In this study, the authors explore the influence of basal friction laws and initialisation procedures on projections of Antarctic ice-sheet evolution, with a particular focus on the Amundsen Sea Embayment. To do so, they use the ice sheet model CISM, initialised with two variants of a forward inversion nudging scheme: the default one, for which basal friction coefficients and ocean temperature corrections are tuned to match observed ice thickness from the Bedmachine dataset, and a novel one (called FEFI), in which flow enhancement factors are, in addition to the basal friction and ocean temperature correction, nudged to match observed ice surface velocities. In both cases, the observed dHdt is imposed as an additional term to the mass transport equation during the initialisation, following van den Akker et al. (2025), forcing the model to reproduce the observed trends in forward simulations. Starting from these two distinct initial states, the ice-sheet model is run forward in time for 1000-2000 years under constant present-day climate conditions. To test the sensitivity to the choice of friction law, friction fields from both initial states are rewritten (following Brondex et al., 2017, 2019) to convert the initial state for other friction laws. This allows the authors to run, for each initial state, forward simulations under four widely used basal friction laws while starting from the same geometry.

When extending their 8 simulations in time, the authors note a higher sensitivity to the choice of basal friction law for the FEFI initial state than for the DI one. Based on this, they conclude that the model can be tuned to be sensitive to the choice of basal friction law or not. However, I am not sure that the results presented in the manuscript really support this statement. In section 4.2.1 and with Figures 8-10, the authors do show sensitivity of the DI simulations to the choice of basal friction law, even though less pronounced than for the FEFI case. I think that caution should be made when stating that ‘the model can be tuned to be sensitive to the choice of basal friction law or not’, as written in the abstract.

To explain the different sensitivities between the simulations, the authors refer to a connection between buttressing and basal sliding in the ASE. However, I find the interpretation of the buttressing analysis in this study somewhat unclear, and I struggle to understand what the authors are trying to demonstrate with the buttressing factors. Although the abstract mentions strong geometry-driven connections, these are difficult to identify in the results section. In particular, it is not entirely clear to me how the comparisons in Figures 10 and 13 support the proposed geometry-driven connection between buttressing and basal sliding. The buttressing numbers shown on the left-hand side of these figures are primarily influenced by differences in ice-shelf geometry at a given time. Therefore, concluding that “buttressing is stronger for one sliding law than another” may be an overinterpretation. Similarly, the increases in velocity following ice-shelf removal (right-hand side of the figures) are more likely driven by the direct influence of the sliding laws on grounded ice velocity (as clearly illustrated in Figure 1) rather than by differences in the buttressing capacity of the ice shelves. I may be misunderstanding the analysis; if so, the results section should be improved to better clarify the influence of buttressing in the simulations.

I am wondering whether the differences in sensitivity observed between simulations initialised with the DI and FEFI methods may partly be explained by the differences in velocity fields between the resulting initial states. While both initialisation methods lead to similar ice sheet geometries that agree well with the observations, the associated velocity patterns differ since the FEFI method allows for a reduction of the misfit with observed ice surface velocities through the tuning of the enhancement factor. The DI initialisation produces an initial velocity field that overestimates flow speeds in the ASE (as shown in Fig. 4), whereas the FEFI inversion reduces this misfit and yields a ‘slower’ initial ASE. My guess is that this difference likely plays a role when the model is extended into the future, delaying the onset of collapse for both Thwaites and Pine Island glaciers in the FEFI case. This delayed response could make the ice sheet more sensitive to differences in basal friction. In contrast, for the DI case, the imprinted dHdt trends combined with faster velocities dominate the ASE signal, leading to a fairly rapid collapse of the region. I may be mistaken, but I think this is a possibility worth exploring. It would be helpful if the authors discuss this aspect more explicitly and provide a clearer visualisation of the differences between the two initial states in the ASE. Current figures make this comparison difficult.

