Review of Willeit and Ganopolski’s “Generalized stability landscape of the Atlantic Meridional Overturning Circulation” by Yvan Romé, University of Leeds  

General comments

The manuscript explores the combined effect of changes in CO2 concentrations and North Atlantic freshwater forcing on the existence of multiple AMOC modes in the fast climate model ClimberX. After plotting the AMOC intensity hysteresis cycles resulting from the two independent parameters and including discussions about the role of the initial AMOC state and the rate of change, Willeit and Ganopolski produced a stability landscape of the AMOC modes in the input space formed by the CO2 concentrations and the freshwater forcing.  

This work offers a new multidimensional approach to understanding AMOC stability in climate models. The stability landscape map is a convincing and comprehensive way to explore the domain of occurrence of AMOC mode shifts. The volume of simulations produced for this article is remarkable, and the experimental design allows advanced conclusions on the effect of AMOC mode shifts on the climate.  

I have, nonetheless, major reservations about the clarity of the manuscript, as well as the justification of some arguments. The manuscript is, at times, difficult to read, and the description of the experiment and the calculations need to be revised to be able to evaluate the validity of the conclusions. 

In summary, this paper is a strong contribution to the highly relevant question of AMOC manuscript in climate models. However, some work is required on the text to support the interpretations and conclusions. I recommend major revisions of the manuscript before publication in ESD. The main concerns I identified are the following. 

• The abstract is not reflective of the work and inconsistent with the conclusion, which is very clear. In particular, the abstract implies that the main aim of the paper is the impact of CO2 concentrations on AMOC stability, instead of, as it is written in the conclusion, performing “a systematic analysis of the AMOC stability in the FWF–CO2 space.”   

• In the introduction, the impact of CO2 on the AMOC stability is said to “remain largely unexplored”, and the freshwater forcing outside of the 20-50°N band to be a rare occurrence. I believe both of these views are outdated, and the introduction is missing key references and discussion points that provide an accurate and comprehensive picture of the current state of the research. If these comments only concerned modern days, it should clearly be stated, and the results from the palaeo community should be discussed. I recommend splitting the second paragraph of the introduction into three parts. A first one on the CO2 effect, including missing references (e.g. Brown and Galbraith 2016, Zhang 2017, Klockmann 2018, Vettoretti 2022), a second one on the FWF including missing references (e.g. Smith and Gregory 2009, Roche 2010, Kageyama 2013, Ivanovic 2018, Romé 2022) and a third one on the need for combined CO2xFWF analysis and an introduction of your paper, which is currently too short.  

• I do not believe that the authors can claim to be the first to attempt to draw a landscape of AMOC stability in the CO2 x freshwater forcing space is true, see Brown and Galbraith 2016 for instance. However, I would say that this paper presents the most comprehensive and robust method up to date. If this claim only applies to modern-day studies of the AMOC, it needs to be clearly stated and put in context with palaeo studies.  

• Significant mode shifts and overshoots on the hysteresis cycles are not discussed in the text. In particular, in Figure 1, the transition in the red solid line around 0.05Sv is remarkable: Is it different from an overshoot? Why is it sustained for about 1000 years? Could this be an occurrence of millennial-scale variability? Could you link this to Willeit 2024?  

• The definition of the different states comes too late in the paper and lacks precision. How do you define the different modes, using the AMOC index, the mixed layer depth or manually? Additionally, How do you calculate the AMOC index? What references did you use for the modern-day deep water formation sites, and how do they compare to your modern mode? Over what time slices was Figure 3 plotted?   

• The interpretation of the freshwater flux needs to be clarified in this article, and it becomes a problem when comparing pre-industrial to modern conditions. Would it not be more accurate to account for changes in CO2 and freshwater forcing when comparing the two? Otherwise, what is the point of using a two-dimensional landscape? In addition, the following statement from the conclusion “Our results indicate a generally stronger and deeper AMOC at equilibrium under warmer climate conditions. This is in contrast to the projected AMOC weakening response to anthropogenic global warming […]” is only valid if one considers the sole CO2 effect, but freshwater forcing is expected to increase with Greenland melt, which could take us into a region of the landscape where all four modes exist. I think the comparison between past, present and future states should include a discussion about the role of excess freshwater induced by ice sheet melting.  

• The details about the construction of the stability landscape is lacking precision and its validity cannot be evaluated. This all the more important as you highlighted the dependence of the direction of variation in Figure 1,2 and B1.  

Specific comments  

Abstract  

• L8 - Can you briefly define the OFF and Modern AMOC states?  

• L11-12 (“In general, the model shows an increase in equilibrium AMOC strength for higher CO2 levels.”) - This does not reflect the actual nature of the work, which goes way beyond this sole aspect. This statement is valid for the standard CO2 experiment in Figure 2, but not consistent with Figure 4 (ex. in Figure 4a, an increase of CO2 can trigger a weak mode). The abstract needs not to focus only on the CO2 experiment but also on the stability landscape. 

Introduction  

• L28 (“There is no consensus as to whether the AMOC is in a monostable or a bistable regime under present climate conditions”) - This needs a reference; I am aware of discussions on the potential weakening of the AMOC, less so about the current state of the AMOC. 

Results  

• L59 (“In particular, there is a range of FWF over which the AMOC has two stable states has two stable states”) – Can you be precise about the range of FWF you are talking about? It also depends on your definition of stability, as I would argue that the dip around 0.05 Sv in Figure 1 is a sign of instability.  

