| 04 May 2026
Future learning and uncertainty reductions in projections of the Amery Ice Shelf catchment, Antarctica
Abstract. Antarctica's Lambert–Amery system is often considered resilient to future climate changes owing to strong buttressing by the Amery Ice Shelf, yet emerging projections through 2300 suggest that sustained ocean warming could substantially alter its long-term mass balance. While recent probabilistic studies quantify present-day parametric uncertainty and propagate it to future sea-level contribution projections, they do not assess how rapidly these uncertainties will contract as forthcoming observations are assimilated. Here we quantify future learning rates for the Amery sector by building a sequential Bayesian calibration workflow that uses present-day (year 2015) as well as synthetic future observations to evaluate how quickly forthcoming data can tighten projections of sea-level contribution through 2300. Using simulations from the MPAS-Albany Land Ice (MALI) model augmented by Gaussian process emulators, we first generate 100 synthetic future observation trajectories of cumulative grounded mass change at 15-year intervals (2030–2300) under a high-greenhouse-gas-emission scenario, drawing from the present-day posterior distributions of six uncertain input parameters related to ice flow, calving, and ice-shelf melting. For each trajectory, we then sequentially recalibrate parameters at each analysis year using the present-day and all synthetic observations available up to that year, and propagate the recalibrated parameter uncertainties to generate updated projections of sea-level contribution. We quantify learning as the reduction in 90 % credible interval widths for both MALI parameters and sea-level contribution projections, characterizing variability across the 100 trajectories to assess uncertainty in the learning rate itself. Results reveal substantial but parameter-dependent learning, with the ice-shelf melt coefficient and basal slip exponent exhibiting the largest uncertainty reduction (≳8-fold by 2300). Learning about future sea-level contribution is time-horizon dependent: end-of-century (2100) projections show limited contraction (30 % reduction in very-likely ranges), whereas year-2200 and year-2300 projections exhibit rapid learning (∼6-fold reduction) after substantial ice-shelf thinning projected around 2150 creates stronger dynamic response which aids parameter learning. These findings indicate that near-term Amery contributions will remain difficult to tightly bound until substantial dynamical changes manifest (post-2150 in these simulations), but that sustained observations through that transition have high impact for reducing long-horizon risk. While our perfect-model assumption and simplified likelihood structure represent simplifications, the results provide guidance for assessing future learning of ice-sheet behavior.
Review of Future learning and uncertainty reductions in projections of the Amery Ice Shelf catchment, Antarctica by Zerbe et al
This manuscript covers an approach to determine how future observations of ice-sheet loss could change parameteric and forecast uncertainty as new observations are made. The analysis focuses on Lambert glacier/Amery ice shelf. An emulator based on a MALI model ensemble is generated and used for Bayesian calibration of future observations to revise assessments of a small number of scalar parameters.
I really like the idea of this manuscript. The effect of future observations is not something generally considered in UQ. The authors are comprehensive by considering a range of future observation trajectories; and the discussion is insightful regarding the results and their physical interpretations.
In terms of general comments, one aspect I will comment on is the complexity of the approach and making it approachable. A GP emulator must be defined; A set of synthetic trajectories must be generated; and for each, bayesian posteriors must be performed at 30 different time instances, for 3 different horizons. When discussing results, I think that methods could do with more systematic descriptions, and improved methods of referring to quantities could be found. In my detailed comments I give some examples. Also, I’m not sure if there is a standard style in the journal for different mathematical objects (scalars, vectors, functions, tensors, etc) — if not, I suggest the authors create their own. For instance, I was unsure whether the named parameters were scalars or vectors until further down.
There is another aspect that I think important enough to make general. The calibrations of future observations use an error model that treats cumulative mass loss at various horizons as independent for reasons of tractability (I assume). But allowing for correlation, I do not believe is intractable, and furthermore I believe disallowing it introduces zero-order errors in the results, to the point of near logical contradiction — I make specific comments about this below. The ignoring of correlations is brought up as a limitation — but simply saying the omission of something is a limitation, when it is as important, and easy NOT to omit, is not enough, and I am hardly the only person who would notice this and think this. The authors need to account for these correlations in their analysis or give a rigorous explanation in-manuscript of why it cannot be done, and what errors it introduces. I am selecting “Major revisions” for this reason, though if I am mistaken or misunderstanding in some way of which I can be convinced, then major revisions may not be necessary.
Specific comments:
L75: say if all parameters are scalar.
I am also unsure whether there are also parameter fields lurking behind that are not being treated probabilistically. For instance, does MALI carry out an adjoint-based calibration of basal friction coefficients in order to reproduce observed velocity patterns, with C_\mu simply a scaling of these values? (And similarly for ice stiffness.) If so, it is worth commenting on whether treating these are “certain” has implications for the study.
