Thoughts on tipping points relevant to Praetorius & Mix (2014)

Tipping points are scary. The response of climate and other environmental systems to external forcing might not be a gradual, reversible change but a flip from one stable state to another. It may be very difficult to reverse this transition. Such tipping points or critical transitions are difficult to prepare for and could cause large social and economic costs. Fortunately, there are strong theoretical expectations that there should be early warning signals such as increasing autocorrelation and variance before a critical transition.

Classic examples of critical transitions between stable states include the onset of Dansgaard–Oeschger events, the Bølling-Allerød interstadial and the Holocene, and the switch between benthic and planktonic dominated lakes as eutrophication increases. Palaeo-scientists have sought to identify early warning signals in proxy records.

If palaeo-proxy data could be used to identify early warning signals of critical transitions, it would be very reassuring. It would imply that even with noisy data, impending critical transitions could be identified decades to centuries before they occur. Alas, not all the attempts are convincing.

A new paper in Science by Praetorius & Mix attempts to find an early warning indicator of the transition from the Last Glacial into the warm Bølling-Allerød.

Praetorius & Mix have produced a high-resolution foraminifera δ18O record from the Gulf of Alaska (GOA) and use a running correlation to show that this record is synchronised with the NGRIP δ18O record from Greenland just before the Bølling-Allerød. They call this synchronisation dynamic coupling and show that dynamic coupling can lead to critical transitions as the pooled variance is higher so that thresholds are more likely to be breached.

I have an alternative hypothesis: that the synchronisation of the GOA and NGRIP records does not cause the transition but is the result of the transition. Praetorius & Mix use a centred 2000-year window for calculating the running correlation; if the Bølling-Allerød transition was initiated in either the North Pacific or Atlantic (or indeed elsewhere) but affects both, the correlation would be expected to start to rise 1000 years before the transition, as soon as the transition enters the moving window.

Gulf of Alaska and NGRIP proxy records (top) and running correlations (bottom). The dashed line in the top panel marks the transition into the Bølling-Allerød. In the bottom panel it marks 500 or 1000 years before this transition.

Gulf of Alaska and NGRIP proxy records (top) and running correlations (bottom). The dashed line in the top panel marks the transition into the Bølling-Allerød. In the bottom panel the dashed lines mark 500 or 1000 years before this transition.

I’ve re-run the analysis of Praetorius & Mix. With a 2000 year window, the zero crossing of the running correlation is exactly 1000 years before the transition.  This is exactly what is expected if the correlation between the proxies is induced by the transition. It provides no evidence that dynamic synchronisation caused the transition.

If we repeat the analysis with a 1000 year moving window, the increase in correlation between the proxies occurs more than 500 years before the transition. So is this evidence for dynamic coupling? Perhaps, but we need to test whether the correlation is higher than expected by chance for two red-noise spectra. This is easily done by simulating many pseudoproxy records that have the same autocorrelation as NGRIP in this time window and finding the correlation between these and the GOA record. If the observed correlation between the GOA and NGRIP proxies is larger than the correlation of GOA and most of the simulated pseudoproxies, the correlation is significant. With 1000 trails, the one-sided p-value is 0.014. Unlike the 2000 year window used by Praetorius & Mix, the 1000 year window used here provides results that are compatible with the dynamic synchronisation hypothesis. The correlation is due to the shared trend in both records during this window, the temporal resolution is not good enough to test if the high frequency variability is also shared, so the results are not as persuasive as one would like.

Even if we accept the results as evidence of dynamic synchronisation as a precursor of critical transitions, dynamic synchronisation, like other early warning signals, may be of little practical use because of the high false alarm rate whenever windowed methods are used, because of the multiple testing. For example, correlations about as large as that preceding the Bølling-Allerød transition occur three times in the Holocene without being followed by a critical transition.


Praetorius, S.K. & Mix, A.C. 2014. Synchronization of North Pacific and Greenland climates preceded abrupt deglacial warming. Science 345, 444-448.

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About richard telford

Ecologist with interests in quantitative methods and palaeoenvironments
This entry was posted in climate, Peer reviewed literature and tagged , , , , . Bookmark the permalink.

2 Responses to Thoughts on tipping points relevant to Praetorius & Mix (2014)

  1. I immediately thought the same when reading the paper.

    • Unless there is some subtle rationale I’m not aware of, I don’t understand how this problem slipped past so many people. I can replicate the essentials of the key figure almost exactly with white noise added to a mean process with the shape of the NGRIP curve – I’ll probably post that later today. I’m in contact with the authors and am considering how best to proceed.

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