Earth System Dynamics
www.earth-syst-dynam.net
2190-4979
2190-4987
3
1
2012
10.5194/esd-3-19-2012
http://www.earth-syst-dynam.net/3/19/2012/
http://www.earth-syst-dynam.net/3/19/2012/esd-3-19-2012.html
http://www.earth-syst-dynam.net/3/19/2012/esd-3-19-2012.pdf
19
32
2012-01-19
Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture
S. Pascale
salvatore.pascale@zmaw.de
J. M. Gregory
M. H. P. Ambaum
R. Tailleux
V. Lucarini
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
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.
Ambaum, M. H P.: Thermal physics of the atmosphere, Wiley-Blackwell, ISBN 978-0-470-74515-1, eBoook: http://dx.doi.org/10.1002/9780470710364doi:10.1002/9780470710364, 256 pp., Chichester, 2010.
Busse, F.: On Howard's upper bound for heat transport by thermal convection, J. Fluid Mech., 37, 457–477, 1969.
Busse, F H.: Bounds for turbulent shear flow, J. Fluid Mech., 41, 219–240, 1970.
Caldeira, K.: The maximum entropy principle: a critical discussion, Climatic Change, 85, 267–269, 2007.
DeGroot, S. and Mazur, P.: Non-equilibrium thermodynamics, Dover, 1984.
Dewar, R C.: Maximum entropy production and the fluctuation theorem, J. Phys A, 38, L371–L381, 2005.
Dewar, R C.: Maximum entropy production as an inference algorithm that translates physical assumption into macroscopic predictions: don't shoot the messenger, Entropy, 11, 931–944, 2009.
Dufresne, J., Fournier, R., Hourdin, C., and Hourdin, F.: Net exchange reformulation of radiative transfer in the CO<sub>2</sub> 15 μm band on Mars, J. Atmos. Sci., 62, 3303–3319, 2005
Dyke, J. and Kleidon, A.: The maximum entropy production principle: its theoretical foundations and applications to the earth system, Entropy, 12, 613–630, 2010.
Edwards, J. and Slingo, A.: Studies with a flexible new radiation code, Part one: Choosing a configuration for a large-scale model, Q. J. Roy. Meteorol. Soc., 122, 689–719, 1996.
Fraedrich, K. and Lunkeit, F.: Diagnosing the entropy budget of a climate model, Tellus~A, 60, 921–931, 2008.
Goody, R.: Sources and sinks of climate entropy, Q. J. Roy. Meteorol. Soc., 126, 1953–1970, 2000.
Goody, R.: Maximum entropy production in climate theory, J. Atmos. Sci., 64, 2735–2739, 2007.
Gordon, C., Cooper, C., Senior, C., Banks, H., Gregory, J., Johns, T., Mitchell, J., and Wood, R A.: The simulation of SST, sea ice extents and ocean heat transports in a version of the Hadley Centre coupled model without flux adjustments, Clim. Dynam., 16, 147–168, 2000.
Grassl, H.: The climate at the maximum-entropy production by meridional atmospheric and oceanic heat fluxes, Q. J. Roy. Meteorol. Soc., 107, 153–166, 1981.
Grassl, H.: Foreword, in: Non-equilibrium thermodynamics and the production of entropy, Springer, 2005.
Grinstein, G. and Linsker, R.: Comments on a derivation and application of the maximum entropy production principle, J. Phys A, 40, 9717–9720, 2007.
Herbert, C., Paillard, D., and Dubrulle, B.: Entropy production and multiple equilibria: the case of the ice-albedo feedback, Earth Syst. Dynam., 2, 13–23, http://dx.doi.org/10.5194/esd-2-13-2011doi:10.5194/esd-2-13-2011, 2011a.
Herbert, C., Paillard, D., Kageyama, M., and Dubrulle, B.: Present and last glacial maximum climates as states of maximum entropy production, Q. J. Roy. Meteorol. Soc., 137, 1059–1069, 2011b.
Ito, T. and Kleidon, A.: Non-equilibrium thermodynamics and the production of entropy, chapter~8, Entropy production of atmospheric heat transport, pages, Springer, 93–106, 2005.
Jaynes, E.: Information theory and statistical mechanics, Phys. Rev., 106, 620–630, 1957.
Jones, C., Gregory, J., Thorpe, R., Cox, P., Murphy, J., Sexton, D., and Valdes, P.: Systematic optimisation and climate simulation of FAMOUS, a fast version of HadCM3, Clim. Dynam., 25, 189–204, 2005.
Jupp, T. and Cox, P.: MEP and planetary climates: insights from a two-box climate model containing atmospheric dynamics, Philos. T. Roy. Soc B, 365, 1355–1365, 2010.
Kleidon, A.: Beyond gaia: thermodynamic of life and earth system functioning, Climatic Change, 66, 271–319, 2004.
Kleidon, A.: Nonequilibrium thermodynamics and maximum entropy production in the earth system, Naturwissenschaften, 96, 653–677, 2009.
Kleidon, A.: A basic introduction to the thermodynamics of the earth system far from equilibrium and maximum entropy production, Philos. T. Roy. Soc B, 365, 1303–1315, 2010.
Kleidon, A., Fraedrich, K., and Kunz, T., and Lunkeit, F.: The atmospheric circulation and the states of maximum entropy production, Geophys. Res. Lett., 30, 2223, http://dx.doi.org/10.1029/2003GL018363doi:10.1029/2003GL018363, 2003.
