Numerical issues in modeling ice sheet instabilities such as binge-purge type cyclic ice stream surging

Hank, Kevin; Tarasov, Lev; Mantelli, Elisa

doi:https://doi.org/10.5194/egusphere-2023-81

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https://doi.org/10.5194/egusphere-2023-81

Preprints

24 Feb 2023

| 24 Feb 2023

Numerical issues in modeling ice sheet instabilities such as binge-purge type cyclic ice stream surging

Kevin Hank, Lev Tarasov, and Elisa Mantelli

Abstract. As in any environmental system, modeling instabilities within the glacial system is a numerical challenge of potentially high real-world relevance. Differentiating between the impacts of physical system processes and numerical noise is not straightforward. Here we use an idealized North American geometry and climate representation (similar to the HEINO experiments, Calov et al., 2010) to examine the numerical sensitivity of ice stream surge cycling in glaciological models. Through sensitivity tests, we identify some numerical requirements for a robust model configuration for such contexts. To partly address model-specific dependencies, we use both the Glacial Systems Model (GSM) and Parallel Ice Sheet Model (PISM).

We show that modeled surge characteristics are resolution-dependent though converging (decreasing differences between resolutions) at higher horizontal grid resolutions. Discrepancies between high and coarse horizontal grid resolutions can be reduced by incorporating a resolution-dependent basal temperature ramp for basal sliding thermal activation. Inclusion of a diffusive bed thermal model reduces the surge cycling ice volume change by ∼33 % as the additional heat storage dampens the change in basal temperature during surge events. The inclusion of basal hydrology, as well as a non-flat topography, leads to increased ice volume change during surge events (∼20 and 17 %, respectively). Therefore, these latter three components are essential if one is endeavoring to maximize physical fidelity in ice stream surge cycle modeling. An abrupt transition between hard bedrock and soft sediment, as in the HEINO experiments, leads to ice stream propagation along this boundary but is not the cause of the main surge events.

Received: 23 Jan 2023 – Discussion started: 24 Feb 2023

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Journal article(s) based on this preprint

10 Oct 2023

Modeling sensitivities of thermally and hydraulically driven ice stream surge cycling

Kevin Hank, Lev Tarasov, and Elisa Mantelli

Geosci. Model Dev., 16, 5627–5652, https://doi.org/10.5194/gmd-16-5627-2023,https://doi.org/10.5194/gmd-16-5627-2023, 2023

Short summary

Kevin Hank et al.

Interactive discussion

Status: closed

AC1: 'Comment on egusphere-2023-81', Kevin Hank, 09 Mar 2023

Dear Readers,
The y-labels in Fig. 6 of the main manuscript are in the wrong order (the top one should be at the bottom).
The updated figure is attached here. We apologize for any confusion.
Kind regards,
Kevin Hank

Citation: https://doi.org/10.5194/egusphere-2023-81-AC1
RC1:
'Comment on egusphere-2023-81', Anonymous Referee #1, 24 Mar 2023

Please see attached pdf comments.

Citation: https://doi.org/10.5194/egusphere-2023-81-RC1
- AC2: 'Reply on RC1', Kevin Hank, 20 Apr 2023
  
  Please see attached pdf.
  
  Citation: https://doi.org/10.5194/egusphere-2023-81-AC2
RC2:
'Comment on egusphere-2023-81', Anonymous Referee #2, 08 Apr 2023

The manuscript "Numerical issues in modeling ice sheet instabilities such as binge-purge type cyclic ice stream surging" by Hank et al. is a study of numerical issues associated with modeling thermal oscillations in ice stream flow. It utilizes the GSM and PISM models, and varies many aspects of the numerical implementation including various details of the thermal and sliding models, resolution in time and space, and a variety of parameters. The central goal of this paper is to demonstrate which aspects of the model implementation are most critical to correctly simulate thermal (aka "binge-purge" oscillations).
The goal of this study is a worthy one, and though the general topic of simulating thermal oscillations in ice sheet models has recieved considerable attention over three decades, a systematic study of the dependence of oscillation characteristics on choices in the numerical implementation has not been done. The main issue I see is that the manuscript in its current form is very challenging to read. It is organized more like a reference guide to a large number of simulations, rather than a discussion of the link between real physical processes, numerical choices and clear recommendations for how to remedy these issues in future simulations. In order to be publishable in a form that will be usable by other researchers, the manuscript needs substantial re-organization, reduction in length and re-writing in places. Below the major issues are listed in more detail (I will wait to comment on minor issues in a subsequent revision):
Major issues:

