The paper examines statistical indicators for Dansgaard-Oeschger (DO) events in the Greenland ice core records and argues that these indicators can serve as signals for a potential weakening of the Atlantic Meridional Overturning Circulation (AMOC). I believe this is an excellent study that contributes significantly to our understanding of the tipping behaviour of the AMOC and is very well presented. While I think the paper can be published as it is, I suggest a few minor points that could improve the presentation of the results:

1.  The authors have used Dansgaard-Oeschger (DO) events as indicators of tipping in the AMOC. They briefly mention this in the abstract (line 5) and later provide some references in the introduction (lines 48-51). However, if the main message of the paper is to propose "robust precursor signals for a possible future AMOC collapse," I think further discussion is required to establish a clear connection between DO events and the transition from a strong to a weak AMOC. I think the paper could benefit from a new section that addresses this point. 
2. It is well established that changes in variance and autocorrelations are good indicators of critical slowing down (occurring during codimension one bifurcations). However, does this approach work as effectively for more complex tipping mechanisms, such as excitability (suggested in section 4 as a possible mechanism)?
3. I would like to draw attention to the rate-induced mechanism, where an excessively rapid change in forcing can tip the system even before reaching the bifurcation point. This mechanism could arise from mechanism 3 (the Hopf bifurcation), where the system can cross the unstable limit cycle (regular threshold) and tip. It could also be relevant to mechanism 4, where the rate of forcing might push the system to cross an irregular threshold in the form of a maximal canard. Please see (Wieczorek et al. 2023) and (O'Sullivan et al. 2023), for more details:
   
   
   
   Wieczorek, Sebastian, Chun Xie, and Peter Ashwin. "Rate-induced tipping: Thresholds, edge states, and connecting orbits." Nonlinearity 36.6 (2023): 3238.
   
   O’Sullivan, Eoin, Kieran Mulchrone, and Sebastian Wieczorek. "Rate-induced tipping to metastable zombie fires." Proceedings of the Royal Society A 479.2275 (2023): 20220647.

This paper by Mitsui and Boers looks at Dansgaard-Oeschger (DO) transitions, which are examples of abrupt transitions in the Earth's past. The authors identify statistical precursor signals (SPS) in the transition from the warm to the cold state, which is evidence of DO transitions being caused by a loss of stability rather than stochastic variability. The Authors propose some dynamical mechanisms to explain this. I thought this was a good paper: the authors have clearly taken time to carefully analyse their results, although I was sad to see the code used in this paper was not shared 'by default'.

The authors may want to consider the following comments.

Broad Comments:

There are lots of time series here: 2 proxy variables, 2 early warning signals, 3 cores, 12 interstadials, 5 window sizes and 6 smoothing spans leading to 3480 analysed time series (when accounting for the fact that not all cores have all interstadials in them), although relatively few give SPS (31%). If there is a common mechanism at work, why is this the case? Can the authors be sure the results are not down to chance? The authors argue that more SPS are observed than would be expected by chance, but none of the time series for each interstadial are truly independent, and there being a false positive in one time series would increase the chance of there being a false positive in another. Furthermore, looking at figure 4d, different cores give different results for the same interstadial, e.g. in GI-20 only 4 cores give any SPS and only one 'robustly'. Different interstadials give different amounts of SPS, for example GI-14 gives many robust SPS but GI-19.2 doesn't. How do the authors account for this?

When looking for SPS, the time series must be decomposed into an slowly changing equilibrium state and fluctuations about that state. As a lot of the signal in this case for SPS comes from 'rebound events' the authors are assuming that the rebound events represent fluctuations rather than changes in the equilibrium state. What is the justification for this?

The authors may want to discuss mechanisms that can lead to changes in variance and autocorrelation not due to changing stability but due other factors. For example, due to changes in the properties of the climate forcing. Furthermore, changes in the statistical properties in the measurement process may also affect the results. For example, measurements in the ice cores further in the past may be more uncertain and therefore noisier, but measurements closer to the present may be less noisy and therefore more correlated. 

Specific Comments:

Line 11: Should be rebound events not rebound event

Line 15: This tipping definition excludes N-tipping, which has no thresholds. Different authors define tipping differently but as there is disagreement over whether DO events are N or B tipping I wonder if it is better to adopt a definition compatible with the Ashwin 2012 typology?

Line 91 "R^2 = 0.95", what fit is this measuring? 

Line 114: The autocorrelation is different to that in Bury et al who have C(tau) = (cos (omega tau)) exp(mu |tau|)

Line 115: Should be "increase or decrease"

Line 117: How do the authors know tau is sufficiently small, especially as omega may also be changing? 

Line 120: Is a linear fit suitable if half of the interstadial is used i.e. 500+ years? Could the stable state be changing nonlinearly in this period?

Line 187: makes reference to interstadials shorter than 1000 years but Line 106 implies the authors are excluding interstadials shorter than 1000 years. Have I misunderstood?   

Line 295-298: "can be shown to be 0.05". I think it would be helpful to show this. When I run the authors code I do not get any output like 0.044 or 0.042, but I may be running the code incorrectly. Is this calculation included in the shared code?

Figure 4d: Could the colormap used in this figure be changed to a diverging colormap, with its centre at 15, so that it is easy to see if an SPS is robust. Currently it is difficult to know if the colours correspond to values larger than or smaller than 15.

Bibliography:

Ashwin 2012 https://doi.org/10.1098/rsta.2011.0306