Application of entropy production extremal principles to simplified climate models

    We study idealized models of the global climate to examine the hypothesis that the climate adjusts to a state of maximum entropy production, as first discussed by Paltridge 1975.  We develop a hierarchy of atmosphere, ocean and coupled box models and maximize the climate entropy production under the constraint of global energy balance.  These are compared to simplified, but dynamically based, climate models.  Entropy production is defined here as , where , is the meridional heat transport from one box to another, and  is the temperature of each box.  The extremal solutions exhibit some notable properties:  (i) they are in plausible agreement with gross measures (heat transport and pole-equator temperature difference) of the present climate  (ii) they are close to the extremal entropy production states diagnosed from simplified climate models in which  is determined by detailed dynamics  (iii) the simplicity of the models allows us to fully investigate the sensitivity of climate entropy production and its extremal state to model parameters.