The Southern Oscillation as an Example of a Simple, Ordered Subsystem of a Complex Chaotic System

Abstract

Complex chaotic systems are systems of high dimension and are unpredictable but often contain subsystems that are simple and predictable. The existence of such simple, ordered subsystems would indicate a predictability of climate if the underlying complex chaotic system is the phase space describing solid earth, oceans, and atmosphere. Often, some components of these systems are only poorly observed. A variational method is proposed in order to determine such parameters indirectly. The dynamic law for the simple, ordered subsystem can be determined once these system variables are known. Two examples are given for this procedure, the forecast of a river outflow and the forecast of the surface pressure at Darwin several months ahead. The model for the latter forecast is two-dimensional in phase space and its design incorporates current knowledge of the physical mechanism of the Southern Oscillation.