ENTROPY AND CLIMATE .2. SIMPLE-MODELS

The possibility that the climate of planet earth might be a state of maximum dissipation was explored by Paltridge through the development of a simple energy-balance model of climate. In this paper we examine the assumptions in Paltridge's model and show that the model can be reduced analytically to a model involving trivial numerical computation. This step exposes the interplay of energy balance, dynamics, and extremum principles. In particular, we highlight the role of a secondary extremum-principle, related to convective activity, which postulates that cloud cover and surface temperature conspire to maximize the sum of sensible- and latent-heat fluxes. We show that this convection hypothesis leads to simple algebraic relations (between cloud cover, surface temperature and horizontal convergence of energy) which could be tested against satellite data. We examine a single-box version of Paltridge's model that exhibits remarkable temperature-regulation through adjustment of cloud cover, and show that the regulation follows from the convection hypothesis rather than the maximum-dissipation hypothesis. Next we investigate the relevance to climate of a theorem on maximum dissipation derived by Ziegler. We reconcile the maximum- and minimum-dissipation 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.