Review of Lambert and Burgard: “Brief Communication: Sensitivity of Antarctic ice-shelf melting to ocean warming across basal melt models."

The Cryosphere Discussion, Paper: 10.5194/egusphere-2024-2358

The manuscript of Lambert and Burgard analyzes the sensitivity of five different basal ice shelf melting parameterizations to an idealized warming of 1°C. The five analyzed basal melting parameterizations are widely used or discussed and differ in complexity. The parameterizations range from point-dependent approaches (quadratic function of the temperature difference between the ocean and local freezing point temperature) to horizontal extensions of models representing different aspects of the ice shelf pump overturning circulation (PICO and Plume model), vertically integrated models solving the Navier-Stokes equation in the upper mixed layer within the ice shelf cavities, to a neural network trained by model output form the cavity-resolving simulations with the NEMO ocean model.

The authors drive these parameterizations with an observational-inspired hydrographical distribution of ocean temperature and salinity, which replicate the main hydrographic conditions for different regions and their ice shelf types (warm vs. cold water ice shelves, for instance), and they retune these parameterizations to reproduce contemporary observational basal melting distributions – except for the neural network due to the limit data base. Afterward, the authors applied a temperature increase of 1°C to analyze how the melting rates change under such a warming. The control run and the warming are analyzed regarding the changes in the overall basal melting rate averages and how melting increases in deeper (ocean depth) parts compared to the overall and shallower ice shelf areas.

In addition to the distinct differences in terms of basal melting amplification due to the warming and the related spatial signatures, all parameterizations show the highest melting amplifications for the warm-water ice shelves located in the Amundsen Sea Embayment, intermediate sensitivities for some ice shelf groups, and a weak reaction to the warming for large cold-water ice shelves (e.g., FRIS, RIS).

It was a pleasure to read the well-structured and prepared manuscript. The figures are of high quality, necessary, and informative.

Various groups are working on the future evolution of the Antarctic Ice Sheet (AIS), where ocean-driven mass loss predominates, and basal melting of floating ice shelves accounts for about 40–66% of the ocean-driven ice mass loss (Rignot et al. 2013; Depoorter et al. 2013; Liu et al. 2015; Davison et al. 2023)⁠. Hence, this study is an important contribution to understanding how different basal melting parameterizations drive future mass loss. Therefore, this work is also highly relevant for studies addressing Antarctica’s sea level contribution in the coming centuries. Since the ocean-driven basal melting is central to the health of Antarctica, this work is also intriguing for the ice sheet modeling community and the coming Ice Sheet Modelling Intercomparison Project (ISMIP).

I recommend the publication of the manuscript after minor corrections.

General comments

The manuscript is well organized and written.

Your manuscript addresses the basal melting enhancement for increased ocean temperatures. Since it is often discussed whether a particular parameterization shows a linear or quadratic behavior for increased temperatures, I wish you could perform an analysis for a temperature rise greater than 1°C, such as 0.5°C or 2°C, add the related results, and indicate if those different parameterizations have a linear or quadratic behavior.

Have you considered including a linear parameterization in addition to the Quadratic parameterization? How would it behave compared to the other parameterizations listed in Section 2.2, Basal melt models (page 3)?

When it comes to the reference of the basal melting rate of (Paolo et al. 2023)⁠, I wish you could compare your reference with other estimates and how large the spread is because it would relate the found sensitivities of the analyzed parameterization to the uncertainty of current basal melting estimates, such as (Rignot et al. 2013; Depoorter et al. 2013; Liu et al. 2015; Davison et al. 2023)⁠.

You may recheck whether you use British or American English. I recognize mostly British English, but you use "e.g.," an American syntax. Please correct it.

Specific comments

Main document

Line 9/L 9: You may add: “… loss is mainly driven by amplified ocean-induced melting … .”

L 13: I'm unsure that "best" is meaningful here. You may rephrase it, e.g., " to as basal melt, is consistently simulated … ."

