Use of Hurst and Renyi analysis to detect and characterize Pacific decadal oscillation impacts on climate variability in Alaska

Jean K. Talbot
Wed, 22 Apr 2026 17:33:39 PDT

While climate systems are known be nonlinear, most statistical tools used to study climate are linear. Two nonlinear analyses are introduced for indicating predictability in climate studies: Hurst analysis and Renyi analysis, the advantages of which are illustrated by applying both to characterize Alaska climate time series 'dynamics' or temporal evolution. These methods are also applied to reanalysis and model data to compare with the observational analysis. Hurst analysis is used to calculate long term predictability in data on a scale of five to 15 years; Renyi analysis is used to quantify the degree of order on a time scale of two to 15 days. The analyses revealed that temperature may be more statistically predictable in certain areas of Alaska during the positive phase of the Pacific Decadal Oscillation (PDO). Circulation effects associated with the PDO shift are found to plausibly cause the change in randomness of the SAT data.