Abstract
The autocorrelation function (ACF) and its relationship to fluctuation analysis (FA) are discussed, based on the reanalysis monthly mean geopotential height at 500 hPa from ECMWF (ERA-20C). ACF provides a measure of the influence of correlation at different time points. The principal pattern ACF shows relatively large positive correlations between every consecutive years in the central Asian continent and the North African continent. However, the confidence intervals of the ACF distributions are generally too wide, and so of low confidence level. It is found that the scaling rule of the ACF breaks down typically, while the distributions of the critical exponent of FA always show patterns. It is also found that the larger values of critical exponent appear in the tropical region, which reflects a larger climate persistence. The critical exponent becomes smaller in the jet stream regions, indicating less year to year reappearance. The characteristic time accounts for the weighted summation of all possible ACFs, which represents a memory length of a certain climate events. In the boreal winter, some robust patterns can be identified by the corresponding distribution of the characteristic time, which provides a unified way of describing the persistence of climate. An approximate relation between the critical exponent of FA and the characteristic time has been found, and such relation is verified by the distributions of these two physical variables.
Acknowledgement
The authors would like to thank Petr Chylek, Carsten Frederiksen, Steve Lambert, Grey Roff, Kristoffer Rypdal, and two anonymous reviewers for their helpful comments.
Disclosure statement
No potential conflict of interest was reported by the authors.