In order to extract the intrinsic information of climatic time series from background red noise, in this paper, we will first give an analytic formula on the distribution of Haar wavelet power spectra of red noise in a rigorous statistical framework.

After that, by comparing the difference of wavelet power spectra of real climatic time series and red noise, we can extract intrinsic features of climatic time series. Finally, we use our method to analyze Arctic Oscillation (AO) which is a key aspect of climate variability in the Northern Hemisphere, and discover a great change in fundamental properties of the AO, commonly called a regime shift or tripping point.

Zhihua Zhang, John C. Moore, Aslak Grinsted, Int. J. Wavelets Multiresolut Inf. Process. 12, 1450020 (2014) [11 pages] doi:10.1142/S0219691314500209