Please find my comments in the attached file.

Review of “Historically consistent mass loss projections of the Greenland ice sheet”.

General comments

The paper by Rahlves et al. presents future projections of the Greenland ice sheet based on the CISM ice flow model. They explored different intialisation strategies, the height-elevation feedback and sensitives to the frontal retreat rate. For the initialization, they rely on a transient basal friction inversion forced by either ERA5 reanalysis data or output from CMIP6 (one CMIP5) ESM climate data; each initialization run received an additional relaxation run to minimize model drift. Future projections are then forced with either direct SMBs or anomalies from the respective ESM. I found the simulation results interesting and a good, detailed study in addition to the more general ISMIP6 intercomparison. Though I found the simulations and results very interesting I cannot recommend the paper for publication yet.

I am in the comfortable position to read the report of reviewer#1. I agree with his/her comments, particularly with the suggestion to construct a “piece of story”. Generally, I found the paper easy to read and well-structured, but several statements are not easy to follow as they are not supported by the results. I have some major points which should be addressed.

• “Piece of story”. From the current research I don’t see the novelty of the results. Methodologically you do large effort for the historical simulations but then the concluded results are very general or not new. As an example: The lines 16-21 (abstract) somehow repeat results that are not new: Sensitivity of glacier (low/mid/high) retreat forcing was shown by Rückamp et al. (2020), ISMIP6 sea level projections (both CMIP5 and 6) were shown by Goelzer et al. (2020) and Payne et al. (2020) (except SSP2-4.5, you refer to it in Line 409), relevance of dynamic vs SMB mass loss by Choi et al. (2021) and Rückamp et al. (2020). I think, the different initialization approaches and their influence are the novelty part of this work, and you should focus on that (as you did partly). You should more highlight, how your work is connected to initMIP (improve initializations) and/or to ISMIP6 (improve projections). Well, both topics are closely connected to each other, but I think it makes a difference when describing the scope.
  
  
  
  
• I found the paper a bit overloaded with experiments not needed. As presented so far, I don’t understand how the different ocean forcings (low, medium, high) and the experiments with and without elevation feedback help do understand the effect initialization approaches on the projections? So please skip these simulations and focus a bit more on the initialization (as in Fig. 7); if that is the overall scope. The grid dependency was not shown although mentioned in the discussion and conclusion. The promised comparison of absolute forcing vs. anomaly forcing (line 76) is very weak and not supported by any figure and not shown in the results section. To my understanding it is rather a technical detail than a comparison (because ERA5 is not available beyond ~2020). So far, I have not understood why you use one CMIP5 model and all other CMIP6 models? Why SSP1-2.6. SSP2-4.5 and SSP5-8.5 scenarios? I case you want to investigate the influence of the initialization on the projections, a few (well selected) projections runs would be enough.

Comment to the CC: Understanding the relevance of the thermal BC is very important, but I don’t think that an ISM that de-couples basal sliding from temperature helps do understand this question (usually, inversion model the infer basal friction are independent of temperature)

Line comments

Line 9: I have some concern. You match the grey area in Figure 4, but how is the spread in SLC before ~1990 explainable?

Line 11. “Atmospheric forcing is downscaled with MAR …”. I am curious what you did in the historical period?  How are the climate data treated in the historical period? You should spend some time describing it, as it is a major difference to the initMIP/ISMIP6 approach where every user come “as is” to ~2015.  I am curious how the retreat parametrization works in the historical period. The ISMIP6 retreat and height gradient parametrization were only available in the future projections in ISMIP6. Maybe it improves the projections once you have a consistent forcing from ~1960 onwards?

Line 13 “Furthermore, we disentangle the importance …”. You should consider dropping it. You focus on the initialization, I guess.

Line 40: What do you mean by ice sheet model uncertainty?

Line 88: There are many higher order models available in the community so please precise „higher order model” or give a reference.

Line 88: How is the 3D temperature field treated in the depth-integrated viscosity? You should also say/discuss if the basal ice flow is coupled to basal temperature or not.

Line 90: Are the 11 vertical layers equally spaced or refined to the base? For a thermomechanical coupled model, I would expect them refined to the base to resolve the shear heating at the base.

Line 90: power law: Please be precise or give a citation which type of law is used (e.q. Budd, Weertman, Coulomb, …).

