High frequency (daily) data analysis of the Southern Oscillation Index. Tsallis nonextensive statistical mechanics approach

Daily data of the Southern Oscillation Index between 1999 and mid-2006 has been analyzed in order to obtain the shape and tails of the partial distribution functions (PDF) of the variability of the index. A model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of the normalized variability for such a climatological index, for small and large time windows, both for small and large variability. The model is linked to Tsallis nonextensive statistics. The transition between the small time scale model of nonextensive, intermittent process and the large scale Gaussian extensive homogeneous fluctuation picture is found to occur at above a ca. 46 days time lag. The intermittency exponent (K) in the framework of the Kolmogorov log-normal model is found to be related to the scaling exponent of the PDF moments. The value of kappa (= 0.25) is in agreement with the intermittency exponent recently obtained for other atmospheric data and for the monthly data, indicating so called scaling universality. We suggest improvements on forecasting along the lines of Tsallis non extensive statistics.