Review of egusphere-2023-2661

This study investigates the role of (1) GIS and WAIS meltwater forcing rate, (2) stochastic noise on meltwater forcing, on AMOC collapse using a 5-box conceptual AMOC model. The paper is technically sound and confirms the idea that the WAIS has a stabilizing effect on the AMOC (proposed by previous studies) even under the influence of forcing rate and noise.  

The paper is worthy of publication in ESD, however additional analysis/revisions are needed. Please see the comments below.  

Additional analysis with realistic meltwater flux forcing: I propose an additional analysis/discussion on the AMOC collapse at the realistic range of forcing parameters (Eq (1) and Eq (2)). First, please provide a realistic range of the forcing parameters in the context of a palaeoclimate event (e.g., MWP-1A) or future climate change (e.g., CMIP6 SSP5-8.5 scenario). Then, discuss the AMOC collapse behavior at this realistic range of meltwater flux. If this specific past/future event is not applicable to the forcing scenario used in this paper (which assumes full melting of GIS and WAIS), I suggest performing an additional experiment. This would provide practical insights into the AMOC collapse in the past/future. Also, it would shore up a weakness of the paper (the weakness of using a highly idealized model with conceptual forcing).

Line 80: The authors consider the time delay between FN (representative of GIS collapse) and FS (representative of WIS collapse) forcing as a key parameter of the AMOC experiment. What is the physical motivation for setting a time delay between them? What is a realistic range of time delay in the context of palaeoclimate and future climate change?

Section 3: Please show the figure that shows together the case of WAIS included and the non-included case for the AMOC collapse (time series would be good). The WAIS-induced stabilization effect is an important key message of this paper, so the direct comparison of these two cases will improve the presentation of the paper (the current version of the figure set is not friendly to readers who are not familiar with the low-order AMOC modeling and dynamical systems theory).

Limation of the conceptual model: The 5-box AMOC model used in this study does not consider the AMOC impact on the WAIS melt. The model considers only a one-way influence from the WAIS melt to the AMOC. However, as the authors explained in the introduction, the collapse of AMOC would increase the Southern Hemisphere temperature and accelerate the WAIS melt, while decreasing the Northern Hemisphere temperature and decelerating the GIS melt. The discussion of this missing physics (which may be very important) should be explained in the paper (probably in Section 6).

L203: Which numerical scheme for stochastic differential equations is used to solve the weak noise case?

Abstract: The key results of the paper are summarized too much in the abstract, and do not give an immediate answer to the question likely to arise from the title (so, what is the role of the forcing rate and noise?). Please revise it.

This study discusses the AMOC stability under meltwater forcing from both Greenland and West Antarctica. The paper is interesting and sound if we accept the conceptual representation of AMOC. However, I struggled when trying to put these discussions in the context of real ocean. It may help the readers by including more comparison with the real world in the revised manuscript. 

In particular, I wonder whether the AMOC sensitivity to WAIS meltwater has been exaggerated too much in this toy model. In a recent paper (https://doi.org/10.1175/JCLI-D-22-0433.1), which uses a more realistic model to examine the overturning responses to meltwater fluxes, they found that the AMOC is rather insensitive to Antarctic meltwater at least on timescales of ~150 years. I think the "overestimated" sensitivity of the AMOC to WAIS meltwater in this toy model is because they parameterize the AMOC strength using density differences between the North Atlantic (n) and Southern Ocean (ts), rather than the density differences between the North Atlantic and the mid-latitude box (t) -- the latter appears more plausible by physics (e.g., https://journals.ametsoc.org/view/journals/phoc/42/10/jpo-d-11-0189.1.xml). Processes in the Southern Ocean could affect the subsurface stratification in the low-mid latitudes, but this connection likely occurs on millennial timescales. 

I also have a few questions regarding the configuration of the AMOC model.

1. Why including the box "ts"? If I read it correctly, the overturning between ts and t is the same as the overturning between s and ts or d and s. 

2. It should be clarified that the meltwater flux is applied as virtual salt flux not as freshwater flux, which won't influence the salinity content in box "t".

3. How is temperature evolved in each box? As the authors mentioned in their introduction, a perturbation to the overturning circulation also modifies the ocean's thermal structure, which necessarily will feedback to the system and may affect the AMOC stability.