Review of “A topographically-controlled tipping point for complete Greenland ice-sheet melt” by Michele Petrini et al.

In the manuscript under review, the authors run ice sheet model simulations of the Greenland Ice Sheet to test for it’s “tipping”. The surface mass balance is created by using elevation-class downscaling from CESM2. Since a temperature correction depending on surface elevation is included in this, the melt-elevation feedback is considered in the simulations. In addition, a simple model for earth deformation is included, which means that a bedrock-uplift feedback can be considered. For different levels of warming, the climate conditions are held constant and the long-term response of the ice sheet to this climate (including the feedbacks mentioned before) is simulated.

Main comment:

1) The usage of terminology in the draft is quite vague. A number of terms are used (“tpping”, “runaway”, “stabilising”, “topographically-controlled tipping point”, “pinning point”....) but they are never defined. As these can be used in different ways in different communities or are not known to me (e.g., topographically-controlled tipping point), it is essential that all these terms are defined and used consistently in the manuscript.

2) My impression is that the authors use “tipping point” as multistability shown by Robinson et al. (2010)? If this is true, however, they do not really show that the threshold they find is a “tipping point”, i.e., a bifurcation point. They show that at some level of SMB, the ice sheet eventually vanishes, but it remains unclear if this is reversible or not? Is there is hysteresis or not? 

3) The study aims to analyse the “SMB threshold for complete melt” but does not include an uncertainty estimate for two essential processes, namely, the lapse-rate temperature correction and the bedrock uplift. At least a variation of these parameters would be expected to test for the robustness of the presented results.

4) The study claims that it identified a “topographically-controlled tipping point”, which I think refers to the “pinning point” that they mention the western margin of GrIS. Importantly, they find that this region deglaciates first in the “full melt” simulations, but stays in the “medium melt” simulations. This is however only an indication for a hypothesis, not a proof. If the authors wanted to prove this statement, they could for example prevent this region from deglaciating in the strong warming simulations (by not changing the SMB there for example) and showing that this means also the rest of the ice sheet does not vanish. Again, here the terminology is unclear: what do you mean here with tipping point? Which is exactly this region, it is only termed the GrIS western margin?

Further comments:

Abstract

- line 12: “highly nonlinear” → “nonlinear” as highly is not quantified.

- line 14 “runaway retreat”, runaway means that the feedback gain of this process if larger than 1, I don’t think that this has been shown yet. Rather, you can say “self-reinforcing”, “self-sustained”.

- line 14: if GIA only delays deglaciation, it does not “stabilise” the margin in the sense of stability analysis. It only affects the timescales.

- line 14-16: this sentence is not clear, reformulate.

- line 16-18: you do not show that this region is the trigger for tipping.

- line 19: what do you mean with “stabilising effect”?

Introduction

- in general the introduction is written as if you are intending to provide an estimate for a tipping point, however, this is not done in this manuscript (see main comments).

- line 24-25: Add a citation for “while until the late 1990s ice discharge has been the main source of ice loss”.

- GIA and it’s effect on GIS stability (papers like Zeitz et al.,2022) is directly relevant to this study and should be discussed in the introduction.

Methods

- A section on the model initialisation is missing. It is pointed to previous studies, but it would be useful to have a quick summary how you initialise and optimise model parameters here.

- lines 97 and following: does the downscaling mean that the SMB that the ice sheet model sees is not equivalent in mass to the fluxes in CESM2?

- line 129: How long does it take to reach the stable ice sheet configuration? What is your criterion for “stability”? Looking at Figure 2, it appears that quite a few runs are still changing (2.5 to 3.8K runs).

- How are the sensitivity runs done? You mention different till friction angle and switching off bedrock uplift – are new equilibrium initial states created for these conditions? If not, do you show the results in Fig A2 relative to a control run?

Results

The concept of a “topographic pinning point” is not clear to me. The results are meant to show that a region in west Greenland is such a “pinning point”, and if it is “un-pinned” the GrIS retreats in all other regions as well. However, the results shows only a correlation between this region being part of the maximum ice sheet extent during oscillations and regions in Greenland being glaciated. And it disappears first. This does not mean that this specific region has any control over other regions being glaciated further away. There is no physical process named through which this pinning point is “stabilising” the other regions of the ice sheet.

- line 139 “exhibits”

- line 139 how do you quantify “highly nonlinear”?

- line 146: please clarify “low GrIS melt is achieved for a decrease in SMB not exceeding 50% of the equilibrium pre-industrial SMB”. This sentence is quite complicated. And why is the pre-industrial SMB an equilibrium SMB?

- line 177: what do you mean with “more stable”?

- line 193: discharge is not included in your experiments except for a fixed

- line 197: please specify where this region is in the figures, e.g., show it in the figures.

- line 197: what is a topographic pinning point?

- line 201: what do you mean with “runaway”?

- line 203: How is this tipping point behaviour? You do not show irreversibility.

Discussion

- line 219: it might be worth giving the numbers here as they diverge quite a lot

- line 241: remove “highly”

Conclusions

- line 290: provide the “other studies”

- lines 291: you do not show that “tipping” depends on the margin – you show that the margin gets lost first.

