Historical SAM index time series: Linear and nonlinear analysis

Abstract

A statistical analysis of 100‐year historic Southern Annular Mode (SAM) time series is carried out, for a set of indices calculated by different methods, in view to understanding their value as simple indicators of climate variability and of the physical processes involved, particularly for the early part of the 20th century. Historic SAM time series available in the literature are analysed together with ones calculated using the 20th‐century reanalysis. A preliminary analysis and comparison is carried out using standard time and space correlations. Distinct differences are observed in the linear relations between the SAM index time series before and after 1950s. A detailed study is carried out using wavelet transform (WT) analysis, in order to better determine the spectral nature and non‐stationarity of the timeseries. The WT spectra reveal an aperiodic, non‐stationary evolution in all cases, with differences in the spectral signature of the various SAM indices during the 20th century. Preferred oscillation periods mainly appear between 2 and 20 years. Important differences between the SAM indices arise from different behaviour on the interannual time scale even in more recent years, as well as non‐stationarity and phase differences on longer time scales. A wavelet coherency (WTC) analysis between the 20th‐century‐reanalysis‐derived SAM time series shows that differences may also arise for indices calculated from the same data source, particularly during the earlier part of the sample. WTC differences appear at times of perturbed El Niño‐Southern Oscillation (ENSO) events. Results using linear as well as a mutual information analysis suggest links between SAM, ENSO, and Pacific‐South American patterns of variability, which may depend on the SAM time series definition. Such behaviour could be due to a combination of factors including the geographic coverage of the SAM calculation methods and data quality, as well as ENSO‐SAM relationships.