The Lorenz Equations
Nonlinear Geoscience

Chaos and the Earth

The earth is a complex, dissipative (friction and eventual decay occur everywhere!) and dynamic system driven by the continuous flow of energy from its interior and the sun, and made up of many interacting parts. While energy dissipates as irrecoverable heat, it is constantly being replenished by its sources. To understand how the Earth works, we not only have to understand the parts of the Earth, but also the way in which those parts interact. In fact, the Earth is a system whose different components interact in a non-linear manner.

In dynamic system Earth, the parts interact and couple with each other such that a change in one of them more likely than not induces changes in all the others that are not proportional to the magnitude of the original change. Nonlinearity means that adding the different actions of the components is not equal to the simple superposition of their effects; in fact, the sum of the parts can produce dramatic new effects reflecting the cooperation among them. In other words, "the whole is more than the sum of its parts." Contrast this with a linear system in which the whole is exactly equal to the sum of its parts.

If we accept that the Earth system is strongly non-linear, then small causes can, and propably will, produce tremendously large effects.

This is the whole idea behind chaos which we will get to shortly. First, let's take an example from ecology to illustrate this important point. The following is paraphrased from the work of American biologist E.O. Wilson:

During the construction of the Panama canal in 1912 rising waters cut off a piece of elevated land foming a new isolate, covered by an evergreen forest. It was named Barro Colorado Island and made into a biological research station. The size of the island, 17 square kilometers, was too small to sustain jaguars and pumas. The prey of the great cats had consisted mainly of agoutis and pacas, outsized rodents that vaguely resemble jackrabbits and small deer. These animals, freed from a major cause of maortality, multiplied to ten times their original numbers. They overexploited their own food, which consists mostly of large seeds that fall from the forest canopy, which caused a reduction in the reproduction and abundance of the tree species that produce the seeds. The effect rippled outward. Other tree species whose seeds are too small to be of interest to the agoutis and pacas benefited from the reduced competition and flourished. Inevitably, animal species specialized to feed on small-seed trees also prospered, and the predators of these animals increased, and the fungi and bacteria parasitizing the small seed trees and associated animals spread, and the microscopic animals feeding on the fungi and bacteria grew denser, and the predators of these creatures increased in turn, and so on across the food web and back again as the ecosystem reverberated from the restriction of its area and consequent loss of its top carnivores.

This is a beautiful example of how small changes can produce great consequences. At the same time, this is a story that can only be told in hindsight. Particular outcomes are contingent on many unpredicatable events. Thus it would be extremely difficult, if not impossible, to be able to accurately predict the actual evolution of such apparently simple ecosystem starting with given initial conditions. There is no known law or model as yet capable of reproducing the story of Barro Colorado given the initial conditions of the the island (area, absence of large predators, tree species).