Shear-margin melting causes stronger transient ice discharge than ice-stream melting according to idealized simulations

Feldmann, Johannes; Reese, Ronja; Winkelmann, Ricarda; Levermann, Anders

doi:https://doi.org/10.5194/tc-2021-327

Preprints

https://doi.org/10.5194/tc-2021-327

Preprints

19 Oct 2021

Status: a revised version of this preprint was accepted for the journal TC and is expected to appear here in due course.

Shear-margin melting causes stronger transient ice discharge than ice-stream melting according to idealized simulations

Johannes Feldmann¹, Ronja Reese^1,2, Ricarda Winkelmann^1,3, and Anders Levermann^1,3,4 Johannes Feldmann et al.

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¹Potsdam Institute for Climate Impact Research (PIK), Potsdam, Germany
²Department of Geography and Environmental Sciences, Northumbria University, Newcastle, UK
³Institute of Physics, University of Potsdam, Potsdam, Germany
⁴LDEO, Columbia University, New York, USA

Received: 13 Oct 2021 – Discussion started: 19 Oct 2021

Abstract. Basal ice-shelf melting is the key driver of Antarctica's increasing sea-level contribution. In diminishing the buttressing force of the ice shelves that fringe the ice sheet the melting increases the solid-ice discharge into the ocean. Here we contrast the influence of basal melting in two different ice-shelf regions on the time-dependent response of an idealized, inherently buttressed ice-sheet-shelf system. Carrying out three-dimensional numerical simulations, the basal-melt perturbations are applied close to the grounding line in the ice-shelf's 1) ice-stream region, where the ice shelf is fed by the fastest ice masses that stream through the upstream bed trough and 2) shear margins, where the ice flow is slower. The results show that melting below one or both of the shear margins can cause a decadal to centennial increase in ice discharge that is more than twice as large compared to a similar perturbation in the ice-stream region. We attribute this to the fact that melt-induced ice-shelf thinning in the central grounding-line region is attenuated very effectively by the fast flow of the central ice stream. In contrast, the much slower ice dynamics in the lateral shear margins of the ice shelf facilitate sustained ice-shelf thinning and thereby foster buttressing reduction. Regardless of the melt location, a higher melt concentration toward the grounding line generally goes along with a stronger response. Our results highlight the vulnerability of outlet glaciers to basal melting in stagnant, buttressing-relevant ice-shelf regions, a mechanism that may gain importance under future global warming.

Johannes Feldmann et al.

Status: closed

RC1:
'Comment on tc-2021-327', Anonymous Referee #1, 16 Nov 2021
The focus of this paper is on the sea-level rise response from localized melting on regions of a buttressing ice shelf. The melting is applied either at the grounding line or along the lateral edges where the topography increases and the downstream flow is slower (Figures 2 & 3), i.e. the shear margins. The difference between the effects of additional melting at the grounding line versus melting below the ice shelf shear margins is notable. And it make sense from a force balance perspective, thinning the shear margin lowers the buttressing balance and the ice stream will accelerate. Similarly, if we considered a unbuttressed ice shelf with a single pinning point, it would be clear that melting at the pinning point would affect the flow more than melting at the grounding line. Although it is an intuitive result with few actionable consequences, I would tepidly support publication in The Cryosphere.

Additional thoughts:

the force balance argument described above doesn't appear in the text and the description of the difference between the grounding line and shear margin melting is too thin.

I find the 'three dimension' description of the simulations as misleading, since SIA/SSA hybrid can have three-components but is still depth integrated.

the second sentence in the abstract is missing a comma before `the melting'.

what is solid-ice? I would replace this with 'grounded' both in the abstract, introduction, and anywhere. Right? Solid, as opposed to what?

it seems like the SM1 is nearly as effective at instigating ice flux as SM2, yet the text in the second paragraph on page 5 is confusing as compared to Figure 4.

lastly, it seems like the authors have discovered for themselves why shear margins are important. Yet I know that others have worked on shear margins, such as Lhermitte et al (2020). I suggest a clearer connection to the existing literature.

