the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 18 Jan 2024
A new 3D full-Stokes calving algorithm within Elmer/Ice (v9.0)
Abstract. A new calving algorithm was developed in the glacier model Elmer/Ice that allows unrestricted calving and terminus advance in 3D. The algorithm used the meshing software Mmg to implement anisotropic remeshing and allow mesh adaptation at each timestep. The development of the algorithm along with the implementation of the crevasse depth law produced a new full-Stokes calving model capable of simulating calving and terminus advance across an array of complex geometries. Using a synthetic tidewater glacier geometry the model was tested to highlight the non-physical parameters that can alter calving. For a system with no clear attractor, model timestep and mesh resolution are shown to alter the simulated calving. In particular vertical mesh resolution had a large impact, increasing calving, as the frontal bending stresses are better resolved. However, when the system had a strong attractor, provided by basal pinning points, non-physical parameters have a limited affect on the terminus evolution. The new algorithm is capable of implementing unlimited terminus advance and retreat as well as unrestricted calving geometries, applying any melt field to the front, use in conjunction with any calving law or potentially advecting variables downstream.
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RC1: 'Comment on egusphere-2023-2778', Gong Cheng, 30 Jan 2024
This manuscript introduces a novel 3D calving model implemented in Elmer/ICE, which is capable of capturing the 3D geometry of the ice terminus. Two groups of numerical experiments, one with pinning points at the ice fronts and one without, are compared. The authors demonstrate that certain choices of non-physical parameters can significantly impact the behavior of the model.
To the best of my knowledge, this manuscript represents the first study attempting to model the 3D geometry of a moving ice front. However, there is still room for improvement before this manuscript can be considered for publication.
Main comments
My main concern is the need to improve the quality of this manuscript. The authors have used non-scientific language, such as 'almost certain' and 'roughly', when drawing conclusions. Additionally, I have noticed that many introductory contents are misplaced in later sections, such as 4.3, 7.1, 7.5, etc. I suggest that the authors rewrite the introduction as well as these sections. Overall, there are several redundant paragraphs in this manuscript that could be significantly shortened.
Regarding the numerical experiments, particularly the mesh resolutions experiments, it is conventionally recommended to test at least 4 different points of each variable in order to draw conclusions related to convergence. These points should span at least 1/2 and 2 times the control resolution.
The significant impact of non-physical parameters on the no pinning point cases appears to be closely related to the CD calving law. I suggest that the authors add a comparison experiment with a rate-based calving law to identify the reason for this strong dependence.
I fully agree that the authors should focus on the key methodological choices and model capabilities. However, as a whole paper, the manuscript should be self-explanatory without requiring readers to read the supplementary materials.
Detailed Comments
- l34, this sentence sounds like incomplete. I would recommend to add a few more sentences to further explain the Linear Elastic Fracture model, and make a comparison with the two previous models.
- l99, I would be more careful to use ‘greatly’. The error depends on the mesh size, and in most of numerical models using level-set approach, the mesh close to the ice front is usually well refined.
- l100, remove ‘Ice-free elements remain dormant.’
- l118, what is the type of the CPUs? I also suggest the authors to give more information about the computational time of all the experiments.
- l120, give → giving
- Figure 1. The texts in the color bar are too small to read
- Section 4.2, in general, this section need a bit more work. For example,
- l132-141, I'm a bit confused about this paragraph. What boundary condition is apply at the fjord wall? If the velocity is solved with a Dirichlet boundary condition parallel to the fjord wall, then the velocity component in the direction of the fjord wall is automatically constrained. Shouldn't the velocity solution be constrained first, instead of fixing the displacement?
- l144, what do 'this' refer to? The previous sentences discuss the issue at the boundary corner, which does not 'provide a better solution...’
- l148-149, ‘the model has the …. lateral margins’, could you explain a bit more in details, what are the ‘boundary elements’ and where is the lateral margins? Are these at the calving front, or at the fjord wall?
- l153, is the normal to the element faces, or to the nodes?
- l159-161, I’m a bit worried about the melting applied at the corner element, as the normal direction is not going to parallel to the wall, which add additional ‘leak of mass’ at the side wall boundary
- Overall, it would beneficial to have a schematic plot of the boundary at the corner between ice front and fjord wall, and refer to the items in the figure when explaining the implementations
- l174-178, these text about how the previous method is implemented should go to the introduction.
