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

Abstract

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 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 variability distributions can be sufficiently well fitted with a χ 2 -distribution. 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 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 κ (= 0.25) is in agreement with the intermittency exponent recently obtained for other atmospheric data.

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

“…Ausloos and Petroni [174] studied the normalized variability of the southern oscillation index (SOI) on different time-scales. Their results indicated a qualitative change in the non-extensivity as the considered scales vary, leading to a classical Boltzmann-Gibbs scaling (q → 1) at larger scales.…”

Introduction to Nonextensive Statistical Mechanics

“…Histograms can be constructed by using values separated by a fixed time lag. They are well fitted by q-Gaussians with q depending on the time lag [292,293]. See Figs.…”

“…The data correspond to the Jan 1866-Jan 2006 period. See[292] for further details. 44 Dependence of q on the (conveniently rescaled) time lag for the SOI.…”

High frequency intrinsic modes in El Niño/Southern Oscillation Index

“…4 we show the signal (dashed line) and the reconstructing function (solid line). The periods used for reconstruction are the following (the parameters A i , B i and φ i obtained by the best fit procedure are summarized in Table 1): 70 months [9], 365 days, 100 days, 76 days, 37 days, 27 days and 24 days.…”