Contrasting different noise models for representing westerly wind bursts in a recharge oscillator model of ENSO

Abstract. Westerly wind bursts (WWBs) have long been known to have a major impact on the development of El Niño events. In particular, they amplify these events, with stronger events associated with a higher number of WWBs. We further find indications that WWBs lead to a more monotonically increasing evolution of warming events. We consider here a noise-driven recharge oscillator model of ENSO. Commonly, WWBs are represented by a state-dependent Gaussian noise which naturally reproduces the amplification of warm events. However, we show that many properties of WWBs and their effects on sea surface temperature (SST) are not well captured by such Gaussian noise. Instead, we show that conditional additive and multiplicative (CAM) noise presents a promising alternative. In addition to recovering the sporadic nature of WWBs, CAM noise leads to an asymmetry between El Niño and La Niña events without the need for deterministic nonlinearities. Furthermore, CAM noise generates a more monotonic increase of extreme warming events with a higher frequency of WWBs accompanying the largest events. This suggests that extreme warm events are better modelled by CAM noise. To cover the full spectrum of warm events we propose a conditional noise model in which the wind stress is modelled by additive Gaussian noise for sufficiently small SSTs and by additive CAM noise once the SST exceeds a certain threshold. We show that this conditional noise model captures the observed properties of WWBs reasonably well.