the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Sensitivity of Future Projections of the Wilkes Subglacial Basin Ice Sheet to Grounding Line Melt Parameterizations
Abstract. Projections of Antarctic Ice Sheet mass loss and therefore global sea level rise are hugely uncertain, partly due to how mass loss of the ice sheet occurs at the grounding line. The Wilkes Subglacial Basin (WSB), a vast region of the East Antarctic ice sheet, is thought to be particularly vulnerable to deglaciation under future climate warming scenarios. However, future projections of ice loss, driven by grounding line migration, are known to be sensitive to the parameterisation of ocean-induced basal melt of the floating ice shelves, and specifically, adjacent to the grounding line – termed Grounding Line Melt Parameterizations (GLMPs). This study investigates future ice sheet dynamics in the WSB with respect to four GLMPs under both the upper and lower bounds of climate warming scenarios from the present to 2500, with different model resolutions and choices of sliding relationships. The variation in these GLMPs determines the distribution and the amount of melt applied in the finite element assembly procedure on partially grounded elements (i.e., elements containing the grounding line). Our findings indicate that the GLMPs significantly affect both the trigger-timings of tipping points and the overall magnitude of ice mass loss. We conclude that applying full melting to the partially grounded elements, which causes melting on the grounded side of the grounding line, should be avoided under all circumstances due to its poor numerical convergence and substantial overestimation of ice mass loss. We recommend preferring options that depend on the specific model context, either 1) not applying any melt immediately adjacent to the grounding line or 2) employing a sub-element parameterisation. Based on our best model results, a tipping point is projected to occur between 2200 and 2300, leading to massive and rapid retreat across the WSB and a significant increase in ice discharge from 200 to 500 Gt a-1. In this context, our simulations suggest that the WSB ice sheet could contribute between 0.23 to 0.34 m to global sea level rise by 2500.
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RC1: 'Comment on egusphere-2024-1005', Tijn Berends, 12 May 2024
Review of Wang et al. (2024): “Sensitivity of Future Projections of the Wilkes Subglacial Basin Ice Sheet to Grounding Line Melt Parameterizations”
By Tijn Berends
Ice-sheet models currently dominate the uncertainty in projections of future sea-level rise. A significant part of this model uncertainty stems from the way the discontinuity of the basal melt rate at the grounding line is treated in spatially discrete models. In this study, the authors present experiments with the Elmer/ice model, where they study the future retreat of the Antarctic ice sheet in the Wilkes basin, using different model resolutions, different sliding laws, and different ways to parameterise sub-shelf melt near the grounding line.
In general, I find this a very well-written paper. The experiments are well-defined, the results are presented clearly and concisely, and the conclusions are well-supported by the evidence presented. Having published a similar paper myself quite recently, I am glad to see that someone now did a better job of it! I do have a few comments that I think should be addressed before publishing, but as none of these should lead to additional experiments, I think these warrant “minor revisions” only.
Major comments
An interesting new feature you present is the “water-column scaling”, which is based on plume modelling studies (although you also cite observation-based papers that suggest that significant melting still occurs at, and even upstream of, the grounding line at several locations in Greenland and Antarctica). However, the way it is presented now in the results is, in my view, slightly confusing. The GLMPs exist in the realm of “model implementation”, i.e. different ways to discretise and solve the same physics. The WCS scheme, however, represents different physics, altering the mass budget of the ice sheet regardless of the choice of model implementation. I think it is important to make this distinction, especially since in the discussion section, you discuss the implications of significant melt upstream of the grounding line.
Both in the abstract and in several places throughout the manuscript, you state that you consider your simulations as actual projections of future mass loss. While I don’t object to this per se, I wonder if this is a good idea. If you want to do this, you will need to provide a lot more information about your experimental set-up (see my technical comments below, about the historical experiments, atmosphere & ocean forcing, etc.). This will add a bunch of extra text to your paper, which won’t do anything for the main story (concerning the GLMPs). I also wonder what the added value is of projections of a single ice-sheet basin, especially one that only contributes 30 cm of sea-level rise at most over the course of nearly five centuries. The main users of ice-sheet projections typically want the mass loss of the entire ice sheet, so they can calculate sea-level rise. As the main focus of your paper seems to be model-oriented, which I think is valuable enough by itself, I advise you to consider removing the label of “projections” from your simulations.
