ENTROPY AND CLIMATE .2. SIMPLE-MODELS

The possibility that the climate of planet earth might be a state of m aximum dissipation was explored by Paltridge through the development o f a simple energy-balance model of climate. In this paper we examine t he assumptions in Paltridge's model and show that the model can be red uced analytically to a model involving trivial numerical computation. This step exposes the interplay of energy balance, dynamics, and extre mum principles. In particular, we highlight the role of a secondary ex tremum-principle, related to convective activity, which postulates tha t cloud cover and surface temperature conspire to maximize the sum of sensible- and latent-heat fluxes. We show that this convection hypothe sis leads to simple algebraic relations (between cloud cover, surface temperature and horizontal convergence of energy) which could be teste d against satellite data. We examine a single-box version of Paltridge 's model that exhibits remarkable temperature-regulation through adjus tment of cloud cover, and show that the regulation follows from the co nvection hypothesis rather than the maximum-dissipation hypothesis. Ne xt we investigate the relevance to climate of a theorem on maximum dis sipation derived by Ziegler. We reconcile the maximum- and minimum-dis sipation theorems of Ziegler and Prigogine in the context of a simple model. Finally, we speculate how the principle of maximum dissipation might be applied in a climate model.