1. Currently, the organization of the manuscript feels like a laundry list of simulations completed and a description of the results, without prioritizing the most important and revealing simulations and little discussion for what the results mean and how they relate to other studies. The study also seems to currently have about 10-15 areas of focus, making it challenging to see which end up actually being important. My recommendation would be to take all the description of simulations where numerical choices don't appear to have much influence on the results and move them into a supplement. They can be summarized in a few sentences perhaps at the end of the results section, but right now they add too much extra to the manuscript making it longer and hard to get through. This includes the sediment-hard bed transition, basal hydrology, basal hydrology instead of temperature ramp and the max time step.
2. The way the results are currently described and presented also contributes to the challenge of reading through this manuscript. There are 15 tables, and it is difficult to understand what all the numbers in the tables mean. Figures 4 and 6 seem like a more intuitive way to present this information (though all the markers and line and shading in Figure 6 need explicit descriptions in the caption and perhaps a legend to be interpretable). There really shouldn't be more than a few tables in the main text of this manuscript, the rest should be relegated to a supplement.
3. The "such as" in the title of the paper is misleading. The only type of ice sheet instability discussed and tested in this paper is a thermal oscillatory instability (or B-P). A more accurate title would be simpler: "Numerical issues in modeling binge-purge type cyclic ice stream surging"
4. Related to #3 and throughout - the term "binge-purge" oscillations has largely fallen out of favor in the ice sheet modeling community. These are more commonly called thermal oscillations or ice stream activation-stagnation cycles. It is OK to mention in the introduction that these have historically been referred to as binge-purge, but it isn't in keeping with the field to continue to refer to them as such throughout.
5. I am quite confused over how numerical noise is defined in this manuscript. It seems in section 3.1.3 that to quantify numerical noise that different solver choices are used. However, depending on the number of iterations occuring between the different tolerances (and the details of how the solver works) it would seem that this method could yield strongly different estimates for the "noise". Additionally, it is unclear why this is the correct bar for determining whether a change is "important", instead of a more physically meaningful quantity. Additionally, the rationale behind the set of simulations detailed in Table 6 is confusing. In a bitwise reproducible code, I don't see why the number of cores used in a simulation should have any influence on the simulations. This makes me concerned about the robustness of other simulations if the number of cores has such an important influence on the results. How reproducible are these results by other researchers? If the same setup is run on a different cluster architecture would the results be different?
6. In section 4 I see the summary of results, but very little discussion of what they mean (in some cases but not others). This seems to me to be the main missing piece of the manuscript to be useful to other researches, a discussion of how these results relate to the theory of thermal oscillations (from Schiavi, Mantelli, Robel, MacAyeal, etc.) and how they might relate to other ice sheet models.

Citation: https://doi.org/10.5194/egusphere-2023-81-RC2
- AC3: 'Reply on RC2', Kevin Hank, 20 Apr 2023
  
  Please see attached pdf.
  
  Citation: https://doi.org/10.5194/egusphere-2023-81-AC3

Interactive discussion

Status: closed

AC1: 'Comment on egusphere-2023-81', Kevin Hank, 09 Mar 2023

Dear Readers,
The y-labels in Fig. 6 of the main manuscript are in the wrong order (the top one should be at the bottom).
The updated figure is attached here. We apologize for any confusion.
Kind regards,
Kevin Hank

Citation: https://doi.org/10.5194/egusphere-2023-81-AC1
RC1:
'Comment on egusphere-2023-81', Anonymous Referee #1, 24 Mar 2023

Please see attached pdf comments.

Citation: https://doi.org/10.5194/egusphere-2023-81-RC1
- AC2: 'Reply on RC1', Kevin Hank, 20 Apr 2023
  
  Please see attached pdf.
  
