Damage strength increases ice mass loss from Thwaites Glacier, Antarctica

Li, Yanjun; Coulon, Violaine; Blasco, Javier; Qiao, Gang; Yang, Qinghua; Pattyn, Frank

doi:https://doi.org/10.5194/egusphere-2024-2916

Preprints

https://doi.org/10.5194/egusphere-2024-2916

Preprints

16 Oct 2024

| 16 Oct 2024

Damage strength increases ice mass loss from Thwaites Glacier, Antarctica

Yanjun Li, Violaine Coulon, Javier Blasco, Gang Qiao, Qinghua Yang, and Frank Pattyn

Abstract. Ice damage plays a critical role in determining ice-shelf stability, grounding-line retreat, and subsequent sea-level rise, as it affects the formation and development of crevasses on glaciers. However, few ice-sheet models have explicitly considered ice damage nor its effect on glacier projections. Here, we incorporate ice damage processes into an ice-sheet model. By applying the upgraded model to the Thwaites Glacier basin, we further investigate the sensitivity of Thwaites Glacier to the strength of the ice damage. Our results indicate that the ice-sheet model enabled with the ice damage mechanics better captures the observed ice geometry and mass balance of the Thwaites Glacier during the historical period (1990–2020), compared to the default model that ignores ice damage mechanics. Ice damage may result in a collapse of Thwaites Glacier on multidecadal-to-centennial timescales and a notable increase in ice mass loss. Moreover, ice mass loss from Thwaites Glacier to the ocean may induce a sea-level rise of 5.0 ± 2.9 cm by 2300, which is more than double the simulation result without ice damage. This study highlights the importance of explicitly representing ice damage processes in ice-sheet models.

Received: 17 Sep 2024 – Discussion started: 16 Oct 2024

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Yanjun Li, Violaine Coulon, Javier Blasco, Gang Qiao, Qinghua Yang, and Frank Pattyn

Status: closed

RC1:
'Comment on egusphere-2024-2916', Tong Zhang, 20 Dec 2024

Please see the attached pdf.

Citation: https://doi.org/10.5194/egusphere-2024-2916-RC1
- AC1:
  'Reply on RC1', Yanjun Li, 28 Mar 2025
  Dear Reviewer,
  We thank you for your constructive feedback, which has helped us improve the manuscript. In response to the comments, we have thoroughly revised the manuscript. The key updates are the following:
  We have improved the writing, formulation and structure of the manuscript to enhance clarity.
  
  Appendix A has been removed and merged into section 2.1, where the model formulation has been extensively revised.
  
  To provide greater clarity on our methodology, we have introduced separate sections for the simulation protocol (Section 2.2) and the initialization (Section 2.3).
  
  Appendix B has been removed and integrated into the results section, which has been thoroughly revised to improve readability.
  
  A comparison of the modeled damage pattern and observations has been added (see Figure 5 in the revised manuscript).
  
  Please refer to the attached document for our detailed responses to each comment.
  Sincerely,
  
  Dr. Yanjun Li (liyj375@mail.sysu.edu.cn)
  
  Sun Yat-sen University
  
  Citation: https://doi.org/10.5194/egusphere-2024-2916-AC1
RC2:
'Comment on egusphere-2024-2916', Ravindra Duddu, 19 Jan 2025
This article presents sensitivity studies using the Kori-ULB ice sheet model to explore the response of Thwaites Glacier (TG) with and without incorporating ice damage. Their main finding is that increasing damage intensity “results in larger retreat of the grounding line, higher ice velocity, thinner ice shelves, more ice mass loss, and a bigger contribution to global sea level rise.” This is generally the consensus among researchers and is not in any way controversial nor groundbreaking; nevertheless, it is of important and interest to The Cryosphere community. The novelty of the article (in my opinion) lies in the set-up of the simulations for TG’s with the calibration of the model using present day data for 1990, historical simulations over 1990-2020, and projections from 2020-2300. However, the description and explanation of the simulation set up and result can be improved.
The authors use the damage model proposed by Sun et al. (2012) that is based on the zero-stress theory. The contribution of this article is that it considers parametric studies by varying two damage parameters C_1 and C_tr, however, I had difficulty in following the model formulation and some of their equations seem to use inconsistent notation. The writing of this article is also not up to the standards of this journal and needs much improvement. The article must undergo major revisions and re-review before it can be considered for publication.
Detailed Comments:
In the abstract and elsewhere in the article, the authors use the term “strength of ice damage” I suggest replacing this term by “intensity of ice damage” so as not to confuse the reader with the strength of ice. Typically, a strength parameter is often used in ice damage models as a material property, so the terminology must be corrected.

