Talento et al. use the climate model of intermediate complexity CLIMBER-X to investigate the critical insolation/CO2 threshold to trigger large scale glacial inceptions. This works mostly follow the idea of Ganopolski et al. (2016) but using a new climate model. It contains also new material with respect to this previous paper, such as an interesting discussion on the role of the AMOC in shaping the ice sheet inceptions.

Overall I enjoy reading the paper. It is nicely written and contain all the relevant information to fully understand the model behaviour. To my opinion it deserves publication in Climate of the Past. I only have a few comments, mostly related to the role of the AMOC, that the authors could consider if they think they are useful.

General comments 

- From l. 175 to 237, the authors selected three combinations that cover the spectrum in terms of insolation / CO2 to achieve inceptions and they discuss the temporal and spatial evolutions of the ice sheets. What we mostly see is that the AMOC is very different for these three simulations. Although I appreciate this section, I found it hard to compare directly these simulations because of the differences in terms of AMOC. I have the feeling that we are not really looking at the impact of insolation/CO2 on ice sheet evolution here but instead we are looking at the impact of inso/CO2 on the AMOC (and ultimately yes, the ice sheet evolution). Perhaps what could have been done is alternative experiments using larger freshwater flux than the ones in Sec. 3.2, in order to have a shutdown state for these three simulations. In doing so, we would have quantified the impact of insolation/CO2 disregarding the state of the AMOC.

- Sensitivity of the AMOC to CO2. The simulations presented here show a general weaker AMOC for lower CO2. The authors suggest that it was also the case in CLIMBER-2 and that some GCMs also display this feature. However, in fact, the majority of GCMs show the opposite: higher CO2 levels are associated with weaker AMOC (e.g. Swingedow et al., 2007; Ma et al. 2021; Fortin et al., 2023), due to several processes (high latitude water cycle intensification, energy dissipation by eddies, etc.). Since the results presented here show a very strong dependence of glacial inception to the AMOC state, I think that a more thorough discussion on how robust are the changes in AMOC can be considered in models (not specifically yours). You might have ideas why lower CO2 leads to weaker AMOC?

Specific comments

- l. 53. By construction, in the radiative scheme of CLIMBER-X there is a logarithm structure with respect to CO2, right? So there is no surprise here.

- l. 64. “(iv)”: be more specific please.

- l. 72. CLIMBER-X is really expected to reproduce the observed decadal variability? This is quite surprising given the model assumptions I guess.

- l. 74. What is the vertical resolution of the oceanic model?

- l. 78. Is there any reference for SEMIX? I know that it has been used before but it could be useful to have a reference here.

- l. 84-85. Reference?

- l. 87. It would have been nice to have a map of the major biases (temperature / precip at least) or a reference here.

- l. 96-97. How do you conserve the water budget while using an acceleration factor? How do you compute your freshwater flux? This is important since it will impact the AMOC in all your simulations.

- l. 98-101. Do you need such a large acceleration factor since CLIMBER-X can perform 10 kyr a day right? Maybe it could have been nice to present a few additional experiments with no acceleration since it can affect your inception threshold.

- l. 101. Why not using a properly spun-up ice sheet instead of using an ad-hoc vertical structure?

- Figure 1. It could have been useful to have indications for the different marine isotope stages in this graph (MIS 5,7,9 and 11).

- l. 156-158. You should perhaps temper this result since CLIMBER-X and CLIMBER-2 are not completely independent. In particular, they share a quite similar atmospheric model (although at a different spatial resolution).

- l. 261-269. Do these experiments display the same AMOC states as when using interactive ice sheets?

- l. 292-293. What about the role of shortwave radiation? The high CO2 simulation have a larger surface temperature, higher precipitation but also smaller shortwave radiation. I am a bit surprised to read here that the positive SMB is explained by larger precipitation rate. In my experience the extent of the accumulation area is primarily driven by temperature/shortwave (i.e. melt).

- l. 336-338. Is this difference explained by AMOC differences, here again?

