the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Surging of a Hudson Strait Scale Ice Stream: Subglacial hydrology matters but the process details don't
Lev Tarasov
Abstract. While subglacial hydrology is known to play a role in glacial dynamics on sub-annual to decadal scales, it remains unclear whether subglacial hydrology plays a critical role in ice sheet evolution on centennial or longer time-scales. Furthermore, several drainage topologies have been inferred but it is unclear which drainage topology is most applicable at the continental/glacial scale. More fundamentally, it is even unclear if the structural choice of subglacial hydrology truly matters for this context.
Here we compare three subglacial hydrology topologies as to their contribution to surge behaviour for an idealized Hudson Strait like ice stream. We use the newly updated model BraHms2.0 and provide model verification tests. BraHms2.0 incorporates each of these systems: two process-based forms dominant in the literature (linked-cavity and poro-elastic) and a non-mass conserving zero-dimensional form (herein termed leaky-bucket) coupled to an ice sheet systems model (the Glacial Systems Model, GSM).
We also assess the likely bounds on poorly constrained subglacial hydrology parameters and adopt an ensemble approach to study their impact and interactions within those bounds.
We find that subglacial hydrology is an important system inductance for realistic ice stream surging but that the three formulations all exhibit similar surge behaviour. Even a detail as fundamental as mass conserving transport of subglacial water is not necessary for simulating a full range of surge frequency and amplitude. However, one difference is apparent: the combined positive and negative feedbacks of the linked-cavity system yields longer duration surges and a broader range of effective pressures than its poro-elastic and leaky-bucket counterparts.
Matthew Drew and Lev Tarasov
Status: final response (author comments only)
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RC1: 'Comment on tc-2022-226', Anonymous Referee #1, 28 Dec 2022
- AC1: 'Reply on RC1', Matthew Drew, 22 Mar 2023
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RC2: 'Comment on tc-2022-226', Anonymous Referee #2, 09 Feb 2023
“Surging of a Hudson Strait Scale Ice Stream: Subglacial hydrology matters but the process details don’t” by Drew and Tarasov presents a subglacial hydrology model implemented in an ice-sheet model geared towards paleo applications. The manuscript describes three versions of the model, a series of verification tests, and the application to a simplified Laurentide Ice Sheet configuration. The authors perform large ensembles with each version of the model to assess parameter sensitivity of the model for applications to ice-sheet thickness and surging. They find that the inclusion of subglacial hydrology improves the surging behavior of the model, but the choice of form of subglacial hydrology among the three forms considered is not critical for primary quantities of interest.
The study is impressive in its thoroughness. The comparison of the different styles of subglacial hydrology models for the application of interest is exhaustive and highlights similarities and differences that are often left to speculation. I also commend the authors for the detailed model verification they perform, which is important but often skipped. The size of the ensembles performed is truly impressive and a great achievement. The size of the parameter space explored provides a lot of confidence on the conclusions. One longstanding problem in subglacial hydrology modeling is not knowing which models to use or what parameter values to use because of the large uncertainty in both choices. The large ensembles described here are one of the few detailed assessments of this issue that I’ve seen.
Despite these strengths, the study suffers from two major issues. First, the cursory consideration of channelized/efficient drainage makes it hard to generalize the results to realistic conditions. Second, the manuscript is long, dense, and feels unfinished. I elaborate on these issues below.
Major Issues
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- Inadequate consideration of efficient/channelized drainage. The authors admit they have implemented a somewhat ad hoc solution to efficient drainage, which is fine, particularly given the long time scale and relatively coarse resolution modeling they are targeting. However, this choice severely limits their ability to address some of the main questions in the manuscript. For example, on line 33 is stated the major question of “And if so, to what extent are the structural details of the hydrological system important for this context, especially given the rest of the system uncertainties?” Similarly, the somewhat provocative title implies the full range of process details have been considered, when arguably the most important process detail has not. I could see two ways to address this issue: revise the model, the simulations, and the manuscript to properly consider efficient drainage, or modify the presentation to more carefully acknowledge this limitation. Obviously, the former is unlikely to be practical. For example, in addition to the examples listed above, line 47 avoids mentioning efficient drainage at all.
- Manuscript is complicated and feels unfinished. The Discussion section is hard to follow and missing many figure references. Additionally, there is no discussion of model limitations (see item 1) or comparison of results to the existing literature. For how long the manuscript is, the conclusion is quite rushed. Specific examples are listed below.
