabilizer to ensure a solution in a situation where there is none. The true solution is the solution with the inertial term in place, computed for small dts. The large-dt solutions for either method are useful if you only care about flow, but not about the transient stress field. That should be made clearer (this was my point about ill-posedness in my first review; the new manuscript says "singular velocities" which is slightly misleading as what it should really say is "there is no solution" since "singular velocity" suggests a local infinity). It's not so much that the method suggested in the paper is *better* than the sea spring for computing transient stresses, its the only way to compute transient stresses following the abrupt removal of a portion of ice.

One particular sentence I'd alter in that regard is ". However, even for a purely viscous model, short time
steps may be necessary to satisfy numerical stability criteria during hydrostatic adjustment that momentarily forces the model outside of the Stokes range." - you've already said that the underlying problem sans the sea spring has no solution (or at least implied it), why not just say that, in this particular configuration, the sea spring method has a solution only because of the regularizing term, but that solution diverges as dt -> 0, and is therefore meaningless. (I'd note that the"small time steps may be necessary" portion doesn't seem to be borne out computationally, as in, if you really don't care about whether you get transient stresses right: both versions of the model, with or without inertial terms, seem to compute just fine with large dt, so long as the inertial model has a sea spring mechanism)

4. This passage is a bit odd:" The unphysically large velocities at small time
steps are magnified by the coupling between effective strain rate and viscosity. As effective strain rates become larger with small time steps, viscosity decreases, causing even greater strain rates." Magnified relative to what? Newtonian ice?

5. Following on from 4: "This problem can be alleviated by using a viscoelastic rheology when examination of short time scale behavior is desired. " - it's not clear to me that this isn't speculation, or what it really means. If by contrast we're looking at this still in the contrast of the non-inertial sea spring model, then the mere change of rheology without introducing inertial terms won't change the fact that the underlying solution is meaningless because force balance is violated. If instead this is about the need to change rheologies becaues a viscous model is inappropriate at the short time scales over which the shelf orientation adjusts to the removal of an ice block, then this is better discussed once the need to include inertial terms has been firmly established (ie after the next subsection". In that case, however, I'm not sure it's easy to make statements about what the change in rheology implies for stresses; after all we now have to worry about elastic waves resulting from the removal of the ice block, and have to take seriously short time steps.. (This seems more like the domain of the sorts of discrete element models used in e.g. Bassis and Jacobs, or HiDEM),

5. I think it's "principal stress" not "principle stress" throughout. I don't think "principle" is ever used as an adjective.

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ED: Publish subject to revisions (further review by editor and referees) (26 Jul 2020) by Valentina Radic

AR by Brandon Berg on behalf of the Authors (06 Aug 2020) Author's response Manuscript

ED: Publish as is (13 Aug 2020) by Valentina Radic

Short summary

Computer models of ice sheets and glaciers are an important component of projecting sea level rise due to climate change. For models that seek to simulate the full balance of forces within the ice, if portions of the glacier are allowed to quickly break off in a process called iceberg calving, a numerical issue arises that can cause inaccurate results. We examine the issue and propose a solution so that future models can more accurately predict the future behavior of ice sheets and glaciers.