- line 294: give the previous modelling studies

- line 297: “includes”, typo

Tables and Figures

- Table 1: The SMB related to the intial values at the start of the repeat-forcing runs, or? Where do the uncertainties in the final volume come from? Why are there no uncertainties in the Min. vol. Time then?

- Table 2: What are the CESM2-only runs? It appears to me that they are not relevant to this study here?

- Figure 2: How are the two axes GrIS integrated SMB (Gt/yr) and mm/yr linked? The GrIS extent changes drastically in the runs, and theoretically, this can cause a change of the integrated SMB while the average SMB remains the same.

- Figure A5, A6: I think these are never referenced.

- Table A1: does this mean you are using a spatially constant geothermal heat flux?

The authors investigate the response of the GrIS volume change to sustained GMT increases that affect the SMB in coupled GCM—ice-sheet-model simulations which branch out at different times from an idealized high greenhouse gas (GHGs) scenario simulation. They find a non-linear (non-gradual) retreat pattern of the GrIS towards the east with increasing GMT that is partly a result of ice pinning on mid-western mountains, but is complicated GIA influences. The authors do a good job in putting their results in perspective by comparing with recent similarly-focus studies and highlight why differences with those studies are likely found. The figures and text are of high quality, and the manuscript is concisely written. I am pleased with the methodology, although I am not an expert on running these kind of model experiments and on the limitations of the one-way coupled experiments presented. In the end I believe the findings are of good value to the community, and I have only few minor comments that I hope the authors will consider to improve the accessibility/readability of the paper.

Minor comments:

In the abstract and L65 the phrase occurs “and we explore the processes controlling the nature of this threshold, [..]“. I would suggest you state upfront which processes you find to control the threshold instead of leaving the reader in suspense.

Please define tipping point carefully as it is usually taken to mean non-reversible state transitions once a threshold (of a control parameter) is reached. It is not sufficiently clear if you take it to mean this, but if so, please give a short account of how this can occur when considering the SMB-height feedback with GIA.

Please define the SMB threshold clearly since you take it to mean Gt/yr in some places, but in other places refer to the GMT increase of some experiment? E.g. in L280-282 you do this nicely, but would be helpful to have a similar clarification earlier.

L66: Not sufficiently clear what “SMB levels” refers to at this point. Please help the reader a bit more here.

L139: “exhibits”

L208: I think it would be helpful to expand on what is meant by “Even though our simulations are not meant to represent realistic scenarios” since you then later go on to compare with, what I would regard, attempts in the literature of make realistic model experiments.

Please consider qualifying early on that “complete ice-sheet melt” also means “complete ice sheet (mass) loss”. E.g. L284 you do this excellently, but having this clearly defined early on, too, would be helpful.

Not sufficiently clear which experiments are fully coupled and which are not; e.g. L247 vs. L266-267 and in conclusions.

The authors present a series of idealised CISM2 future simulations, ran within the CESM2 architecture and forced with different initial states coming from a published CISM2/CESM2 simulation. They identify a threshold in the initial SMB forcing beyond which the GrIS completely melts. They discuss the competing effects of the melt and the GIA and identified a pinning point in the midwestern margin that stabilises the ice sheet in the higher SMB/lower temperature simulations. The supplementary videos were particularly useful in that regard. They also compared their results to other studies and discussed how differences in the models could be a source of difference in the behaviour of the ice sheet. I liked the references to the similarities with the last interglacial, as modellers usually tend to focus on time period only.

I have, however, a concern with the use of the term tipping point in the title and in the manuscript (see main comment). Nevertheless, the study is interesting and its main result (i.e. the identification of an SMB threshold for complete melt and the mitigating effect of the GIA) should still be published, provided that the author address this concern, which has also been raised by the other referees. 

Below my main comment are some minor comments on the text and on the figures and tables, and some typos/grammatical mistakes corrections.

1/ Main comment

The vague use of the of the term tipping point bothers me a bit. It is not defined, which makes it difficult to take the main message out the introduction and is at times a bit vaguely used to talk about long term effects of strong feedbacks. The stricter definitions of tipping points involve irreversibility and hysteresis (though some looser definitions accept reversibility) and the idea that the mechanism will still be self-perpetuating even after the initial perturbation has stopped. Although the GrIS being a tipping point of the climate system is accepted in the literature, the irreversible aspect and if this is applicable to your study is not discussed in the manuscript either.

Please clarify your use of tipping point by providing a definition and discussing how it is applicable to the SMB threshold for complete melt in your specific case. If you find that the definition of tipping point does not apply here, please carefully rewrite some sentences to avoid the misuse of the term.

2/ Minor comments

You are using a mix of British and American English, please homogenise. I spotted the use of modelling (British spelling), color (American spelling) and both British and American spellings for parametrisation/parametrization. You also use both parametrize and parameterize. It looks like both are correct but could you stick to one spelling?

Introduction

The first paragraph is really long, can you divide it into several smaller ones? The SMB-height feedback appears in the middle of the paragraph. It is the main focus (along with the competing effect of the GIA) of your work but it doesn’t really stand out in the text.