Minor Issues
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16: If there is space in the abstract work limit, concisely state the feedbacks that the linked-cavity model has that the other don’t.
20: “leading *to*”
24: Consider adding some more recent references as examples here (e.g. work in west Greenland about seasonal and diurnal variations).
28: I’m not sure “topology” is the right word here and throughout the manuscript. topology is defined as “the way in which constituent parts are interrelated or arranged”. I think what you may mean is system form or structure.
29: You could be as far as to say these issues limit application of subglacial hydrology models generally.
39: Also consider the mechanisms of (Bassis et al., 2017).
49-51: This detail would be more appropriate in the Methods than the Introduction.
56-59: These details are also distracting in the Introduction.
64: quantify what you mean by “large”. These ensembles are impressively large for ice-sheet model standards.
72: In terms of the two modes evolving to each other, it is important to mention the hysteresis in evolution (Schoof, 2010).
84: Include the citation for this statement. (Flowers and Clarke, 2002)
93: Add citations, e.g. (Rada and Schoof, 2018)
113: The mass conservation equation should be moved to section 2.1. As presented, it implies that it is unique to the poro-elastic model, but it also applies to the linked-cavity model.
119: Again, add reference for this equation (Flowers and Clarke, 2002)
146: missing reference
165: spelling: Arakawa. Also provide a reference for this terminology (Arakawa and Lamb 1977)
168: “modified version of Schoof (2010) as in that of Werder et al. (2013) and Bueler and van Pelt (2015)” It is unclear what is meant by this – each of those papers are very dense.
175: formatting problem around “e.g.”
Eq. 9: replace curly braces with parentheses
181: add comma after “surging”
194: This statement seems to be a repeat of line 191.
220: Did you consider the semi-analytic solution presented in (Bueler and van Pelt, 2015)?
250: Did you attempt to assess if the rate of convergence matches the numerical order of the discretization? (same for spatial resolution in sec. 3.3.3)
Why were different domains used for the temporal and spatial resolution convergence tests?
Fig. 1: What are the other variables than effective pressure? Only effective pressure is mentioned in the text on line 259.
289: missing closing parenthesis.
300: Please state the model resolution. Also mention the model time step used somewhere in section 4.
335: Other references to consider for conductivity ranges: (Hewitt, 2011; Hager et al., 2022)
344: Please clarify how ice velocity provides a lower bound on water flow speed. Is the assumption that water moves with the ice and shares the same speed?
348: Are you applying a flow law here? If so, state what it is.
351: Reword this sentence to make it clear that this equation is what Flowers et al. did, not a certain relationship. Also, it is not clear how you are using this relationship.
356-363: This methodological detail should be moved to the model description.
395: Is this the equation from Schoof? If so, please add the citation here as well.
405-408: There is no description of how these parameters are used in GSM. Please add that here or to the model description.
4.12: Please divide this section into a portion describing the ensemble design and a separate section describing the results.
416: These are very large numbers of runs for ice-sheet modeling! Can you provide some details about how long a single run and/or entire ensemble takes to run and what computational resources were used?
418: Please add a table listing the parameters varied in each ensemble. The parameter sensitivity figures and discussion are extremely hard to follow without knowing what the parameters are.
428: Is there a reference for this sieve technique? Regardless, can you provide a more explicit definition of what that means? Also, did you consider performing a formal Bayesian calibration to the desired ice-sheet thickness instead? It would seem you have large enough sample sizes to do that.
436: Similarly, is there a reference for the non-parametric sensitivity method you are employing here, or is it novel to the study? Why not using existing non-parametric sensitivity methods?
450: Why is the dummy parameter not identical before and after sieving? Also, why do the unsieved KDFs in Figure 7 a and b drop off near the minimum and maximum values in the range?
What is the difference between Figures 7 and 12? Why is Figure 12 introduced after Fig. 7 on line 452?
459: Please justify why an inflection indicates which parameters could be fixed. Also, justify fitting a polynomial to categories of data. It does not seem that you do anything with the categories of sensitive and insensitive parameters, so this extra complexity might not be needed.
460: “The change in sensitivity metric from one parameter to the next highest is not strictly monotonic”. They look monotonic. Are they sorted by increasing KDF diff? If so, by definition, they increase monotonically.
463: Can you could identify which parameter are hydrology-related (and possibly other categories) in the figure using a color or symbol? That would greatly help the utility of this figure in conveying which classes of parameters are most important (which could be discussed in 465-471).
