  Like any fluid heated from below, the atmosphere is subject to vertical
instability which triggers convection. Convection occurs on small time and
space scales, which makes it a challenging feature to include in climate
models. Usually sub-grid parameterizations are required. Here, we develop an
alternative view based on a global thermodynamic variational principle. We
compute convective flux profiles and temperature profiles at steady-state in an
implicit way, by maximizing the associated entropy production rate. Two
settings are examined, corresponding respectively to the idealized case of a
gray atmosphere, and a realistic case based on a Net Exchange Formulation
radiative scheme. In the second case, we are also able to discuss the effect of
variations of the atmospheric composition, like a doubling of the carbon
dioxide concentration.
