the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 Jun 2022
ISMIP-HOM benchmark experiments using Underworld
Abstract. Numerical models have become an indispensable tool for understanding and predicting the flow of ice sheets and glaciers. Here we present the full-Stokes software package Underworld to the glaciological community. The code is already well established in simulating complex geodynamic systems. Advantages for glaciology are that it provides a full-Stokes solution for elasto-visco-plastic materials and includes mechanical anisotropy. Underworld uses a material point method to track the full history information of Lagrangian material points, of stratigraphic layers and of free surfaces. We show that Underworld successfully reproduces the results of other full-Stokes models for the benchmark experiments of the ISMIP-HOM project. Furthermore, we test FE meshes with different geometries and highlight the need to be able to adapt the finite-element grid to discontinuous interfaces between materials with strongly different properties, such as the ice-bedrock boundary.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2022-492', Frank Pattyn, 12 Jul 2022
The paper describes a particular application of the Underworld model. Underworld2 is an open-source, particle-in-cell finite element code tuned for large-scale geodynamics simulations, which allows for the tracking of history information through the high-strain deformation associated with fluid flow. In this paper, Underworld is applied to large-scale ice flow and compared to known solutions given by other full-Stokes model following the benchmark experiments given in Pattyn et al. (2008). The authors demonstrate that the results of their model is in overall agreement with results for other full-Stokes models, which shouldn't be surprising. The major differences are related to different numerical approaches that are imbedded in Underworld and the authors show what numerical approach is more appropriate for this particular application.While this is in itself an interesting model application, to me this is a stepping stone towards a more in-depth study of ice dynamics/mechanics and especially ice rheology. Indeed, Underworld is a far more sophisticated model than the application to an isotropic ice mass without taking into account kinematic constraints (the geometry is fixed for most experiments with exception for experiment F). The authors mention a series of potential applications in the introduction, but it remains a limited list. In the outlook section, the potential is again given for improving flow laws of ice, but it remains limited to this (radar stratigraphy isn't mentioned anymore). A more exhaustive discussion of where potentially Underworld can be applied and how it can improve our understanding of ice mechanics, rheology, fabric, etc. would be more than welcome. Especially the link with ice core and seismic/radar studies are of importance. For instance, studies based on phase-sensitive radar (pRES) allow for quantifying COF in ice sheets using polarimetry and could greatly profit from the full capability of Underworld (e.g., Ershadi et al. (2022) and reference herein; Drews et al., 2015). Other examples are the elastic and visco-elastic response on short time scales due to drainage of supraglacial lakes within ice shelves, which have an effect on the ice shelf rheology (Banwell et al., 2019; MacAyeal et al., 2021), to name a few. Strengthening and emphasising this part is important, as Underworld has certain advantages over other ice sheet models, but also certain limitations. Ice sheet models, and definitely the majority that participated in ISMIP-HOM, are designed to make prognostic runs of ice sheets and glaciers across different time scales. Certain approximations are therefore made to make them computationally efficient and their focus is often on more complex boundary conditions to deal with atmosphere and ocean interaction, for instance. Underworld can be used to study certain aspects of ice dynamics, as the examples cited above. This should be stressed and strengthened.Minor comments:Line 48: The correct website: https://frank.pattyn.web.ulb.be/ismip/welcome.html (12/7/2022), but all material is also found on the TC website, which is maybe better to cite.Figure 4: I guess these are examples of the type of mesh and not the actual meshing used (it seems rather coarse to me). Mesh resolution is discussed later, but it would be informative to express the different mesh sizes used (not only in number of degrees of freedom, but also in number of x,z or x,y,z).Line 249: This is the