The writing in the paper can be improved and may need professional writing help, as I found typos and grammatical errors. For example, in the abstract “ice sheet model enabled with the ice damage mechanics…” change as “ice sheet model including damage mechanics”

The first sentence of the introduction begins with “Damage of glaciers …” For the sake of clarity and information, please define what you mean by damage in the context of ice sheet, especially at the scale you are defining damage. As we know, damage can be described at multiple scales all the way from microns (grain boundaries crack in the microstructure) to kilometers (rifts in ice shelves). Also, the introduction is a bit sparse with references on damage models incorporated into either shallow shelf models or full Stokes models. As a suggestion, I would like to bring to the authors ice shelf scale studies incorporating damage into SSA (Huth et al., 2021b, 2023; Ranganathan et al., 2024).

Line 63 – Please clarify what you mean by 2.5D. Different authors use this in different ways. Is the thermal part 3D whereas the flow part 2D, is that right?

On Line 70 – put CDM in parentheses, also CDM typically stands for continuum damage mechanics. Also, change the next sentence as “Damage d(tau_1) includes a local source term d_1(tau_1) and an advection term due to ice flow d_tr.” Also, damage is not a conserved variable. The damage evolution equation is not necessarily related to either mass or momentum but it rather a type of non-conserved phase field variable. Therefore, you should say “Damage advection due to ice flow …”

I do not follow Eq. (3) for d(tau_1), you are taking max of certain quantities, but because there are so many parentheses, I am not able to follow what you are stating. Also, aren’t d_s, d_s+d_b and C_1*h s all positive quantities so then why do you need to have the max(0,..) function, why can’t you just simply take the max of the three non-zero quantities. I am also not clear how d_tr is defined in Eq. (4). Even though it may be well described in Sun et al., (2017) it would be useful discuss the definition of d_tr for completeness. The notation in the Appendix A is hard to follow as well (see my comments below on Appendix A).

Line 90 – Was the inversion to obtain ice sheet initial conditions only performed once and was used as the starting point for all simulations. Also, more details on the inverse would be useful for the general reader, unless Coulon et al. (2024) has it all in detail. Please add a sentence to clarify.

Line 92 – Assuming that present day is undamaged is unrealistic, but it is an assumption. Perhaps, you can add a clarification that it can be interpreted as relative damage with respect to the initialized state. In the sentence below you report RMSE, perhaps it is a bit more helpful to report relative RMSE as a percentage.

Line 98 – The term local damage is used to define the damage production term to highlight the fact that damage can also advect from upstream. However, both advection and production terms are local damage whereas nonlocal damage refers to those approaches that incorporate a nonlocal length scale (Duddu, 2020; Huth 2021b). Also, on Line 101, why not say parameter values, why use the term parameter members. I would replace the word members with values in this context throughout the paper.

Line 114 – Add statement to clarify what “different physics” the Ctrl_cal experiments consider as opposed to the damage experiments.

Line 141 – Replace the term “the strength of ice damage” with “the intensity of ice damage” throughout the paper. In Table 1, the acronym SLC is not

Line 150 – The description here could be improved. Is it correct that so this ignoring damage underestimates ice mass change by more than an order of magnitude, that is 2.1 (without damage) instead of 38.3 (with damage) or 28.1 (Ctrl_cal)?

Figure 4 – This is an important figure, and the results can be explained better with a sentence. The way I understand the light red and green corresponding to the lowest damage do not produce any significant retreat compared to the observed GL and central profile. Is the black line in subfigure (b) the observed elevation, please clarify.

Line 219 – The sea level rise by year 2300 is about 5 – 8 cm. This seems quite small. Is this cumulative sea lever rise or is it sea level rise. From what I recall, the question always was if Antarctica could contribute to a meter or more of sea level rise by 2300. Does this mean that Thwaites is not going to be a major contributor for sea level rise?

Line 233 – It is stated that “The increased ice velocity and decreased ice thickness further stimulate damage formation and propagation.” I am not sure if decreased ice thickness would always stimulate damage formulation. As the ice thickness is reduced the driving stress could also be reduced and this could reduce damage formation. Perhaps, my reasoning is wrong, but the authors could comment on this.

