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A Possible Explanation for Low Correlation Dimension Estimates for the Atmosphere

Shafiqul IslamDepartment of Civil and Environmental Engineering, University of Cincinnati, Cincinnagi, Ohio

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Rafael L. BrasRalph M. Parsons Laboratory, Massachusetts institute of Technology, Cambridge, Massachusetts

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Ignacio Rodriguez-IturbeRalph M. Parsons Laboratory, Massachusetts institute of Technology, Cambridge, Massachusetts

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Abstract

There have been numerous attempts to detect the presence of deterministic chaos by estimating the correlation dimension. The values of reported correlation dimension for various geophysical time series vary between 1.3 and virtually infinity (i.e., no saturation). It is pointed out that analyzing variables that depend on physical constraints and thresholds, like precipitation, may lead to underestimation of the correlation dimension of the underlying dynamical system.

Abstract

There have been numerous attempts to detect the presence of deterministic chaos by estimating the correlation dimension. The values of reported correlation dimension for various geophysical time series vary between 1.3 and virtually infinity (i.e., no saturation). It is pointed out that analyzing variables that depend on physical constraints and thresholds, like precipitation, may lead to underestimation of the correlation dimension of the underlying dynamical system.

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