Line 91: Maybe I missed it, but in the results sections, you don’t show the grid dependency. Therefore, your conclusions (e.g. Lines 21, 369/370, 414) are not supported.

Line 92: please define date of “present-day”

Line 93: Are bedrock and elevation smoothed? Please explain why it is smoothed.

Line 94: I don’t understand “prescribed”. Do you mean initialized? Because it then evolved … (Line 96). How do you treat temperate ice?

Line 94-103: I am bit confused about the terminology used here. You use “climate forcing” and “atmospheric forcing” from ESM’s. I understand what you mean, but please differentiate between climate and atmospheric forcing/data and what is finally used for the ISM. I suggest something like (very basic): “We use ESM climate data which has been downscaled in order to prescribe an appropriate boundary condition for the ISM.”

Line 103: Please explain briefly, why the elevation-feedback parametrization is necessary (MAR is running on stationary surface elevation).

Line 103: Maybe add “… anomalies with respect to reference period”.

Line 121/122 Is 1960 really present-day?

Line 129: ice sheets (don’t use plural for ice sheet unless you refer to GIS and AIS) -> ice sheet configurations

Line 129: relaxation: if the relaxation belongs to the initialization procedure, I would not explicitly name it later. Should be clear form the init-approach described here (see captions of Figure 1 and 2.). I do understand this further relaxation. I would have been expected that the inverse transient approach minimizes the drift already. The additional 1000/500 years make the approach a bit questionable …  and how they final states (geometry, ice masks, ice velocity) correspond to the target. This could be presented and explored better.

Line 134 to 136: I found “ensemble” confusing here. It is only one climate forcing experiment (ERA5) and not an ensemble. Maybe use “initialization approach”?

Line 135 and Line148/149: What match well? And how is ‘well’ defined? That is no shown.

Line 141: computer resources: Is 4, 8, 16km really very expensive (with 11 layers temperature-coupled) compared to e.g. Blatter-Pattyn or FS (11layers and temperature-coupled) with a much higher resolution? I guess a 4km resolution with your model is rather cheap … But I can only guess without having any number.

Line 142-144 the paragraph is not well connected to the text. Suggest dropping it.

Line 145: “Historical period”:  I found this chapter much too short. The title of your paper is “Historically consistent …”. For me, there are many open questions. So, I am wondering how the retreat parametrization is behaves in that period? What about the height-elevation feedback? Is that changing over time?  What really means “historically consistent”, that was never mentioned.

Line 153/154: “Note that ESM’s …” Please give a reference. Basically, ESMs generate no SMB.

Line 152 and 166: This contradicts with your statement in Line 103 where you say that anomalies (and absolute) are used. Well, ok, I re-read it: so please make it more prominent in the text where needed …

Line 155: add that sensitivities are also performed to grid resolution

Line 184: ACCESS-initialization -> please rewrite: “… except for the ESM ACCESS of the ESM-init ensemble”. Is there a need to mention ACCESS separately? I mean, the full range of -41Gt to -110Gt (about 0.1-0.3mm SLE over 100 years) is very small compared to the projections and the historical runs.

Line 188: observational data -> observed geometry/ice mass. Well, its not surprising that the initial state matches the observed geometry, because that’s the target of the initialization (although I don’t how the additional relaxation works … ) . But I am curious how the ice surface velocity matches observations.

Line 189: maybe rewrite to: “…the limited ability of the inversion in the initialization approach …”. You may also consider that floating ice in your simulations is directly calved off.

Line 190: You introduce the simulation ID ERA5-init, so please use it: Figure 1 shows the state of ERA5-init (with medium ocean forcing).

Line 191 common pattern in what? Please be precise.

Line 192: ERA5-initialization -> ERA5-init

Line 193: I don’t understand why you focus on the comparison of ERA5-init to ESM-init with NorESM. I found the argument that it is the in-house product very weak and not well supported. In case you want to focus on the in-house model drop all other experiments and refresh the title

Line 200: “This is a residual …” -> could be tied together with statement in Line 188.

Line 205 The simulation ESM-SMB init is not introduced. Do you mean you use the SMB of NorESM from the ESM-init ensemble? Anyway, I found the paragraph “To further explore …” hard to follow, because it is not demonstrated with figures/numbers.