Starting a new paragraph here would be a good idea. You could also put a bit more emphasis on this process to attract the reader’s attention. This could be done by putting your definition of tipping point just before (if you can justify the use of the words tipping point) or by rewritting line 36 to 38. In particular, line 36 says that the SMB-height feedback is ‟another important source for future GrIS mass loss”. This is absolutely true but, without developing a bit more on the feedback, you make it sound like you’re just discussing another source of ice loss instead of the main point of your work. 

The competition between melt and GIA is also an important point in your work but you only mention at the end of your introduction that CISM2 takes into account the effects of GIA. Please add a sentence about the fact that it will counterbalance the effect of the melt and influence how melt is evolving throughout the simulations.

Method

Lines 115 - 127:  I’m not sure I understand things correctly here. From section 2.3 I understand that your work starts from the already existing CESM2/CISM2 simulation of Muntjewerf et al., 2020b and that you use different points in time from that simulation to force CISM2 in your simulation. In line 115 you also mention that you run CISM2 within the CESM2 architecture. Do you mean that you completely bypass the atmospheric and land modules and directly force CISM2 with the SMB from the already existing Muntjewerf simulation? If yes, is it the novel forcing method that you mention at the beginning of the section. If not, do you mean you’ve been running the same configuration as Muntjewerf et al. and used snapshots of it as initial conditions and that the SMB was calculated during your runs?

You also mention later (in the discussion) that CISM2 is not bi-directionnally coupled to CESM2. This is a shortcoming of your study as it makes the comparison with Gregory et al. 2020 a bit more difficult since, as you also say in the discussion, you don’t take into account the effects of a changing ice sheet geometry on the local climate. Please add a sentence after line 120 mentioning the absence of coupling the other way, that it doesn’t take into account the effect of the ice sheet on the climate and a justification of why you’re doing it that way. I suppose that the only reason, which is entirely justifiable, is that the computing ressources that would be needed to do that would be almost astronomical.

Results

Line 145-147: can you add the equilibrium pre-industrial value in the text to make it easier to compare? Like you did at the beginning of the discussion section.

Line 160: ‟timescales for ice loss increase sharply…” Do you mean the timescale needed to reach the final volume/equilibrium?

Discussion

Line 215: what type of applied corrections do you mean?  I thought you meant that the Lofverstrom simulation was not coupled but line 218 tells me this is not the case.

Line 246: please add that the model used in Gregory et al. is bi-directionally coupled here since you mention that the version of CESM/CISM you are using is not in the next sentence → ‟used an ISM bi-directionnally coupled to”

3/ Figures and tables

Figure 1: This is the most important figure of the paper but it’s a bit cluttered, which makes it a bit difficult to interpret. A few suggestions to improve the readability:

• Increase the space between the 2 subfigures to separate them more clearly
• Increase the width of both of them a bit if also possible
• Remove ‟run” in figure 1a legend
• Use a slightly less thick font for axis labels

Table 1: please move the units with the column titles so that the focus can be on the numbers only

Figures A1 and A2: can you make the axis titles and labels as big as in the other figures?

Figure A2 caption: close bracket before ‟. On the left”

Figure 2A caption: 40 kyrs instead of 40 000 years to be consistent with the rest of the paper.

Figures A5 and A6 are not referenced in the text.

4/ Typos, grammatical mistakes and punctuation

I am not a native speaker so please double check my typos/grammar corrections. I tried to avoid adding punctuation as this can be a personal preference but I still included a few suggestions that, I think, improve readability.

First author affiliation: is there a space missing in Climate&Environment?

Introduction

Line 1: currently storing 

Line 26: commas around ‟as of today”

Line 45: no comma in ‟either explicitly, or parametrized”

Line 49: commas around ‟during the last interglacial period (LIG…)”

Line 51: suggests

lines 55-57: This is a really long sentence. Cutting it after warmer climate and starting a new one with However improves readability

Method

Line 81: model instead of Model

Line 103: -2°C and 0°C instead of K

line107: missing space after 1°

line126: SMBs instead of SMB

line127: ‟results from a compromise” instead of ‟results as a compromise”

Results

Line 139: exhibits

Line 140: misplaced space in ‟Table1, the”

Line 163: ‟longest” instead of ‟highest”

Line 174: comma after ‟consequently” (or no comma before)

Line 175: missing video reference (xxx)

Line 177: Fig. 2 - missing space

Line 180: ‟from 3 to 12%” instead of ‟between 3% and 12%”

Line 183: oscillations

Line 197: acts

Line 200: permanently loses

Line 205: ‟in around 15kyrs or less” or ‟around 15kyrs or sooner”

Discussion

Line 218: comma before ‟as a consequence”

Line 218: no comma after ‟SMB”

lines 249-250: commas around ‟which … feadback” + lead or leads (increase in precipitation leads to or these processes lead to)?

Line 258: ‟agrees well with Zetz et al., 2022 and Plach et al., 2019”

Line 262: also limited

Line 286: promotes

Line 286: which in turn yields

Line 290: has also been

Line 297: includes