the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 Oct 2025
Disentangling uncertainty in ISMIP6 Antarctic sub-shelf melting and 2300 sea level rise projections
Abstract. Ocean-driven ice shelf melting is a major contributor of present and future ice loss from the Antarctic Ice Sheet. In the Ice Sheet Model Intercomparison Project (ISMIP6) Antarctic 2300 projections, sea level rise varies widely, from -0.6 to 4.4 m, highlighting significant uncertainty. Here, we assess drivers of this spread, focussing on sub-shelf melting and dynamic ice loss as well as sectors that have the potential for large-scale, rapid ice loss: the Amundsen Sea, Filchner-Ronne, and Ross sectors, and the Aurora and Wilkes Subglacial Basins. We derive two sensitivity factors for each ISMIP6 simulation: a) a melt sensitivity factor, describing how simulated sub-shelf melt rates respond to ocean thermal forcing changes; and b) a dynamic ice loss sensitivity factor, describing how simulated dynamic ice loss (and hence sea level contribution) responds to cumulative sub-shelf melt changes. Melt sensitivities range from 1.5–21.3 ma−1 K−1, with no clear dependency on the melt parameterisation. Model simulations cluster into two groups based on calving strength. The dynamic ice loss sensitivities range from 0.1 to 2.6 (unitless), with larger variations in the Amundsen sector, and Aurora and Wilkes Subglacial Basins. These sensitivity factors are good predictors of short-term integrated melting and sea level rise, respectively, but are less robust on longer time scales. Our findings show that these factors explain much of the ensemble spread in projected ice loss to 2300. We recommend to further constrain these factors, and advocate for their use in model calibration and emulator design, with the ultimate aim of explaining uncertainties in future projections of sea level rise from Antarctica.
Competing interests: Some authors are members of the editorial board of the Cryosphere.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-4069', Anonymous Referee #1, 27 Jan 2026
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RC2: 'Comment on egusphere-2025-4069', Anonymous Referee #2, 09 Apr 2026
In this study, the authors evaluate the ISMIP6 model experiment results to identify the dominant sources of uncertainties in sub ice shelf melting and dynamic sea level rise. To do so, the authors define two linear scaling factors: the melt sensitivity (MS), which is derived from an assumed linear relationship between shelf-average basal melt anomalies and average thermal forcing anomalies, and the dynamic sensitivity (DS), which characterises another assumed linear relationship between cumulative basal melt anomalies and dynamic ice loss. These factors, along with a categorical climate forcing variable and an observed/qualitative classification of modeled calving are used as the basis for decomposing variance in the model outputs across the ISMIP6 ensemble. Analysis of variance results in the conclusion that MS and DS factors are significant contributors to the uncertainty of the ensemble results, explaining about 75% of the variance in the dynamic sea level projections. The authors seem to present this as the primary result of their work. However, the results from the 3-way ANOVA deserve more of a highlight, especially the transition of the leading contributor to BMB uncertainties from melt sensitivity to calving groups.
General Comments:
- Linear Regression: The authors do a good job in acknowledging the limitations of using linear approximations to derive MS and DS, particularly in Discussions. However, several regression choices lack justification or explanation in the Methods, making it challenging to infer the motivation behind them. For instance, the purpose of the linear regressions shown in Figure 6 is unclear — they appear to serve as an evaluation of MS correlation with total melt change (is this total melt anomaly?) in sectors where predefined calving groups don’t present a clear distinction in basal mass balance anomaly time series. I could not find any additional justification for this regression, or why a regression was chosen compared to a nonparametric statistical test suited to the data. It is recommended that the authors provide a consolidated description of all linear regression analyses in an expanded Methods section, including the purpose of each. This should also include a clear statement of the assumptions underlying each regression: for example, assumptions about residual independence, homoscedasticity, and linearity. This is particularly important for any regression analyses involving MS or DS and variables used in their derivation, where circularity in the relationships could affect interpretation.