Line 265 – The long-term projections of TG’s evolution (2020-2300) differ between the Ctrl_cal and those with damage. It would be good to remind the reader, quantitatively and qualitatively what are these differences by 2300. Also, important to note that we will not know which of the two projections is realistic. I do not think we can simply state that incorporating damage mechanics improves the projections without some validation. This needs more discussion.

Line 330 – Grant number is missing and typed as XX

Appendix A – This section needs to undergo a thorough revision. Please see the comments below:

The notation is poorly chosen, for example stress and strain are tensors, but they are denoted as scalars. Eqs. (A1) and (A2) need to be corrected.

In Eq. (A3) the first term on the RHS is (h-tau_1), which does not make sense because h ice thickness and tau_1 is the first principal stress. You cannot subtract two quantities with different units.

Line 359 tau_1 cannot be determined by setting it equal to depth of crevasses, stress and depth are different physical quantities.

In Eq. (A8) u should be bold as it represents the ice velocity, which is a vector, otherwise the divergence operator does make any sense.

I do not understand how the sentence above Eq. (A9) about crevasse closure leads to the specific definition of damage in (A9)

Line 379 – Please explain what the term “model collapse before 2300” means.

Line 381 – it is not clear what is meant by “averagely” in the next sentence, maybe say “on an average” instead. Also, 7 – 10 cm of global sea level rise seems on the lower end, when other works are exploring the possibility of 1 – 3 m of sea level rise (e.g. DeConto and Pollard, 2016).

Table A1 – How is RMSE calculated, please give more details and perhaps consider relative RMSE to report it as percentages.

Figure A1 – why is the flowline marked in subfigures (a) and (b)

Figure A3 – what is the reason the gray and blue model lines are not matching well in the top region but matching well in the bottom region, which is apparent from subfigure (b).

Figure A4 – please add a sentence to clarify how ice mass loss is calculated.

Figure A5 – what does model collapse mean.
Citation: https://doi.org/10.5194/egusphere-2024-2916-RC2
- AC2:
  'Reply on RC2', Yanjun Li, 28 Mar 2025
  Dear Reviewer,
  We thank you for your constructive feedback, which has helped us improve the manuscript. In response to the comments, we have thoroughly revised the manuscript. The key updates are the following:
  We have improved the writing, formulation and structure of the manuscript to enhance clarity.
  
  Appendix A has been removed and merged into section 2.1, where the model formulation has been extensively revised.
  
  To provide greater clarity on our methodology, we have introduced separate sections for the simulation protocol (Section 2.2) and the initialization (Section 2.3).
  
  Appendix B has been removed and integrated into the results section, which has been thoroughly revised to improve readability.
  
  A comparison of the modeled damage pattern and observations has been added (see Figure 5 in the revised manuscript).
  
  Please refer to the attached document for our detailed responses to each comment.
  Sincerely,
  
  Dr. Yanjun Li (liyj375@mail.sysu.edu.cn)
  
  Sun Yat-sen University
  
  Citation: https://doi.org/10.5194/egusphere-2024-2916-AC2

Status: closed

RC1:
'Comment on egusphere-2024-2916', Tong Zhang, 20 Dec 2024

Please see the attached pdf.

Citation: https://doi.org/10.5194/egusphere-2024-2916-RC1
- AC1:
  'Reply on RC1', Yanjun Li, 28 Mar 2025
  Dear Reviewer,
  We thank you for your constructive feedback, which has helped us improve the manuscript. In response to the comments, we have thoroughly revised the manuscript. The key updates are the following:
  We have improved the writing, formulation and structure of the manuscript to enhance clarity.
  
  Appendix A has been removed and merged into section 2.1, where the model formulation has been extensively revised.
  
  To provide greater clarity on our methodology, we have introduced separate sections for the simulation protocol (Section 2.2) and the initialization (Section 2.3).
  
  Appendix B has been removed and integrated into the results section, which has been thoroughly revised to improve readability.
  
  A comparison of the modeled damage pattern and observations has been added (see Figure 5 in the revised manuscript).
  