L82: there is mention of a GP emulator; readers should not need to refer to another paper to see this. Could a brief intuitive explanation be given? My understanding from Wernecke 2020, whom you cite, is that an PCA (SVD) analysis is done and the temporal expressions of the spatial eigenvectors are the things that are replaced by GPs (which are, as I understand it, essentially brownian bridges). A truncated set of spatial eigenvectors is retained; can you say how many are retained, and how this decision impacts posterior uncertainty? And that said, I might be misunderstanding, so an intuitive explanation would be helpful.
L93: need to say how this is defined (is grounded mass volume above floatation), how error is defined, either here or point to the section where it is done. We should not need to consult jantre to get the basic idea.
L114, present day posterior: where do you discuss the present day posterior density calculation.
L125: i think the specific form(s) of bayes rule need to be given here. it is difficult to envision the likelihood function. And while it becomes clear later, it is not clear here that you are treating each of the 100 trajectories as a separate realisation to be learned from in order to find statistics of learning, that should be made clear.
L137. This seems like a zero-order error you are introducing, and I do not see why you would do it. If the loss from, say, 2100 to 2110 is independent of the loss from 2015 to 2100, and both are gaussian, then the loss from 2015 to 2110 is the sum of the two, and finding the statistical properties of the correlation between this and loss to 2100 seems a simple known problem. By treating cumulative loss to 2100 and cumulative loss to 2110 as independent you are surely skewing the posterior uncertainties in a nonnegligible way — ignoring the correlations could overestimate reduction in uncertainty.
L144: this makes more sense now but I hadn’t realized you are treating each observational trajectory independently.
L148-151: confused — this is how you generated the synthetic data, no? Why are you introducing it again?
L152-153: again confused -- this seems a necessary step to (a) synthetic observations and (b) likelihood evaluation. yet it is badged as "probabilistic future learning". or maybe this is the forward propagation of uncertainty. as it is not clear how this is done (monte carlo or MCMC?) please give more detail on this, using eqns if necessary.
L154-156: isn’t this what you said you did at lines 144-146? I’m very confused now.
Figure 2, “Sample from present-day posterior” in legend. im not sure I understand this — are these the parameters in the specific realization in the 100-member ensemble used for synthetic generation?
L217, 4.17 [2.80-5.09] mm. My understanding of what this describes is WAY off, which needs to be remedied, or this does not make sense. It is saying that with the information available in 2090, there is *uncertainty* of about 4 mm SLR in the cumulative SLR by 2100. I don’t see how this is possible, unless all of the SLR from 2015-2100 is presumed to happen in the last decade. More generally, and at least assuming gaussian statistics, I would expect the uncertainty in a future value of a cumulative sum at a certain time to go to zero as that time is approached. And this is precisely because the cumulative sums at different times correlate with each other. And so I wonder if what I’m seeing is a consequence of treating these cumulative sums as independent.
L239-241. interesting. as the level of buttressing is not always the same, is the degree of buttressing a factor as well, and can this be looked at in this context?
L243-244: i disagree with interpretation. if floating ice is not providing backstress its removal will not affect discharge, providing little information/learning even if ice is lost rapidly.
L279, point 2: this is true of the basal friction coefficient scaling too, comment?
L290-291: i think it would be useful to do to Furst-type analysis of the buttressing number as his numbers do not apply to these new modelled configurations of the ice shelf.
L296-297: again, this does not make sense to me -- such uncertainty for something 10 years in the future? means im missing something in my understanding
L304-306: is it just the change in forcing, or does the change in the system itself play a role? Thwaites glacier is likely to keep retreating and thinning greatly over the next 50-100 years without any changes to forcing.
L313-314: is this because the projections at 2100 are so small that, in absolute terms, they are still well below uncertainties at 2200?
L331, “slightly larger than the mid-trajectory mean”, please remind us what parts of the figure to look like. i thought the uncertainty of the credible interval was the beige shaded area. the half-widht of this is far less than the across trajectory mean
L339 remove “an”
L339 “more gradual” than what??
L346: this is interesting but please show rigorous statistics on these claims of relationships in Figs 9 and 10.
L416-7: a very good point.
L429: the answer then is to not use diagonal covariance matrices, even if it takes longer to converge..
L431: “in reality” — please explain why this is so difficult to incorporate?
L440: Recinos reference: here, overconfidence was due to unrealistically small errors in observations. (Which I think you are admitting by treating cumulative mass losses as independent..)
Section 4.5: i think this would benefit from a review of the literature around Optimal Experimental Design.