The paper presents a series of model experiments on the evolution of Thwaites Glacier over the next centuries using an ice sheet model forced by several climate models. The paper demonstrates that the historical imbalance of the glacier matters a lot for its future stability and its potential for 'collapse'. Thee authors also put forward a limit in global temperature increase for which the glacier could 'collapse'.

The paper is rather lengthy and could benefit from some trimming, which would make the message clearer. Especially the experiments of steady state versus transient initialization are of interest, followed by the forcing experiments. The introduction on the different ways of initializing models could be shortened, as the importance for the paper is to make the distinction between steady state and including imbalance.

Overall, I find this an interesting study that with some polishing and a few clarifications (see below) I would recommend for publication.

Line 14: model -> models

Line 14: what models are meant here. I guess climate models and not ice sheet models. Please specify.

Line 19: Collapse occurs 58 times in the text, but it is never defined what is exactly meant by collapse of the ice sheet. Later on (onset of collapse' is used, which also requires a clarification.

The introduction is quite long giving a complete overview of different methods of initialization. It is quite interesting in itself, but is not necessarily guiding the reader towards the core of the paper, i.e., that starting a historical simulation from an observed imbalance results in different response of TG compared to starting from steady-state conditions. It is not so much the way an initialization is done, but what the imbalance is that counts for understanding the remaining of the manuscript.

Line 91: Our null hypothesis is that the GMSL rise from the present-day mass loss rates is independent of the GMSL rise caused by an increase in ocean thermal forcing, i.e. that the present-day mass loss rates do not influence future forced projections.

Quite confusing. I would suggest to remove the mention to GMSL. It is about mass loss either caused by a given imbalance due to a grounding line retreat some time ago, or due to the current applied ocean forcing. I don't see how GMSL rise can be caused from thermal forcing (except thermal expansion, but that is not what you are talking about I presume).

Line 100: Is a spatial resolution of 4km sufficient to guarantee grounding line migration (see for instance discussion in Pattyn et al., 2013). Maybe briefly state what is done to facilitate grounding line migration at such spatial resolution.

Line 109: The regularized Coulomb friction law was already used in Joughin et al (2019), and is based on the work of Schoof and Gagliardini. (Joughin, I., Smith, B. E., and Schoof, C. G.: Regularized Coulomb Friction Laws for Ice Sheet Sliding: Application to Pine Island Glacier, Antarctica, Geophys. Res. Lett., 46, 4764–4771, https://doi.org/10.1029/2019gl082526, 2019.)

Line 121: The reference that marine sediments are likely more prevalent in submarine basins may be a bit outdated. There are more recent studies that have investigated the probability of sediment versus hard bed of Antarctica. See for instance: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2021RG000767 and https://www.nature.com/articles/s41561-022-00992-5

It shows a larger diversity of possible outcomes for regions lying below sea level.

Line 127: What are these parameters (Ho, tau, r L)? How do they influence your optimization? It is not defined what these parameters are about.

Line 158: See my remark of Line 100: is this the way grounding line migration is dealt with? Interpolation of friction within partially floating cells AND subshelf melt as well? It has been shown in Seroussi and Morlighem (https://tc.copernicus.org/articles/12/3085/2018/)  that it increases the sensitivity of grounding line retreat big time. Some discussion is needed.

Line 165: isn't this not too much different than keeping the calving front fixed, as you probably need quite high melt rates to have the front retreating through melting alone.

Line 181: Is an initialization of 10 ka enough for the temperature field to reach an equilibrium?

Table 1:  Overall, I found the figures in the supplementary material more of interest than the first few figures shown in the manuscript. Therefore, some information of figures S4 and S5 could be transferred to the main manuscript and replace table 1. One way of representing this is as in Martin et al, (2011) Figure 15 (https://tc.copernicus.org/articles/5/727/2011/tc-5-727-2011.pdf), so that different regions of the ice sheet/ice shelf system are represented.

Figure 3: Is not showing integrated mass loss, but mass contribution to SL in terms of GSLR and % of VAF. Mass loss also comprises that mass that is lying underneath floatation level.

