Simplified Two-Dimensional Model for Global Atmospheric Dynamics

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.