The long-term memory of climatic changes: theoretical foundation and observational confirmation
The multi-scale climatic changes take the dominant long-term memory or long-term persistence.In this paper,based on the knowledge from fractional integral,power spectrum and self-correlation function,the mechanism resulted in this feature has been derived that the exponent of power spectrum is twice the order of fractional integral.Finally,this theoretical relation has been confirmed by the results from the observational temperature record analysis by the method of detrended fluctuation analysis.