Self-organization of the Earths climate system versus Milankovitch-Berger astronomical cycles

TL;DR

This paper models the Earth's climate variations by decomposing Antarctic temperature data into cyclic and stochastic components, each with distinct self-organizing processes, and compares their mathematical properties to understand climate dynamics.

Contribution

It introduces a mathematical framework distinguishing cyclic and stochastic climate processes with self-organization, linking them to astronomical cycles and multifractal analysis.

Findings

Cyclic component modeled as an auto-oscillating system with constant period.

Stochastic component analyzed through multifractal spectrum comparison.

Models suggest interconnected but distinct climate variability processes.

Abstract

The Late Pleistocene Antarctic temperature variation curve is decomposed into two components: cyclic and high frequency, stochastic. For each of these components, a mathematical model is developed which shows that the cyclic and stochastic temperature variations are distinct, but interconnected, processes with their own self-organization. To model the cyclic component, a system of ordinary differential equations is written which represent an auto-oscillating, self-organized process with constant period. It is also shown that these equations can be used to model more realistic variations in temperature with changing cycle length. For the stochastic component, the multifractal spectrum is calculated and compared to the multifractal spectrum of a critical sine-circle map. A physical interpretation of relevant mathematical models and discussion of future climate development within the context of this work is given.