  Citation: https://doi.org/10.5194/egusphere-2023-81-AC2
RC2:
'Comment on egusphere-2023-81', Anonymous Referee #2, 08 Apr 2023

The manuscript "Numerical issues in modeling ice sheet instabilities such as binge-purge type cyclic ice stream surging" by Hank et al. is a study of numerical issues associated with modeling thermal oscillations in ice stream flow. It utilizes the GSM and PISM models, and varies many aspects of the numerical implementation including various details of the thermal and sliding models, resolution in time and space, and a variety of parameters. The central goal of this paper is to demonstrate which aspects of the model implementation are most critical to correctly simulate thermal (aka "binge-purge" oscillations).
The goal of this study is a worthy one, and though the general topic of simulating thermal oscillations in ice sheet models has recieved considerable attention over three decades, a systematic study of the dependence of oscillation characteristics on choices in the numerical implementation has not been done. The main issue I see is that the manuscript in its current form is very challenging to read. It is organized more like a reference guide to a large number of simulations, rather than a discussion of the link between real physical processes, numerical choices and clear recommendations for how to remedy these issues in future simulations. In order to be publishable in a form that will be usable by other researchers, the manuscript needs substantial re-organization, reduction in length and re-writing in places. Below the major issues are listed in more detail (I will wait to comment on minor issues in a subsequent revision):
Major issues:

1. Currently, the organization of the manuscript feels like a laundry list of simulations completed and a description of the results, without prioritizing the most important and revealing simulations and little discussion for what the results mean and how they relate to other studies. The study also seems to currently have about 10-15 areas of focus, making it challenging to see which end up actually being important. My recommendation would be to take all the description of simulations where numerical choices don't appear to have much influence on the results and move them into a supplement. They can be summarized in a few sentences perhaps at the end of the results section, but right now they add too much extra to the manuscript making it longer and hard to get through. This includes the sediment-hard bed transition, basal hydrology, basal hydrology instead of temperature ramp and the max time step.
2. The way the results are currently described and presented also contributes to the challenge of reading through this manuscript. There are 15 tables, and it is difficult to understand what all the numbers in the tables mean. Figures 4 and 6 seem like a more intuitive way to present this information (though all the markers and line and shading in Figure 6 need explicit descriptions in the caption and perhaps a legend to be interpretable). There really shouldn't be more than a few tables in the main text of this manuscript, the rest should be relegated to a supplement.
3. The "such as" in the title of the paper is misleading. The only type of ice sheet instability discussed and tested in this paper is a thermal oscillatory instability (or B-P). A more accurate title would be simpler: "Numerical issues in modeling binge-purge type cyclic ice stream surging"
4. Related to #3 and throughout - the term "binge-purge" oscillations has largely fallen out of favor in the ice sheet modeling community. These are more commonly called thermal oscillations or ice stream activation-stagnation cycles. It is OK to mention in the introduction that these have historically been referred to as binge-purge, but it isn't in keeping with the field to continue to refer to them as such throughout.
5. I am quite confused over how numerical noise is defined in this manuscript. It seems in section 3.1.3 that to quantify numerical noise that different solver choices are used. However, depending on the number of iterations occuring between the different tolerances (and the details of how the solver works) it would seem that this method could yield strongly different estimates for the "noise". Additionally, it is unclear why this is the correct bar for determining whether a change is "important", instead of a more physically meaningful quantity. Additionally, the rationale behind the set of simulations detailed in Table 6 is confusing. In a bitwise reproducible code, I don't see why the number of cores used in a simulation should have any influence on the simulations. This makes me concerned about the robustness of other simulations if the number of cores has such an important influence on the results. How reproducible are these results by other researchers? If the same setup is run on a different cluster architecture would the results be different?
6. In section 4 I see the summary of results, but very little discussion of what they mean (in some cases but not others). This seems to me to be the main missing piece of the manuscript to be useful to other researches, a discussion of how these results relate to the theory of thermal oscillations (from Schiavi, Mantelli, Robel, MacAyeal, etc.) and how they might relate to other ice sheet models.