S. Lhermitte, S. Sun, C. Shuman, B. Wouters, F. Pattyn, J. Wuite, E. Berthier, and T. Nagler. Damage accelerates ice shelf instability and mass loss in Amundsen Sea Embayment. PNAS, 117(40):24735–24741, 2020
Citation: https://doi.org/10.5194/tc-2021-327-RC1
- AC1: 'Reply on RC1', Johannes Feldmann, 05 Feb 2022
  
  The comment was uploaded in the form of a supplement: https://tc.copernicus.org/preprints/tc-2021-327/tc-2021-327-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/tc-2021-327-AC1
RC2:
'Comment on tc-2021-327', Anonymous Referee #2, 16 Nov 2021
This study evaluates the sensitivity of ice flux from ice streams to the location of sub-ice shelf meltwater. In particular, the authors compare localized sub-ice shelf melting that occurs in the trunk of the ice shelf to melting that occurs in the shear margin, where ice velocity decreases rapidly. In model runs of PISM, they find that localized melting in the shear margins affects ice flux more than melting in the trunk of the ice stream and they suggest that this is due to the slower velocities in the shear margin. The study seems comprehensive and is laid out in an intuitive manner. The paper itself is well-written. I believe there is much to think about when it comes to the effects of shear margin dynamics on ice shelf buttressing, and I am heartened to see studies tackling this question. There are some comments below that may improve the readability and clarity of the paper.

In general, while I follow the logic of the underlying dynamics that cause shear margin melting to affect ice flux more than melting in the trunk, I felt that this argument could have been presented more clearly in the paper. While the discussion section does introduce a number of interesting points, I found it to be missing a clear explanation for the reasons behind the disparity in flux response. There is some explanation in the results section in lines 17-25 of page 5, but I found this explanation to be a bit buried in the results section and quite short given that this appears to be the primary physical explanation for the results of the paper.

I also wondered if the study needed more of a formal connection to other shear margin studies that consider the effect of shear margin dynamics on ice shelf/ice stream stability. For example, Alley and others 2019 proposes a physical mechanism for the localization of melt underneath ice shelf shear margins, and invoking these studies would strengthen the motivations of this work quite a bit. Further, there’s been quite a bit of work done on heating in shear margins which suggest that shear margins are likely to be quite warm (and even temperate), and I would be interested to know whether this may further increase basal melting in these regions given that the ice is already quite warm (see: Suckale and others 2014, Perol and Rice 2015, Haseloff and others 2019).

In the last paragraph of the study the authors discuss implications for Antarctic ice stream dynamics. In particular, they mention observations of enhanced melting in ice stream margins, which provides significant motivation for the work presented in this study. I believe it may be useful as a takeaway for the reader to either expand on these observations and provide a clearer link between the work in this study and those observations or to suggest what these observations and the physical mechanism proposed in this study may mean for how we represent and model ice sheet dynamics.

In the discussion of the results, I found myself losing track of the different perturbation experiments and some of the acronyms. It may be useful to have a table of the different experiments and the corresponding the melt rates.

Line 22 on page 4: I wondered whether “efficiency of the melting” was a clear descriptor of Equation 1, rather than something like “sensitivity of the flux to melt rate”.

Lines 7-12 on page 8: the comparison of melt rates in this study to melt rates estimated in ice shelves may be more useful in the “Setup and experimental design” section as a motivation for the choice of melt rates, as I found myself wondering how you chose the melt rates and whether they were physical

Does the width of the shear margin matter? If the shear margin is quite wide and thus velocities are going to zero slowly (i.e. if the flow law exponent is lower), would this dampen the effect of melting in the shear margin?

Citations

Alley, K.E., Scambos, T.A., Alley, R.B., Holschuh, N. (2019) Troughs developed in ice-stream shear margins precondition ice shelves for ocean-driven breakup. , 5(10), doi: 10.1126/sciadv.aax2215

Suckale J, Platt JD, Perol T and Rice JR (2014) Deformation-induced melting in the margins of the West Antarctic ice streams. , 119(5), 1004–1025 (doi: 10.1002/2013JF003008)

Perol T and Rice JR (2015) Shear heating and weakening of the margins of West Antarctic ice streams. , 42(9), 3406–3413, ISSN 00948276 (doi: 10.1002/2015GL063638)

