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).

Thursday, November 11, 2010

Dynamic stability in probability density plots

Probability density diagrams of the two dimensional phase space portraits of climate proxies show two forms of stability. The first is the obvious form--stable (in this case, ice volumes) over comparatively long periods of time, broken up by brief periods of rapid change where the ice volume changes to another metastable state.

Using a stacked time series (from Huybers, 2004), we observe a different form of stability--one in which repeated cycles of growth and decay generate ring structures in the probability density plot.
Just as a car driving around a track at a constant speed is a form of stability, so are the two "limit cycles" inferred in the frame above. The system is stable, even though it is in a constant state of motion.

In the animation below (click and with luck it will run), the probability density space is characterized in the early Quaternary (about the first half of the animation) by stable cycles, which give the ring forms as in the still image shown above, but in the late Quaternary, the rings disappear and are replaced by probability peaks.

Both segments of the record show multi-stability, but the forms of individual metastable states in the early Quaternary differ from those of the late Quaternary.

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