  We present a simplified model of the atmosphere of a terrestrial planet as an
open two-dimensional system described by an ideal gas with velocity $\vec{v}$,
density $\rho$ and temperature $T$ fields. Starting with the Chern-Simons
equations for a free inviscid fluid, the external effects of radiation and the
exchange of matter with the strata, as well as diffusion and dissipation are
included. The resulting dynamics is governed by a set of nonlinear differential
equations of first order in time. This defines an initial value problem that
can be integrated given the radiation balance of the planet. If the
nonlinearities are neglected, the integration can be done in analytic form
using standard Green function methods, with small nonlinearities incorporated
as perturbative corrections in a consistent way. If the nonlinear approximation
is not justified, the problem can be integrated numerically. The analytic
expressions as well as the simulations of the linear regime for a continuous
range of parameters in the equations is provided, which allows to explore the
response of the model to changes of those parameters. In particular, it is
observed that a 2.5% reduction in the emissivity of the atmosphere can lead to
an increase of 7C degrees in the average global temperature.
