MEP and planetary climates: insights from a two-box climate model containing atmospheric dynamics.

A two-box model for equator-to-pole planetary heat transport is extended to include simple atmospheric dynamics. The surface drag coefficient CD is treated as a free parameter and solutions are calculated analytically in terms of the dimensionless planetary parameters eta (atmospheric thickness), omega (rotation rate) and xi (advective capability). Solutions corresponding to maximum entropy production (MEP) are compared with solutions previously obtained from dynamically unconstrained two-box models. As long as the advective capability xi is sufficiently large, dynamically constrained MEP solutions are identical to dynamically unconstrained MEP solutions. Consequently, the addition of a dynamical constraint does not alter the previously obtained MEP results for Earth, Mars and Titan, and an analogous result is presented here for Venus. The rate of entropy production in an MEP state is shown to be independent of rotation rate if the advective capability xi is sufficiently large (as for the four examples in the solar system), or if the rotation rate omega is sufficiently small. The model indicates, however, that the dynamical constraint does influence the MEP state when xi is small, which might be the case for some extrasolar planets. Finally, results from the model developed here are compared with previous numerical simulations in which the effect of varying surface drag coefficient on entropy production was calculated.