Line 222: I am bit confused about the negative and positive signs of SLC (i.e. negative signs == loose mass). Maybe it would be more intuitive to show SLC relative to 1960 or as change to initial ice mass.

Line 223:

(1) ESM-initialized simulations -> ESM-init

(2) Fig 4b -> Fig. 4

(3) I guess observations == IMBIE?

Paragraph 3.2

(1) First of all, I found it very interesting that all simulations start with a large SLC spread in ~1960 and then converge towards 2015. Any explanation for that?

(2) In legend of Fig. 4: ERA5 medium, low , high -> ocean forcing? What is applied to the ESM’s? Medium, low, high or no ocean forcing? Please explain. Ah, ok. It is explained in the figure caption. Suggest dropping ERA5 low & high as you do not refer to these simulations in the text. IMBIE “max corr“ and “uncorr.” and they grey shaded box needs further explanation.

(3) Would it be possible to add an observational dataset from 1960 onwards? That would help to judge the different models.

(4) “fairly well”, “agree closely”, “strong agreement (Line 237)”: How do you specify agreement? Though the SLE is an integrated scalar value, I am curious if you can say a bit more about spatial patterns?  Without giving any number like e.g. RMS it is hard to follow. In the IMBIE period it seems that all models behave well, I cannot see that ERA5 behaves much better than some of the models from the ESM-init ensemble (like MPI-ESM1-2HR or IPSL-CM6A-LR).

(5) Your interpretation with interannual and interdecadal variability is very speculative as it is not shown by any numbers or figures.

Line 233: Maybe add after “… set to 0” that the forcing is then representative for the 1960-1989 period (reference period), if so. I am curious to see a figure. I would have expected that some models have a negative SLE in 2100 (mass gain) to reach the 1960-1989 state.

Line 237: drop “interannual variability”. That was not shown and I don’t see the context.

Line 237: I am not fully convinced. Reaching a small model drift is a difficult task and not always the intention: E.g. ‘paleo spin-ups’ aim to reach the trend of observational period. Generally inverse/data assimilation models have a larger drift, but they match observations (at least for the date of the inversion). So, you did transient inversion and another relaxation. How does your model results ‘perform’ in 1960?

Figure 5 caption: ERA5-initialization -> ERA5-init. What is the simulation ESM-own SMB?

Maybe try to use another color scheme that shows the different SSP scenarios. Its hard to follow the “linear” statement in Line 242.

Line 244-245 What is the motivation to compare rates of 2040-50 and 2090-2100 with observations?

Line 257: I am trying to follow. Both, ESM-init and ERA5-init are in balance due to the relaxation. If you add an anomaly, the simulated SLE of the ISM is in both cases (ESM init vs ERA5 init) rather similar, or? That’s not surprising as they own the same climate forcing.

Line 269 “… ice thickness of the initialized ice sheets …” -> initial ice thickness

Line 271: it is bit confusing. What is the difference between “(ESM-initialization - ERA5-initialization)“ and “(ESM-initialized - corresponding ERA5-initialized) “

Section 3.3.1. I acknowledge the detailed results of this chapter. But I don’t see the new results and how they are related to previous studies.

Line 290 and 300: to be honest, I get a bit lost with all the different scenarios. “fully forced”, “partially forced”, medium/low/high ocean forcing; “SMB-only”, “Retreat-only” and “No-SMB-height-feedback-experiment” vs NorESM or the fully ensemble. A table could help.

Line 310-317: That’s a good analysis. But I don’t see how it is related the overarching aim of the paper.

Line 342: “exceed” is not a fair comparison as you use different scenarios (CMIP5 vs CMIP6, see Payne et al (2020)).

Around Line 395: Maybe I missed that comparison in the methods/results section. What do you mean with baseline SMB? Directly comparable: I guess, they are identical. Some equations would help.In my understanding, you have in the anomaly approach:

SMB(t)=SMB_ESM_1960-1989 + SMB_ESM(t) - SMB_ESM_1960-1989

which is identical to the absolute approach

SMB(t)=SMB_ESM(t).

Line 406: I think, another restriction is the retreat parametrization, which “overrides” the ISM dynamics.

Line 414: the grid dependency was not shown.

Code and data availability: Retreat masks and MAR forcing for the historically period for all ESM should be made available.