Figure 8: Please make it explicit what the sieve criterion being evaluated in this figure is.
Section 4.13: This section would benefit from referring to some examples of what identified surges look like. It looks like that is what Figure 9 is, but it is never referenced in the text! Also, I recommend changing the section title to something like “Definition of surge metrics”.
500: The percentages listed are much smaller than 1/3-1/4.
509: “runs with *surge* events”
Fig. 10: You use the term “Heinrich event metrics” in the caption, but in the text you say “surge events”. Please use a consistent terminology, because this is an ad hoc working definition, and it will reduce confusion. Also, I wonder if line plots would be easier to distinguish the 4 models – they are hard to differentiate as is.
510-521: This text looks like it should belong in the following section (5.1). Or consider removing it. What is the purpose of analyzing the surge duration as a function of frequency? This part of the manuscript is hard to follow, and I question what value it adds. Unless there is clear use for this information, I recommend removing this section to reduce the complexity of an already complex paper.
524: The parenthetical statement should not be parenthetical, as it is critical for understanding what was done. Also, please reword it (e.g. three and twelve what?).
525: “sensitivity ranking” – Is this referring to Figure 12? I’m feeling very lost in this section.
527-533: Again, coloring/marking the parameters by type is needed to make this figure interpretable.
535: Is this referring to Figure 13? Also, is this the whole ensemble, or one of the sieved subsets? From Fig. 13 caption it looks like the entire ensemble. I’m not sure that is useful given the arbitrary nature of the parameter ranges considered. Why use the whole ensemble for this?
536: “stark difference” Why? Please elaborate.
General: I recommend a table defining and naming the various ensemble subsets (sieved results). The text can then refer to those subsets unambiguously.
Figure 13: How are both the whole ensemble and the warm-based portion of the ensembles shown in this one figure?
551-561: This section is hard to follow and seems to be getting into specific details. Also, these results are not shown anywhere, making it harder to assess these statements. I suggest removing these paragraphs.
554: Figure reference missing.
570: This result may be a feature of the specific friction law used, which is fairly ad hoc. The paper is lacking a discussion section on model limitations and comparison to other studies. Please add such a section. For example, (Hewitt, 2013) compares poroelastic and linked cavity formulations.
References===========
Bassis, J. N., Petersen, S. V., and Mac Cathles, L.: Heinrich events triggered by ocean forcing and modulated by isostatic adjustment, Nature, 542, 332–334, https://doi.org/10.1038/nature21069, 2017.
Bueler, E. and van Pelt, W.: Mass-conserving subglacial hydrology in the Parallel Ice Sheet Model version 0.6, Geosci. Model Dev., 8, 1613–1635, https://doi.org/10.5194/gmd-8-1613-2015, 2015.
Flowers, G. E. and Clarke, G. K. C.: A multicomponent coupled model of glacier hydrology 1. Theory and synthetic examples: MULTICOMPONENT HYDROLOGY, 1, THEORY, J. Geophys. Res., 107, ECV 9-1-ECV 9-17, https://doi.org/10.1029/2001JB001122, 2002.
Hager, A. O., Hoffman, M. J., Price, S. F., and Schroeder, D. M.: Persistent, extensive channelized drainage modeled beneath Thwaites Glacier, West Antarctica, The Cryosphere, 16, 3575–3599, https://doi.org/10.5194/tc-16-3575-2022, 2022.
Hewitt, I. J.: Modelling distributed and channelized subglacial drainage: the spacing of channels, J. Glaciol., 57, 302–314, https://doi.org/10.3189/002214311796405951, 2011.
Hewitt, I. J.: Seasonal changes in ice sheet motion due to melt water lubrication, Earth and Planetary Science Letters, 371–372, 16–25, https://doi.org/10.1016/j.epsl.2013.04.022, 2013.
Rada, C. and Schoof, C.: Subglacial drainage characterization from eight years of continuousborehole data on a small glacier in the Yukon Territory, Canada, Subglacial Processes, https://doi.org/10.5194/tc-2017-270, 2018.
Schoof, C.: Ice-sheet acceleration driven by melt supply variability, Nature, 468, 803–806, https://doi.org/10.1038/nature09618, 2010.
Citation: https://doi.org/10.5194/tc-2022-226-RC2 - AC2: 'Reply on RC2', Matthew Drew, 22 Mar 2023
Matthew Drew and Lev Tarasov
Matthew Drew and Lev Tarasov
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