- l179, add ‘,’ between ‘algorithm’ and ‘Mmg’
- l179, move ‘(version 5.5.4 or later)’ to l177
- l180-182, l187-188, l192-193, The author repeatedly mentions that "Mmg must be run in serial, but Elmer is in parallel." These redundant sentences heavily influence the reading experience. I would recommend merging these sentences into one paragraph.
- l185, what does anisotropic mean? Horizontally, or vertically? The authors need to define the concept at the first time introducing it.
- l192-195, shorten these two sentences to one.
- l196-197, these sentences are redundant. As I understand correctly, ‘Surface and bottom are projected because they need to be projected. Free surface solvers are used on ‘A’ because free surface cannot be solved on non-A’ I would recommend to rewrite these sentences.
- l201-203, Here, together with the following paragraphs, I suggest the author first explain the details about the failure, then how to cure the failure
- l205-206, these two ‘if’s are also redundant. merge them.
- l209, what is ‘a saved mesh’
- l210-211, what is ‘level set implementation fails across the range of input parameters provided’? Give a concrete example. Why ‘calving cannot occur’ then?
- l212, what is ‘remeshing fails on all input parameters’?
- l219, how is the new solution checked, to ensure not to use unrealistic velocity?
- l227, why ‘plus one second’? Does this mean one has to always use time step at one second?
- Figure 4, row 5, the center box ‘Success? Mesh quality sufficient?’ has two ‘Yes’ arrows, which way should ‘Yes’ go?
- l262-269, these are pretty standard numerical analysis theory, I suggest the authors to replace this paragraph with a review of literature, and shorten the length.
- l269-274, I could not fully agree with the author’s arguments here. Every numerical method for time dependent problem has numerical errors associated with the time scheme. No matter what type of calving law, the errors are due to the approximation of the time derivative in the time dependent equations. In this case, it comes from the free surface equations. I agree the way no-physical rate-based law update the ice geometry is different from rate-based law, but this does not lead to the conclusion that it is time step independent.
- section 6.2, after reading this section several times, it is still not clear to me what adaptive time stepping method is used in this study. To me understanding, adding small timesteps is just a safeguard after the adaptive time stepping. I suggest the authors to rewrite this section, and spend the first few paragraphs to explain what adaptive time stepping method they used in this work.
- l303-306, in most numerical models, the common reason to use adaptive time stepping is to improve efficiency of the transient simulation, while maintaining desired accuracy. In general, adaptive time stepping method is more efficient than constant time stepping in terms of getting the final solution of a long term simulation. I would strongly recommend to revise this section.
- l309-312, what is the purpose to mention ‘fine meshes at ice streams’? This sounds like ‘others did A, we are going to do B’
- l313, could you provide a reference about ‘increasing exponentially’. Otherwise, I would say it is n^3 to n^4
- Figure 6, the fonts in the figures are too tiny
- l350, ‘a linear increase in calving’, in terms of rate or ice front position?
- l359, what is the reduction in element size? from where?
- l359, ‘Secondly, …’ this is still due to a more accurate representation of the crevasses, which falls in ‘Firstly’. You need to further explain this point, or merge it to the first argument.
- l362-366, this paragraph is too weak. The authors claim that a fine mesh resolution should always be used, but then did not go for it.
- Table 1 has the names of the two columns swapped. The retreat rate of no pinning points should be larger than that of those with pinning points.
- Section 7.1, the authors spend the first sentence talking about the new calving model, but the rest of the paragraph is a review of other models, which should either be placed in the introduction, or be removed. l388, ‘A second important opportunity…’, what is the first opportunity?
- l397, remove the discussion about calving laws, since calving law has its own section in the next paragraph
- Section 7.3, the title of the section says ‘other calving laws’, however, the authors spend half of the paragraph talking about CD, which is the one already implemented. I suggest to rewrite this section with more in-depth discussion about other calving laws, and move the CD parts to future implementation.
