States of maximum entropy production in a one-dimensional vertical model with convective adjustment

We investigate the hypothesis that the atmosphere is constrained to maximize its entropy production by using a one-dimensional (1-D) vertical model. We prescribe the lapse rate in the convective layer as that of the standard troposphere. The assumption that convection sustains a critical lapse rate was absent in previous studies, which focused on the vertical distribution of climatic variables, since such a convective adjustment reduces the degrees of freedom of the system and may prevent the application of the maximum entropy production (MEP) principle. This is not the case in the radiative-convective model (RCM) developed here, since we accept a discontinuity of temperatures at the surface similar to that adopted in many RCMs.
For current conditions, the MEP state gives a difference between the ground temperature and the air temperature at the surface ≈10 K. In comparison, conventional RCMs obtain a discontinuity ≈2K only. However, the surface boundary layer velocity in the MEP state appears reasonable (≈m s^?1). Moreover, although the convective flux at the surface in MEP states is almost uniform in optically thick atmospheres, it reaches a maximum value for an optical thickness similar to current conditions. This additional result may support the maximum convection hypothesis suggested by Paltridge (1978 ).