Correlation Dimension Estimates of Global and Local Temperature Data

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  • 1 Ralph M. Parsons Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

The author has attempted to detect the presence of low-dimensional deterministic chaos in temperature data by estimating the correlation dimension with the Hill estimate that has been recently developed by Mikosch and Wang. There is no convincing evidence of low dimensionality with either global dataset (Southern Hemisphere monthly average temperatures from 1858 to 1984) or local temperature dataset (daily minimums at Auckland, New Zealand). Any apparent reduction in the dimension estimates appears to be due large1y, if not entirely, to effects of statistical bias, but neither is it a purely random stochastic process. The dimension of the climatic attractor may be significantly larger than 10.

Abstract

The author has attempted to detect the presence of low-dimensional deterministic chaos in temperature data by estimating the correlation dimension with the Hill estimate that has been recently developed by Mikosch and Wang. There is no convincing evidence of low dimensionality with either global dataset (Southern Hemisphere monthly average temperatures from 1858 to 1984) or local temperature dataset (daily minimums at Auckland, New Zealand). Any apparent reduction in the dimension estimates appears to be due large1y, if not entirely, to effects of statistical bias, but neither is it a purely random stochastic process. The dimension of the climatic attractor may be significantly larger than 10.

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