Haseloff M, Hewitt IJ and Katz RF (2019) Englacial Pore Water Localizes Shear in Temperate Ice Stream Mar- gins. , 124(11), 2521–2541, ISSN 2169-9003 (doi: 10.1029/ 2019JF005399)
Citation: https://doi.org/10.5194/tc-2021-327-RC2
- AC2: 'Reply on RC2', Johannes Feldmann, 05 Feb 2022
  
  The comment was uploaded in the form of a supplement: https://tc.copernicus.org/preprints/tc-2021-327/tc-2021-327-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/tc-2021-327-AC2
RC3:
'Comment on tc-2021-327', Anonymous Referee #3, 14 Dec 2021
The manuscript "Shear-margin melting causes stronger transient ice discharge than ice-stream melting according to idealized simulations" by Feldmann et al. investigates a relatively straightforward question: where does melting of ice shelves matter most? A lot of previous work has focused on the along-flow direction when addressing this question, while the authors focus on the across-stream direction. They apply localised melt either directly at the grounding line or in the shear margins. Maybe unsurprisingly they find that persistent melting matters most where the ice is slowest, which is in the shear margins of an ice shelf in their experiments.

The paper builds heavily on Reese et al. (2018) and is similar to Zhang et al (2020) and thus not overly novel in its approach. Nevertheless, I think it is worth pointing out that spatial variation in melting matters and to try to identify regions where melting is most influential. My main points of criticisms are:

I think a more systematic investigation involving more locations would have greatly benefitted the paper and would have allowed a more systematic analysis of the role of distributed melt.

The findings of the paper are really quite straightforward, and I don't see the need for 8 figures in the main text plus an additional 5 in the appendix to convey the results. Figures 1, 3, 4 and subsets of figures 5 and 6 would in my opinion suffice.

Ice stream shear margins are interesting for many authors because they are regions of enhanced warming with implications for ice flow and stability of ice shelves. I think this could be mentioned in the text.

The paper title is a bit misleading -- being familiar with the large body of literature on ice stream shear margins, I didn't expect the paper to solely focus on isothermal ice shelf margins.

The paper is well-written, but somewhat selective (not to say negligent) in its discussion of existing literature. Relevant studies worth mentioning include (just to name a few)

Alley KE, Scambos TA, Alley RB, Holschuh N. Troughs developed in ice-stream shear margins precondition ice shelves for ocean-driven breakup. Science advances. 2019 Oct 1;5(10):eaax2215.

Alley KE, Scambos TA, Siegfried MR, Fricker HA. Impacts of warm water on Antarctic ice shelf stability through basal channel formation. Nature Geoscience. 2016 Apr;9(4):290-3.

Hunter P, Meyer C, Minchew B, Haseloff M, Rempel A. Thermal controls on ice stream shear margins. Journal of Glaciology. Cambridge University Press; 2021;67(263):435–49.
Citation: https://doi.org/10.5194/tc-2021-327-RC3
- AC3: 'Reply on RC3', Johannes Feldmann, 05 Feb 2022
  
  The comment was uploaded in the form of a supplement: https://tc.copernicus.org/preprints/tc-2021-327/tc-2021-327-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/tc-2021-327-AC3

Status: closed

RC1:
'Comment on tc-2021-327', Anonymous Referee #1, 16 Nov 2021
The focus of this paper is on the sea-level rise response from localized melting on regions of a buttressing ice shelf. The melting is applied either at the grounding line or along the lateral edges where the topography increases and the downstream flow is slower (Figures 2 & 3), i.e. the shear margins. The difference between the effects of additional melting at the grounding line versus melting below the ice shelf shear margins is notable. And it make sense from a force balance perspective, thinning the shear margin lowers the buttressing balance and the ice stream will accelerate. Similarly, if we considered a unbuttressed ice shelf with a single pinning point, it would be clear that melting at the pinning point would affect the flow more than melting at the grounding line. Although it is an intuitive result with few actionable consequences, I would tepidly support publication in The Cryosphere.

Additional thoughts:

the force balance argument described above doesn't appear in the text and the description of the difference between the grounding line and shear margin melting is too thin.

