Abstract The recharge oscillator (RO) model has been successfully used to understand different aspects of the El Niño‐Southern Oscillation (ENSO). Fitting the RO to observations and climate model simulations consistently suggests that ENSO is a damped oscillator whose variability is sustained and made irregular by external weather noise. We investigate the methods that have been used to estimate the growth rate of ENSO by applying them to simulations of both damped and self‐sustained RO regimes. We find that fitting a linear RO leads to parameters that imply a damped oscillator even when the fitted data were produced by a model that is self‐sustained. Fitting a nonlinear RO also leads to a significant bias toward the damped regime. As such, it seems challenging to decide whether ENSO is a damped or a self‐sustained oscillation by fitting such models to observations, and the possibility that ENSO is self‐sustained cannot be ruled out.

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