Citation: https://doi.org/10.5194/egusphere-2023-81-RC2
- AC3: 'Reply on RC2', Kevin Hank, 20 Apr 2023
  
  Please see attached pdf.
  
  Citation: https://doi.org/10.5194/egusphere-2023-81-AC3

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Kevin Hank on behalf of the Authors (27 Jun 2023) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (30 Jun 2023) by Ludovic Räss

RR by Anonymous Referee #2 (17 Jul 2023)

Suggestions for revision or reasons for rejection

This is an updated version of the manuscript with new title "Numerical issues in modeling thermally and hydraulically driven ice stream surge cycling" by Hank et al. It is greatly improved based on revisions responding to prior reviews. I think it has more logical flow and clearer messages about the importance of various modeling choices in simulating ice stream surging.

In some ways I think the revision does not quite go far enough in paring down the level of detail in the manuscript and the amount of repetition in describing the results (mainly in the amount of recapping of results in section 4 right after they are described in a similar level of detail in section 3). However, I also recognize that stylistic suggestions regarding the structure of papers are ultimately up to the authors. As someone who has worked on this problem and is predisposed to being very interested in the topic, I found it hard to get through the 40+ pages of painstaking detail on this suite of modeling experiments as a linear reading experience. It may be that most readers will use this paper as a reference guide, without reading it in its entirety. Even in such a form, it will be a useful contribution to the field. Ultimately it is up to the authors to decide whether it is worth substantially reducing the level of detail in sections 2 and 4. In section 2, there are places where modeling detail not pertinent to the questions defined in this study could be moved to a supplement or even just cited out to a previous paper. In section 4, there are many descriptions of results that are also given in section 3 which could be removed. Section 1.3 could be greatly shortened by just stating the questions you set out to answer. The first ~20 lines of section 5 recap results right after a section that is largely recapping of results. Overall, I think it is possible for this manuscript to be 25% shorter without losing much of the important detail of interest to readers.

One other major concern that remains from the first review is that it does not seem like a parameterization should be explicitly made to be resolution-dependent. It is unclear that the "optimal" temperature ramp parameters for coarse resolution would be the same between GSM and other models, and its unclear what is gained by designing the parameterization this way since it will undoutedly affect many others metrics beyond those which are the focus of this study. Additionally, it appears that the result of "compensation" of temperature ramp parameters for resolution difference are not even definitive, so why not just exclude this aspect of the discussion?

Below I have listed many minor suggestions on the writing as promised in my first review:

Throughout: apostrophes are not consistent in their direction
Throughout: the term parameter "vector" is more typically called a parameter "set"
Ln 8: high -> fine
Ln 17: delete sentence one
Ln 17: The relevance of ice sheet modeling...of numerical implementations.
Ln 21: significant -> realistic
Ln 31: work -> heat
Ln 34: work -> heating
Ln 34: delete "or to"
Ln 35: delete "decreased basal friction"
Ln 36: delete "loosened sediment"
Ln 41: note sure if this is what is typically meant by a "pinning point" as used in the glaciology literature. This is more commonly called a "sticky spot".
Ln 44: delete "quasi"
Ln 46: As a result of the physics involved and the behaviors expected
Ln 52: ...related to the physical system being modeled and those related to the numerical implementation.
Ln 53: Delete "numerical...surging" sentence. You list 4 studies right after this on this topic, and theres at least 5 more. I wouldn't call this "limited".
Ln 61: delete "however, only"
Ln 63: ...behavior, but an in-depth...
Ln 66: ...entirely absent from the literature.
Ln 67, 68, 71: time steps -> time step size
Ln 83: delete "with this as a starting point,"
Ln 84: model equations are not a numerical choice, they are a component of the system this is being modeled.
Ln 92: delete "high variance"
Ln 96: delete "especially"
Ln 167: "a priori" is two words
Ln 213: shelf-shallow ice
Ln 217: further automated reductions
Ln 246: Stokes model is currently infeasible over glacial cycle time scales
Ln 264: We configure the GSM
Ln 309 (and throughout): the term "one-at-a-time" is not really necessary (it doesn't matter whether you sample in serial or in parallel)
Ln 326: colon typo in citations
Ln 439: do the surge characterisitics change with the threshold for activating SSA? I was surprised that this numerical choice was not tested, given how exhaustive this study is otherwise.
Ln 457: "numerical induced bifurcation" is not the right terminology. This behavior is typically called "spontaneous symmetry breaking" and it was previously identified in the context of ice stream in Sayag and Tziperman, 2011)
Ln 473: early on you say that you won't be comparing the GSM to the PISM results directly, but then you do here?
Ln 502: there should be an explanation in the main text as to why the number of cores affects the solution. Many readers while find this to be concerning.
Ln 509: given that both models have tolerances that can be changed, why not use the same criteria for defining MNEEs in both models? This difference seems to make things unnecessarily complicated.
Ln 515: is this just noise in the initial condition or at every time step?
Ln 527: but is the implicit coupling scheme more accurate (for example with respect to grid spacing)
Ln 634-651: the discussion here is confusing and could be shortened and clarified
Ln 656,657: leads to more, longer, and higher amplitude surges.
Ln 741: the correct way to describe these results is that the solution exhibits "convergence", but is not "converged"
Figure 12: It would be clearer to plot the surge characteristics/metrics with respect to grid spacing. This is the typical plot made in convergence studies.
Section 3.4.2: it is difficult to take anything away from this convergence study since half of the simulations did not finish. Would make more sense to just delete this section an add a sentence at end of previous section saying that PISM is too computationally intensive to conduct a robust convergence study.
Ln 788-794: I struggled with this paragraph because it is not clear that is possible to compare the magnitude of sensitivity to very different kinds of changes to parameters and other numerical choices. It would be better to just whether changes were greater or less than MNEEs. Isn't that the point of defining these?
Ln 800: error with respect to the...
Ln 811-812: why do you expect this? Seems to be quite a big claim.
Ln 880-881: I'm not sure that this can be generalized since this hydrological model is quite simple and doesn't simulate many things other subglacial hydrology models do, like the increase in effective pressure with the development of channelized hydrology.
Ln 964: given the difference in configurations should we even expect to get temperature spokes in these simulations? fast flow is confined to a narrow strip which is different from the EISMINT simulations.
Ln 970: ...is the physical modeling choices and numerical sensitivity that must be considered when modeling ice stream...
Ln 973: Analytical solutions
Ln 974: models are needed to further...

Hide

ED: Publish subject to minor revisions (review by editor) (17 Jul 2023) by Ludovic Räss

AR by Kevin Hank on behalf of the Authors (08 Aug 2023) Author's response Author's tracked changes Manuscript

ED: Publish subject to minor revisions (review by editor) (17 Aug 2023) by Ludovic Räss

AR by Kevin Hank on behalf of the Authors (24 Aug 2023) Author's response Author's tracked changes Manuscript

ED: Publish subject to technical corrections (28 Aug 2023) by Ludovic Räss

AR by Kevin Hank on behalf of the Authors (30 Aug 2023) Author's response Manuscript

Journal article(s) based on this preprint

10 Oct 2023

Modeling sensitivities of thermally and hydraulically driven ice stream surge cycling

Kevin Hank, Lev Tarasov, and Elisa Mantelli

Geosci. Model Dev., 16, 5627–5652, https://doi.org/10.5194/gmd-16-5627-2023,https://doi.org/10.5194/gmd-16-5627-2023, 2023

Short summary

Kevin Hank et al.

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https://doi.org/10.5194/egusphere-2023-81-supplement

Data sets

Supplementary material for "Numerical issues in modeling ice sheet instabilities such as binge-purge type cyclic ice stream surging" Kevin Hank https://doi.org/10.5281/zenodo.7529646

Kevin Hank et al.

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Physically meaningful modeling of geophysical system instabilities is numerically challenging, given the potential effects of purely numerical artifacts. Here we explore the sensitivity of ice stream surge activation to numerical and physical model components. We find that surge characteristics exhibit a resolution dependency but converge at higher horizontal grid resolutions and are significantly affected by the incorporation of bed thermal and subglacial hydrology models.


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