I find the 'three dimension' description of the simulations as misleading, since SIA/SSA hybrid can have three-components but is still depth integrated.

the second sentence in the abstract is missing a comma before `the melting'.

what is solid-ice? I would replace this with 'grounded' both in the abstract, introduction, and anywhere. Right? Solid, as opposed to what?

it seems like the SM1 is nearly as effective at instigating ice flux as SM2, yet the text in the second paragraph on page 5 is confusing as compared to Figure 4.

lastly, it seems like the authors have discovered for themselves why shear margins are important. Yet I know that others have worked on shear margins, such as Lhermitte et al (2020). I suggest a clearer connection to the existing literature.

S. Lhermitte, S. Sun, C. Shuman, B. Wouters, F. Pattyn, J. Wuite, E. Berthier, and T. Nagler. Damage accelerates ice shelf instability and mass loss in Amundsen Sea Embayment. PNAS, 117(40):24735–24741, 2020
Citation: https://doi.org/10.5194/tc-2021-327-RC1
- AC1: 'Reply on RC1', Johannes Feldmann, 05 Feb 2022
  
  The comment was uploaded in the form of a supplement: https://tc.copernicus.org/preprints/tc-2021-327/tc-2021-327-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/tc-2021-327-AC1
RC2:
'Comment on tc-2021-327', Anonymous Referee #2, 16 Nov 2021
This study evaluates the sensitivity of ice flux from ice streams to the location of sub-ice shelf meltwater. In particular, the authors compare localized sub-ice shelf melting that occurs in the trunk of the ice shelf to melting that occurs in the shear margin, where ice velocity decreases rapidly. In model runs of PISM, they find that localized melting in the shear margins affects ice flux more than melting in the trunk of the ice stream and they suggest that this is due to the slower velocities in the shear margin. The study seems comprehensive and is laid out in an intuitive manner. The paper itself is well-written. I believe there is much to think about when it comes to the effects of shear margin dynamics on ice shelf buttressing, and I am heartened to see studies tackling this question. There are some comments below that may improve the readability and clarity of the paper.

In general, while I follow the logic of the underlying dynamics that cause shear margin melting to affect ice flux more than melting in the trunk, I felt that this argument could have been presented more clearly in the paper. While the discussion section does introduce a number of interesting points, I found it to be missing a clear explanation for the reasons behind the disparity in flux response. There is some explanation in the results section in lines 17-25 of page 5, but I found this explanation to be a bit buried in the results section and quite short given that this appears to be the primary physical explanation for the results of the paper.

I also wondered if the study needed more of a formal connection to other shear margin studies that consider the effect of shear margin dynamics on ice shelf/ice stream stability. For example, Alley and others 2019 proposes a physical mechanism for the localization of melt underneath ice shelf shear margins, and invoking these studies would strengthen the motivations of this work quite a bit. Further, there’s been quite a bit of work done on heating in shear margins which suggest that shear margins are likely to be quite warm (and even temperate), and I would be interested to know whether this may further increase basal melting in these regions given that the ice is already quite warm (see: Suckale and others 2014, Perol and Rice 2015, Haseloff and others 2019).

In the last paragraph of the study the authors discuss implications for Antarctic ice stream dynamics. In particular, they mention observations of enhanced melting in ice stream margins, which provides significant motivation for the work presented in this study. I believe it may be useful as a takeaway for the reader to either expand on these observations and provide a clearer link between the work in this study and those observations or to suggest what these observations and the physical mechanism proposed in this study may mean for how we represent and model ice sheet dynamics.

In the discussion of the results, I found myself losing track of the different perturbation experiments and some of the acronyms. It may be useful to have a table of the different experiments and the corresponding the melt rates.

Line 22 on page 4: I wondered whether “efficiency of the melting” was a clear descriptor of Equation 1, rather than something like “sensitivity of the flux to melt rate”.

Lines 7-12 on page 8: the comparison of melt rates in this study to melt rates estimated in ice shelves may be more useful in the “Setup and experimental design” section as a motivation for the choice of melt rates, as I found myself wondering how you chose the melt rates and whether they were physical

Does the width of the shear margin matter? If the shear margin is quite wide and thus velocities are going to zero slowly (i.e. if the flow law exponent is lower), would this dampen the effect of melting in the shear margin?