Overall, the main focus of this paper is to demonstrate how initialisation choices strongly constrain modelled behaviour. The implications of the initialisation procedure for how we interpret model sensitivity and the range of future ice-sheet responses have already been shown previously (e.g., Seroussi et al., 2019), and this study brings another piece of evidence to support that. That said, the authors should be careful not to overinterpret their results. Relying solely on an initialisation method that explicitly targets observed surface thinning rates raises concerns about overfitting, especially in the ASE, where trends are significant. It is important that the authors clearly acknowledge the limitations of this approach. To strengthen the analysis, I recommend adding some simulations. For example, the same experiments could be performed, but without incorporating the surface thinning rate (dH/dt) in the mass transport equation. I don’t believe this would require too much additional work and could reinforce the analysis. 

In terms of presentation, the manuscript would benefit from improved clarity in the figure captions. For several figures (e.g., Figures 9, 10), captions lack some key information, e.g., whether the results are from the DI of FEFI initialisation procedure. The reader needs to search for the information within the text. Efforts should be made to ensure that the captions and figures are as self-explanatory as possible. Similarly, I find the Results section difficult to follow. The storyline lacks clarity, and the key messages are scattered throughout the text, making it difficult to identify the main findings. I recommend reorganising this section to improve its logical flow and highlight the key results more clearly. In addition, I would suggest that the authors put more emphasis on the adjusted FEFI initialisation procedure that they present. I think that this is a key contribution of this study. A method allowing for a reduced misfit for both ice thicknesses and ice surface velocities is very valuable, and it deserves to be more clearly highlighted in the paper. 

Despite these limitations, this is an interesting and valuable study. With revisions that address the concerns raised above and the comments below, I believe the manuscript could be suitable for publication.

Specific comments:

Abstract

l.10: Those two starting sentences are somewhat contradictory. Maybe reformulate as, e.g., ‘Previous studies do not agree on the magnitude of the influence of basal friction laws in sea-level projections’.

l.18: What is meant by underdetermined here? This should be clarified.

l.18-19: This is quite a strong claim, and I am wondering how constructive it is to make. I think stating that model results are dependent on modelling choices and the initialisation procedure is sufficient. You can indeed tune your model to force it towards a given behaviour, but this does not mean that modelling results are not useful. This underscores the importance of validating model outputs against observations.

Introduction: 

l.42: It can be worth mentioning that the second category of basal friction laws was originally developed to capture the behaviour of sliding over deformable till, in contrast to the first category, which typically represents sliding over hard beds.

l.49: ‘If the thicker ice shelf persists’ – This implies that increased grounding line flux leads to a thicker ice shelf, which I am not sure is necessarily the case. Buttressing capacity is also simply influenced by changes in the shape/geometry of the ice shelf.

l.64: ‘showing the importance of ice-shelf buttressing’ – I leave it up to the authors whether they want to keep this or not, but this may feel out of place, as it comments on a result while still stating the study’s goals. 

l.71-72: I am not entirely convinced by the reasoning presented here. I am not sure that having a compensating effect from buttressing means that the ice sheet evolution is not sensitive to the choice of the basal friction law. These are two distinct processes which both contribute to the ice dynamics. The combination of both leads to the ice-sheet response.

Methods

l.130: Could you clarify what is meant by ‘linearised’ stress balance here?

l.133: Which Eq. 1 are you referring to?

l.162-163: Maybe specify that both numbers correlate well for the theoretical case of MISMIP+ but show low correlation when applied ot Antarctica.

l.182: For a smoother transition, briefly remind what Cc/Cp is.

l.186: So if I understand correctly, you aim for an a priori field of Cc. Can you comment on the influence of r?

l.187-189: How sensitive are the results to the choice of Cr? It would be interesting to comment on this.

l.196: It is the ocean temperature which is tuned, isn't it? I suggest clarifying this in the sentence.

l.200: Do I understand correctly that you are not applying the temperature corrections per basin provided in Jourdain et al. 2020, but rather calculate it yourself locally through this nudging procedure?

l.205: What is the initial value attributed to the enhancement factor when starting the inversion? And what is the default value used in the default initialisation?

l.229-230: Can you specify how exactly you define such a conflict?

l.252: Refer to the figure showing the comparison between modelled and observed velocities here.

l.255: Which version of Bedmachine are you using?

l.273: For clarity, please remind what those datasets are.

l.279: Please clarify what could be such a physically implausible behaviour.

l.300: This seems to be missing from the supplementary material.

l.302: I don't believe you specified the spatial resolution used for your simulations anywhere. This is important information that should be included somewhere in the methods section.

