Boot et al. study the “multiple equilibria window” (MEW) of the Atlantic Meridional Overturning Circulation (AMOC) in a coupled ocean-carbon cycle box model. Specifically, they study the interactions between the AMOC and the carbon cycle, and show, among other things, that:

1. AMOC off states have lower atmospheric pCO2

2. the MEW widens when more carbon is added to the system.

I think that this is an exciting paper. The model seems reasonable (and indeed is based on multiple previous studies) and the methodological approach is sound. The AMOC and its nonlinear behaviour are subjects of great relevance, both with respect to present or future tipping risk as well as for understanding paleoclimate dynamics, and the paper derives some interesting new insights. I always appreciate seeing dynamical systems approaches (and indeed, AUTO) used for these purposes. However, I do think that the paper’s key insights are still a little obscured behind the modelling details, and I recommend a few revisions to bring them out more clearly.

Specific comments:

First, it’s challenging on an initial read to keep track of all of the cases and what they mean. This is challenging to get around without major rewrites (which I do not think are needed), but I think at minimum Table 1 could be made more helpful by describing clearly what all the lambda values represent. This could be done either within the table itself, or perhaps more productively in the caption.

Next, Figure 1: I think it’s worth mentioning explicitly in the caption that the strength of the AMOC downwelling is set by the meridional density gradient between ts and n. Understanding exactly how AMOC strength is set in the model will help readers later on when mechanisms are explained.

Figure 3: I found this quite confusing at first read, not least because of the overlap between many of the curves. If the key point of this figure is to show the general shape of the AMOC bifurcation diagram as well as to illustrate that off states have lower pCO2, perhaps it might be worth showing only this: i.e. AMOC vs E_a and pCO₂ vs E_a for one single case (and moving the other cases to the Appendix). This is not essential, but I offer it as a suggestion.

Figure 4: my first comment is that this is really big compared to other figures that strike me as equally important, e.g. 5a. Second, it seems like what really matters are not the blue and orange lines themselves but the spaces they demarcate – why not label them accordingly? e.g. the region between the lines is precisely the MEW, the region above the blue line is one where only the off state is stable, and the region below the orange line is that where only the on-state is stable. Third, why not include CO2 levels as a second x-axis at the top of the graph which maps nonlinearly onto E_s? I think these changes would make the figure vastly easier to understand at first glance.

Figure 5: My main comment here is that this could be much larger. For example, it seems like 5a shows a major result of the paper, but it’s small and hard to read. Maybe a and b could be on the top row and c in the middle on the bottom row? Also, it’s worth mentioning in the caption the result from Caves et al. (2016) that total carbon content has varied between 24,000 and 96,000 Pg C, to make the reader understand immediately that the changes explored in the figure are reasonable.

Figure 6. I guess this is probably a Latex quirk, but it’s strange to me that it’s placed after the Appendix and all of the references – this makes it easy to miss at first glance. It would be good to place it much more prominently near the end of the text. Finally, I suggest replacing dTC/dt with d[DIC]/dt (if indeed that’s what’s meant).

More minor comments:

Line 20: It may be worth mentioning studies reporting a present-day AMOC weakening, e.g. Caesar et al. (2018), Boers (2021), Ditlevsen and Ditlevsen (2023)

Lines 37-38: I’m not directly familiar with the studies by Barker et al., but at a glance it seems like these are primarily observational (i.e. not model-based). It may be worth mentioning this, as it highlights the novelty of the authors’ work.

Line 38: “of how”?

Line 54: “eddy-induced” (consistent with wind-induced)

Line 87: “to form the model used...”

Line 97: I suggest always using “riverine flux” instead of “river flux” for clarity; “river flux” is repeated a number of times throughout the paper.

Line 106/Eq. (1): It seems like there is a sum over all j missing here?

Line 128/Eq. (4): do you have some more justification for this? e.g. the 0.81 power law?

Line 151: Eq. (6): The linear dependence on atmospheric CO2 here (e.g. as opposed to other powers) is a fairly strong assumption that should probably be discussed.

Line 189: (Andersson et al. 2017)

Line 233: I think the usage of “saddle nodes” is confusing, and recommend that every instance of this be replaced with “saddle-node bifurcations”.

Figure 4: which case are these results from?

Line 325: and rate-induced tipping, see e.g. Alkhayuon et al. (2019), Lohmann and Ditlevsen (2021)

Line 345: space after (Eq. A2)

Table B1 caption: “based on Cimatoribus et al. (2014)”. similar in B2-B4.

