Dust flux, Vostok ice core

Dust flux, Vostok ice core
Two dimensional phase space reconstruction of dust flux from the Vostok core over the period 186-4 ka using the time derivative method. Dust flux on the x-axis, rate of change is on the y-axis. From Gipp (2001).

Friday, March 2, 2012

Snapshots of multistability in the climate system

Today the World Complex presents images from the recently redrafted movie of the probability density plot of the proxy record for global ice volume over the past two million years. The reason for the redrafting was to shorten the window, improving the resolution of the individual frames.

The methodology for deriving these plots from original data has been previously described here. The O-18 data used below are from Shackleton et al. (1990). Variations in O-18 in the deep ocean reflect global volumes of glacial ice.

This figure is a map of a ice-volume phase space over the interval 189 ka to 39 ka (ka = thousand years ago). There are three distinct regions of higher probability (grey areas) in phase space, which represent stable global glacial volumes. This figure suggests that over the interval in question, there were three stable global ice configurations--one corresponding roughly to the interglacial condition we have today (at lower left), and two more with considerably more (glacial) ice--and that transitions from one to another happened relatively rapidly. As the probability of any state outside of the three LSAs is low, global climate change was rapid during the interval in question. Glacial ice volumes therefore have three conditions of equilibrium, which are punctuated by brief episodes of rapid change. Using our dynamic interpretations from previous articles, we have inferred three areas of Lyapunov stability in the time delay state space of global ice volume.

The graph only tells us about global ice volume, but not where the ice is. Thus we cannot infer the global glacial configurations for each of the three LSA.

In the 699-519 ka interval (still Late Quaternary) we still see multiple areas of stability. There may be a limit cycle in the low volume section of probability density diagram.

The interval 1509-1359 ka was characterized by a large limit cycle, with a couple of particular regions of higher probability. The high probability peak at lower left represents an area of Lyapunov stability. Limit cycle behaviour in the ice volume system suggests oscillatory growth and decay of ice sheets.

This plot shows a limit cycle and two areas of Lyapunov stability. The lower one, near (3.5, 3.5) is the same as the one in the next figure above. The second area of attraction, near (3.9, 3.9) is present in the figure at representing the interval 1599-1449 ka above.

In general, limit cycle behaviour is more common in the Early Quaternary, and simple LSA multistable behaviour is more common in the Late Quaternary. This observation is reinforced in observations of reconstructed phase space portraits of smoothed C-13 measurements from cibicidoides sp. (Raymo et al., 2004).

The C-13 data is purported to represent oceanographic conditions and are reflective of overall glacial conditions, with lower values corresponding to glacial maxima (Bickert et al., 1997). The phasing of variability in the C-13 differs from that of O-18 at different frequencies and is thought to reflect changes in oceanographic flow at least partially in response to glacial cycles (Raymo et al., 2004).

In the Early Quaternary, the probability density plots of the reconstructed state space mainly suggest limit cycle behaviour. The period of the oscillations is approximately 41 ky.

In the Late Quaternary, the oceanographic state is more suggestive of multiple metastable equilibria, punctuated by brief episodes of rapid change.

Limit cycle behaviour is still observed in some windows in the Late Quaternary . . .

 . . . but multiple equilibria is the predominant state in the Late Quaternary. 

I have recently completed epsilon machine reconstructions for the 13C predictive states (at least the forward-evolving e-machines as described briefly here in the references) and will be posting these shortly.


Bickert, T., Curry, W. B., and Wefer, G., 1997. Late Pliocene to Holocene (2.6-0 Ma) western equatorial Atlantic deep-water circulation: Inferences from benthic stable isotopes. In Shackleton, N. J., et al. (eds.), Proceedings of the Ocean Drilling Program, Scientific Results, v. 154: 241-254.

Raymo, M. E., Oppo, D. W., Flower, B. P., et al., 2004. Stability of North Atlantic water masses in face of pronounced climate variability during the Pleistocene. Paleoceanography, v. 19: 13p. doi: 10.1029/2003PA000921.

Shackleton, N. J., A. Berger, and W. R. Peltier, 1990. An alternative astronomical calibration of the Lower Pleistocene timescale based on ODP site 677, Trans. R. Soc. Edinburgh, Earth Sci., 81: 251-261.

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