Line 307: I don't think that delta T can be considered an inverted parameter, as there is not inversion method used. Maybe use 'optimized'.

Figure 4 and Line 349: instead of pointing the readers to a supplementary figure S6 just to find out where a little line is drawn, it would be more informative to mention in the caption where this line is situated as a function of present-day GL position (i.e., XX km inland from the current GL position). This line is also defined as bedrock ridge and important as onset of collapse. What is meant by onset of collapse (see also remark on collapse in general)?

Line 400: I wouldn't call these simulations outliers. They are valid solutions for that given forcing. Just that these forcings are relatively low in melt and high in accumulation and therefore result in less mass loss than other forcings. This is not the definition of an outlier.

Summary:

In this manuscript, the authors perform numerical simulations of the Antarctic ice sheet using the CISM model and test the impact of the initialization method (including or not the present-day thickness rate change during the model initialization phase) on the future simulations, based on both idealized forcings and projections using climate model conditions. They find that the inclusion of thickness change rate impacts the results mostly in the ASE as it is already experiencing large changes. They also conclude that the response to additional forcing is not linear, with the future changes compared to present-day conditions very different for the two initialization methods.

The paper is usually well-written and clear, and the figures appropriate. The conclusions are well supported by the results provided. However, there are number of aspects that can be improved to make the paper clearer, including the ESM and simulations used, the ability of the two methods to capture current thickness changes, the metrics to consider that a basin collapsed, and limit repetitions between the results and discussions. Below are some major and minor suggestions to improve the manuscript.

Major comments:

• The paper mentions 7 ESMs in several instances, but only 5 ESMs are actually used, from which 7 simulations are used. This needs to be clarified throughout the text.
• Unlike the other ESMs, the NorESM simulations are only run until 2100 (and not 2300), so the patterns compared in figures 1 and 2 are shown for different times for the different simulations. Since high-emission scenarios are based on continued increases in emission after 2100, the temperature and overall conditions are very different at these two times. I am not asking to remove or redo these simulations, but this should be made very clear as soon as the simulations are described and reminded each time the patterns are compared and maybe additional figures are needed (for example for 2100).
• One of the initialization methods includes the dH/dt rate as a constraint, so an additional metric to measure how the two methods are able to match dH/dt at the beginning of future simulations would be useful. This would also balance the other metrics that are all about present-day conditions at a given time and not about rate of changes.
• In the collapse of the Ronne and Filchner-Ronne basins, the threshold for collapse initiation is 10% IVAF, but the collapse is considered for 100 mm GMSL. I don’t understand why a similar absolute number is used for both basins? There is no reason why a similar number should be used for both basins since they don’t hold the same amount of ice. So using also a percentage of the ice contained or IVAF for both basins would be more relevant and would lead to a better comparison of the timescale these two basins take to “collapse”.
• S3 shows the extents used for the different basins. Ronne-Filchner does not include all of the Filchner ice shelf of the glaciers feeding in there. So it would be good to update this basin to include all of Filchner ice shelf and all the glaciers feeding it.
• The discussion and result sections are sometimes repetitive, with the discussion spending a lot of time repeating some of the results. Restructuring them would help to remove some of the repetitions. I think also the discussion could do a better job at comparing with previous studies looking at both the entire Antarctic ice sheets and specifically for Thwaites and Pine, whose collapse is discussed in details here.

Minor comments:

l.13: “projections”: specify projections of what and over what period

l.14: “most models project some or severe” -> “while most models project some moderate to severe”

l.16: “uniform ocean”: the main text describes the perturbation to be only in the ASE sector

l.18: “seven ESMs”: there are only 5 ESMs from which outputs for 7 simulations are used. There are a lot of confusions about these ESMs, so make sure it is clear what is used. Also ESM has not been defined

l.19: TG was not defined

l.20: GMSL was not defined so far. Also is that GMSL from Thwaites or also other basins?

l.24: “coming 5 centuries”: you want to be more nuanced, it does not happen for that long or at least not in all the cases

l.29-31: this is the main conclusion, so start with this sentence before going into the details of the results.

