Earth System Dynamics Discussions www.earth-syst-dynam-discuss.net 2190-4995 2 1 2011 10.5194/esdd-2-393-2011 http://www.earth-syst-dynam-discuss.net/2/393/2011/ http://www.earth-syst-dynam-discuss.net/2/393/2011/esdd-2-393-2011.html http://www.earth-syst-dynam-discuss.net/2/393/2011/esdd-2-393-2011.pdf 393 434 2011-05-23 MEP solution for a minimal climate model: success and limitation of a variational problem S. Pascale J. M. Gregory M. H. P. Ambaum R. Tailleux V. Lucarini Department of Meteorology, University of Reading, UK Met Office Hadley Centre, Exeter, UK Department of Mathematics, University of Reading, UK NCAS-Climate, University of Reading, UK Maximum Entropy Production conjecture (MEP) is applied to a minimal 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 number of degrees of freedom, and test its realism by comparing it with a GCM output. An order-of-magnitude evaluation of contributions to the material entropy production (≈50 mW m−2 K−1) due to horizontal and vertical processes within the climate system is carried out by using ad hoc temperature fields. It turns out that approximately 40 mW m−2 K−1 is the entropy production due to vertical heat transport and 5–7 mW m−2 K−1 to horizontal heat transport. 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