  Please refer to the attached document for our detailed responses to each comment.
  Sincerely,
  
  Dr. Yanjun Li (liyj375@mail.sysu.edu.cn)
  
  Sun Yat-sen University
  
  Citation: https://doi.org/10.5194/egusphere-2024-2916-AC1
RC2:
'Comment on egusphere-2024-2916', Ravindra Duddu, 19 Jan 2025
This article presents sensitivity studies using the Kori-ULB ice sheet model to explore the response of Thwaites Glacier (TG) with and without incorporating ice damage. Their main finding is that increasing damage intensity “results in larger retreat of the grounding line, higher ice velocity, thinner ice shelves, more ice mass loss, and a bigger contribution to global sea level rise.” This is generally the consensus among researchers and is not in any way controversial nor groundbreaking; nevertheless, it is of important and interest to The Cryosphere community. The novelty of the article (in my opinion) lies in the set-up of the simulations for TG’s with the calibration of the model using present day data for 1990, historical simulations over 1990-2020, and projections from 2020-2300. However, the description and explanation of the simulation set up and result can be improved.
The authors use the damage model proposed by Sun et al. (2012) that is based on the zero-stress theory. The contribution of this article is that it considers parametric studies by varying two damage parameters C_1 and C_tr, however, I had difficulty in following the model formulation and some of their equations seem to use inconsistent notation. The writing of this article is also not up to the standards of this journal and needs much improvement. The article must undergo major revisions and re-review before it can be considered for publication.
Detailed Comments:
In the abstract and elsewhere in the article, the authors use the term “strength of ice damage” I suggest replacing this term by “intensity of ice damage” so as not to confuse the reader with the strength of ice. Typically, a strength parameter is often used in ice damage models as a material property, so the terminology must be corrected.

The writing in the paper can be improved and may need professional writing help, as I found typos and grammatical errors. For example, in the abstract “ice sheet model enabled with the ice damage mechanics…” change as “ice sheet model including damage mechanics”

The first sentence of the introduction begins with “Damage of glaciers …” For the sake of clarity and information, please define what you mean by damage in the context of ice sheet, especially at the scale you are defining damage. As we know, damage can be described at multiple scales all the way from microns (grain boundaries crack in the microstructure) to kilometers (rifts in ice shelves). Also, the introduction is a bit sparse with references on damage models incorporated into either shallow shelf models or full Stokes models. As a suggestion, I would like to bring to the authors ice shelf scale studies incorporating damage into SSA (Huth et al., 2021b, 2023; Ranganathan et al., 2024).

Line 63 – Please clarify what you mean by 2.5D. Different authors use this in different ways. Is the thermal part 3D whereas the flow part 2D, is that right?

On Line 70 – put CDM in parentheses, also CDM typically stands for continuum damage mechanics. Also, change the next sentence as “Damage d(tau_1) includes a local source term d_1(tau_1) and an advection term due to ice flow d_tr.” Also, damage is not a conserved variable. The damage evolution equation is not necessarily related to either mass or momentum but it rather a type of non-conserved phase field variable. Therefore, you should say “Damage advection due to ice flow …”

I do not follow Eq. (3) for d(tau_1), you are taking max of certain quantities, but because there are so many parentheses, I am not able to follow what you are stating. Also, aren’t d_s, d_s+d_b and C_1*h s all positive quantities so then why do you need to have the max(0,..) function, why can’t you just simply take the max of the three non-zero quantities. I am also not clear how d_tr is defined in Eq. (4). Even though it may be well described in Sun et al., (2017) it would be useful discuss the definition of d_tr for completeness. The notation in the Appendix A is hard to follow as well (see my comments below on Appendix A).

Line 90 – Was the inversion to obtain ice sheet initial conditions only performed once and was used as the starting point for all simulations. Also, more details on the inverse would be useful for the general reader, unless Coulon et al. (2024) has it all in detail. Please add a sentence to clarify.

Line 92 – Assuming that present day is undamaged is unrealistic, but it is an assumption. Perhaps, you can add a clarification that it can be interpreted as relative damage with respect to the initialized state. In the sentence below you report RMSE, perhaps it is a bit more helpful to report relative RMSE as a percentage.

Line 98 – The term local damage is used to define the damage production term to highlight the fact that damage can also advect from upstream. However, both advection and production terms are local damage whereas nonlocal damage refers to those approaches that incorporate a nonlocal length scale (Duddu, 2020; Huth 2021b). Also, on Line 101, why not say parameter values, why use the term parameter members. I would replace the word members with values in this context throughout the paper.

Line 114 – Add statement to clarify what “different physics” the Ctrl_cal experiments consider as opposed to the damage experiments.

Line 141 – Replace the term “the strength of ice damage” with “the intensity of ice damage” throughout the paper. In Table 1, the acronym SLC is not

Line 150 – The description here could be improved. Is it correct that so this ignoring damage underestimates ice mass change by more than an order of magnitude, that is 2.1 (without damage) instead of 38.3 (with damage) or 28.1 (Ctrl_cal)?

