|Overall, this revised manuscript provides an excellent proof of concept for using Early Warning Indicators (EWI) as a tool for diagnosing the Marine Ice Sheet Instability in ice sheet model simulations. The revision now also serves as an excellent primer on the theory and practice of calculating EWIs that will be useful to those in the glaciology community who are new to this topic. My overall recommendation is that this paper is now close to being ready for publication, with a few more suggestions, which could be classified as "minor".|
My more substantive suggestions:
1. In my original review I was fairly convinced that this study primary utility was as a proof of concept for showing how EWI could be identified observationally for MISI. However, in this version, it isn't until lines 352-354 that it became clear to me the exact utility of using EWI-type analysis on simulation output, beyond as a proof of concept. Here the authors state that this approach could be useful to lower the computational expense needed to verify the presence of bifurcations in a model simulations (i.e. without very long simulations). As a modeler, I find this to be a compelling argument, and should be front and center in the paper, particularly in the first section where you are trying to entice readers to continue learning more about EWIs.
2. Not to hammer too hard on the window length issue, but I think there needs to be a bit more discussion of two points.
(a) First off, on lines 280-282, you state 300 years is "the shortest window size for which the DFA indicator provides an accurate prediction for all tipping event". What does "accurate" mean in this context? From Figure 7, I would guess you mean where Kendall's Tau has a maximum, but why does that make this window the most accurate way to determine whether a tipping point will occur? In principal, wherever 0<tau<1 is indicative of increasing indicator, so one could argue that window lengths anywhere from 200 to 400/500 years seem to work in this regard.
(b) There is also still not much investigation of window lengths relevant to observational time scales (i.e. decades). I wonder if increasing the forcing rate to levels that might be relevant to modern climate change (i.e. degrees/century) would make short window lengths more useful? This is perhaps beyond the scope of the paper, but if its computationally feasible to run a few simulations with higher forcing rate, and re-calculate figure 7 for those forcing rates, you could begin to answer the questions of whether it would be possible to use modern observations to calculate EWIs.
3. In my opinion, the point that is made throughout about separating tipping points by using slow forcing is a bit off the mark. Because you are not doing fully steady-state simulations, it is not clear that you have shown that these are actually three discrete tipping points (in the traditional sense of a bifurcation diagram which traces the stable manifold of the system). In the real system, these three tipping points likely involve a grounding line retreating over a region of reverse sloping bed with some prograde bumps. Perhaps if the forcing were even slower, there would be places where the grounding line stabilizes on these bumps, subdividing these tipping points even further. On the other hand, for realistically fast forcing rates, you would have a "tipping point cascade" that might look like one single rapid retreat. This would still be of interest, and could be valuable to identify using EWI since it is closer to what we are likely to see in reality. This is all to say that without a completely steady-state analysis it seems a bit premature to argue that you have found the three actual tipping points in the system, when there may be more in a mathematical sense, or when they might combine into one tipping event under real forcing.
Line 12: what does "this" refer to in this sentence?
Line 18: indicators in model simulations robustly detect
Line 23: delete "a major component of the earth system" to make sentence clearer
Line 27: If grounding line retreat causes grounding line flux to increase
Line 31: a small perturbation results in the system
Line 43: delete "externally forced" since there needs to be an external forcing trigger for MISI to occur in the first place
Line 47: I'm not sure you need to mention the lower stable branch since technically it does not "participate" in the bifurcation (and there doesn't need to be a lower stable branch at all to have a saddle node bifurcation)
Line 46-55: It would be useful to indicate what are the assumptions under which it is the case that MISI is a saddle-node bifurcation? i.e. that bed slope is negligible and changes very slowly in space (i.e. Schoof 2007/2012)
Line 51: parameter range
Line 58 and elsewhere: I always thought this was called "critical slowing down". A cursory search in the literature indicates that this is the most common usage and should perhaps be used that way here if you want readers to relate this to the broader EWS literature.
Line 76: are you calling these EWI or EWS? You use both in the same sentence
Section 2.1: So, I am typically loathe to reference my own papers, but I think it bears noting that Robel et al. 2018 shows analytically that the response time (calculated directly from the eigenvalues of the system) increases towards the MISI bifurcation (see Fig. 3 in that paper).
Line 123-124: This sentence could be written a bit more clearly since its unclear what you are saying about variance here
Line 154: typo at exponent
Line 191: Also, by using realistic noise you can assess EWI detectability that would be expected in observations
Line 199: How do you know what is not related to system recovery time? Sentence is a bit vague
Line 220-224: can you be clearer about the different interpretations of tau=1 and 0<tau<1?
Line 247: MISI event begins
Line 314: of ice flow are
Line 337: and also decreasing window length?
Line 346: related to issue #3 above, but it isn't clear why this cascade is a problem from the POV of EWI detectability
Line 349: tipping points is one that
Figure 4: in panel (b) you have open markers where you have done steady-state calculations, but not in panel (a), so it is unclear where you have actually done simulations to determine steady-states.