States of maximum entropy production in a onedimensional vertical model with convective adjustment

Abstract

We investigate the hypothesis that the atmosphere is constrained to maximize its entropyproduction by using a one-dimensional (1-D) vertical model. We prescribe the lapse rate in theconvective layer as that of the standard troposphere. The assumption that convection sustainsa critical lapse rate was absent in previous studies, which focused on the vertical distributionof climatic variables, since such a convective adjustment reduces the degrees of freedom of thesystem 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 accepta 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 temperatureand the air temperature at the surface ≈10 K. In comparison, conventional RCMs obtain adiscontinuity ≈2 K only. However, the surface boundary layer velocity in the MEP stateappears reasonable (≈3 m s^-1). Moreover, although the convective flux at the surface in MEPstates is almost uniform in optically thick atmospheres, it reaches a maximum value for anoptical thickness similar to current conditions. This additional result may support the maximumconvection hypothesis suggested by Paltridge (1978).