*Journal of the Atmospheric Sciences*, **58**, 3650-3665.

Adam H. Sobel

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

Johan Nilsson

Department of Meteorology, University of
Stockholm, Stockholm, Sweden.

Lorenzo M. Polvani

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

**Abstract**

Horizontal temperature gradients are
small in the tropical atmosphere, as a consequence of the smallness
of the Coriolis parameter near the equator. This provides a strong
constraint on both large-scale fluid dynamics and diabatic
processes. This work is a step towards the construction of
a balanced dynamical theory for the tropical circulation
which is based on this constraint, and
in which the diabatic processes are explicit and
interactive.

The authors first derive the basic fluid-dynamical scaling under the ``weak
temperature gradient'' (WTG) approximation in a shallow water
system with a fixed mass source representing an externally imposed
heating. This derivation follows an earlier similar one by
Held and Hoskins, but extends the analysis to the
nonlinear case (though on an f-plane), examines the resulting
system in more detail, and presents a solution for an axisymmetric
``top-hat'' forcing. The system is truly balanced, having no
gravity waves, but is different
from other balance models in that the heating is included
a priori in the scaling.

The WTG scaling is then applied to a linear moist model in which
the convective heating is controlled by a moisture variable
which is advected by the flow. This moist model is derived from
the Quasi-Equilibrium Tropical
Circulation Model (QTCM) equations of Neelin and Zeng, but
can be viewed as somewhat more general. A number
of additional approximations are made in order to consider balanced
dynamical modes, apparently not studied previously, which owe their
existence to interactions of the moisture and flow fields. A
particularly interesting mode arises on an f-plane with a constant
background moisture gradient. In the limit of low frequency and
zero meridional wave number this mode has
a dispersion relation mathematically identical to that of a barotropic
Rossby wave, though the phase speed is eastward (for moisture
decreasing poleward in the background state) and the propagation
mechanism is quite different. This mode also has significant positive
growth rate for certain low wave numbers. The
addition of the beta effect complicates matters.
For typical parameters,
when beta is included the direction of phase propagation is
ambiguous, as the effects of the background gradients in moisture
and planetary vorticity appear to cancel to a large degree.
Possible relevance to intraseasonal variability and easterly wave
dynamics is briefly discussed.