- Section 7.5, most of the text in the section should be relocated in the introduction. Previous models suffer from 3D ice front geometry is the reason of doing this study, but not the ‘capability and potential’ of this model.
- l449-450, remove ‘have been shown ….cores.’, since the author did not mention any high performance computing details in the whole manuscript, ‘1000 cores’ does not mean anything to the reader.
- l453, remove ‘Some improvements to increase the computational efficiency of the algorithm are ongoing but currently the model is robust’, this is not conclusion.
Citation: https://doi.org/10.5194/egusphere-2023-2778-RC1 -
AC1: 'Reply on RC1', Iain Wheel, 13 Mar 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2023-2778/egusphere-2023-2778-AC1-supplement.pdf
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RC2: 'Comment on egusphere-2023-2778', Stephen Cornford, 19 Feb 2024
Wheel and others present a new method for the treatment of calving in glaciers. This is an urgent problem in the numerical modelling of glaciers, with calving being perhaps the most important physical mechanism that is (usually) not represented well in models. That is partly because the physics is not well understood (or, rather, is not well represented at scale) in most models, and partly because the numerical methods usually fall short in some way. The paper makes use of a sophisticated multiple stage treatment, essentially creating new unstructured meshes whose boundary is (in part) coincident with the moving calving front and finely space near that front where numerical error would otherwise be large. Given that, this paper should be welcome progress, and I think that it could be welcome progress but only after substantial revisions, including additional numerical experiments and improvements to presentation are complete.
Major comment 1: numerical experiments
The model capabilities are demonstrated with two closely related sets of experiments: they differ in that experiment 1 (unpinned) has no pinning point and experiment 2 (pinned) has two. Here, a pinning point is a local rise in the bedrock where the glacier front will tend to less motion. These are idealized experiments, and well chosen to demonstrate the ultimate capabilities of the model. However, the results are not sufficient to demonstrate convergence with mesh spacing, and clearly show that the results do *not* converge with decreasing time step in either the pinned or unpinned case. The authors do note the lack of convergence in the unpinned case where it is most obvious.
Looking at table 1 (a summary of all experiments), we see that as the time step decreases (2d->1d->1/2d-1/4d) the retreat rate in the pinned case (BTW the column labels are incorrect in table 1) follows the sequence 2.51,3.31,2.99,3.67. This is not convergent: the difference between successive elements is not decreasing. This might improve with yet smaller time steps. In the unpinned case (which is at least as likely in real glaciers as the pinned case) the sequence is clearly diverging. As it stands the method cannot be used with any confidence.
As for space convergence: pick four resolutions following a geometric sequence for each case (e.g 80,40,20,10 m). Then correct (or not correct) behaviors will be evident. It does look from the figures presented as though the unpinned case will not be convergent but the pinned case might be.
Many authors would hide these flaws (or not check at all) and I don’t think they are fatal for the paper, but further experiments could show why they occur. The text hints (and I think is probably correct) that the crevasse depth law is the cause rather than the remeshing procedure per se. But this can be tested: carry out simulations with a simple calving rate.
 Major comments 2: presentation
I found the paper quite disorganized, at multiple levels. In my opinion it requires a wholesale rewrite.
At the highest level, the sections are not arranged in the usual hierarchy. Sections 1,2,3 are (overall) introductory material, section 4 mixes methods with some discussion (why the method might fail). Section 5 repeats the last part of section 4. Section 6 should detail the experiments, but includes some material (discussion of the CFL condition) that applies to all cases. Section 7 is a discussion section. The paper would benefit from organization in the conventional manner.
Some paragraphs change subject midway. One example: the paragraph starting at line 101starts talking about the computational difficulty of remeshing, but then switches to need for it, then back. Another: starting at 171 the text is about the need for updated remeshing procedures, but then introduces some specific issue around parallel computing. This is best dealt with by saying how the model works first and later describing (as is done to some extent) parallel computing issues and solutions.
Many parts of the text are difficult to understand, they are usually descriptions of some model behaviors or feature without examples of quantification, so as a reviewer I am not able to say whether they are likely to be correct or not. This is particularly acute in section 4.4, where numerous algorithmic details are mentioned but it is not clear how they are implemented – following this paper to implement the ideas in (say) ISSM would be impossible.
