Realistic ENSO Dynamics Requires a Damped Nonlinear Recharge Oscillator

Abstract

The dynamics of the El Ni\~no-Southern Oscillation (ENSO) are succinctly captured by the Recharge Oscillator (RO) framework. However, to simulate ENSO realistically, careful choices must be made regarding the RO's key parameters. In particular, nonlinear parameters govern how well the model reproduces ENSO asymmetries-El Ni\~no events tend to be stronger but relatively short, often transitioning into La Ni\~na, whereas La Ni\~na events are typically weaker but may last longer. While amplitude asymmetry has been studied within the RO framework, duration and transition asymmetries remain less explored and their causes are debated. In this study, by systematically exploring the RO parameter space-rather than relying on commonly used fitting methods-we identify optimal parameter values that successfully capture key linear and nonlinear ENSO characteristics. In doing so, we revisit several foundational elements of the RO framework. First, we analytically derive the phase relationship between temperature and heat content anomalies, showing that it depends on the signs of the Bjerknes feedback and the ocean damping timescale. We show that self-sustained oscillations fail to reproduce the observed kurtosis of Ni\~no indices. We further derive an analytical expression for the power spectrum and argue that incorporating red noise forcing, rather than white noise, introduces unnecessary complexity. The most realistic yet simplest RO configuration is a strongly damped oscillator, with a decay timescale shorter than the dominant period, forced by multiplicative white noise and influenced by weak deterministic nonlinearities. Identifying these minimal components preserves the RO framework's clarity and isolates the core physical processes underlying ENSO behavior.