Figure 4 – This is an important figure, and the results can be explained better with a sentence. The way I understand the light red and green corresponding to the lowest damage do not produce any significant retreat compared to the observed GL and central profile. Is the black line in subfigure (b) the observed elevation, please clarify.

Line 219 – The sea level rise by year 2300 is about 5 – 8 cm. This seems quite small. Is this cumulative sea lever rise or is it sea level rise. From what I recall, the question always was if Antarctica could contribute to a meter or more of sea level rise by 2300. Does this mean that Thwaites is not going to be a major contributor for sea level rise?

Line 233 – It is stated that “The increased ice velocity and decreased ice thickness further stimulate damage formation and propagation.” I am not sure if decreased ice thickness would always stimulate damage formulation. As the ice thickness is reduced the driving stress could also be reduced and this could reduce damage formation. Perhaps, my reasoning is wrong, but the authors could comment on this.

Line 265 – The long-term projections of TG’s evolution (2020-2300) differ between the Ctrl_cal and those with damage. It would be good to remind the reader, quantitatively and qualitatively what are these differences by 2300. Also, important to note that we will not know which of the two projections is realistic. I do not think we can simply state that incorporating damage mechanics improves the projections without some validation. This needs more discussion.

Line 330 – Grant number is missing and typed as XX

Appendix A – This section needs to undergo a thorough revision. Please see the comments below:

The notation is poorly chosen, for example stress and strain are tensors, but they are denoted as scalars. Eqs. (A1) and (A2) need to be corrected.

In Eq. (A3) the first term on the RHS is (h-tau_1), which does not make sense because h ice thickness and tau_1 is the first principal stress. You cannot subtract two quantities with different units.

Line 359 tau_1 cannot be determined by setting it equal to depth of crevasses, stress and depth are different physical quantities.

In Eq. (A8) u should be bold as it represents the ice velocity, which is a vector, otherwise the divergence operator does make any sense.

I do not understand how the sentence above Eq. (A9) about crevasse closure leads to the specific definition of damage in (A9)

Line 379 – Please explain what the term “model collapse before 2300” means.

Line 381 – it is not clear what is meant by “averagely” in the next sentence, maybe say “on an average” instead. Also, 7 – 10 cm of global sea level rise seems on the lower end, when other works are exploring the possibility of 1 – 3 m of sea level rise (e.g. DeConto and Pollard, 2016).

Table A1 – How is RMSE calculated, please give more details and perhaps consider relative RMSE to report it as percentages.

Figure A1 – why is the flowline marked in subfigures (a) and (b)

Figure A3 – what is the reason the gray and blue model lines are not matching well in the top region but matching well in the bottom region, which is apparent from subfigure (b).

Figure A4 – please add a sentence to clarify how ice mass loss is calculated.

Figure A5 – what does model collapse mean.
Citation: https://doi.org/10.5194/egusphere-2024-2916-RC2
- AC2:
  'Reply on RC2', Yanjun Li, 28 Mar 2025
  Dear Reviewer,
  We thank you for your constructive feedback, which has helped us improve the manuscript. In response to the comments, we have thoroughly revised the manuscript. The key updates are the following:
  We have improved the writing, formulation and structure of the manuscript to enhance clarity.
  
  Appendix A has been removed and merged into section 2.1, where the model formulation has been extensively revised.
  
  To provide greater clarity on our methodology, we have introduced separate sections for the simulation protocol (Section 2.2) and the initialization (Section 2.3).
  
  Appendix B has been removed and integrated into the results section, which has been thoroughly revised to improve readability.
  
  A comparison of the modeled damage pattern and observations has been added (see Figure 5 in the revised manuscript).
  
  Please refer to the attached document for our detailed responses to each comment.
  Sincerely,
  
  Dr. Yanjun Li (liyj375@mail.sysu.edu.cn)
  
  Sun Yat-sen University
  
  Citation: https://doi.org/10.5194/egusphere-2024-2916-AC2

Yanjun Li, Violaine Coulon, Javier Blasco, Gang Qiao, Qinghua Yang, and Frank Pattyn

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Short summary

We incorporate ice damage processes into an ice-sheet model and apply the new model to Thwaites Glacier. The upgraded model more accurately captures the observed ice geometry and mass balance of Thwaites Glacier over 1990–2020. Our simulations show that ice damage has a notable impact on the ice sheet evolution, ice mass loss and the resulted sea-level rise. This study highlights the necessity for incorporating ice damage into ice-sheet models.


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