Results



Figure 4-5: It would be interesting to see the inverted ocean temperature perturbation field for the entire ice sheet. It could be included in the supplementary material while still providing an opportunity to visualise it. In contrast, since your focus is on the ASE, it would be useful to illustrate the influence of both initialisation procedures more clearly. One way to do so would be to include a figure that compares maps of velocity and thickness misfits zoomed into the ASE region and placed side by side. Currently, the need to switch between figures and zoom in makes direct comparison difficult.

Figure 6: Similarly, I would be interested to see the resulting enhancement factors for the whole ice sheet.

l.355-356: I don’t fully understand why the thickness bias in the EAIS interior has grown compared to the DI. It could be worth commenting on this.

l.356-357: There are quite some differences in some regions, for example, the Aurora Basin. Specifically, this is a region for which the thickness misfit is larger with FEFI than with DI. What is unclear to me is that this region is not a region where the velocity misfit has been improved with the FEFI initialisation. How would you explain this? It would be worth commenting on this.

l.360: How do you explain the fact that the thickness misfit in the shelves is larger with FEFI than DI?

Figure 6: I am not sure what Figure 6b represents. Is it the change in velocity compared to DI? Or is it a zoom on the velocity misfit with respect to the observations? The caption should be clarified. If it is the change in velocity compared to DI, then a zoom on the velocity misfit with respect to the observations would be useful.

l.384-386: I am not sure what you mean to say by this statement. Wouldn't the same be true for DI initialisation?

l.413-415: One could argue that the same is true for the simulations starting from DI, even though it is less pronounced.

l.426-427 Isn’t this the case for PIG and not TG? Overall, I don't find the results description in this paragraph to be very straightforward. It would be good to try to improve it. It is not obvious to me from Figure 8 that the grounding lines of the power law and PP law and the schoof and ZI laws are grouped together.

l.424-428: So, it seems that the results of the DI experiments are still fairly sensitive to the choice of the basal friction law. Is that correct?

Figure 8-9: Specify in the captions that those results are for the DI initial state.

l.433: I’d suggest removing the ‘much’. The GL retreat seems roughly similar, even though slightly more retreated for the power law. I would also say that retreat is slightly more pronounced for the ZI law at year 750 than for the power law.

Figure 10: I’d suggest specifying that the area shown is not the same for the buttressing number and the absolute velocity increase. I was initially a little confused. You could also mark the zoomed area, or simply show the same area for both to make it easier to compare.

l.468-469: I am not sure that I agree with this statement. Due to the different geometries at year 500, it is difficult to attribute differences in buttressing to friction laws. Instead, I would attribute those differences to the evolving geometries themselves, which are, of course, influenced by the friction laws. The analysis is more informative at year 250, when the geometries are still comparable. In this case, I find that the pattern of the buttressing numbers at year 250 is very similar for both friction laws. The velocity increase differs, but it seems to me that this difference results from the friction law’s influence on the ice flow response, rather than from differences in the buttressing effect itself. In other words, the buttressing is similar, but the response to loss of buttressing is highly dependent on the friction law, as expected. Overall, I am not convinced that these acceleration numbers provide a valid approach to quantify or isolate a potential influence of basal friction on the buttressing capacity.

l.486: Again, I think that this is quite a strong statement. I agree that Figure 7 showing the evolution of the volume above flotation shows less sensitivity to the choice of friction law with DI than with FEFI. However, you just showed that results with DI are sensitive to the choice of friction law.

l.487: To which glacier collapse are you referring? I'm assuming Thwaites. In lines 407-411, you referred to three stages of retreat for those experiments. Am I correct in understanding that the PIG collapse is triggered after 600 years in all simulations? This should be clarified. It would be interesting to show the pattern of mass loss for all simulations, which could be included in the supplementary materials. Since you don't have many simulations, this sounds feasible and would help clarify the interpretation of the results.

l.491: I think you mean Fig. 7?

l.492: What experiment is this for? Based on the DI results presented above, it seemed like the TG and PG collapsed fairly simultaneously, didn't they? Fig. 12 also seems to show this.