• L61 - Does “preindustrial conditions” mean 0 Sv in this case? Also, according to the methods, this experiment has pre-industrial CO2 concentrations but a modern-day ice sheet. I would be more careful about using “pre-idustrial” conditions, what about "initial state" instead? 

• L63 (“suggesting a prominent role of convective instability”) - Could you show that this is a convective instability, showing deep water formation sites activity, for example?  

• L65 - “This is the result of a collapse of deepwater formation […] of observed past Dansgaard-Oeschger events.” : Here again, the manuscript is missing a plot with the deep water sites dynamics to verify this statement, and a reference about convection in D-O records.  

• L67 – A definition of what the authors mean by Off, Weak, Modern-day, Strong  is needed at this point of the paper.  

• L82 (“which is possibly more relevant for the ongoing global warming”) - I disagree, both CO2 and meltwater discharge are relevant to future climate changes.  

• L85-93 - I find the wording of this section confusing. Is the rate of CO2 increase in this paper slower than the “slow” increase in Gérard and Crucifix? How do you explain that you see a strengthening of the AMOC when Gérard and Crucifix 2024 saw a decrease? Could this simply mean that the AMOC response to CO2 is highly uncertain and model dependent?  

• L105 (“For CO2 above ∼250 ppm, the convection pattern resembles the present-day state with deep water forming in the Labrador Sea and in the Nordic Seas”) - Are you talking about Willeit et al. 2024 or this manuscript?  

• L156 (“If the climate would be in equilibrium with present-day CO2 concentrations of ∼420 ppm, the model suggests that the Modern AMOC state would not be stable, but that the AMOC would rather be in the Strong state instead”) – Back to the point about the interpretation of future freshwater forcing, would the accelerated melt of Greenland not move the system along the Modern AMOC conditions diagonal instead? Otherwise, this is a major caveat of the analysis that needs to be discussed (although, arguably, the last paragraph of the discussion introduces this idea of model dependency).  

• Figure 4 - Good Figure but missing information about the criteria used for the clustering of the AMOC states. Is it purely based on the AMOC index, or on the mixed layer depth?  

• Figure 5 - I think this is the most important Figure of the paper and it deserves to be bigger. Also, why are the Off mode treated differently than the different modes? It makes the Figure difficult to interpret at first reading. Could you use different colours or shading and include all four states in the stability landscape?  

• L181 - This is a good section and a convincing way to perform this analysis. However, as you showed, the sea ice extent is driving the most significant temperature changes, so I think it would be good to conclude on the impact of less extensive Arctic sea ice in future climate on these results.  

Discussion  

• L186 - Can you say a word about the Modern and Off AMOC modes. 

SI  

• L256 - The paths used in Figure A1 need to be clearly explained in the Figure or the text, otherwise it is impossible to validate the protocol in Figure 4. Do they correspond to the black or the green arrows? Do they include the standard experiments?   

• Figure B2 does not have a caption.  

Technical corrections 

Introduction  

• L17 - Do you have an example of a “societal” change?  

• L19 - Add Bellomo 2021 for state-of-the-art climate model references. 

Results  

• L51 – “Willeit et al. (2020)” to “(Willeit et al., 2020)  

• L69 (“most AMOC hysteresis experiments to date have been performed with FWF at lower latitudes (usually between 20N and 50N)”) – Needs references.  

• L71 (“In our hysteresis experiment”) – Change to “In Figure 1”, there are multiple hysteresis experiments in this paper.  

• L80 (“give the wrong impression that the AMOC Off state is also stable”) – Is it a wrong impression or relative to the rate of meltwater discharge? Can you give an order of magnitude of the expected meltwater discharge for future melting or during a D-O event/Heinrich event?  

• L83 – “In an experiment where” to “In Figure 2”?  

• L94 (“two discrete transition”) - what do you mean by discrete? Abrupt?  

• Figure 2 - It is difficult to distinguish the solid and dotted lines on this Figure. Maybe two columns?  

• L110 (“but this has been shown to not be a requirement for the existence of millennial-scale variability”) – Vague, can you say more?  

• Figure 3 - The Figure needs to be bigger. Please add labels to the colour-bars. Does seasonal mean winter in this case?  

• L130 - “net freshwater flux” to “net surface freshwater flux”.  

• L133 (“for CO2 doubling”) – I would say “for double the amount of CO2” because you are not doing a CO2 doubling experiment, which, as you highlighted, could have a different impact on the AMOC.  

• L139 - “in the model the net surface freshwater flux into the whole Atlantic Ocean shows the opposite trend” to “the net surface freshwater flux into the whole Atlantic Ocean shows the opposite trend in our model”?  

• L144 - remove “a stabilizing effect”?  

• L150 - “can be investigating by tracing their stability through” to “can be investigated by tracing the AMOC response in”  

• L169 - “to explore the pure effect of the different AMOC states on climate” to “to isolate the effect of the changes of AMOC states on the climate”.  

• Figure 6: Can you use a different colour scheme for the temperature?  

Discussion  

• L193 - “explains” to “demonstrates”?  

• L202 (“anthropogenic global warming”) - Add Bellomo 2021 to the references for state-of-the-art climate models. 

SI  

• Figure B1: Hard to distinguish the solid and dotted lines on this Figure. Maybe two columns?