**The
ENSO-Spectrum: **A **Result
of Deterministic Chaos**

**or Stochastic Forcing?**

*]in-Sang
van STORCH *,

Institute 0£
Meteorology, University Hamburg, Germany

*Bin *W *ANG and Zhua *W *ANG*

School 0£ Ocean and
Earth Science and Technology, University 0£ Hawaii at Manoa, Honolulu, HI
96822, USA

**Abstract **-The spectrum of ENSO is studied using both observational data and
integrations with coupled models of various complexities. The observed ENSO
spectrum is characterized by a *w *-2-s1ope ( where *w *is frequency)
at high frequencies, a spectral plateau at low frequencies, and a broad
spectral maximum at about one cycle every 3 to 4 years. This smooth spectral
shape is reproduced by the coupled GCMs, but not by the simplified coupled
models. The simple models produce spectra with significant peaks and a *w *-4-
slope at high frequencies. The roles of two mechanisms, deterministic chaos and
stochastic forcing, in de- termining the ENSO spectrum are studied using a
simple non-linear dynamical model, which captures the low-order dynamics of
ENSO and produces, in the presence of the annual cycle, chaotic' behaviors. The
two mechanisms affect the spectrum in different ways. Even though deterministic
chaos Is able to spread variance over a large range of time scales, It alone
cannot produced the w-2-slope in the non-linear model considered. In contrary,
a strong enough stochastic forcing will ultimately produce a *w *-2-slope
at high fre" quencies. The physical meaning of a strong stochastic forcing
is discussed. The unrealistic spectra ob- tainedwith the simple models suggest
the limited utility of simple models in making probability forecasts of ENSO.