It is important and interesting to conduct a set of well-designed 1000-year-long abrupt stabilization simulations to understand the final-state response of global climate to various stabilized external forcing levels. In this study, the EC-Earth3 model estimates a range of 1.4 K to 9.6 K global mean surface temperature (GMST) increase relative to preindustrial level if the external forcing is suddenly stabilized at specific levels in historical (1990) and SSP5-8.5 (2100). The evolution of the pattern of surface warming, and precipitation change in the long simulations clearly reveal the effect of the deep ocean heat storage and its feedback to global and regional surface climate at a long time scale. The results are well presented and advance our understanding of the equilibrium response of global climate to different levels of anthropogenic forcing. Some concerns are the interpretation of the underlying mechanism for deep ocean warming and its non-linear response to different magnitudes of external forcing.

Minor comments:

(1) Lines 5-7, 141-142: The author may need to compare the climate sensitivity of EC-Earth3 with other CMIP6 models when estimating the GMST response and associated Paris Agreement target.

(2) Lines 38-39, the upper ocean fast warming and the slow but persistent deep ocean warming are well noted in the results from the experimental and diagnostical approach of Held et al. (2010) and Long et al. (2014). The deep ocean feedback on the surface warming pattern and precipitation change is also discussed in Zappa (2020), King et al. (2020), Kim et al. (2022), etc.

(3) Figure 7: the shift of the precipitation trend (dry to wet; wet to dry) is mainly distributed at the boundary of the regions with negative and positive precipitation trends, which may not be significant. The role of internal variability can be large during stabilization simulation, especially for precipitation change. The author may pay attention to these issues and related conclusions. However, it is worthy to discuss the precipitation pattern with significant trends during the stabilized period following the mechanisms proposed by Chadwick et al. (2013a, b).

(4)  Lines 260-262: This fact can actually be explained by the fast upper ocean and slow deep ocean response to increasing external forcing. As long as the GHG forcing is gradually increased in SSP5-8.5, the upper ocean warms much faster than the deep ocean and would accumulate more heat in the upper ocean, leaving a relatively small fraction of deep ocean heat storage.

(5)  Lines 320-328, 348-352: The deep ocean warming in the Indo-Pacific Ocean is also a result of the heaving effect of the inter-basin water redistribution due to AMOC weakening, which is evident maximizes at 300-3000m layer (Sun et al. 2022). The underlying mechanisms of deep ocean warming may differ substantially between the Indo-Pacific and Atlantic Oceans. It is necessary to show the response of Indo-Pacific and Atlantic Ocean temperature and meridional overturning circulation, respectively, in Figs. 9 and 11. The dynamical effect of the ocean circulation change and non-linear recovery of AMOC may also be important in explaining global deep ocean temperature change and hence OHC change under different levels of stabilized external forcing.

Refs:

Chadwick, R., I. Boutle, and G. Martin, 2013a: Spatial patterns of precipitation change in CMIP5: Why the rich do not get richer in the tropics. J. Climate, 26, 3803–3822.

Chadwick, R., P. L. Wu, P. Good, and T. Andrews, 2013b: Asymmetries in tropical rainfall and circulation patterns in idealised CO2 removal experiments. Climate Dyn., 40, 295–316.

Held, I. M. et al. Probing the fast and slow components of global warming by returning abruptly to preindustrial forcing. J. Clim. 23, 2418–2427 (2010).

Long, S.-M., S.-P. Xie, X.-T. Zheng, and Q., Liu, 2014: Fast and slow responses to global warming: Sea surface temperature and precipitation patterns. J. Climate, 27, 285–299.

Kim, SK., Shin, J., An, SI. et al. Widespread irreversible changes in surface temperature and precipitation in response to CO2 forcing. Nat. Clim. Chang. 12, 834–840 (2022). https://doi.org/10.1038/s41558-022-01452-z

King, A.D., Lane, T.P., Henley, B.J. et al. Global and regional impacts differ between transient and equilibrium warmer worlds. Nat. Clim. Chang. 10, 42–47 (2020). https://doi.org/10.1038/s41558-019-0658-7

Sun, S., Thompson, A. F., Xie, S. P., & Long, S. M. (2022). Indo-Pacific warming induced by a weakening of the Atlantic meridional overturning circulation. Journal of Climate, 35(2), 815-832.

Review of “Multi-centennial evolution of the climate response and deep ocean heat uptake in a set of abrupt stabilization scenarios with EC-Earth3” by Federico Fabiano and co-authors

The paper surveys the response of one model to a range of stabilization scenarios sampling many forcing levels of CO2. The authors discuss the response of surface warming patterns, precipitation, sea ice and deep ocean heat storage in the different scenarios. The text is well written, easy to follow, and the figures are clear and convey the points the authors make in the text.

My big issue with this paper is that there is no hypothesis, one single very general and in a sense irrelevant question (which is not answered beyond what is known about it already), no increased understanding of a concrete physical process, and a poor embedment in the literature for some of the metrics’ surveyed. It is merely *reported* or “explored” how one model responses to a range of forcing scenarios. “What happens in this model?” is not a scientific question.

The subject itself is interesting, not too well studied and does actually have open scientific questions. Hence, instead of merely surveying all sorts of “measures”, I suggest the authors develop 1-3 specific questions and hypotheses (from the current understanding of these timescales presented in the literature). I point out below which questions I think merit attention but these are only suggestions to illustrate where my thinking stems from.

Minor and major comments are mixed below.

