General comments

It is of great importance to understand the risks of tipping of the Atlantic Meridional Overturning Circulation (AMOC). This is often done using climate models, however, these are known to have biases, in particular, freshwater biases in the Indian and the Atlantic Ocean, which might affect the model evaluations of AMOC stability. It is therefore of great interest to quantify how such biases might affect model outputs. This is the goal of the paper. The paper conducts larger simulation studies of CLIMBER-X, an Earth System Model of intermediate complexity to study the effect of biases in surface freshwater flux on AMOC tipping behavior. Several scenarios of biases are introduced in the Indian and Atlantic Ocean, as well as the reference level with no bias. Then they perform hysteresis experiments on all scenarios, where the surface freshwater forcing is slowly ramped up in the North Atlantic until the AMOC collapses; subsequently, the forcing is reversed until the AMOC recovers again. 

The paper shows that the AMOC stability is hugely affected by freshwater biases. This is an important result, and underpins the importance of being careful when drawing quantitative conclusions from climate models regarding tipping elements, in particular the AMOC.

 The paper is very well written, the methods well chosen and executed and statements, conclusions, methods and goals clearly detailed. Figures are of high quality.

Congratulations with a really nice work.

Technical corrections

It is confusing with the notation REF for the reference model. It looks like there is an error with a reference. This is not important, just a suggestion to change the notation.

The authors have undertaken a focussed study of AMOC hysteresis for a plausible (CMIP-informed) range of biases in surface freshwater forcing over the Indian and Atlantic oceans. Using an Earth System Model of Intermediate Complexity, CLIMBER-X, a substantial impact on AMOC stability is evident, a result that should be of interest to those engaged in a wide range of AMOC monitoring, modelling and related research.

Following the pioneering study of Stommel (1961), the interplay of freshwater forcing and transport was highlighted more recently by Rahmstorf (1996), which along with emerging paleo evidence (Broecker 2010, and references therein) attracted wider interest to the issue of AMOC stability. This sub-field has since developed incrementally over the last 30 years, and this manuscript is a useful contribution to our understanding of model dependence of AMOC hysteresis.

It appears from Fig. 1a that the ‘REF’ configuration of CLIMBER-X has a bistable AMOC, in that there are two stable states (on and off) at Freshwater Forcing = 0 Sv. This is noteworthy, as are monotable or bistable AMOCs evident in subsequent 18 hysteresis experiments. This aspect of AMOC stability is central to the issue of hysteresis, S₁, S₂ and H, worthy of comment in results and discussion.

The authors are appropriately cautious in discussion, not least due to the limitations of CLIMBER-X, which likely lacks key feedbacks. In particular, the imposed freshwater fluxes (over Atlantic and Indian oceans) are held fixed throughout the experiments. This is highly artificial, as one might expect teleconnected changes to E-P across the global ocean, as part of the coupled response to a collapsing (or recovering) AMOC. Also implicit in this study is the longstanding assumption that the AMOC is buoyancy forced from the north, while others have long argued that the AMOC is mechanically forced from the south (reviewed by Kuhlbrodt et al. 2007). Given the here-acknowledged importance of changes in the SA, and the NA-SA density difference, are feedbacks involving the Southern Ocean - specifically wind-driven and eddy-mediated dense water upwelling - worthy of note?

The manuscript is succinctly written, with well-crafted figures that convey a rich level of information. I close with the following specific comments:

1. Introduction: References to the earlier/earliest studies of AMOC hysteresis and stability (see above) would be appropriate, in the opening part of the Introduction
2. Sect. 2.2: In the hysteresis experiment, freshwater forcing in the Atlantic, in the zone 20-50N, is increased/decreased at 0.05 Sv/yr; later in the discussion, this is briefly justified and discussed, but it would be appropriate to justify in Sect. 2.2, also the zone (notably south of convection sites).
3. Sect. 2.2 / Fig. 2: Where is Fig. 2 referenced in the main text? This would naturally be at lines 111-115
4. Sect. 3.3, lines 221-222: Analysis of density compensation of changes in salinity and temperature in the IA experiments needs some elaboration; I inferred that the Atlantic bias primarily affects the NA while the Indian bias affects SA, in opposite senses – is this correct?
5. Summary and discussion, lines 251-252: Regarding ‘other processes, e.g., atmospheric feedbacks’, there is scope to expand on this to discuss the effects of changing atmospheric heat and moisture transports, wind stress curl (NA subpolar gyre) and Ekman dynamics (Southern Ocean), on the AMOC (collapsing or recovering).

References

Broecker, W.S., 2010. The Great Ocean Conveyor: Discovering the Trigger for Abrupt Climate Change. Princeton University Press, ISBN: 978-0-691-14354-5.

Kuhlbrodt, T., Griesel, A., Montoya, M., Levermann, A., Hofmann, M., Rahmstorf, S., 2007. On the driving processes of the Atlantic meridional overturning circulation. Rev. Geophys. 45. https://doi.org/10.1029/2004RG000166, RG2001.

Rahmstorf, S., 1996. On the freshwater forcing and transport of the Atlantic thermohaline circulation. Clim. Dyn. 12, 799–811. https://doi.org/10.1007/s003820050144.

Stommel, H., 1961. Thermohaline convection with two stable regimes of flow. Tellus 13, 224–230.