Tsallis nonextensive statistical mechanics of El Nino Southern Oscillation Index

Abstract: The shape and tails of partial distribution functions (PDF) for a climatological signal, i.e. the El Nino SOI and the turbulent nature of the ocean-atmosphere variability are linked through a model encompassing Tsallis nonextensive 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 variabil- ity distributions can be sufficiently well fitted with a chi-square-distribution. The transition between the small time scale model of nonextensive, intermittent process and the large scale Gaussian exten- sive homogeneous fluctuation picture is found to occur at above ca. a 48 months time lag. The intermittency exponent ($\kappa$) 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.