Dimension Analysis of Climatic Data

Abstract

It has been conjectured that the unpredictability of climatic systems is due to strange attractors (SAs) in the configuration space dynamics. One climatic record, the oxygen isotope ratio data from deep-sea cores that pertains to long periods on the order of one million years and provides direct correlation with the glaciation-deglaciation periods, seemed to indicate (under earlier analysis) a low dimensional attractor of correlation dimension D2 ≈ 3.1. Our present reanalysis of this data in light of recent methods suggested by Broomhead and King (BK) is at variance with that result. Two (model) four-variable systems that support chaotic strange attractors are examined using an analysis similar to BK to investigate the practical drawbacks of using a short time-series vis-a-vis the estimation of attractor dimension.