Technical comments
Abstarct: the water column scaling is not mentioned in the abstract
L 54-55 “Modelling studies suggest that ice sheet models are more sensitive to melt rates near the grounding line than to cavity-integrated melt rates beneath ice shelves” What about Joughin et al., 2021: “we find only minor sensitivity to melt distribution (<6%), with a linear dependence of ice loss on the total melt”
L 59-60 “…due to the discretisation of the ice sheet model, there inevitably exist grid cells or elements at the grounding line where ice is partially grounded and partially floating” In fixed-grid models, yes. Maybe not something to discuss here, but should we eventually move to moving-grid models?
L 88 “…such as the Shallow Shelf Approximation we use here” I’ve always wondered what the impact of this choice is when combined with an inversion method. Near the grounding line it’s probably fine, but further inland there should at present be at least some vertical shearing going on. The SSA neglects this, so the inversion must by necessity overestimate the basal slipperiness to compensate. Near the end of your projections, the grounding line might retreat into this area of overestimated slipperiness, artificially amplifying the retreat (see also the “compensating errors” in Berends et al., 2022 - https://tc.copernicus.org/articles/17/1585/2023/tc-17-1585-2023.pdf). Not something to investigate here, obviously, but maybe something to mention.
L 98 “The locations of calving front and inland boundary are held fixed throughout the simulations” This needs some elaboration. Is the ice not allowed to advance beyond that front but allowed to retreat within it, or is the front really fixed? If so, how? Do you apply a minimum ice thickness to maintain a thin shelf within the observed front?
Eq. 3 Nitpicking, I know, but please don’t use cursive in subscripts (h_af).
L 123-124 “m is a positive exponent, often related to the creep exponent n of Glen’s law (Glen, 1958) as m = 1/n. Here we use m = 3, following Hill et al. (2023)” This seems contradictory. Do you deviate from the “often” used relation of m=1/n (as typically n=3), or is there a typo somewhere and should I read m=1/3?
L 145 Here too, if you use regular instead of cursive, the “JregEη2” term probably will look a lot cleaner.
L 162-163 “…we initiate historical runs to smoothly transition the model past an initial adjustment phase in the forward transient simulations (Fig. 2). The historical runs span 20 years, from 1995 to 2015.” If you really want to present your simulations as actual projections, this part will need more information. How exactly are your historical simulations forced in terms of atmosphere and ocean? How does your modelled trend in ice mass/thickness compare to observations? What year is the BedMachine dataset supposed to represent, and how does that affect the results, given that you used it to initialise your model in 1995?
L 173-174 “In "sub-element melt 1" (SEM1), melt is applied to the entire area of partially floating elements, but its magnitude is reduced based on the fraction area of the floating ice in the element” Do I understand it correctly then that this is identical to the “partial melt parameterisation (PMP)” of Leguy et al. (2021) and Berends et al. (2023)?
L 175-177 “In the "sub-element melt 3" (SEM3), an increased number of 20 integration points are used during the finite element assembly procedure within any partially floating element” Does this mean that the entire stress balance is solved with a much higher resolution at the grounding line? If so, how does that affect the error in the velocity solution related to the discontinuous basal friction there?
Eq. 7 Sorry for the nitpicking again, but I’d use a single-letter variable for SMB, since combined with the cursive font it now reads like “S times M times B”.
Eq. 8 I think it would be really valuable to include a figure here comparing the spatial patterns of basal melt underneath one of the shelves with and without the water column scaling.
L 201-205 As with the historical simulations, if you wish to present your results as projections, you will need to provide more information here. Did you include the ISMIP6 “cavity-extrapolated ocean forcing”? What kind of temperatures does this produce in the very deep trenches in the Wilkes basin? Why did you use output from two different ocean models for SSP1 and SSP5?
L 206-211 Do I understand it correctly that you only performed the inversion with the Weertman law, and then converted the resulting friction coefficients to the Coulomb law to maintain the same basal friction?
Fig. 10 No need to label every 15-year interval in the legend, maybe draw contours every 20 years but label only every 100? (apart from that, great figure!)
