*Ocean-Atmosphere Interaction and Climate Variability* (AGU
monograph, in press), C. Wang, S.-P. Xie, and J. A. Carton, Editors.

Adam H. Sobel

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

Christopher S. Bretherton

Department
of Atmospheric Sciences, University of Washington, Seattle, WA.

Hezi Gildor

Department of Environmental
Sciences and Energy Research,
Weizmann Institute of Science, Rehovot, Israel.

Matthew E. Peters

Department
of Applied Mathematics, University of Washington, Seattle, WA.

**
Abstract**

The authors consider a set of simple models for the divergent component of
the tropical atmospheric circulation, and the associated precipitation field.
A number of strong simplifying assumptions are made, leaving deep convection
and radiation (both simply parameterized) as the key processes in the models.

The first case considered is that of fixed SST, with an SST gradient imposed
across the domain, in the limit of zero convective time scale or strict
quasi-equilibrium (SQE). Steady solutions are found for sufficiently
weak cloud-radiative feedback. As the parameter controlling the strength
of the cloud-radiative feedback is increased, the region of nonzero
precipitation shrinks in size and the precipitation grows stronger there.
For cloud-radiative feedback stronger than a particular value, steady solutions cannot be found, and numerically obtained time-dependent solutions blow up.
In the next case considered, the slab ocean lower boundary condition is used.
In this case the behavior is dramatically different. In the steady solutions,
the strength of the radiative feedback now has little effect on the size of the precipitating region. The finite convective time scale changes the
stability criterion, and when the steady solutions become unstable,
rather than blowing up, well-behaved radiative-convective oscillations
set in. The mechanism for these oscillations is essentially local
radiative-convective or surface flux convective instability, so
they can be studied at a single point. Their frequencies are intraseasonal,
and some inferences can be drawn from them about how ocean coupling affects
the Madden-Julian oscillation.

The simplicity of the models allows a relatively complete understanding of
their behavior.
The sensitivity of the solutions to the key parameters, especially the
convective time scale and the radiative feedback parameter, are discussed
in some detail.