The El Niño stochastic oscillator

Abstract

A stochastic model is fitted to the observed NINO3.4 time series between 1951–1995. The model is nothing more than the complex version of a first-order autoregressive process. The autocorrelation of this stochastic oscillator model is an exponentially decaying cosine, specified by three parameters: a period, a decay time, and a phase shift. It fits the observed NINO3.4 autocorrelation quite well. Anomalies during an El Nino can be characterized to a large extent by a single, irregularly oscillating, index. Equatorial wave dynamics and delayed-oscillator models have been used to explain this behaviour, and it has been suggested that El Nino might be a stable phenomenon excited by weather noise. Assuming this is the case, the stochastic oscillator has a direct physical interpretation: the parameters of the oscillation can be linked to dynamical models of the delayed-oscillator type, and the noise terms represent random influences, such as intraseasonal oscillations. Long Monte Carlo simulations with the stochastic oscillator show substantial decadal variability and variation in predictability. The observed decadal variability is comparable, except for the rather large rise in the long-term mean around 1980. The observed seasonal dependence of El Nino behaviour is not compatible with the natural variability of a stationary stochastic oscillator. Formulating the model in terms of standardized anomalies takes into account some of the seasonal dependence. A stochastic oscillator forecast model has a skill approaching that of more comprehensive statistical models and may thus serve as an appropriate baseline for the skill of El Nino forecasting systems.