only mention of x,z mesh size in the paper. What are other used? Do you think the highest resolution employed is sufficient to solve the problem? This can be tested by comparing the results for different resolutions and see whether or not this converges. What is the highest mesh resolution used? Is this sufficient for the purpose of this study and how may this potentially hamper other detailed studies of ice dynamics?Line 345: You should essentially compare your result with the analytical solution rather than the numerical solution of two other models. Having said that, I realised that the analytical solution is not given in the repository of the ISMIP-HOM results. I added the matlab file from my archives that can be used for this purpose.Conclusions: Please refrain from a bulleted list and write a section in plain text.ReferencesBanwell, A.F., Willis, I.C., Macdonald, G.J. et al. Direct measurements of ice-shelf flexure caused by surface meltwater ponding and drainage. Nat Commun 10, 730 (2019). https://doi.org/10.1038/s41467-019-08522-5Drews, R., Matsuoka, K., Martín, C., Callens, D., Bergeot, N., and Pattyn, F. (2015), Evolution of Derwael Ice Rise in Dronning Maud Land, Antarctica, over the last millennia. J. Geophys. Res. Earth Surf., 120, 564– 579. doi: 10.1002/2014JF003246.Ershadi, M. R., Drews, R., Martín, C., Eisen, O., Ritz, C., Corr, H., Christmann, J., Zeising, O., Humbert, A., and Mulvaney, R.: Polarimetric radar reveals the spatial distribution of ice fabric at domes and divides in East Antarctica, The Cryosphere, 16, 1719–1739, https://doi.org/10.5194/tc-16-1719-2022, 2022.MacAyeal, D., Sergienko, O., Banwell, A., Macdonald, G., Willis, I., & Stevens, L. (2021). Treatment of ice-shelf evolution combining flow and flexure. Journal of Glaciology, 67(265), 885-902. doi:10.1017/jog.2021.39
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RC2: 'Comment on egusphere-2022-492', Anonymous Referee #2, 21 Jul 2022
General comments
The paper presents an application of the Underworld software, initially developed for geodynamical applications, to solve ice flow problems using the Full Stokes formulation. Underworld uses the material point method and shows interesting potential in addressing challenges related to ice flow modelling. The paper mostly reports about benchmarking Underworld using the ISMIP-HOM benchmark experiments. Besides the benchmarking exercise, the paper provides some technical details related to the treatment of sharp boundaries and solver performance. Efforts towards better resolving physical processes with the respect to ice flow are valuable. Underworld shows potential to include complex rheologies and exposes both a mechanical and thermal solver, for both 2D and 3D configurations.
Although reporting overall good results for the selected benchmarks, the paper is missing some results and discussion about the actual and claimed new and interesting features Underworld could actually handle. These features such as incorporating anisotropy, complex rheologies or thermo-mechanical coupling, points advanced already in the abstract, would truly provide a step forward in our understanding of complex processes affecting ice flow. To turn the current paper draft into a contribution making some impact, I would be very enthusiastic about seeing actually Underworld addressing some of the challenges (e.g. as listed on Line 71) and discussing them.
I would thus suggest, besides addressing the specific comment listed hereafter, to add a couple of examples that actually demonstrate the features a 2D and 3D MPM code can provide, with particular focus on mechanical anisotropy and complex rheology, in a major revision.
Specific comments
l.10: "solution for elasto-visco-plastic materials and includes mechanical anisotropy." that's exciting! Please provide some example as this is the main motivation of using Underworld.
l.13: "Furthermore,we" -> Furthermore, we.
l.19: "ice 1h" is not an abvious concept. consider providing some additional information or making it clear that you are defining "1h".
l.24: The recent development on "complex rheologies" goes beyond the 3 articles cited here. Consider including recent work by Ranganathan and Minchew (see http://glaciers.mit.edu/publications).
l.31-32: Maybe even more important, the strong dependence of ice rheology, i.e. viscosity, on temperature…
l.59 & Eq.1: If you have both σ and P, then your σ actually stands for the deviatoric stress tensor, usually denoted as τ. If you want to consider the full (and not "absolute") stress tensor, then you should remove the pressure derivative in Eq. (1). Please correct.
