Tsallis non-extensive statistical mechanics of El Niño southern oscillation index

The shape and tails of partial distribution functions (PDF) for a climatological signal, i.e., the El Niño SOI and the turbulent nature of the ocean–atmosphere variability are linked through a model encompassing Tsallis non-extensive statistics and leading to evolution equations of the Langevin and Fokker–Planck type. 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. This normalized variability distributions can be sufficiently well fitted with a χ2-distribution. The transition between the small time scale model of non-extensive, intermittent process and the large-scale Gaussian extensive homogeneous fluctuation picture is found to occur at above ca. a 48 months time lag. The intermittency exponent (κ) 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 is in agreement with the intermittency exponent recently obtained for other atmospheric data.