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# Simplified Two-Dimensional Model for Global Atmospheric Dynamics

Jun 2022

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

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