Eq.4: η_ice, consider using italic text only for math variables. Here ice is not a variable thus the italic should not be used. Please correct the other math notation for consistency.
Table 2: "basal shear stress parallel x", what does parallel x stands for? Please precise.
l.71: "Some of these challenges" consider including some of these in your results (see general comment).
l.216: Basal condition section. The solution of adding a viscous layer is not the most proper implementation of basal boundary condition. Since the ice-bedrock interface is crucial, it would very interesting to see how the proposed ad-hoc boundary condition implementation performs with respect to a more serious implementation of traction boundary conditions.
l.229: CPU time consumption section. It would interesting to get slightly more information in this section, namely regarding the hardware used as the SMP system (l.237) is not the most common processor one would have. Also, it would be interesting to know how much RAM the compute server had.
l.233-234: The number of DoFs depends on the element type also.
l.242: You only report 2D scaling and performance. What about 3D? Any data available. This would be very interesting as well in order to compare.
l.255: "cp Fig. 7c", what's cp?
l.273: Section Specific results. What’s the logic behind having some results in SI, while others in the article. I guess it’s fine doing so, but it would be good to state about the strategy as it is not obvious as such to the reader. Also, why not having all or most figures in the main paper, potentially as appendix. This would be much more valuable.
l.277: complimentary" -> "complementary" I guess.
l.282: Experiments B. Experiment B 3D shows not a so good fit in the Figure S5 at 5km, and in Figure S6 for 5 and 10km. Please provide more information on why, or try to get the discrepancy fixed.
l.327: "Fig.9shows" -> add space.
l.353: "Underworld2" where does Underworld2 come from. Until now, you always referred to Underworld.
l.367: Section conclusion. please refrain from using bullet point list
l.378: Here as well, potentially very exciting, but nothing is shown in this paper. Consider adding material regarding these features.Figures:
For all figures, consider:
- adding axes information
- using bigger font
- homogenising the style
- using panel names (a,b,etc) in descriptions instead of left, right
- Work on the overall styleCitation: https://doi.org/10.5194/egusphere-2022-492-RC2 -
AC1: 'Comment on egusphere-2022-492', Till Sachau, 18 Oct 2022
Our sincere thanks to both reviewers for their generally supportive and helpful comments, which certainly improved the quality of the manuscript. We tried to address every points they raised in our reply.
For better readability we attach a pdf-file with the replies to each reviewer.
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-492', Frank Pattyn, 12 Jul 2022
The paper describes a particular application of the Underworld model. Underworld2 is an open-source, particle-in-cell finite element code tuned for large-scale geodynamics simulations, which allows for the tracking of history information through the high-strain deformation associated with fluid flow. In this paper, Underworld is applied to large-scale ice flow and compared to known solutions given by other full-Stokes model following the benchmark experiments given in Pattyn et al. (2008). The authors demonstrate that the results of their model is in overall agreement with results for other full-Stokes models, which shouldn't be surprising. The major differences are related to different numerical approaches that are imbedded in Underworld and the authors show what numerical approach is more appropriate for this particular application.While this is in itself an interesting model application, to me this is a stepping stone towards a more in-depth study of ice dynamics/mechanics and especially ice rheology. Indeed, Underworld is a far more sophisticated model than the application to an isotropic ice mass without taking into account kinematic constraints (the geometry is fixed for most experiments with exception for experiment F). The authors mention a series of potential applications in the introduction, but it remains a limited list. In the outlook section, the potential is again given for improving flow laws of ice, but it remains limited to this (radar stratigraphy isn't mentioned anymore). A more exhaustive discussion of where potentially Underworld can be applied and how it can improve our understanding of ice