- Statistical Analysis Descriptions: The Methods section on ANOVA lacks sufficient detail to support interpretation of the results, which has led to key analysis choices being scattered across the Results section. Notably, the definitions of the calving groups introduced in Section 3.1.2 and the definitions of the categorical variables used in Section 3.1.4 would be more appropriately placed in the Methods (or at minimum the Supplement). More broadly, the statistical analysis workflow would benefit from a clearer, unified description that establishes how ANOVA, the calving group classifications, and the categorical variable definitions fit together as a coherent analytical framework. Additionally, the Kruskal-Wallis H-test is introduced in the Methods but does not appear to be referenced again, leaving it unclear where its results are reported and interpreted. The authors should either clarify where these results appear and explain how this test relates to the broader analysis.
- Further Support for Calving Group Selection: The authors present a thorough regional and sector-level analysis of their calving group classification (Section 3.1.2) in addition to admitting that this classification is qualitative, which is appreciated. However, the validity of these groupings would be more convincingly established if a formal test of statistical difference were applied directly to the BMB anomaly time series across groups, perhaps through a functional ANOVA or a similar trajectory-based test. Statistically significant differences in time series between the defined groups should also remove the need for the linear regression . This is particularly important given that the calving groups serve as a categorical factor in the subsequent variance decomposition: if the groups are not statistically distinguishable in their BMB anomaly trajectories, the interpretation of the ANOVA results rests on a qualitative classification.
- Figure Organization and Styling: Several figures in the main text present information that is either peripheral to the central discussion or duplicative of content covered in the narrative, while figures that are directly relevant to key results have been relegated to the Supplement. The authors should conduct a systematic review of figure placement, prioritising figures that support the main claims of the paper in the main text and moving ancillary material to the Supplement. In some cases, minor additions or removals of individual panels would substantially improve clarity. Specific instances are identified in the detailed comments.
Specific Comments:
Figure 1: I recommend using a different color scheme or changing the order of the groups being plotted, otherwise all three subplots are far too crowded to actually discern the differences from each climate model forcing. The authors can also consider splitting the plots by climate forcing groups.
48-52: This sentence is far too long and contains too much information to be clear. Splitting this up into separate sentences is recommended.
78: Descriptions for the abbreviations of initialization procedures should be included in the Table 1 caption, even if they are present in the main text of the section.
135: How do the authors anticipate that the PICO derived forcings are approximately similar to the extrapolated thermal forcings? Consider adding a reference or elaborate.
165: Shouldn’t the term in the denominator be Shelfarea instead of delta Shelfarea?
180-185: Figures S2 and S3 are far too small. We should be able to see the trends referenced in the text.
188-189: Why was this choice made? Would it not make more sense to unify the derivation process of MS factors for each experiment? Since MS feeds directly into the variance decomposition, methodological inconsistency risks confounding physical differences in melt sensitivity with artefacts of the derivation approach. The authors should further justify this choice and report how the variance fractions change under a unified derivation scheme.
195-198: This paragraph would fit better in Section 2.1
213–220: If a unified derivation (i.e. using the same sections of the experiment timeseries) method was applied for DS but not for MS, the authors should explicitly justify the inconsistency.
265-274: If this result is derived from the Kruskal-Wallis H-test for the MS factor, it should be stated explicitly. Same applies to any Kruskal-Wallis H-test results reported for the DS factor.
344: The descriptions of the melt sensitivity bins are not very easy to understand. Authors should consider using/adding equations/inequalities to be more precise.
359: Is the unexplained contribution here the 3-way interaction? If so, the authors should be consistent with Figure 7.
Figure 10: The referenced observations from this plot would be more evident if the data encoded in the colormap was represented in two additional scatter plots showing any potential linear correlation of dSLR with MS and DS factors respectively.
Citation: https://doi.org/10.5194/egusphere-2025-4069-RC2
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- 1
Beckmann et al. analyze ice-sheet model outputs from ISMIP6. They are concerned with disentangling different sources of uncertainty. I think the main finding of the paper is that the initially most significant, melt-related uncertainty declines past 2100, after which calving-related uncertainty becomes the most significant uncertainty source.
General comments:
1) TF time series: The authors face a major challenge in terms of inferring the thermal forcing present through the simulations, that was however absent from the outputs. They choose to simply interpolate temperature to the modeled ice base geometries (which are present in the output), independent of what parameterization (producing the resulting TF) was actually used. It remains unclear whether that quantity has anything to do with the actual parameterized TF. I think it needs to be shown (or referenced if that has already been done elsewhere) how well these two quantities are actually related. This could be done, for example in some separate ice sheet model run where the TF inferred and TF calculated are evaluated for all parameterizations used in the analyzed ensemble.