Kleidon, A., Fraedrich, K., Kirk, E., and Lunkeit, F.: Maximum entropy production and the strenght of boundary layer exchange in an atmospheric general circulation model, Geophys. Res. Lett., 33, L08709, http://dx.doi.org/10.1029/2005GL025373doi:10.1029/2005GL025373, 2006.
Kunz, T., Fraedrich, K., and Kirk, E.: Optimisation of simplified GCMs using circulation indices and maximum entropy production, Clim. Dynam., 30, 803–813, 2008.
Lorenz, E.: Generation of available potential energy and the intensity of the general circulation, Pergamon, Tarrytown, N.Y., 1960.
Lorenz, R., Lunine, J., Withers, P., and McKay, C.: Titan,Mars and Earth: Entropy production by latitudinal heat transport, Geophys. Res. Lett., 28, 415–418, 2001.
Lucarini, V.: Thermodynamic efficiency and entropy production in the climate system, Phys. Rev E, 80, 021118, http://dx.doi.org/10.1103/PhysRevE.80.02118doi:10.1103/PhysRevE.80.02118, 2009.
Lucarini, V., Fraedrich, K., and Ragone, F.: New results on the thermodynamic properties of the climate, J. Atmos. Sci., 68, 2438–2458, 2011.
Malkus, W.: Outline of a theory of turbulent shear flow, J. Fluid Mech., 1, 521–539, 1956.
Malkus, W.: Borders of disordrs: in turbulent channel flow, J. Fluid Mech., 489, 185–198, 2003.
Malkus, W. V R.: The heat transport and spectrum of thermal turbulence, P. Roy. Soc. Lond A, 225, 196–212, 1954.
Martyushev, L. and Seleznev, V.: Maximum entropy production principle in physics, chemistry and biology, Phys. Rep., 426, 1–45, 2006.
Murakami, S. and Kitoh, A.: Euler-Lagrange equation of the most simple 1-d climate model based on the maximum entropy production hypothesys, Q. J. Roy. Meteorol. Soc., 131, 1529–1538, 2005.
Nicolis, C. and Nicolis, G.: Stability, complexity and the maximum dissipation conjecture, Q. J. Roy. Meteorol. Soc., 136, 1161–1169, 2010.
Noda, A. and Tokioka, T.: Climates at minima of the entropy exchange rate, J. Meteorol. Soc. Jpn., 61, 894–908, 1983.
Ozawa, H. and Ohmura, A.: Thermodynamics of a global-mean state of the atmosphere: A state of maximum entropy increase, J. Climate, 10, 441–445, 1997.
Ozawa, H., Ohmura, A., Lorenz, R., and Pujol, T.: The second law of thermodynamics and the global climate system: a review of the maximum entropy production principle, Rev. Geophys., 41, 1018, http://dx.doi.org/10.1029/2002RG000113doi:10.1029/2002RG000113, 2003.
Paltridge, G.: Thermodynamic dissipation and the global climate system. Q. J. Roy. Meteorol. Soc., 107, 531–547, 1981.
Paltridge, G W.: Global dynamics and climate-a system of minimum entropy exchange, Q. J. Roy. Meteorol. Soc., 101, 475–484, 1975.
Paltridge, G W.: The steady state format of global climate, Q. J. Roy. Meteorol. Soc., 104, 927–945, 1978.
Pascale, S., Gregory, J., Ambaum, M., and Tailleux, R.: Climate entropy budget of the HadCM3 atmosphere-ocean general circulation model and FAMOUS, its low-resolution version, Clim. Dynam., 36, 1189–1206, 2011a.
Pascale, S., Gregory, J., Ambaum, M., and Tailleux, R.: A parametric sensitivity study of entropy production and kinetic energy dissipation using the FAMOUS~AOGCM, Clim. Dynam., doi 10.1007/s00382–011–0996–2, in press, 2011b.
Peixoto, J P. and Oort, A.: Physics of the Climate, Springer-Verlag, New York, 1992.
Pope, V D., Gallani, M L., Rowntree, P R., and Stratton, R A.: The impact of new physical parametrizations in the Hadley Centre climate model – HadAM3, Clim. Dynam., 16, 123–146, 2000.
Pujol, T.: Eddy heat diffusivity at maximum dissipation in a radiative-convective one-dimensional climate model, J. Meteorol. Soc. Jpn., 81, 305–315, 2003.
Pujol, T. and Fort, J.: States of maximum entropy production in a one-dimensional vertical model with convective adjustments, Tellus~A, 54, 363–369, 2002.
Reichler, T. and Kim, J.: How well do coupled models simulate today's climate? B. Am. Meteorol. Soc., 89, 303–311, 2008.
Rodgers, C.: Minimum entropy exchange principle-reply, Q. J. Roy. Meteorol. Soc., 102, 455–457, 1976.
Schulman, L L.: A theoretical study of the efficiency of the general circulation, J. Atmos. Sci., 34, 559–580, 1977.
Shimokawa, S. and Ozawa, H.: On the thermodynamics of the oceanic general circulation: entropy increase rate of an open dissipative system and its surroundings, Tellus~A, 53A, 266–277, 2001.
Smith, R. S., Gregory, J. M., and Osprey, A.: A description of the FAMOUS (version XDBUA) climate model and control run, Geosci. Model Dev., 1, 53–68, http://dx.doi.org/10.5194/gmd-1-53-2008doi:10.5194/gmd-1-53-2008, 2008.
Trenberth, K., Fasullo, J., and Kiehl, J.: Earth's global energy budget, B. Am. Meteorol. Soc., 90, 311–324, 2009.