Figure 3 is overall a very useful figure, providing a set of diagrams that explain the whole procedure well. Â It does have a minor flaw: there are no scales and figures are presented at different scales. I can make out what is going on in each case, but published figures should be made with more care. The color scale legend labels in panels a and h are too small.
Â
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Citation: https://doi.org/10.5194/egusphere-2023-2778-RC2 -
AC2: 'Reply on RC2', Iain Wheel, 13 Mar 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2023-2778/egusphere-2023-2778-AC2-supplement.pdf
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AC2: 'Reply on RC2', Iain Wheel, 13 Mar 2024
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-2778', Gong Cheng, 30 Jan 2024
This manuscript introduces a novel 3D calving model implemented in Elmer/ICE, which is capable of capturing the 3D geometry of the ice terminus. Two groups of numerical experiments, one with pinning points at the ice fronts and one without, are compared. The authors demonstrate that certain choices of non-physical parameters can significantly impact the behavior of the model.
To the best of my knowledge, this manuscript represents the first study attempting to model the 3D geometry of a moving ice front. However, there is still room for improvement before this manuscript can be considered for publication.
Main comments
My main concern is the need to improve the quality of this manuscript. The authors have used non-scientific language, such as 'almost certain' and 'roughly', when drawing conclusions. Additionally, I have noticed that many introductory contents are misplaced in later sections, such as 4.3, 7.1, 7.5, etc. I suggest that the authors rewrite the introduction as well as these sections. Overall, there are several redundant paragraphs in this manuscript that could be significantly shortened.
Regarding the numerical experiments, particularly the mesh resolutions experiments, it is conventionally recommended to test at least 4 different points of each variable in order to draw conclusions related to convergence. These points should span at least 1/2 and 2 times the control resolution.
The significant impact of non-physical parameters on the no pinning point cases appears to be closely related to the CD calving law. I suggest that the authors add a comparison experiment with a rate-based calving law to identify the reason for this strong dependence.
I fully agree that the authors should focus on the key methodological choices and model capabilities. However, as a whole paper, the manuscript should be self-explanatory without requiring readers to read the supplementary materials.
Detailed Comments
- l34, this sentence sounds like incomplete. I would recommend to add a few more sentences to further explain the Linear Elastic Fracture model, and make a comparison with the two previous models.
- l99, I would be more careful to use ‘greatly’. The error depends on the mesh size, and in most of numerical models using level-set approach, the mesh close to the ice front is usually well refined.
- l100, remove ‘Ice-free elements remain dormant.’
- l118, what is the type of the CPUs? I also suggest the authors to give more information about the computational time of all the experiments.
- l120, give → giving
- Figure 1. The texts in the color bar are too small to read
- Section 4.2, in general, this section need a bit more work. For example,
- l132-141, I'm a bit confused about this paragraph. What boundary condition is apply at the fjord wall? If the velocity is solved with a Dirichlet boundary condition parallel to the fjord wall, then the velocity component in the direction of the fjord wall is automatically constrained. Shouldn't the velocity solution be constrained first, instead of fixing the displacement?
- l144, what do 'this' refer to? The previous sentences discuss the issue at the boundary corner, which does not 'provide a better solution...’
- l148-149, ‘the model has the …. lateral margins’, could you explain a bit more in details, what are the ‘boundary elements’ and where is the lateral margins? Are these at the calving front, or at the fjord wall?
- l153, is the normal to the element faces, or to the nodes?
- l159-161, I’m a bit worried about the melting applied at the corner element, as the normal direction is not going to parallel to the wall, which add additional ‘leak of mass’ at the side wall boundary
- Overall, it would beneficial to have a schematic plot of the boundary at the corner between ice front and fjord wall, and refer to the items in the figure when explaining the implementations
- l174-178, these text about how the previous method is implemented should go to the introduction.
- l179, add ‘,’ between ‘algorithm’ and ‘Mmg’
- l179, move ‘(version 5.5.4 or later)’ to l177
- l180-182, l187-188, l192-193, The author repeatedly mentions that "Mmg must be run in serial, but Elmer is in parallel." These redundant sentences heavily influence the reading experience. I would recommend merging these sentences into one paragraph.
