A Non-Gaussian Stochastic Model for the El Ni\~no Southern Oscillation

A non-autonomous stochastic dynamical model approach is developed to describe the seasonal to interannual variability of the El Ni~no-Southern Oscillation (ENSO). We determine the model coefficients by systematic statistical estimations using partial observations involving only sea surface temperature data. Our approach reproduces the observed seasonal phase locking and its uncertainty, as well as the highly non-Gaussian statistics of ENSO. Finally, we recover the intermittent time series of the hidden processes, including the thermocline depth and the wind bursts.