Line 9 “the most striking feature being a drastic acceleration to the warming in the Southern Ocean” – the fact that the Southern Ocean lags warming is decades old and definitively not surprising or worth reporting. See e.g. review in Armour et al. 2016. This paper does not add any new knowledge to the subject.

p.2 “One fundamental question remains unanswered: which will be the equilibrium state of the climate once all of the warming linked to a specific level of forcing is realized? “ – so what is the answer? What do you show which goes beyond Li et al. 2013, Rugenstein et al. 2019, Mitevski et al. 2021? How does this equilibrium state relate to the policy implication the study is motivated with? Why does this state matter? Has the real climate system ever been in that state or is it expected to move there (I don’t think so)? What is “the state of the climate”? Why is are the spatial patterns relevant? How far into the final equilibration are your simulations in the year 3000?

Computational costs are mentioned as the reason for few equilibrated simulations. First of all there are not so few around by now, and second, this argument was true ten years ago, but not anymore today. There are km-scale simulations by now which used order of magnitude more computational resources than argued about there, initial conditions ensembles with tenths of thousands of years, perturbed parameter simulations with several thousand years. Equilibrating simulations might not have the strongest lobby, but it is not correct anymore that the computational resources are not existing. Somewhat related, Li et al. 2013 and Zickfeld et al. 2013 are mentioned but these papers are ten years old and the discussion has moved on. What do modern EMICs say about the issues? Are they even still around? What features of the equilibration or the equilibrium do EMICs and GCMs share and where do they differ and how? What do these differences tell us about the real world? Do we trust GCMs more just because they also have clouds, which we know are extremely parameterized?

Following, the LongRunMIP project is mentioned once but not at all discussed. The project has 14 or so models, some of which have three forcing levels. The literature discusses things like equilibration timescales of the surface warming pattern, the deep ocean, the Atlantic meridional overturning circulation, top of the atmosphere radiative imbalance, polar amplification, ENSO and the temperature dependence of feedbacks. Where do the findings discussed here go beyond that? Other recent effort include Dunne et al. 2020 who gathers simulations longer than 800 years and some models CMIP6 extended their required protocol to well beyond 150 years of step forcings (see e.g. list in Bloch-Johnson et al. 2021). It is argued that most of these simulations are step forcings. However, they find exactly the same things as pointed out here. Until when does the scenario before the stabilization matter? Does it matter at all? For what?

Page 6 line 150, stabilization – more relevant than surface temperature would be the top of the atmosphere energy imbalance or the surface flux imbalance or the accumulated ocean heat content. How can the surface temperature be equilibrated, while the TOA is not (as can be seen in 4 but would be more obvious in a timeseries)? Through which processes do the deep ocean and TOA communicate at these timescales? Is the connection between deep ocean, surface, and top of the atmosphere forcing dependent?

Sea ice/Fig.3 are actually one of the least explored issues in my understanding of the literature. Open research questions could be whether you can predict the forcing level at which sea ice will collapse or stay below a certain threshold? What sets the rate of decay of sea ice – the global warming, local warming? How relevant is the sea ice response to the non-linear behavior of the ocean heat uptake? How unrealistic is this response shown here given the fixed ice sheets? Is this time evolution dependent on the rather large mean-state bias? Sea ice feedback itself is pretty dependent on that (e.g., Kajtar et al. 2021).

An interesting unexplored question around Fig.4 would be what causes radiative feedbacks (the slope of the lines) to be more negative with increasing forcing levels? See Jonah Bloch-Johnson et al. 2021 who finds that most models do the opposite than your model (increasing feedbacks with increase forcing, although this seems to be extremely model dependent) and Mitevski et al. 2021 for this being discussed earlier and pointing out the open questions around feedback temperature and feedback forcing dependence.

Is b100 actually stabilizing at -0.2Wm^-2?, Fig.4 doesn’t look like it?

Page 10 line 200 “This is well known… due to larger thermal inertia…” Mike Byrne has a range of papers showing that this is actually not the correct explanation for the land-ocean contrast. If the thermal inertia argument was true, in the equilibrium ocean and land should have the same warming – which they don’t suggested by Fig.5 and even after 4000 years they are not (LongRunMIP). What processes set the land-ocean heating contrast equilibration? When does the contrast equilibrate?

Section 4 The forcing dependence of the overturning circulation has been discussed a while ago by Rugenstein et al. 2016 (with the same findings as here, except that the Southern Ocean overturning played a larger role) and more recently by Mitevski et al. 2021. These papers discuss the non-linear dependence of the ocean heat uptake to forcing and that warming in the equilibrium is not homogeneously distributed. However, there are open questions around this: How model-dependent is this non-linearity? What sets its dependence? Does is matter for more practical issues like the end-of-the-21^st-century temperatures? Can we learn something about tuning parameters, like diffusivity or vertical mixing, from this behavior? Does the type of forcing matter, i.e. are the response to aerosol and CO2 forcing additive when it comes to ocean heat uptake? Practically, how do we include this effect when estimating climate sensitivity for example from the last glacial maximum or very warm periods in the past?

I don’t ask for all these questions to be answered in a new version of a manuscript. But developing a few questions and according hypotheses well should result in a paper which goes beyond reporting.

Armour et al. 2016 Southern Ocean warming delayed by circumpolar upwelling and equatorward transport

Dunne et al. 2020 Comparison of Equilibrium Climate Sensitivity Estimates From Slab Ocean, 150‐Year, and Longer Simulations

Rugenstein et al 2016 Nonlinearities in patterns of long-term ocean warming

Mitevski et al. 2021 Non-Monotonic Response of the Climate System to Abrupt CO2 Forcing

Bloch-Johnson et al. 2021 Climate Sensitivity Increases Under Higher CO2 Levels Due to Feedback Temperature Dependence

Kajtar et al. 2021 CMIP5 Intermodel Relationships in the Baseline Southern Ocean Climate System and With Future Projections