Analytical probability density function for the statistics of the ENSO phenomenon: Asymmetry and power law tail

This letter has two main goals. The first one is to give a physically reasonable explanation for the use of stochastic models for mimicking the apparent random features of the El Ninõ–Southern Oscillation (ENSO) phenomenon. The second one is to obtain, from the theory, an analytical expression for the equilibrium density function of the anomaly sea surface temperature, an expression that fits the data from observations well, reproducing the asymmetry and the power law tail of the histograms of the NIÑO3 index. We succeed in these tasks exploiting some recent theoretical results of the author in the field of the dynamical origin of the stochastic processes. More precisely, we apply this approach to the celebrated recharge oscillator model (ROM), weakly interacting by a multiplicative term, with a general  deterministic complex forcing (Madden‐Julian Oscillations, westerly wind burst, etc.), and we obtain a Fokker‐Planck equation that describes the statistical behavior of the ROM.