2) MS factor normalization: The normalization by area in the calculation of the MS factor seems to be problematic for comparing different ice shelves, whose melt rate distributions have different shapes. This normalization choice, rather than a more fundamental physical reason, is probably why large ice shelves have lower, and small ice shelves higher MS factors. This choice does not affect the variability of the derived MS time series, and therefore doesn't affect conclusions about the uncertainty attribution. However, this choice does affect the discussion about geographic variability of the MS factor across regions.
3) MS (and DS) factor derivation from data: There were a few fitting choices listed in the paper, and there is a fairly complicated and sometimes confusing explanation of how different choices and methods were used for different models and regions, but the reasoning isn't always very convincing. Perhaps it is just a problem with presentation, but I was not left with the impression that the derivation of the factors is particularly robust. I think this should be addressed somehow, but I don't have a good recommendation. Perhaps starting with a goal of what timescales/regimes these MS/DS factors should be useful for (rather than the applicability range being an outcome) could be a good start, but I am not entirely sure.
4) There are multiple instances of interpretation of results that do not seem to be reflected in the figures or based on the formulas provided, and rather seem based on observational understanding of the system, however, without showing that the modeled results are consistent with these observations (e.g. comment 458 below). In general, more frequent figure referencing would help, and perhaps even completely solve this concern.
In-line comments:
18: 'will' feels a bit too definitive
22: Do you also want to specify scenario for the lower bound of sea-level rise projections as you do later for the upper bound?
27: Sentence starting 'The largest sources...' too long to be clear, please rephrase or break up.
34: "show a much larger spread, with no clear correspondence to the climate forcing (Fig. 1b)." - this seems to be the case only after some time can you clarify if that is the case? Also can't really see that clearly because the plotting order seems to be by color - perhaps it would be better to interlace the colors
35: and also a s function of the CMIP model output
44: Coriolis is not a property like salinity or temperature. The whole parenthesis isn't really clear actually - just remove or actually list processes that are simplified or missed.
47: Probably worth adding a citation to and ESM that actually has coupled ice sheet - e.g., Siahaan 2022
102: Please provide reasoning why you restrict your analysis only to high-emissions scenarios
127: rather then "acting" something like "that would have acted" to indicate that you are trying to infer something close but not exact to the the field that was used in the simulations but was not saved.
128: what is the climate dataset? do you mean the ocean thermal forcing dataset mentioned earlier? If yes, please keep terminology consistent.
125-130: I am not following here. Why do you linearly interpolate properties, rather than using the Jourdain extrapolation algorithm that was actually used in the simulations? If these results were close, why would the more complicated Jourdain extrapolation actually ever be used?
135: I don't agree with this statement about consistency. It is not important to have one single method for all parameterizations, the important thing is to recover the thermal forcing at the ice shelf base equally well (with respect to what was actually present at the time of simulation) for all parameterizations.
131: 'may differ slightly' seems like an understatement
155: I am not sure about the purpose of the note. Perhaps add references that do either of the two approaches so that there is some context?
Equation 1: What is the meaning of c? Shouldn't there be at time t = 0, 0 change in TF and BMB, therefore making c = 0? In that case the fit should be forced to pass through 0 - indeed from fig S3 there is a strange offset in the black, relative to blue lines which seems to be caused by nonzero c.
Also, TF has also already been shelf averaged, correct? in that case it seems that the shelf area just cancels on both sides, no?
165: How is TF defined? In situ - freezing temperature at each ice shelf base location, correct? Can you make that explicit somewhere, if that is what you do?
170-175: Could you please include these plots with fits from which you derive MS (and analogously for DS) in the supplement so that we have a sense of how reasonable it is to fit a line to there? Ok, later on I see there is an example in S3, so perhaps cite it earlier? Also, can you provide examples from each end of the spectrum of Fig S2? Since the goodness of fit and melt factor value follow the same curve, I wonder what that actually says about the utility of the melt factor across all models, so some figures would help there.
