THE SOURCE DOCUMENT FROM WHICH THIS POST IS DERIVED >> [LINK]

FIGURE 1  

FIGURE 2

A CHAOS THEORY OF GLACIATION CYCLES

1. There is no satisfactory explanation for glaciation cycles because the theories proposed impose a fixed periodicity that is not found in the data; as well the progress of both the rise to glacial maximum and fall to interglacial are interrupted by brief reversals at millennial time scales as seen in the video above that shows the formation and decay phases of the Last Glacial Period. For at least two million years the size of the mass of ice accumulation in the high northern latitudes has followed a cyclical pattern; growing at times to cover most of the northern continents during glaciation and then receding to approximately where it is today in interglacial periods.
2. The traditional theory of the glaciation cycle, first forwarded by Milutin Milankovitch, attempts to link the earth’s precession, tilt, and eccentricity to glaciation cycles. The theory implies that the length of glaciation cycles is fixed at integer multiples of the precession cycle of 26,000 years. But this is not what we see in the data where we find a more random and chaotic time scale of glaciation cycles. The evidence suggests that icy periods last from 20 to 100 thousand years and interglacials between 7 and 20 thousand years. These time scales are not integer multiples of the precession period. The non-periodic nature of the phenomenon has not been adequately addressed in the Milankovitch theory.
3. Another mystery of glaciation cycles is that within any icy period there are violent cycles of ice melt that don’t make it all the way to an interglacial. During the meltdown, 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. He says 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.
4. Linear causation theories such as these subsume that for any given climactic state there is a 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.
5. Many natural systems exhibit non-linear dynamics and are meta-stable. In these systems many different “equilibrium” states are possible and even the slightest trigger (the proverbial butterfly) can bring about substantial changes in the equilibrium state. A graphical model of meta-stability is shown in Figure 1. The ball in the deep bowl 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 shallow bowl is in meta-stable 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.
6. We propose 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 glaciations, interglacials, Heinrich events, and, most importantly, the non-periodicity of these events. In a purely solar and atmospheric view of these changes, the waxing and waning of the ice fraction can be 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. However, as described by James Edward Kamis [LINK] , random and unpredictable geothermal events can also intervene and play a role in glaciation cycles. Therefore, a simplistic and periodic theory of glaciation cycles is unlikely to provide a satisfactory explanation for what is likely to be a phenomenon of non-linear dynamics. 
7. The chaos model shown in Figure 2 demonstrates the surprising impact of non linear dynamics. 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 insert non-linear dynamics into the system.
8. We find that large swings in the ice fraction is possible under these chaos conditions. “Glaciation periods”, that is, high ice fractions, form naturally and tend to persist. Just as naturally the ice recedes in 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 non-linearity in the heating function and without imposing an external causal force.
9. 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. This is the dynamic that can be set off in either direction by minute random effects. It appears that nonlinear dynamics play a role in these ice cycles and the attempt to explain these cycles purely in a cause and effect deterministic way does not address the observed chaotic behavior.
10. Another source of the chaos in glaciation cycles may arise from called Hurst persistence, often seen in time series data, in which random changes tend to persist. This effect is demonstrated in a Youtube video that appears below [LINK].
11. Yet another theory of glaciation cycles is proposed by James Kamis (and also by Ben Wouters in the comments section below). Kamis says that because we are interglacial creatures, we tend to see glaciation cycles from an interglacial perspective where interglacial is the norm and glaciation is the oddity that needs to be explained. However, the earth spends most of its time in the glaciation state and somewhere between 10% to 15% of its time in an interglacial state, so that glaciation is the norm and it is interglacials that need explaining and the earth’s own geological forces and geothermal heat provide all the energy we need to explain interglacials [LINK] .

HURST PERSISTENCE IN TIME SERIES DATA