An improved noise model for representing westerly wind bursts in the recharge oscillator model of ENSO

Abstract

Westerly wind bursts (WWBs) have long been known to have a major impact on the development of El Ni\~no events. In particular, they amplify these events, with stronger events associated with a higher number and stronger WWBs. We consider here a noise-driven recharge oscillator model of ENSO. Commonly, WWBs are represented by a state-dependent Gaussian noise that naturally reproduces the amplification of warm events. However, we show that many properties of WWBs and their effects on sea surface temperature (SST) are better captured by a conditional additive and multiplicative (CAM) noise, which presents a promising alternative to represent WWBs. In addition to recovering the sporadic nature of WWBs, CAM noise leads to an asymmetry between El Ni\~no and La Ni\~na events without the need for deterministic nonlinearities. Furthermore, CAM noise generates SST dynamics 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 observed bulk statistical properties of ENSO equally well as the commonly used multiplicative Gaussian red noise model, but additionally better reproduces dynamical signatures such as the increased number of WWBs preceding large El Ni\~no events.