mechanics, rheology, fabric, etc. would be more than welcome. Especially the link with ice core and seismic/radar studies are of importance. For instance, studies based on phase-sensitive radar (pRES) allow for quantifying COF in ice sheets using polarimetry and could greatly profit from the full capability of Underworld (e.g., Ershadi et al. (2022) and reference herein; Drews et al., 2015). Other examples are the elastic and visco-elastic response on short time scales due to drainage of supraglacial lakes within ice shelves, which have an effect on the ice shelf rheology (Banwell et al., 2019; MacAyeal et al., 2021), to name a few. Strengthening and emphasising this part is important, as Underworld has certain advantages over other ice sheet models, but also certain limitations. Ice sheet models, and definitely the majority that participated in ISMIP-HOM, are designed to make prognostic runs of ice sheets and glaciers across different time scales. Certain approximations are therefore made to make them computationally efficient and their focus is often on more complex boundary conditions to deal with atmosphere and ocean interaction, for instance. Underworld can be used to study certain aspects of ice dynamics, as the examples cited above. This should be stressed and strengthened.Minor comments:Line 48: The correct website: https://frank.pattyn.web.ulb.be/ismip/welcome.html (12/7/2022), but all material is also found on the TC website, which is maybe better to cite.Figure 4: I guess these are examples of the type of mesh and not the actual meshing used (it seems rather coarse to me). Mesh resolution is discussed later, but it would be informative to express the different mesh sizes used (not only in number of degrees of freedom, but also in number of x,z or x,y,z).Line 249: This is the only mention of x,z mesh size in the paper. What are other used? Do you think the highest resolution employed is sufficient to solve the problem? This can be tested by comparing the results for different resolutions and see whether or not this converges. What is the highest mesh resolution used? Is this sufficient for the purpose of this study and how may this potentially hamper other detailed studies of ice dynamics?Line 345: You should essentially compare your result with the analytical solution rather than the numerical solution of two other models. Having said that, I realised that the analytical solution is not given in the repository of the ISMIP-HOM results. I added the matlab file from my archives that can be used for this purpose.Conclusions: Please refrain from a bulleted list and write a section in plain text.ReferencesBanwell, A.F., Willis, I.C., Macdonald, G.J. et al. Direct measurements of ice-shelf flexure caused by surface meltwater ponding and drainage. Nat Commun 10, 730 (2019). https://doi.org/10.1038/s41467-019-08522-5Drews, R., Matsuoka, K., Martín, C., Callens, D., Bergeot, N., and Pattyn, F. (2015), Evolution of Derwael Ice Rise in Dronning Maud Land, Antarctica, over the last millennia. J. Geophys. Res. Earth Surf., 120, 564– 579. doi: 10.1002/2014JF003246.Ershadi, M. R., Drews, R., Martín, C., Eisen, O., Ritz, C., Corr, H., Christmann, J., Zeising, O., Humbert, A., and Mulvaney, R.: Polarimetric radar reveals the spatial distribution of ice fabric at domes and divides in East Antarctica, The Cryosphere, 16, 1719–1739, https://doi.org/10.5194/tc-16-1719-2022, 2022.MacAyeal, D., Sergienko, O., Banwell, A., Macdonald, G., Willis, I., & Stevens, L. (2021). Treatment of ice-shelf evolution combining flow and flexure. Journal of Glaciology, 67(265), 885-902. doi:10.1017/jog.2021.39
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RC2: 'Comment on egusphere-2022-492', Anonymous Referee #2, 21 Jul 2022
General comments
The paper presents an application of the Underworld software, initially developed for geodynamical applications, to solve ice flow problems using the Full Stokes formulation. Underworld uses the material point method and shows interesting potential in addressing challenges related to ice flow modelling. The paper mostly reports about benchmarking Underworld using the ISMIP-HOM benchmark experiments. Besides the benchmarking exercise, the paper provides some technical details related to the treatment of sharp boundaries and solver performance. Efforts towards better resolving physical processes with the respect to ice flow are valuable. Underworld shows potential to include complex rheologies and exposes both a mechanical and thermal solver, for both 2D and 3D configurations.