l.35: “ice sheet modelled sea level” -> “modeled ice sheet contribution to sea level”

l.37: “increases” -> “increases rapidly”

l.43: “choice of the model” -> “choice of the ice sheet model”

l.52: you also want to remind before this sentence that there are many other differences and then say a main difference is the initialization.

l.54: comma after AIS

l.57: Larour et al. 2012 does not use the mass change rate: they use static data assimilation with the stress balance equation only and there is no additional term in the cost function related to the mass change. You want to check that it is really the case for the other citations.

l.58-59: this sentence should go before the previous one, so first the generic method and then the specific about the mass change.

l.64: add a reference for the inconsistencies, for example Seroussi et al. 2011

l.66: “The other”: the other what? Other models?

l.74: remove “at grid point base”

l.77: remove “will”

l.80: I don’t understand, you just said it is investigate the role of the present-day mass change a few sentences ago, so why are you saying here the present-day mass change rates was not included? You also want to explain what you mean by “forced” ( in general I found this term a bit confusing throughout the text”

l.81: again what does forced mean?

l.81: “using firstly” -> “first using”

l.87: I don’t understand why you say 21^st century climate change since most climate model used simulate changes until 2300

l.90: rather than talking about a null hypothesis, I would rephrase to say that you are testing or investigating the impact of the initial conditions and the importance of capturing the present-day imbalance. You can even say it is common in intercomparison to subtract a control run with constant climate conditions to better compare model results, like what is done in ISMIP6

l.91: comma missing after i.e.

l.94: “forced simulations” -> “future projections” or just “simulations” (or realistic simulations)

l.103: don’t use higher-order here: this is typically used for the Blatter-Pattyn approximation and could be confusing for people used to that

Eq.1.3: I don’t think you need the \beta u_b part here: this wrongfully gives the impression that the basal stress varies linearly with basal velocity, which is not the case as shown in the last part of the equation

l.111-114: it is not clear what is done for the effective pressure N, can you add the equation if can be described easily with an equation or rephrase this sentence to make it more clear how N is calculated.

 l.123: this linear description of the coefficient was derived for Greenland if it’s from Aschwanden et al., 2013. Did you check how results from Antarctica compare to that and if a similar relationship can be used? Part of the reason I am asking is that we also find some good and simple relationship to describe the friction in Greenland but could never find a similar relationship for the friction for Antarctica.

l.130: mention what this observational dataset is (climatology combining all observations over the past couple of decades or something like that)

 l.141: “matches”: what is the target of this match? Extent? Or thickness? Or something else?

Eq.1.7: what does this quantity represent?

l.161: references for the calving laws: I would go back and cite the papers that originally introduced the different calving laws

l.167: the “ice shelf thinning” is included in your calving, it is actually the only thing included since calving happens when the ice gets thin enough. The impact of large stresses or strain rates on the other hand are not included.

l.172: “initialization” -> “initial state”

Eq.1.8: there is no need to introduce a variable F for the flux divergence, since it is simply H \bar{u}. It is more common and will make things easier to simple use that instead of introducing a new variable.

l.184: I think that on top of looking at the long-term drift, it would be useful to also look at the instantaneous thickness change at the beginning of the projections (using present-day conditions for the forcing) to assess the impact of including the mass change term and seeing how the two runs compare to observations. It would be a very useful and complementary metric to the thickness and velocity misfit and you already have the data used for dH/dt. So I would compare the mass change and add the results in Table 1.

l.184: what does “without forcing mean”? you always need to have forcings at the ice/atmosphere and ice/ocean interfaces? So do you mean that the forcing is constant or unchanged compared to the initialization phase?

l.187: For which run is the 0.04% change? I would put number for both cases

l.191: “Continuation simulations” is not very clear. Maybe experiments or future projections would be a better description of this section.

l.197: there are not seven ESMs used in this study, only 5 ESMs from which outputs from 7 simulations are used, this should be made very clear right away. So this paragraph needs to be clarified. Maybe it would be easier to have a short section of idealized experiments and another one on projection experiments in which you talk about both the projections and the ESMs (so merging with section 2.4)

l.200: explain how the repeating is done

l.200: “one where the forcing” mention which one right away (maybe that would be easier after the ESMs are mentioned hence the suggestion to slightly reorganize)

l.201: “last datapoint”: what is the impact of using just 1 datapoint as opposed to an average over 10 or 20 years? If that year has anomalously high or low SMB (or ocean thermal forcing) it might bias the results. Without necessarily rerunning all the experiments with an average value, you can add some discussion (here or in the discussion section) about how 2300 compares to over years around that time.

l.212: how about the other two climate models? What are their ECS and how does it compare with rest of the ESMs?