References:

Alkhayuon, H., Ashwin, P., Jackson, L. C., Quinn, C., & Wood, R. A. (2019). Basin bifurcations, oscillatory instability and rate-induced thresholds for Atlantic meridional overturning circulation in a global oceanic box model. Proceedings of the Royal Society A, 475(2225), 20190051.

Boers, N. (2021). Observation-based early-warning signals for a collapse of the Atlantic Meridional Overturning Circulation. Nature Climate Change, 11(8), 680-688.

Caesar, L., Rahmstorf, S., Robinson, A., Feulner, G., & Saba, V. (2018). Observed fingerprint of a weakening Atlantic Ocean overturning circulation. Nature, 556(7700), 191-196.

Ditlevsen, P., & Ditlevsen, S. (2023). Warning of a forthcoming collapse of the Atlantic meridional overturning circulation. Nature Communications, 14(1), 1-12.

Lohmann, J., & Ditlevsen, P. D. (2021). Risk of tipping the overturning circulation due to increasing rates of ice melt. Proceedings of the National Academy of Sciences, 118(9), e2017989118.

In this manuscript, Boot and co-authors couple a physical box model of the AMOC to a carbon cycle box model. This tackles an interesting and largely unanswered question of how the carbon cycle and the AMOC influence each other, with a particular focus on whether and how the carbon cycle may impact the stability of the AMOC. The paper is overall well written. It builds on previous work such that the two box models are well established in their own right. I have two (related) main concerns and in the current form of the manuscript I was not able to tell whether these concerns are indeed pointing to fundamental issues with the approach and results, or whether it is rather an issue of presentation. 

1) Is the coupling of the 2 full models needed to answer what I interpret as the central question: how does the MEW depend on atmospheric CO2 concentrations? This is related to another fundamental aspect I am concerned with: The very purpose of idealized box models is to reduce the complexity of a system to a small number of leading-order processes which can then be probed in detail to gain intuitive understanding. The model developed here with ~30 ODEs is so complex that I wonder whether much intuitive understanding can be gained? Furthermore, from the figures presented it appears that many of the processes included have no or barely any notable impact on the processes that are being studied (see the overlapping curves in Fig 3 and the many almost identical lines in Figure 5). From my reading of Figure 4 a key process driving changes in MEW is the increase of Es with increased CO2? In that case, why not, for example, take the physical AMOC model and force it with Es (as constrained by the CMIP6-derived CO2) and consider the resulting changes in the MEW? Although I wonder whether this would be rather similar to the original work of Cimatoribus et al (2014)?

2) Is the combined model suitable to probe the size of the MEW? In my reading of the results, the size of the MEW (the distance between the dot-dashed and dashed lines in Fig 3) is barely impacted at all by accounting for different processes - even when the CO2 concentrations (right column of Fig 3) change quite notably. Similarly, the MEW size in Fig 5 is either completely or mostly insensitive to changes in the processes that are accounted for and also to total carbon content. I find this quite remarkable, since this is a very complex non-linear model and the authors consider a wide range of feedbacks and forcings etc, yet the MEW is largely constant. Again, as far as I can tell the main sensitivity is to Es (or atmospheric CO2) in Fig 4. This makes me wonder whether the title of the study should rather be something along the lines of "Robustness of AMOC MEW to changes in marine carbon cycle"?

These comments are intended to highlight the questions that arose for me when I read the manuscript, and as I said above much of my skepticism may be the result of a lack of clarity of presentation. The other reviewer had some constructive ideas of how the presentation could be improved and that may alleviate some of my concerns above as well. I will further add that I have little expertise in the carbon cycle aspect of this work, which certainly hindered my interpretation. Nevertheless, I believe that a substantial reduction in the complexity of the model and the range of feedbacks and other processes may be required to be able to meaningfully shed light on the governing processes. As it stands, I found it difficult to assess the value of both the approach and the results. 

As a final comment, I was noting the absence of any model validation or comparison to previous formulations. At one point the authors state that they had to add two boxes to ensure realistic CO2 values. The original version apparently had very low CO2 under AMOC collapse, and the authors state that most previous modeling studies found increases in CO2 under AMOC collapse. However, the results in Fig 3 still show substantial reductions in CO2 when going from the AMOC "on" to the "off" state. In my reading this prompts open questions as to how this work compares to previous studies. To instill confidence in this novel coupled model, I would argue that some form of validation is needed.