Mixed mode oscillations of the El Ni\~no-Southern Oscillation

Very strong El Ni\~no events occur sporadically every 10-20 years. The origin of this bursting behavior still remains elusive. Using a simplified 3-dimensional dynamical model of the tropical Pacific climate system, which captures the El Ni\~no-Southern Oscillation (ENSO) combined with recently developed mathematical tools for fast-slow systems we show that decadal ENSO bursting behavior can be explained as a Mixed Mode Oscillation (MMO), which also predicts a critical threshold for rapid amplitude growth. It is hypothesized that the MMO dynamics of the low-dimensional climate model can be linked to a saddle-focus equilibrium point, which mimics a tropical Pacific Ocean state without ocean circulation.