ESD Earth System Dynamics ESD Earth Syst. Dynam. 2190-4987 Copernicus Publications Göttingen, Germany 10.5194/esd-3-19-2012 Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture Pascale S. 2 1 Gregory J. M. 3 4 Ambaum M. H. P. 1 Tailleux R. 1 Lucarini V. 2 5 Department of Meteorology, University of Reading, Reading, UK Meteorologishes Institut, Klimacampus, University of Hamburg, Hamburg, Germany NCAS-Climate, Meteorology Building, University of Reading, Reading, UK Met Office Hadley Centre, Exeter, UK Department of Mathematics and Statistics, University of Reading, Reading, UK 19 01 2012 3 1 19 32 Copyright: © 2012 S. Pascale et al. 2012 This work is licensed under the Creative Commons Attribution 3.0 Unported License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/3.0/ This article is available from https://esd.copernicus.org/articles/3/19/2012/esd-3-19-2012.html The full text article is available as a PDF file from https://esd.copernicus.org/articles/3/19/2012/esd-3-19-2012.pdf

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<sup>−2</sup> K<sup>−1</sup> of material entropy production is due to vertical heat transport and 5–7 mW m<sup>−2</sup> K<sup>−1</sup> to horizontal heat transport.

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