  The skill of the statistical as well as physics-based coupled climate models
in predicting the El Ni\~no-Southern Oscillation (ENSO) is limited by their
inability to represent the observed ENSO nonlinearity. A promising alternative,
namely a deterministic nonlinear dynamical model derived from an observed ENSO
timeseries, however, has remained elusive. Here we discover such a
phenomenological nonlinear dynamical model that embodies known physical
processes responsible for the self-sustained quasi-oscillatory character of the
ENSO and its observed spectrum of variability. High predictive potential of the
model is demonstrated and the intrinsic nonlinearity of the ENSO is shown to be
critical for overcoming the Spring Predictability Barrier to a large extent.
The unique methodology presented here has the potential for constructing
similar models for other geophysical systems.