Figure 11: What basal friction law is shown on this figure? This should be clarified in the caption.

l.503: PIG collapse slower than TG – Is this only for the FEFI inversion? The timing of collapse between TG and PIG seems rather equivalent in the DI case.

Figure 13: I think this is the other way around, as described in the caption. Also, to make sure I understand correctly, is the speedup in the bottom row observed in just one model timestep? The positions of the grounding lines between the top and bottom rows seem quite different. Did this occur in only one timestep? Also, please clarify in the caption what model year is represented in the figure.

l.522: hardly matters – I find this to be a rather strong statement. I agree that a more pronounced speedup is seen with the ZI sliding law, but it also seems like grounding line retreat has been triggered within one timestep in response to the killing of the ice shelves.

l.522-523: I do not see how the difference in acceleration is smaller for FEFI than for DI. Figures 13 and 10 seem fairly comparable to me. Am I missing something? 

Section 4.3: I am not convinced by the added value of this section. Stating that the integrated basal melt flux is nearly equal to the grounding line flux for TG seems like an overinterpretation to me. This may be true for the FEFI case, but only prior to the collapse. The same could be said for the ZI-DI case in PIG, though. Therefore, I am having difficulty identifying a key message in Figure 14. Perhaps I have misunderstood the section. If so, it is worth improving its clarity.

Discussion

l.552: It would be interesting to include a statement in the discussion, either in this paragraph or elsewhere, about the role of subglacial hydrology and also the influence of meltwater in the grounding zone (e.g. Hewitt and Bradley). The current simple representation of effective pressure surely influences the ice-sheet response highlighted in this study.

l.553: It is worth noting that both Barnes and Gudmundsson and Wernecke et al. focus on much shorter timescales (decadal). At similar timescales, all of your simulations would likely agree with the results of those two studies, probably as a consequence of your initialisation procedure using present-day dhdt rates.

l.579-583: It is important to emphasise the influence of the initialisation procedure, in which the model is forced to imprint present-day DHDT trends. First, extending this present-day trend into the future dominates your simulation's response on shorter timescales (decadal to centennial). It is only once a significant grounding line retreat is triggered in your simulations, at different times due to differences in the initial states, that the influence of the basal friction laws kicks in. To what extent do you think your conclusions apply to this particular inversion procedure? It is likely that the basal friction field has been overfitted to match the observed dHdt. One alternative would be to apply the nudging scheme to an earlier ice sheet state and then assess whether the model can reproduce historical trends. In that case, different parameter fields might produce valid initial states but result in different model behaviours, highlighting how the initialisation procedure constrains the simulations. Since the observed dHdt has been imposed on the model, it is difficult to determine which parameter values would improve the match to observations. Tuning the basal friction field to match present-day trends prevents testing its ability to capture changes in mass balance in response to varying boundary conditions.

l.597-598: It is worth mentioning that the FEFI initialisation reduces the overestimation of observed surface velocities in the ASE. This could be a key factor in explaining why the FEFI initial state experiments showed delayed retreat compared to the DI ones. This delayed retreat leaves more room for the influence of basal friction on the rate of GL retreat. In contrast, for the DI initial state, the response is dominated by the imprinted fast flow in the ASE, leaving less room for the basal friction law.

Conclusion

l.616-618: It would be interesting to discuss potential ways to address this issue. For example, by including initial state uncertainty in ensembles of simulations? 

Technical corrections: 

l.27: double spacing at the end of the line: ‘(TG),  is’

l.34: ‘Sources of modelled ice sheet uncertainty’ – replace by ‘Sources of uncertainty in modelled ice sheet behaviour’ ?

l.56: consistency in citation formatting: ‘e.g., Brondex et al., 2017; Sun et al., 2020, Brondex et al., 2019)’. This is the case at several places in the manuscript.

l.58: same: (ABUMIP; Sun et al., 2020) 

l.93: ‘Eq 1.4 and is referred to’ – remove ‘and’

l.382: ‘depending on’

Figure 9: mix up between bottom and top row for Power Law / ZI.