L 15: You may add: "… currently remain rare and computationally too expensive to run … ."

L 62: You may expend the sentence: “that mimics the overturning circulation in the cavity; known as ice-shelf pump (Lewis and Perkin 1986)“.

L 72: Do you think the three-equation model is linear with respect to the temperature forcing? If so, please consider modifying the sentence "commonly adopted 'thre-equations parameterization,' which is linear in the temperature forcing, and the overturning … ."

L 84: You may add some information about CDW to address a wider audience, e.g., “… a warm layer of Circumpolar Deep Water (CDW), which a temperature of ≥0°C.”

L 87: You may modify “The subsurface warm water mass … .”

L 88: Please delete “where possible”

L 90–91: I do not fully agree with the description of the water masses since the lowest temperature of HSSW corresponds to ocean water’s surface freezing point temperature (about -1.87°C). In contrast, the water mass that is supercooled in relation to the surface freezing point temperature is Ice Shelf Water (ISW). The interaction of the HSSW with the ice shelf base transforms it into ISW. Please clarify this point.

L 94: You may delete: “the exact values of”

L 95: I am unsure, but should it be "… division of the ice shelves between Cold and Cool, … ."

L 94–95: Since you create and use idealized ocean forcing, you may want to drop "cannot be sufficiently constrained by observations" since the idealization of observations is not necessarily identical. You may describe it like this: "Several experimental choices are made, such as … Cold and Cool case. Considering the idealized forcing, the value selection has a subjective component.”

L 99: You may replace the verb: “… ice shelf, we restrict CDW intrusion into … .”

L 109–112: Long sentence. You may consider splitting and rearranging it with the following sentence. For instance: "As changes … higher than ice-shelf averages (e.g., Jourdain et al., 2020). Hence, we additionally define the 'deep amplification,' where the nondimensional metric … ice-shelf average."

L 122–124: It is unclear how the effective turbulent temperature exchange velocity is determined. Please clarify.

L 140 and L 141–142: Intriguing that the spreading factor is 100 = O(10 m yr-1)/O(0.1 m yr-1) in the first case and only 10 =O(5 m yr-1)/O(0.5 m yr-1) for the Plume Model and Neural Network.

L 162–164: You speculate that the selected minimum layer thickness may overestimate the heat transport. Would a thicker or thinner layer thickness reduce the heat transport?

L 187 and 189: First, I was confused about what "linear sensitivities" and "quadradic sensitivities" mean. I guess you may something line “(T_cold – T_warm)/ Delta T” and “(T_cold – T warm)**2/Delta T “, or? Please clarify it.

L 228: I am afraid I have to disagree that we can not avoid it, but it could be essential. Furthermore, some models/parameterizations may only be fit for some purposes. Therefore, reducing the intermodel spread might be misleading. Instead, knowing the limitations of the models and coming to a generalized description might be more critical.

L 232: I am unsure about the style guide of Copernicus journals, but should each quantity have its own units so that it comes to "67% to 240%"?

L 197: You may be more implicit with your message: "… by the quadratic sensitivities (Fig. 3c), having on average the highest sensitivity, with values … ."

L 240: I am unsure if you would like to extend the sentence: "… melt enhancement in the deeper regions and none towards lowest depths: PICO … ."

Figure

Figures 1 b—g) and 2 a—e): Great figures and a very smart way to use the available space to plot the ice shelf regions around Antarctica. Since your color bars have a "whitish" color around zero (0), it is not always clear what values are along the ice shelf edge facing the ocean. Would it help to color the ocean (e.g., gray) and, therefore, mark the ice shelf edge?

Bibliography

Davison, Benjamin J., Anna E. Hogg, Noel Gourmelen, Livia Jakob, Jan Wuite, Thomas Nagler, Chad A. Greene, Julia Andreasen, and Marcus E. Engdahl. 2023. “Annual Mass Budget of Antarctic Ice Shelves from 1997 to 2021.” Science Advances 9 (41): 1–12. https://doi.org/10.1126/sciadv.adi0186.