Citations

Alley, K.E., Scambos, T.A., Alley, R.B., Holschuh, N. (2019) Troughs developed in ice-stream shear margins precondition ice shelves for ocean-driven breakup. , 5(10), doi: 10.1126/sciadv.aax2215

Suckale J, Platt JD, Perol T and Rice JR (2014) Deformation-induced melting in the margins of the West Antarctic ice streams. , 119(5), 1004–1025 (doi: 10.1002/2013JF003008)

Perol T and Rice JR (2015) Shear heating and weakening of the margins of West Antarctic ice streams. , 42(9), 3406–3413, ISSN 00948276 (doi: 10.1002/2015GL063638)

Haseloff M, Hewitt IJ and Katz RF (2019) Englacial Pore Water Localizes Shear in Temperate Ice Stream Mar- gins. , 124(11), 2521–2541, ISSN 2169-9003 (doi: 10.1029/ 2019JF005399)
Citation: https://doi.org/10.5194/tc-2021-327-RC2
- AC2: 'Reply on RC2', Johannes Feldmann, 05 Feb 2022
  
  The comment was uploaded in the form of a supplement: https://tc.copernicus.org/preprints/tc-2021-327/tc-2021-327-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/tc-2021-327-AC2
RC3:
'Comment on tc-2021-327', Anonymous Referee #3, 14 Dec 2021
The manuscript "Shear-margin melting causes stronger transient ice discharge than ice-stream melting according to idealized simulations" by Feldmann et al. investigates a relatively straightforward question: where does melting of ice shelves matter most? A lot of previous work has focused on the along-flow direction when addressing this question, while the authors focus on the across-stream direction. They apply localised melt either directly at the grounding line or in the shear margins. Maybe unsurprisingly they find that persistent melting matters most where the ice is slowest, which is in the shear margins of an ice shelf in their experiments.

The paper builds heavily on Reese et al. (2018) and is similar to Zhang et al (2020) and thus not overly novel in its approach. Nevertheless, I think it is worth pointing out that spatial variation in melting matters and to try to identify regions where melting is most influential. My main points of criticisms are:

I think a more systematic investigation involving more locations would have greatly benefitted the paper and would have allowed a more systematic analysis of the role of distributed melt.

The findings of the paper are really quite straightforward, and I don't see the need for 8 figures in the main text plus an additional 5 in the appendix to convey the results. Figures 1, 3, 4 and subsets of figures 5 and 6 would in my opinion suffice.

Ice stream shear margins are interesting for many authors because they are regions of enhanced warming with implications for ice flow and stability of ice shelves. I think this could be mentioned in the text.

The paper title is a bit misleading -- being familiar with the large body of literature on ice stream shear margins, I didn't expect the paper to solely focus on isothermal ice shelf margins.

The paper is well-written, but somewhat selective (not to say negligent) in its discussion of existing literature. Relevant studies worth mentioning include (just to name a few)

Alley KE, Scambos TA, Alley RB, Holschuh N. Troughs developed in ice-stream shear margins precondition ice shelves for ocean-driven breakup. Science advances. 2019 Oct 1;5(10):eaax2215.

Alley KE, Scambos TA, Siegfried MR, Fricker HA. Impacts of warm water on Antarctic ice shelf stability through basal channel formation. Nature Geoscience. 2016 Apr;9(4):290-3.

Hunter P, Meyer C, Minchew B, Haseloff M, Rempel A. Thermal controls on ice stream shear margins. Journal of Glaciology. Cambridge University Press; 2021;67(263):435–49.
Citation: https://doi.org/10.5194/tc-2021-327-RC3
- AC3: 'Reply on RC3', Johannes Feldmann, 05 Feb 2022
  
  The comment was uploaded in the form of a supplement: https://tc.copernicus.org/preprints/tc-2021-327/tc-2021-327-AC3-supplement.pdf
  
  Citation: https://doi.org/10.5194/tc-2021-327-AC3

Johannes Feldmann et al.

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Short summary

We use a numerical model to simulate the flow of a simplified Antarctic-type outlet glacier with an attached ice shelf. We find that after a few years of perturbation such a glacier responds much stronger to melting in the lateral parts of its ice shelf than to melting in the central part of its ice shelf. Since continued global warming likely will increase the melt rates under the Antarctic ice shelves the mechanism found and explained in this study might gain importance in the future.


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