Fig.1: rather than spin-up, I would use present-day or observations or climatology

Fig.1 caption: not all models have values for 2280-2300 since NorESM simulations stop in 2100. Make sure this is very clear throughout the text, since it explains to a large extent the patters of SMB and ocean thermal forcing (not as much warming in high-emission scenarios by 2100 compared to 2300)

l.219: “as” -> “similar to”

l.226: Why do you show the average of the last 20 years (2280-2300) on the figure but then use only the last year (2300) to continue the projections? That seems a bit inconsistent.

l.235: NorESM simulations stop in 2100 that that will explain a lot of the different for this model, especially for the high-emission scenario. Same for l.239: the only high-emission scenario that is different is NorESM, to a large extent because it is not comparing for the same year so the comparison is biased.

Fig.2: here again, NorESM RCP585 stands out because it is warming by 2100 and not 2300 and the warming continues after 2100 in this scenario.

Fig.2 captions: what do you mean by “modelled” SMB here? Is that the SMB values used during the initialization?

Fig.251: You should also add a metric to compare the dH/dt trend at the very beginning of the future projections

l.256: Goelzer et al. 2020 is a paper on Greenland, so I am not sure how much we can compare velocity and thickness errors for the Greenland and Antarctic ice sheet simulations?

l.259: comparing the ice fluxes at the grounding line is a great idea. Could you add that to table 1?

l.270: you still have the same target data for both initialization, so I am confused why the error would be so much larger in one case if the same target is included in both?

Table 1: add a metric for the dH/dt change at the beginning of the projections, and one for the grounding line mass flux.

Fig.3 caption: you have a and b on the panels, so I would use that in the caption instead of left and right

l.304: “broader” –> “entire”

l.305: “earlier”: what are you referring to? Earlier than what?

l.306: “increases linearly”: it is not clear on Fig.3 that you are discussing here that there is a linear increase. It looks like this is more clear on Fig.5, so I would reorganize this part.

l.306: “more pronounced”: what do you mean by that? In one case, it is steady-state (with no temperature change) and in the other on it changes because of the initialization method, so it sounds obvious that there will be a large difference in the case of the steady-state. But maybe I am missing something.

l.314: remove period after “Fig. S6)”

Fig.4: add a legend with the blue and red lines as well as the blue and red stars

Fig.4 caption: use a and b instead of left and right since you already have then on the figures

l.326: I still think the null hypothesis is confusing, so I would reformulate to say something like: investigate the impact of different initial conditions

l.328: “simulations. These results are shown in Figure 4.” -> “simulations (Figure 4)”

l.331: remove “already”

l.333-334: rephrase this sentence: The response to warming conditions is impacted by the modeled initial conditions …

l.337: remove “than in equilibrium”

Fig.5 caption: Overall title would be more representation with something like: Impact of ocean warming on collapse and maximum GMSL …

Fig.5 caption: “added” -> “additional”

l.352: “an ice dynamical limit” -> “a limit on the onset of collapse”

l.352: “2 degrees”: if the collapse would happen earlier with more than 2 degrees of warming, then that’s not the definition of a limit: it would the case if you had an asymptotic value regardless of how warm the ocean gets

l.354: “rate of sea level rise keeps on intensifying”: is that also from the same ASE region or is there also mass loss from other sections or glaciers outside of Pine Island and Thwaites?

l.362: “Until 2150”: how do you find 2150 as the transition from the initialization to the forcing dominated uncertainty?

l.363-364: Rephrase this sentence, it is very confusing.