Depoorter, M.A, J.L. Bamber, J.A. Griggs, J.T.M. Lenaerts, S.R.M. Ligtenberg, M.R. van den Broeke, and G. Moholdt. 2013. “Calving Fluxes and Basal Melt Rates of Antarctic Ice Shelves.” Nature 502 (7469): 89–92. https://doi.org/10.1038/nature12567.

Lewis, E. L., and R. G. Perkin. 1986. “Ice Pumps and Their Rates.” Journal of Geophysical Research: Oceans 91 (C10): 11756–62. https://doi.org/10.1029/JC091iC10p11756.

Liu, Yan, John C Moore, Xiao Cheng, Rupert M Gladstone, Jeremy N Bassis, Hongxing Liu, Jiahong Wen, and Fengming Hui. 2015. “Ocean-Driven Thinning Enhances Iceberg Calving and Retreat of Antarctic Ice Shelves.” Proceedings of the National Academy of Sciences 112 (11): 3263–68. https://doi.org/10.1073/pnas.1415137112.

Paolo, Fernando S., Alex S. Gardner, Chad A. Greene, Johan Nilsson, Michael P. Schodlok, Nicole-Jeanne Schlegel, and Helen A. Fricker. 2023. “Widespread Slowdown in Thinning Rates of West Antarctic Ice Shelves.” The Cryosphere 17 (8): 3409–33. https://doi.org/10.5194/tc-17-3409-2023.

Rignot, E., S. Jacobs, J. Mouginot, and B. Scheuchl. 2013. “Ice-Shelf Melting Around Antarctica.” Science 341 (6143): 266–70. https://doi.org/10.1126/science.1235798.

Review: “Brief Communication: Sensitivity of Antarctic ice-shelf melting to ocean warming across basal melt models”

E. Lambert and C. Burgard (egusphere-2024-2358)

Summary

This paper applies five approaches to ice shelf basal melt modeling to the 40 largest Antarctic ice shelves in order to compare their sensitivity to an idealized ocean warming scenario. These include more established approaches such as a simple parameterization of pointwise melt rates based on the regional hydrography and local ice base slope and more complex parameterizations accounting for meltwater advection and refreezing, and a newer machine learning approach using a neural network. The neural network is trained on output from a 1/4º NEMO simulation, which employs the same three-equation melt parameterization used in the intermediate complexity models. The aim of the neural network approach is to capture more of the complex spatial structure of basal melt rates without the prohibitively high computational cost of the full NEMO simulation.

The ocean conditions of the 40 ice shelves are classified into 6 categories based on their deep and near-surface temperatures and thermocline depths, each with an idealized “reference” temperature and salinity profile. Simulations are run for each ice shelf with its reference hydrography and then with a (salinity-compensated) 1ºC warming applied to the deep waters. The resulting melt rate distributions for the reference simulations are compared to observed melt rates to evaluate the fidelity of each modeling approach, and the warm simulations are compared with the reference to evaluate the sensitivity to warming.

The results show large differences in the spatial distribution of melt rates, even in the reference simulations which were calibrated to have the same average magnitude. The increases in the warming scenario vary among the models in both magnitude and distribution. However the models generally agree that the fastest-melting ice shelves under present day conditions are also most sensitive to warming.

Characterizing these differences is useful to the Antarctic Ice Sheet/Ocean modeling community. I recommend this paper to be published with some revisions.

General comments

The paper is well-structured and concise, with the figures in particular accommodating a huge amount of information in an impressively small package.

My major question is related to the sensitivity calculations and comparison with other studies. Because there was only one warming experiment, the quadratic sensitivities were calculated using the additional point of zero melt at the freezing point. Is this a common approach to calculating climate sensitivity? Would it be possible/valuable to conduct an additional simulation with a larger forcing in order to better constrain both the linear and quadratic sensitivities? If feasible, this could also allow one to evaluate whether the sensitivity of each model (and/or ice shelf system) is better characterized as linear or quadratic.

