*J. Climate*, **16**, 3978-3992.

Adam H. Sobel

Department of Applied Physics and Applied Mathematics and Department of Earth and Environmental Sciences,
Columbia University, New York, NY

Hezi Gildor

Lamont-Doherty Earth Observatory
of Columbia University, Palisades, NY

**Abstract**

The authors introduce a simple model for the time-dependent
evolution of tropical "hot spots", or localized regions where the
sea surface temperature (SST) becomes unusually high for a limited
period of time. The model consists of a simple zero-dimensional
atmospheric model coupled to an ocean mixed layer. For plausible
parameter values, steady solutions of this model can become unstable
to time-dependent oscillations, which are studied both by linear
stability analysis and explicit time-dependent nonlinear simulation.
For reasonable parameter values, the oscillations have periods
ranging from intraseasonal to subannual. For parameter values only
slightly beyond the threshold for instability, the oscillations
become strongly nonlinear, and have a recharge-discharge character.

The basic mechanism for the instability and oscillations comes from
cloud-radiative and wind-evaporation feedbacks, which play the same
role in the dynamics and are lumped together into a single
parameterization. This is possible because, under the assumption
that the shortwave and longwave radiative effects of high clouds
cancel at the top of the atmosphere, their net effect is only to
transfer energy from ocean to atmosphere exactly as a surface flux
does, and because the two processes are observed to be approximately
in phase on intraseasonal time scales. Both feedbacks move energy
from the ocean to the atmosphere in convective regions, intensifying
the convection and thus destabilizing the system. The same energy
transfer cools the ocean, which eventually (but not instantaneously,
because of the mixed layer's heat capacity) reduces the SST enough
to render the model stable to deep convection, shutting off the
convection. At that point the SST begins warming again under the
resulting clear skies, starting the cycle over.

The authors also examine the forced linear response of the model, in
a weakly stable regime, to an imposed atmospheric oscillation. This
is meant to crudely represent forcing by an atmospheric
intraseasonal oscillation. The model's response as a function of
mixed layer depth is not monotonic, but has a maximum around 10-20
meters, which happens to be close to the observed value in the
western Pacific warm pool.