- l185, what does anisotropic mean? Horizontally, or vertically? The authors need to define the concept at the first time introducing it.
- l192-195, shorten these two sentences to one.
- l196-197, these sentences are redundant. As I understand correctly, ‘Surface and bottom are projected because they need to be projected. Free surface solvers are used on ‘A’ because free surface cannot be solved on non-A’ I would recommend to rewrite these sentences.
- l201-203, Here, together with the following paragraphs, I suggest the author first explain the details about the failure, then how to cure the failure
- l205-206, these two ‘if’s are also redundant. merge them.
- l209, what is ‘a saved mesh’
- l210-211, what is ‘level set implementation fails across the range of input parameters provided’? Give a concrete example. Why ‘calving cannot occur’ then?
- l212, what is ‘remeshing fails on all input parameters’?
- l219, how is the new solution checked, to ensure not to use unrealistic velocity?
- l227, why ‘plus one second’? Does this mean one has to always use time step at one second?
- Figure 4, row 5, the center box ‘Success? Mesh quality sufficient?’ has two ‘Yes’ arrows, which way should ‘Yes’ go?
- l262-269, these are pretty standard numerical analysis theory, I suggest the authors to replace this paragraph with a review of literature, and shorten the length.
- l269-274, I could not fully agree with the author’s arguments here. Every numerical method for time dependent problem has numerical errors associated with the time scheme. No matter what type of calving law, the errors are due to the approximation of the time derivative in the time dependent equations. In this case, it comes from the free surface equations. I agree the way no-physical rate-based law update the ice geometry is different from rate-based law, but this does not lead to the conclusion that it is time step independent.
- section 6.2, after reading this section several times, it is still not clear to me what adaptive time stepping method is used in this study. To me understanding, adding small timesteps is just a safeguard after the adaptive time stepping. I suggest the authors to rewrite this section, and spend the first few paragraphs to explain what adaptive time stepping method they used in this work.
- l303-306, in most numerical models, the common reason to use adaptive time stepping is to improve efficiency of the transient simulation, while maintaining desired accuracy. In general, adaptive time stepping method is more efficient than constant time stepping in terms of getting the final solution of a long term simulation. I would strongly recommend to revise this section.
- l309-312, what is the purpose to mention ‘fine meshes at ice streams’? This sounds like ‘others did A, we are going to do B’
- l313, could you provide a reference about ‘increasing exponentially’. Otherwise, I would say it is n^3 to n^4
- Figure 6, the fonts in the figures are too tiny
- l350, ‘a linear increase in calving’, in terms of rate or ice front position?
- l359, what is the reduction in element size? from where?
- l359, ‘Secondly, …’ this is still due to a more accurate representation of the crevasses, which falls in ‘Firstly’. You need to further explain this point, or merge it to the first argument.
- l362-366, this paragraph is too weak. The authors claim that a fine mesh resolution should always be used, but then did not go for it.
- Table 1 has the names of the two columns swapped. The retreat rate of no pinning points should be larger than that of those with pinning points.
- Section 7.1, the authors spend the first sentence talking about the new calving model, but the rest of the paragraph is a review of other models, which should either be placed in the introduction, or be removed. l388, ‘A second important opportunity…’, what is the first opportunity?
- l397, remove the discussion about calving laws, since calving law has its own section in the next paragraph
- Section 7.3, the title of the section says ‘other calving laws’, however, the authors spend half of the paragraph talking about CD, which is the one already implemented. I suggest to rewrite this section with more in-depth discussion about other calving laws, and move the CD parts to future implementation.
- Section 7.5, most of the text in the section should be relocated in the introduction. Previous models suffer from 3D ice front geometry is the reason of doing this study, but not the ‘capability and potential’ of this model.
- l449-450, remove ‘have been shown ….cores.’, since the author did not mention any high performance computing details in the whole manuscript, ‘1000 cores’ does not mean anything to the reader.
- l453, remove ‘Some improvements to increase the computational efficiency of the algorithm are ongoing but currently the model is robust’, this is not conclusion.