Tables 3 & 4 That’s a lot of numbers, consider replacing by a bar graph or something else to visualise.
Fig. 12 The graphs are suddenly much thicker, I like it! Please use these thick lines for the other figures too.
Fig. 13 Do you expect these lines to become straight when using a double-logarithmic scale?
L 325-326 “Due to the distinct mechanism of the model implementation, the GLMPs they used differ from the four explored in our study” Worth mentioning here that the resolutions used in these square-grid models are much coarser than what you used, so you would expect significant dependence on resolution there even if melt at the grounding line is resolved perfectly.
L 332-340 I think this is a crucial discussion. As far as I’m aware, all studies that have looked at GLMPs to date have implicitly assumed zero melt underneath grounded ice. If that assumption is wrong (as the studies you cite suggest), then obviously none of the simulations are ever going to get the “correct” answer, regardless of what GLMP they use. This is the “physics vs. model implementation” discussion I meant!
All figures: please use a larger font size for the axis labels, legends, etc. Imagine you’re in the back of the room at EGU!
Citation: https://doi.org/10.5194/egusphere-2024-1005-RC1 -
RC2: 'Comment on egusphere-2024-1005', Anonymous Referee #2, 22 May 2024
Summary:
The authors conduct a comprehensive study of ice dynamics sensitivity to grounding line melt parametrization, together with variations in mesh resolution, friction law and water column scaling, and emissions scenario. The study is focused on the Wilkes Subglacial Basin (WSB) region of East Antarctica. Experiments are run out to the year 2500 and grounding line dynamics as well as changes in total ice mass are evaluated.
Generally, melt parameterizations shows better convergence with resolution, except the NMP under the Coulomb law with water column scaling, where finer resolutions increase ice mass loss. This behavior is attributed to the NMP underestimating melt in partially grounded elements, which is inherent to the parameterization. SEM1 and SEM3, while providing more accurate average melt rates, do not necessarily improve convergence and often overestimate mass loss at coarse resolutions. Under high emission scenarios, differences in grounding line melt parameterizations performance are amplified, affecting ice mass loss predictions significantly. Overall, SEM and NMP outperform FMP, with each showing varying degrees of superiority depending on the scenario.
Overall, I think this study is well presented and is an interesting contribution with both location specific and general takeaways. It provides new and useful details on model dependence on parameterization and focuses on an important and understudied region of East Antarctica that needs more attention.
Major points:
- Since this study is a sensitivity test, it would be really nice to see a comparison figure at the end showing all of the results. For example, this could display total ice mass over time (like existing plots) but show the results from melt parameterizations, emission scenarios, friction law, water column scaling, and model resolution. Currently, I find myself having to flip back and forth between all the result figures. A big comparison figure with all the results (or most important results) would help a lot with this.
- As there is growing community interest in the WSB region, I would like to know what additional constraints the authors think would make the biggest difference for numerical simulations since this study shows that the melt parameterization affects both the timing of a tipping point and the overall magnitude of ice mass loss. This is sort of generally touched on but I think it should be expanded on in some more detail in the discussion.
- I would like to see something added about the choice of SSA over a higher order approximation of full stokes, since SSA has limitations in accurately representing grounding line dynamics. I understand that in order to run all of these experiments, SSA is probably the only computationally manageable option. But I would like to see the limitations addressed somewhere, i.e. is it possible that SSA could be inadequate for resolving processes that affect the results of this study?
- In the conclusion you say that the 1km grid isn’t fine enough resolution for capturing the grounding line dynamics. Since it is so common to use even coarser resolutions than this for large scale ice sheet models, is there anything more the authors can add to this discussion? Would you say that high resolution should be prioritized above all else for modeling grounding line dynamics?
Minor points:
- I think it would be useful to have all the experiments introduced earlier in the paper. Right now only some of them are introduced early on and then others are introduced about half way through.
- L 84: could use a little more specifics rather than just the obvious results, discussion, conclusion.
- Fig 3: Add outline box in a) showing the region displayed in b)- e)
- Fig 4: Units should be added
Citation: https://doi.org/10.5194/egusphere-2024-1005-RC2
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