Is ENSO a self-sustained or a damped oscillation?

The recharge oscillator (RO) model has been used to describe and understand different aspects of the El Niño Southern Oscillation (ENSO). One application involves fitting the RO model to observations or model output to identify if ENSO is a self-sustained or a damped oscillation driven by external weather noise such as westerly wind bursts. Fitting the linear recharge oscillator to observations and climate model simulations consistently yields an asymptotically stable system. This suggests that ENSO can be represented by a damped oscillator whose variability is sustained and made irregular by external stochastic forcing. We investigate the accuracy of methods that have been used to estimate the recharge oscillator parameters and their implied period and growth rate for ENSO using simulations of both linear and nonlinear recharge oscillators. Ultimately, we find that fitting the RO does not allow for robustly differentiating between a damped or a self-sustained regime. Specifically, 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. As such, it seems challenging  to conclude whether ENSO is a damped or a self-sustained system by fitting the recharge oscillator model to observations. It is therefore possible that ENSO could be described instead by a self-sustained oscillator.