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WBM1996: A CHAOS MODEL OF GLACIATION CYCLES

Posted on: May 24, 2020

WBM POSTS ARE MY LOST WORKS FOUND IN THE WAY BACK MACHINE 

 

bandicam 2020-05-25 07-24-44-229

There is no satisfactory explanation for glaciation cycles . For at least two million years the size of the northern polar ice cap has followed a cyclical pattern; growing at times to cover most of the northern continents in the glaciated state and then receding to approximately where it is today during the “interglacial” periods. The traditional theory of this cycle is the one proposed by Milutin Milankovitch. The theory attempts to link the earth’s precession, tilt, and obliquity of the orbit to glaciation cycles.

The period of the earth’s precession is 26,000 years; so we would expect ice formation to peak and to have warm interglacials every 26,000 years or so. But this is not the case. The evidence suggests that icy periods last from 20 to 100 thousand years and interglacials between 7 and 20 thousand years and not integer multiples of the precession period. The non-periodic nature of the phenomenon has not been adequately addressed in the Milankovitch theory of glaciation cycles.

Another mystery of the glaciation cycle is that within any icy period there are violent ice melt cycles. During the meltdown phase of these cycles large chunks of ice slide out to sea and the continental ice sheets get thinner. But within a few years it begins to get thicker again. The commonly held explanation for this behavior is due to Hartmut Heinrich. Heinrich postulates that as the ice gets thicker it acts as insulation and allows internal heat from the earth to melt the bottom of the ice and cause glacial flows. The problem with the Heinrich theory is that evidence suggests that glacial flows are not regional but global and at such a large scale that synchronization of localized hot spots is highly improbable.

Theories such as these subsume a cause and effect mechanism for these ice cycles in which for any given climactic condition there is a corresponding stable steady state ice level on the northern continents; and that any change from the steady state level can only be caused by a significant event with sufficient energy to cause the change. But this is not always the case in nature. Many natural systems exhibit non-linear dynamics and are metastable. In these systems many different “equilibirium” states are possible and even the slightest trigger (the proverbial butterfly) can bring about substantial changes in the equilibrium state.

A graphical model of metastability is shown below. The ball in the upper frame is in stable equilibrium. It will require a great deal of energy to shift the ball to another equilibrium state and if such a shift is observed a theory like that of Heinrich or Milankovitch might be required. The ball in the lower frame is in metastable equilibrium. Although it appears to be in steady state, many other steady state conditions are equally likely and minute random events can make wholesale changes to the position of the ball.

 

We propose here that ice formation in the northern continents is such a system. The time series of ice fractions is in chaotic equilibrium at wildly different levels of ice. The non-linearity in the system is imposed by the annual summer/winter heat cycles and by the reflective nature of ice. Such a non-linear model may be used to explain glaciation, interglacials, Heinrich events, and non-periodicity of these events. The waxing and waning of the ice fraction is nonlinear because ice is melted by heat that the planet has absorbed from sunlight; and the heat absorbed by the planet is a function of the ice fraction because ice reflects sunlight. This kind of inter-relationship is known to create chaotic behavior as shown in a video representation of a mathematical model of such a system at the end of this post.

The chaos model shown below demonstrates the surprising impact of this non linear behavior. In the model, a sine function is used to generate the annual incident solar radiation on the northern hemisphere of the tilted earth as it rotates on its axis and revolves around the sun. We begin the simulation with an assumed size of the polar cap which has a tendency to grow unless melted by solar radiation. A small perturbation (1%) is added to the solar radiation function to account for random effects.

We find that large swings in the ice fraction are possible under these conditions simply due to chaotic behavior. The glaciation states (high ice fractions) form naturally and tend to persist. Just as naturally the ice recedes into brief interglacial periods. What’s more surprising is the existence of the Heinrich events within these epochs. Both the glaciation cycle and the Heinrich events are produced as a result of a nonlinearity and chaos in the heating function and without imposing an external causal force in a purely cause and effect relationship.

The more ice you have the less energy gets absorbed and even more ice can be formed. Conversely, the more ice you melt, the more energy you can absorb and more ice you can melt. Chaos derives from the behavior of this dynamic because it can be set off in either direction by minute random effects. We propose that it is this non-linearity that is responsible for periods of otherwise inexplicable growth in ice formation and periods of melting and shrinking of the ice fraction.

A Youtube video of chaotic behavior due to the so called Hurst Persistence in time series data is shown below.

 

 

 

 

 

1 Response to "WBM1996: A CHAOS MODEL OF GLACIATION CYCLES"

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