Citation: https://doi.org/10.5194/egusphere-2023-2778-RC1 -
AC1: 'Reply on RC1', Iain Wheel, 13 Mar 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2023-2778/egusphere-2023-2778-AC1-supplement.pdf
-
RC2: 'Comment on egusphere-2023-2778', Stephen Cornford, 19 Feb 2024
Wheel and others present a new method for the treatment of calving in glaciers. This is an urgent problem in the numerical modelling of glaciers, with calving being perhaps the most important physical mechanism that is (usually) not represented well in models. That is partly because the physics is not well understood (or, rather, is not well represented at scale) in most models, and partly because the numerical methods usually fall short in some way. The paper makes use of a sophisticated multiple stage treatment, essentially creating new unstructured meshes whose boundary is (in part) coincident with the moving calving front and finely space near that front where numerical error would otherwise be large. Given that, this paper should be welcome progress, and I think that it could be welcome progress but only after substantial revisions, including additional numerical experiments and improvements to presentation are complete.
Major comment 1: numerical experiments
The model capabilities are demonstrated with two closely related sets of experiments: they differ in that experiment 1 (unpinned) has no pinning point and experiment 2 (pinned) has two. Here, a pinning point is a local rise in the bedrock where the glacier front will tend to less motion. These are idealized experiments, and well chosen to demonstrate the ultimate capabilities of the model. However, the results are not sufficient to demonstrate convergence with mesh spacing, and clearly show that the results do *not* converge with decreasing time step in either the pinned or unpinned case. The authors do note the lack of convergence in the unpinned case where it is most obvious.
Looking at table 1 (a summary of all experiments), we see that as the time step decreases (2d->1d->1/2d-1/4d) the retreat rate in the pinned case (BTW the column labels are incorrect in table 1) follows the sequence 2.51,3.31,2.99,3.67. This is not convergent: the difference between successive elements is not decreasing. This might improve with yet smaller time steps. In the unpinned case (which is at least as likely in real glaciers as the pinned case) the sequence is clearly diverging. As it stands the method cannot be used with any confidence.
As for space convergence: pick four resolutions following a geometric sequence for each case (e.g 80,40,20,10 m). Then correct (or not correct) behaviors will be evident. It does look from the figures presented as though the unpinned case will not be convergent but the pinned case might be.
Many authors would hide these flaws (or not check at all) and I don’t think they are fatal for the paper, but further experiments could show why they occur. The text hints (and I think is probably correct) that the crevasse depth law is the cause rather than the remeshing procedure per se. But this can be tested: carry out simulations with a simple calving rate.
 Major comments 2: presentation
I found the paper quite disorganized, at multiple levels. In my opinion it requires a wholesale rewrite.
At the highest level, the sections are not arranged in the usual hierarchy. Sections 1,2,3 are (overall) introductory material, section 4 mixes methods with some discussion (why the method might fail). Section 5 repeats the last part of section 4. Section 6 should detail the experiments, but includes some material (discussion of the CFL condition) that applies to all cases. Section 7 is a discussion section. The paper would benefit from organization in the conventional manner.
Some paragraphs change subject midway. One example: the paragraph starting at line 101starts talking about the computational difficulty of remeshing, but then switches to need for it, then back. Another: starting at 171 the text is about the need for updated remeshing procedures, but then introduces some specific issue around parallel computing. This is best dealt with by saying how the model works first and later describing (as is done to some extent) parallel computing issues and solutions.
Many parts of the text are difficult to understand, they are usually descriptions of some model behaviors or feature without examples of quantification, so as a reviewer I am not able to say whether they are likely to be correct or not. This is particularly acute in section 4.4, where numerous algorithmic details are mentioned but it is not clear how they are implemented – following this paper to implement the ideas in (say) ISSM would be impossible.
Figure 3 is overall a very useful figure, providing a set of diagrams that explain the whole procedure well. Â It does have a minor flaw: there are no scales and figures are presented at different scales. I can make out what is going on in each case, but published figures should be made with more care. The color scale legend labels in panels a and h are too small.
Â
Â
Citation: https://doi.org/10.5194/egusphere-2023-2778-RC2 -
AC2: 'Reply on RC2', Iain Wheel, 13 Mar 2024
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2023-2778/egusphere-2023-2778-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Iain Wheel, 13 Mar 2024
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