Relatedly, where the sensitivities calculated in this study are compared to published estimates (e.g. lines 187-192), it would be helpful to include at least a brief description of the approaches of those studies and how they differ from the present work. Certainly the reader can visit those references for more detail but I think that a bit of context within the text would be helpful and appropriate. There are a few other points where I think more discussion would be appropriate which I have highlighted in the line-by-line comments.

Line-by-line comments

Abstract: “diversity in basal melt forcing is presently unavoidable to prevent underestimating uncertainties in future projections.” This statement is confusing to me because it’s separated from the initial mention of sea level rise and also I’m not sure what you mean by “unavoidable.” I would say something like “a range of basal melt forcings should be applied to incorporate this uncertainty in future projections of sea level rise.”

Line 138: It might be helpful to refer here to the ice shelf label numbers, i.e. “(10-14 and 27 in Figure 1a)”.

Line 141: Does this imply that the contrast is reproduced better in the other models? Please clarify.

Line 168-170: This has me a little confused about how the Neural Network approach works. I guess it is trained on simulations that include seasonality, but when given an ocean temperature profile modeled on winter conditions, the resulting melt pattern effectively represents an annual mean — is this true? (It doesn’t seem like this has much impact on the melt sensitivity calculation since it looks like a lot of that signal cancels out, at least looking at Filchner-Ronne and Ross.)

Line 177: At times I found it slightly confusing that “deep amplification” can refer to either the actual melt rate or the melt rate response/anomaly — this is a place where I think it is a bit unclear and you could clarify by writing “Combining the average melt rate response and its deep amplification…”

Line 187-192: Why do you think the sensitivities calculated in this study are so much lower than previous estimates? Are there key contrasts with the approaches taken in those papers that can help the reader interpret your findings?

Line 195: To me this is a somewhat uncommon use of the word “consensual,” I would omit it as you’ve already said earlier in the sentence that the models agree so I don’t think it’s necessary (or it could be replaced with “consistent”).

Line 196-199: Some patterns begin to emerge here but they weren’t immediately obvious to me with the large number of names, not all of which were completely familiar. One simple thing that would make it easier to parse is to reverse the order that you list the ice shelves in the sentence so they are in the same order as they are shown in Figure 3. You could also consider noting in the text what ocean conditions apply to each ice shelf, or including the number of each ice shelf corresponding to the legend in Figure 1a to make it easier to refer back. 

Line 203: except for Getz.

Line 208-210: What was the method/approach used by the study you’re comparing to, and is there a clear reason to think that result is more realistic?

Line 220-229: From what you’ve shown, I don’t think it’s possible to “reduce the intermodel spread” in reference to this suite of models because they are fundamentally so different from one another. 

Rather, if the goal is to improve sea level projections, it seems to me that it’s important to prioritize the regions of the ice shelf that exert the greatest influence on ice sheet dynamics and consider which models seem most trustworthy in those settings. Thinking of results from Reese et al. (2018) showing the disproportionate sensitivity of upstream ice dynamics to thinning in narrow channels near the grounding line, it’s concerning to me that the Neural Network is trained on a model that likely performs worst in those areas. (But maybe you disagree!) On the other hand, if the goal is to capture the change in spatial distribution of basal melt more broadly under warmer ocean conditions, the Neural Network may be a good choice.

I know you are limited in how much you can say about which model is “better” but I think it could add to the value of this paper if you went a bit further into the discussion of the implications of your findings.

Figures 1 & 2: I think it would be helpful if you could add a coastline, or some shading to either the ocean or land, to help orient and delineate the ice shelves in the “puzzle” subplots.

additional reference:

Reese, R., Gudmundsson, G.H., Levermann, A. et al. The far reach of ice-shelf thinning in Antarctica. Nature Clim Change 8, 53–57 (2018). https://doi.org/10.1038/s41558-017-0020-x