175: Is it the abruptness of the change, or the fact that the geometry changed enough? And if it is simply the latter, does that mean that your method is good for estimating melt rate in static ice shelf cavities, but no so good for evolving ice shelf cavities? And how much shape evolution is too much for it?
Fig S2: x labels on the bottom of the right column are incorrect. Also, what is the grey dashed line and why are there two legends - please clarify in the caption.
Fig S3: the legend for the bottom 3 panels is at the top panels and the legend for the top three panels is missing.
Also, can you visually mark the time period to which the line is fitted? (for example by different color of dots)
181: What is 2K in TF<2K?
185: I don't understand why it is reasonable to use a different fitting method for different model simulations, since what is compared at the end of the day, are the coefficients across simulations. Because of that, it seems to me more important to have the same method for each simulation used for a given sector, then the same methods used for all sectors within a simulation. Still though, it feels that the same method should be used for all of these, if all are to be compared. Ultimately, I think it is important to show and communicate whether these choices influence the results or not, and I don't think I got that out of reading the paper.
Equation 3: same as eq 1 - what is the physical meaning of d, can you provide analog of figs S2 and S3 for DS?
3.1.2: I am not clear on if you are classifying models based on calving laws implemented, or if you simply noticed a bimodal distribution in the results and you are pointing out that observation.
291: can you call it G1 etc same as in Fig 5?
290-310: can you add figure references to statements? Also elsewhere in the paper.
320: Is it delta BMB not BMB here and further in the section?
329: Why don't you do this for all sectors?
338: What do you mean by "basal mass balance evolution is dominated mainly by the calving group"? Are you saying that the same bimodal distribution that you observe in ice shelf are change also appears in delta BMB? Or do you mean something else?
Similarly, what do you mean by "basal mass balance evolution is explained solely by the MS factor"
Fig 9: Why don't the IMAU models have different regions shown? Do all regions have the same factor value for this model? - ok I see later this is mentioned in the text, please add to figure also.
399: Figure reference to statement please.
409: Figure ref please.
450: I think the term 'predict' is incorrect here and elsewhere, I think 'diagnose' would be more accurate.
458: I don't think it is the control value of TF but the change in TF that would give rise to high MS factor (see Eq 1). Further, is the highest change in TF actually taking place in the Amundsen Sea - some figure that would show the continental shelf TF anomaly time series for the different regions would be useful.
460-480: Isn't the reason for the difference between low MS factor at Filchner-Ronne and high MS factor at Amundsen just the fact that you normalize by ice shelf area? And if that is the case, what does that really tell us about the usefulness or meaning of this MS factor? I understand the desire to normalize by area, but I am not convinced in this case it is very meaningful. The reason for that is that fundamentally, melting (and change in melting) is highest at deeper portions of the ice shelves, and smaller, shorter ice shelves (Amundsen) have higher fraction of high-melting portions than big ice shelves (Filchner-Ronne) - so I think your MS factor differences just reflect this fact. Conversely, if you do not normalize, you would probably get much higher MS volume flux factors for bigger ice shelves than smaller ice shelves, which is also not very informative. But perhaps there is some better metric that takes into account the distribution of melt rates over ice shelves and compares their distributions in a more meaningful way than a simple average, which seems more appropriate for gaussian distributions (I don't think melt rates on an ice shelf are necessarily gaussian).
505: Is there even any physical reason you would expect MS and DS factors to correlate? If yes, perhaps start with that as a motivation. Reading the results often feels like you are just correlating random time series and waiting if something pops out of it (so the danger there is spurious correlation).
531: Can you elaborate on how these factors would be useful? Do you mean using them to train emulators? They don't seem too robust, especially across a range of different regimes, so it seems far better to just strain the emulators on the data that was used to produce the MS and DS factors.
536-537: So those calving groups G1 and G2 actually have different sets of calving parameterizations? If that is the case that should have been stated clearly in results already (maybe I missed that, but was definitely confused when reading results).
551: Resolution of which model? Of the ice sheet model? Or of the melt rate parameterization (if such a thing applies)?
567-568: So what else then probabilistic projections is appropriate? Or are no projections appropriate at all at this point for these sectors?
569-576: You seem to suggest that the high sensitivity in these regions comes from modeling choices, but what if it is simply 'intrinsic variability' - that is high sensitivity as a result of particular group of geometries and locations?