Estimate of the average timing for strong El Niño events using the recharge oscillator model with a multiplicative perturbation

El Niño Southern Oscillation (ENSO) is the leading mode of tropical Pacific variability at interannual timescales. Through atmospheric teleconnections, ENSO exerts large influences worldwide, so that improved understanding of this phenomenon can be of critical societal relevance. Extreme ENSO events, in particular, have been associated with devastating weather events in many parts of the world, so that the ability to assess their frequency and probability of occurrence is extremely important. In this study, we describe the ENSO phenomenon in terms of the Recharge Oscillator Model perturbed by multiplicative deterministic chaotic forcing, and use methodologies from the field of Statistical Mechanics to determine the average time between El Niño events of given strengths. This is achieved by describing the system in terms of its probability density function, which is governed by a Fokker Planck equation, and then using the Mean First Passage Time technique for the determination of the mean time between extreme events. The ability to obtain analytical solutions to the problem allows a clear identification of the most relevant model parameters for controlling the frequency of extreme events. The key parameter is the strength of the multiplicative component of the stochastic perturbation, but the decorrelation timescale of the stochastic forcing is also very influential. Results obtained with this approach suggest an average waiting time between extreme events of only some tens of years.