Although reporting overall good results for the selected benchmarks, the paper is missing some results and discussion about the actual and claimed new and interesting features Underworld could actually handle. These features such as incorporating anisotropy, complex rheologies or thermo-mechanical coupling, points advanced already in the abstract, would truly provide a step forward in our understanding of complex processes affecting ice flow. To turn the current paper draft into a contribution making some impact, I would be very enthusiastic about seeing actually Underworld addressing some of the challenges (e.g. as listed on Line 71) and discussing them.
I would thus suggest, besides addressing the specific comment listed hereafter, to add a couple of examples that actually demonstrate the features a 2D and 3D MPM code can provide, with particular focus on mechanical anisotropy and complex rheology, in a major revision.
Specific comments
l.10: "solution for elasto-visco-plastic materials and includes mechanical anisotropy." that's exciting! Please provide some example as this is the main motivation of using Underworld.
l.13: "Furthermore,we" -> Furthermore, we.
l.19: "ice 1h" is not an abvious concept. consider providing some additional information or making it clear that you are defining "1h".
l.24: The recent development on "complex rheologies" goes beyond the 3 articles cited here. Consider including recent work by Ranganathan and Minchew (see http://glaciers.mit.edu/publications).
l.31-32: Maybe even more important, the strong dependence of ice rheology, i.e. viscosity, on temperature…
l.59 & Eq.1: If you have both σ and P, then your σ actually stands for the deviatoric stress tensor, usually denoted as τ. If you want to consider the full (and not "absolute") stress tensor, then you should remove the pressure derivative in Eq. (1). Please correct.
Eq.4: η_ice, consider using italic text only for math variables. Here ice is not a variable thus the italic should not be used. Please correct the other math notation for consistency.
Table 2: "basal shear stress parallel x", what does parallel x stands for? Please precise.
l.71: "Some of these challenges" consider including some of these in your results (see general comment).
l.216: Basal condition section. The solution of adding a viscous layer is not the most proper implementation of basal boundary condition. Since the ice-bedrock interface is crucial, it would very interesting to see how the proposed ad-hoc boundary condition implementation performs with respect to a more serious implementation of traction boundary conditions.
l.229: CPU time consumption section. It would interesting to get slightly more information in this section, namely regarding the hardware used as the SMP system (l.237) is not the most common processor one would have. Also, it would be interesting to know how much RAM the compute server had.
l.233-234: The number of DoFs depends on the element type also.
l.242: You only report 2D scaling and performance. What about 3D? Any data available. This would be very interesting as well in order to compare.
l.255: "cp Fig. 7c", what's cp?
l.273: Section Specific results. What’s the logic behind having some results in SI, while others in the article. I guess it’s fine doing so, but it would be good to state about the strategy as it is not obvious as such to the reader. Also, why not having all or most figures in the main paper, potentially as appendix. This would be much more valuable.
l.277: complimentary" -> "complementary" I guess.
l.282: Experiments B. Experiment B 3D shows not a so good fit in the Figure S5 at 5km, and in Figure S6 for 5 and 10km. Please provide more information on why, or try to get the discrepancy fixed.
l.327: "Fig.9shows" -> add space.
l.353: "Underworld2" where does Underworld2 come from. Until now, you always referred to Underworld.
l.367: Section conclusion. please refrain from using bullet point list
l.378: Here as well, potentially very exciting, but nothing is shown in this paper. Consider adding material regarding these features.Figures:
For all figures, consider:
- adding axes information
- using bigger font
- homogenising the style
- using panel names (a,b,etc) in descriptions instead of left, right
- Work on the overall styleCitation: https://doi.org/10.5194/egusphere-2022-492-RC2 -
AC1: 'Comment on egusphere-2022-492', Till Sachau, 18 Oct 2022
Our sincere thanks to both reviewers for their generally supportive and helpful comments, which certainly improved the quality of the manuscript. We tried to address every points they raised in our reply.
For better readability we attach a pdf-file with the replies to each reviewer.
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Haibin Yang
Justin Lang
Paul D. Bons
Louis Moresi
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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