l.365-366: remove “blue” and “red” as there colors do not reflect the types of simulations

l.366: “collapse”: what do you use to consider that the ASE collapsed?

l.371: “The forcing then rules the response” rephrase or remove that sentence

l.379: the UKESM simulations actually has the largest/fastest AIS mass loss

l.383: remove “in our simulations”

l.386: “profoundly”: quantify what you mean in terms of percentage difference or something like that

l.401: “only one”: there are several lines that are above the extrapolated mass change in the beginning of the run and until 2250

l.402: “absence of any future forcing”: is that future forcing or continuing with the same constant present-day conditions? Also it’s not possible to not have a forcing, there are always prescribed conditions, even if they are zero SMB and melt.

l.404: “run towards 2100” -> “run only until 2100 and conditions from 2100 are repeated after that”. Also this needs to be made clear much earlier, as soon as you describe the EMS simulations

Fig.6 caption: remove “on the right”. Also “unforced” is not clear, and you always have a forcing, even if it’s zero

l.420: “high-warming” -> “high-emission”

l.424: “respectively disappear and completely unground entirely by 2500” –> “completely ungrounded by 2500”

l.426: “does” -> “do”

l.427: “simulations” -> “in simulations”

l.428: “deglaciate” -> “also deglaciate”

Fig.7: remove the parts that are already floating at the beginning of the experiments on panel b, so it is more clear what areas do unground

l.441: “considerably”: quantify what you mean

l.444: If you want to use the abbreviation FR, I suggest you introduce earlier in the paper and consistently use it throughout the text

Fig.8: I am not sure why different colors are used for the three basins because it does not add much. Instead I would continue using the same colors for the different ESM simulations for consistency with the other figures

Fig.8: Why do you show the thermal forcing for PIG, thwaites and Larsen when the other panels show Filchner-Ronne, Ross and ASE? Try to keep it consistent for the three metrics reported

Fig.8 caption: “per basin”: mention which basins you are looking at instead

Fig.8 caption: remove the last sentence since the figure is only until 2300

l.468: “100 mm of GMSL”: why use an arbitrary number of GMSL and not a fraction of the basin contribution to GMSL as is done for the initiation? I don’t know the difference between the Ross and Filchner-Ronne basins, but there is no expectation that they hold the same amount of ice. That could also make changes in the results reported in table 4 and give insights into the timing to deglaciate these two basins, and how they compare. Finally, why not include also ASE in table 4?

l.476: remove “typically”

Fig.9 caption: why “extra”? I am not sure I understand what you mean here, what are you comparing it to?

l.520: “present” -> “show”

l.522: “considerably”: add some numbers to quantify

l.530: “does not occur before 2100”: you want to compare your numbers with previous studies such as Robel et al. 2019, Joughin et al. 2014, etc.

l.532: “extreme warming”: you see already a very large difference, and 2 degrees is quite a lot, so I would rephrase this sentence

l.533: Why does the peak rate continues to increase? Where is the ice coming from and what is the mechanism that leads to this continued increase?

l.536-539: rephrase this positively to highlight the new finding (also will has three “l”s in the manuscript)

l.551 and following: this is all repeating information that are already mentioned in the results section, so try to go beyond the results reported and compare with other studies for example

l.570: missing parenthesis

l.576: remove “which “

l.588: missing comma after i.e.

l.590: “our ESM” -> “the ESM”

l.591: “decreasing”: for what period is that? It looks like it first increases and then decreases?

l.602: “use” -> “improve this aspect by using”

l.607: “from 2100”: as mentioned earlier, this should be made clear from the beginning

l.615: “calving ceased entirely”: I don’t understand, it can continue retreating if the ice is thing enough to allow ice front retreat

l.617: “modeled front positions” -> “ice thickness”. This seems contradictory to the calving scheme described based on ice thickness only

l.622: “by” -> “with” and remove “up”

l.628: “whether or not include the present-day” –> “to include or not the present-day”

l.630: “with” -> “over”

l.633: “depedent” -> “dependent”

l.636: “shelfs”???

Fig.S3: why is Filchner ice shelf and the glaciers feeding it not entirely in the Filchner-Ronnee domain?