- l. 410. Not necessarily, e.g. Harder et al. (2017).

- l. 426. It is quite variable geographically and depends on continentality, seasonality of precipitation etc.

- l. 431. I guess it comes from the temporal integral between the beginning and the end of the melt season? Why these are different for insolation and temperature then, if in both case the integral is over two month around the peak value?

Reference

Fortin, A. S., Dufour, C. O., Merlis, T. M., & Msadek, R. Geostrophic and Mesoscale Eddy Contributions to the Atlantic Meridional Overturning Circulation Decline Under CO 2 Increase in the GFDL CM2-O Model Suite. Journal of Climate, 1-42 (2023).

Harder, P., Pomeroy, J. W., & Helgason, W. Local-scale advection of sensible and latent heat during snowmelt. Geophysical Research Letters, 44, 9769–9777 (2017).

Ma, X., Liu, W., Burls, N.J. et al. Evolving AMOC multidecadal variability under different CO2 forcings. Clim Dyn 57, 593–610 (2021).

Swingedouw, D., Braconnot, P., Delecluse, P. et al. Quantifying the AMOC feedbacks during a 2×CO2 stabilization experiment with land-ice melting. Clim Dyn 29, 521–534 (2007).

The manuscript « New estimation of critical insolation-CO₂ relationship for triggering glacial inception » by Talento et al. presents a very interesting discussion on the main forcing involved in glacial inceptions. The paper is well written and the scientific content well organized. I have a few comments below that the authors might use to improve their manuscript. Overall, this paper clearly deserves being published in Climate of the Past.

Main comments.

1 - This study is presented as a theoretical work aimed at better understanding the relative role of insolation and CO2 in the triggering of glacial inception, with the objective to better predict “future glaciations and the effect that anthropogenic CO₂ emissions might have on them”. This paper is indeed fully relevant in this respect. It complements a previous study (Ganopolski et al. 2016) made with a simpler model. But in contrast to this previous paper based on CLIMBER-2, CLIMBER-X appears to be a rather new model. In particular, it is not clear how well it can simulate the actual glacial inceptions observed during the Quaternary. The authors are citing a preprint (Willeit et al. 2023b) concerning the last glacial inception, but it is difficult to evaluate how well this new model configuration behaves on the other inceptions. I would appreciate some discussions or comments on this point, for instance by building on improvements made versus CLIMBER-2, or by discussing a bit more the simulations corresponding to the actual last 4 inceptions, among the 19 simulations performed. It would strengthen the paper to put these results against observations, even if they are not fully comparable.

2 - It is not discussed if climate sensitivity is different, or very similar, in CLIMBER-X versus CLIMBER-2 (I suspect the latter), if the radiative code is identical or not. Such information would be critical to assess such statements as (line 155): “values for alpha and beta might not be strongly model-dependent”. This would likely not hold with very different climate sensitivity to CO₂ forcing. A few lines of information on CLIMBER-X in this respect would be useful.

3a - Line 89-90: biais correction on temperature. It is all right to use such a procedure, but it would be necessary to have some discussion on possible impacts on the final results. The hidden assumption is that the biaises should remain constant, whatever the climate and the ice-sheet evolution. Is it realistic?

3b - There is no mention of “biais correction” on precipitation. I read through Willeit et al. (2023b) Appendix B but found no information on this point. I had a look at Willeit et al. (2022) but could not really evaluate precipitations at high latitude. Are precipitations from SESAM good enough?

These two points may be critical for instance in the discussion of Hsmx65_LCO2_Fixice (cold) versus Lsmx65_HCO2_Fixice (snowy).

Minor comments.

4 - (line 96): “sea level (which affects land-sea mask)”. I guess this concerns the atmospheric model, but not the ocean model (bathymetry)? Or does the ocean have a bathymetry which adapt to ice-sheet induced changes ?

5 - (line 170, legend Fig 2) CLIMEBR -> CLIMBER

6 - (line 241) understating -> understanding