Abstract
Abstract. The objective of this paper is to reconsider the Maximum Entropy Production conjecture (MEP) in the context of a very simple two-dimensional zonal-vertical climate model able to represent the total material entropy production due at the same time to both horizontal and vertical heat fluxes. MEP is applied first to a simple four-box model of climate which accounts for both horizontal and vertical material heat fluxes. It is shown that, under condition of fixed insolation, a MEP solution is found with reasonably realistic temperature and heat fluxes, thus generalising results from independent two-box horizontal or vertical models. It is also shown that the meridional and the vertical entropy production terms are independently involved in the maximisation and thus MEP can be applied to each subsystem with fixed boundary conditions. We then extend the four-box model by increasing its resolution, and compare it with GCM output. A MEP solution is found which is fairly realistic as far as the horizontal large scale organisation of the climate is concerned whereas the vertical structure looks to be unrealistic and presents seriously unstable features. This study suggest that the thermal meridional structure of the atmosphere is predicted fairly well by MEP once the insolation is given but the vertical structure of the atmosphere cannot be predicted satisfactorily by MEP unless constraints are imposed to represent the determination of longwave absorption by water vapour and clouds as a function of the state of the climate. Furthermore an order-of-magnitude estimate of contributions to the material entropy production due to horizontal and vertical processes within the climate system is provided by using two different methods. In both cases we found that approximately 40 mW m−2 K−1 of material entropy production is due to vertical heat transport and 5–7 mW m−2 K−1 to horizontal heat transport.
Highlights
The total material entropy production of the climate system has been estimated from general circulation models to be about 50 mW K−1 m−2 and most of it is associated with the hydrological cycle whereas only a small (10 %) fraction is associated with large scale meridional heat transport (Ambaum, 2010; Fraedrich and Lunkeit, 2008; Pascale et al, 2011a)
This paper provides insights into the application of Maximum Entropy Production conjecture (MEP) to a simple four-box model of climate able to represent both horizontal and vertical heat fluxes and temperature gradients, which are the major characteristics of our climate system
By keeping insolation and optical properties of each atmospheric box fixed, a MEP solution can be found with numerical values of temperatures and heat fluxes reasonably realistic given the simplicity of the model
Summary
A recent reappraisal of MEP (Dewar, 2009; Dyke and Kleidon, 2010) as an inference algorithm that passively translates physical assumptions into macroscopic predictions (Maximum Entropy or, colloquially, MaxEnt, Jaynes, 1957) gives a quite different interpretation. The total material entropy production of the climate system has been estimated from general circulation models to be about 50 mW K−1 m−2 and most of it is associated with the hydrological cycle whereas only a small (10 %) fraction is associated with large scale meridional heat transport (Ambaum, 2010; Fraedrich and Lunkeit, 2008; Pascale et al, 2011a).
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