Abstract

The observed ENSO statistics exhibits a non-Gaussian behavior, which is indicative of the presence of nonlinear processes. In this paper, we use the Recharge Oscillator Model (ROM), a largely used Low-Order Model (LOM) of ENSO, as well as methodologies borrowed from the field of statistical mechanics to identify which aspects of the system may give rise to nonlinearities that are consistent with the observed ENSO statistics. In particular, we are interested in understanding whether the nonlinearities reside in the system dynamics or in the fast atmospheric forcing. Our results indicate that one important dynamical nonlinearity often introduced in the ROM cannot justify a non-Gaussian system behavior, while the nonlinearity in the atmospheric forcing can instead produce a statistics similar to the observed. The implications of the non-Gaussian character of ENSO statistics for the frequency of extreme El Niño events is then examined.

Highlights

  • The observed El Niño Southern Oscillation (ENSO) statistics exhibits a non-Gaussian behavior, which is indicative of the presence of nonlinear processes

  • Because we are interested in evaluating the role of the nonlinearities in the ENSO dynamics, modeled by the perturbed Recharge Oscillator Model (ROM), we would need an Fokker–Planck Equation (FPE) for the Probability Density Function (PDF) of the SST anomalies that fully retains the nonlinear nature of the interaction between the ENSO variables of interest (h, the SST anomaly (TE) ) and the collective variable ξ (t) of Equation (15)

  • Starting from the fact that the ENSO statistics has some clear non- Gaussian features, in this paper, we use the results of some recent papers, and we analyze further the statistics of the ENSO, with the specific goal of discussing which non-linear dynamics might be responsible for them

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Summary

Non-Gaussian-Nonlinear Features of the ENSO Statistics

It is well established that some aspects of the El Niño Southern Oscillation (ENSO) have a non-Gaussian statistics, a characteristic that is indicative of some underlying nonlinear process. The latter approach has been largely used in the context of the foundation of statistical mechanics and thermodynamics and, more recently, in the oceanographic field by some of the authors [17,26,27] It aims at starting from more realistic deterministic systems (instead of the stochastic ones), and by using projection- perturbation procedures, it allows managing the cases in which the time scale separation between the dynamics of the part of interest and that of the rest of the system is not so large: this is the reason why in this work, we shall focus on the projection-perturbation approach, which has been applied to the multi-scale. We shall obtain a general FPE for the perturbed linear/non-linear ROM representing the ENSO dynamics, and we will compare some general statistical features resulting from the FPE (such as the stationary PDF, the relaxation properties and the average timing of the events) with observations, to infer the specific nature of the nonlinearities of the ENSO modeled by the ROM.

The Dynamics of the Components of the ENSO
Is a Possible Internal Nonlinearity Relevant?
The Multiplicative Nature of the Forcing
The Fokker–Planck Equation Guiding the Statistics of the ROM
Inference of the Statistical Features of the ROM from Observations
The Covariance Matrix of the ROM and the Comparison with the ENSO Data
Signatures of a Nonlinear Perturbation
Inferring the FPE Coefficients from Data
Discussion and Conclusions
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