|In my opinion, the authors have managed to come up with a much clearer and more transparent manuscript. It is now clear to me what the authors do and why: The fundamental question is whether one can distinguish from the speleothem record if the abrupt monsoon switches are associated with bifurcations or with switches between permanent alternative states. The authors point to this question and show that their potential model is in line with the bifurcation hypothesis. In principle, I think that this result just merits a publication because I see no killing argument against it. However, it still remains unclear to me to what extent the author’s results are any evidence for the bifurcation hypothesis in contrast to a sophisticated speculation. I hope that further research will tackle this question more thoroughly, and that the authors still improve their manuscript, by addressing some of the following points. |
The authors state that their potential model should “supplement the analysis of the speleothem records and help interpret the results”. I rather think that this model is at the heart of the analysis and that the message of the paper rests on this model. It is thus important to argue why it is an appropriate model, and why alternative explanations (e.g. nonlinear response to forcing, or stochastic resonance) are less plausible, ideally by using statistical tests to refute some hypothesis. The fact that the authors come up with a model that describes the abrupt changes as bifurcations does not prove that the model is more likely to be true than any other model. Although the way the authors derive the model is now transparent, it is not very transparent to me how sensitive the results are to different choices during the model derivation. The fact that a simpler approach fails due to a negative leading coefficient indicates that the model is not robust. I still wonder how robust the results are to the choices during the model derivation. For example, why is the solar forcing a linear term added to the potential U? Why not say that the four parameters of U all depend on time?
The authors do not find “early warnings” though they would be expected if their bifurcation hypothesis was true, and argue that the time series are too short and the noise level is too large for a detection. Is there any further line of evidence to substantiate this claim? How robust is the noise level estimate?
I think it is sensible in this context to check the dependence of “early warnings” on noise level and resolution, using the potential model, as the authors do. However, it is not clear to me whether the results confirm the claim that most transitions are below detectability, while termination II is above detectability. At which length of the record would the signal become significant? I think this is something else than examining the resolution because of the autocorrelation in the time series (see my point on characteristic timescale below).
By the way, just from looking at the data, the time series from Hulu cave does not occur bimodal to me, and the shifts are less abrupt / less permanent. The authors often refer to “the speleothem data”, but I have the impression it is only the Sanbao record they use for their potential model, while they still analyse early warnings in the Hulu record. This seems to be contradictory.
Further (minor) remarks
Another problem that I think remains in the revised manuscript is the lack of a physical mechanism to explain the relaxation time of the system. The authors correctly point out in line 102 that
“Detecting the phenomenon of critical slowing down relies on a timescale separation, whereby the timescale forcing the system is much slower than the timescale of the system’s internal dynamics, which is in turn much longer than the frequency of data sampling the system (Held and Kleinen, 2004).” However, I missed an explanation why this timescale separation applies to the East Asian monsoon (why should monsoon respond much slower to forcing than the resolution of the record, i.e. ~100 years?). Also, this seems to be at odds to the often cited Zickfeld/Levermann/Schewe model which seems to have a much faster timescale given the rapid processes in the atmosphere. I guess it must be the model’s parameters determined by the ocean that somehow adjust slowly to the change in insolation?
line 97: “While it has been theoretically established that autocorrelation and variance should both increase together (Ditlevsen and Johnsen, 2010; Thompson and Sieber, 2011), there are some factors which can negate this, discussed in detail in Dakos et al. (2012b, 2014).”
I still don’t see clearly why this is noted here. What does it tell about the author’s results? Would they expect an increasing variance in case of the monsoon, and why (not)? As autocorrelation and variance do increase together before termination II, where is the problem?
The test for trends in Kendall’s Tau seem to be done via surrogate time series, which I think is a good idea. But it seems that the surrogate time series have no autocorrelation because it is destroyed by the shuffling. The true data is autocorrelated and thus trends are less robust. Wouldn’t the trend significance then be overestimated? The authors refer to Dakos et al. (2008), and the approach seems to correspond to their H0_1 - one could instead use their Null-hypothesis 2 and/or 3, which take autocorrelation into account.
I have the impression the term “tipping point analysis” has been made up by the authors and is very vague. One could instead refer to particular steps in the statistical analysis by using established conventions. Moreover, “noise-induced transition” is not the right term for a random shift of the system into a different attractor basin. As far as I know the term does not refer to one particular event in a stationary time series but to the sudden change of a system’s long-term statistics when the noise level is changed. For example, see books and articles by Berglund, Gentz, Horsthemke and Lefever on this topic.
I still think that some figures are not required, for example
Fig. 1: c, d;
Fig. 6 and 7: c, d.
Fig. 10: I suggest to use individual potential plots, or arrows between potentials and time periods in the record, or write the letter directly next to the line in the plot.
The caption of Fig. 11 is incomprehensible to me.