ACP Atmospheric Chemistry and Physics ACP 1680-7324 Copernicus GmbH Göttingen, Germany 10.5194/acp-10-9729-2010 Thermodynamics of climate change: generalized sensitivities Lucarini V. 1 2 3 Fraedrich K. 4 Lunkeit F. 4 Department of Meteorology, University of Reading, Earley Gate, P.O. Box 243, Reading RG6 6BB, UK Department of Mathematics, University of Reading, Whiteknights, P.O. Box 220 Reading RG6 6AX, UK Walker Institute for Climate System Research, University of Reading, Reading RG6 6AR, UK Meteorologisches Institut, Klima Campus, University of Hamburg, Grindelberg 5, 20144 Hamburg, Germany 18 10 2010 10 20 9729 9737 This is an open-access article ditributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. This article is available from http://www.atmos-chem-phys.net/10/9729/2010/acp-10-9729-2010.html The full text article is available as a PDF file from http://www.atmos-chem-phys.net/10/9729/2010/acp-10-9729-2010.pdf

Using a recent theoretical approach, we study how global warming impacts the thermodynamics of the climate system by performing experiments with a simplified yet Earth-like climate model. The intensity of the Lorenz energy cycle, the Carnot efficiency, the material entropy production, and the degree of irreversibility of the system change monotonically with the CO<sub>2</sub> concentration. Moreover, these quantities feature an approximately linear behaviour with respect to the logarithm of the CO<sub>2</sub> concentration in a relatively wide range. These generalized sensitivities suggest that the climate becomes less efficient, more irreversible, and features higher entropy production as it becomes warmer, with changes in the latent heat fluxes playing a predominant role. These results may be of help for explaining recent findings obtained with state of the art climate models regarding how increases in CO<sub>2</sub> concentration impact the vertical stratification of the tropical and extratropical atmosphere and the position of the storm tracks.

 References % vor jede Referenz Becker, E., Frictional heating in global climate models, Mon. Weather Rev., 131, 508–520, 2003. Chou, C., Neelin, J. D., Chen, C.-A., and Tu, J.-Y.: Evaluating the "Rich-Get-Richer" Mechanism in Tropical Precipitation Change under Global Warming, J. Climate, 22, 1982–2005, 2009. Danabasoglu, G. and Gent, P. R.: Equilibrium Climate Sensitivity: is it accurate to use a slab ocean model?, J. Climate, 22, 2494–2499, 2009. Dewar, R.: Maximum entropy production and the fluctuation theorem, J. Phys. A: Math. Gen., 38, L371–L381, 2005. Fraedrich, K.: Simple Climate Models, in: Progress in Probability 49, edited by: Imkeller, P. and von Storch, J.-S., Birkhäuser, Berlin, 65–110, 2001. Fraedrich, K. and Lunkeit, F.: Diagnosing the entropy budget of a climate model, Tellus A, 60, 921–931, 2008. Fraedrich, K., Jansen, H., Kirk, E., Luksch, U., and Lunkeit, F.: The planet simulator: towards a user friendly model, Meteorol. Zeitschrift, 14, 299–304, 2005. Frierson D. M. W.: Robust increases in midlatitude static stability in simulations of global warming, Geophys. Res. Lett., 33, L24816, doi:10.1029/2006GL027504, 2006. Grinstein G. and Linsker R.: Comments on a derivation and application of the 'maximum entropy production' principle, J. Phys. A: Math. Theor., 40, 9717–9720, 2007. Held, I. M.: The Gap between Simulation and Understanding in Climate Modeling, Bull. Amer. Meteor. Soc., 86, 1609–1614, 2005. Hernández-Deckers, D. and von Storch, J.-S.: Energetics Responses to Increases in Greenhouse Gas Concentration, J. Climate, 23, 3874–3887, doi:10.1175/2010JCLI3176.1, 2010. IPCC: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, Cambridge, 2007. Johnson D. R.: Entropy, the Lorenz Energy Cycle and Climate, in: General Circulation Model Development: Past, Present and Future, edited by: Randall, D. A., Academic Press, New York, 659–720, 2000. Kleidon, A. and Lorenz, R. D. (eds.): Non-equilibrium thermodynamics and the production of entropy: life, Earth, and beyond, Springer, Berlin, 2005. Kleidon, A., Fraedrich, K., Kirk, E., and Lunkeit, F.: Maximum entropy production and the strength of boundary layer exchange in an atmospheric general circulation model, Geophys. Res. Lett., 33, L06706, doi:10.1029/2005GL025373, 2006. Kunz, T., Fraedrich, K., and Kirk, E.: Optimisation of simplified GCMs using circulation indices and maximum entropy production, Clim. Dyn., 30, 803–813, 2008. Kushner, P. J., Held, I., and Delworth, T. W.: Southern Hemisphere atmospheric circulation response to global warming, J. Climate, 14, 2238–2249, 2001. Lenton, T. M., Held, H., Kriegler, E., Hall, J. W., Lucht, W., Rahmstorf, S., and Schellnhuber, H. J.: Tipping elements in the Earth's climate system, P. Natl. Acad. Sci., 105, 1786–1793, 2008. Lorenz, E. N.: Available potential energy and the maintenance of the general circulation, Tellus, 7, 157–167, 1955. Lucarini, V.: Response Theory for Equilibrium and Non-Equilibrium Statistical Mechanics: Causality and Generalized Kramers-Kronig relations, J. Stat. Phys., 131, 543–558, 2008a. Lucarini, V.: Validation of Climate Models, in: Encyclopedia of Global Warming and Climate Change, edited by: Philander, SAGE, Thousand Oaks, 1053–1057, 2008b. Lucarini, V.: Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system, J. Stat. Phys., 134, 381–400, 2009a. Lucarini, V.: Thermodynamic Efficiency and Entropy Production in the Climate System, Phys Rev. E, 80, 021118, doi:10.1103/PhysRevE.80.021118, 2009b. Lucarini, V. and Fraedrich K.: Symmetry breaking, mixing, instability, and low frequency variability in a minimal Lorenz-like system, Phys. Rev. E, 80, 026313, doi:10.1103/PhysRevE.80.026313, 2009. Lucarini, V. and Ragone, F.: Energetics of PCMDI/CMIP3 Climate Models: Net Energy Balance and Meridional Enthalpy Transports, Rev. Geophys. doi:10.1029/2009RG000323, 2010. Lucarini, V., Fraedrich, K., and Lunkeit, F.: Thermodynamic analysis of snowball earth hysteresis experiment: Efficiency, entropy production, and irreversibility, Q. J. Roy. Meteorol. Soc., 136, 2–11, 2010. Myhre, G., Highwood, E. J., Shine, K. P., and Stordal, F.: New estimates of radiative forcing due to well mixed greenhouse gases, Geophys. Res. Lett., 25, 2715–2718, 1998. Ozawa, H., Ohmura, A., Lorenz, R. D., 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, doi:10.1029/2002RG000113, 2003. Paltridge, G. W.: Climate and thermodynamic systems of maximum dissipation Nature, 279, 630–631, 1979. Paoletti, S., Rispoli, F., and Sciubba, E.: Calculation of exergetic losses in compact heat exchanger passages, ASME AES, 10, 21–29, 1989. Pascale, S., Gregory, J. M., Ambaum, M. H. P., and Tailleux, R. G.: Climate entropy budget of the HadCM3 atmosphere-ocean general circulation model and of FAMOUS, its low-resolution version, Clim. Dyn., doi:10.1007/s00382-009-0718-1, 2009. Peixoto, J. and Oort, A.: Physics of Climate, Springer, New York, 1992. Ruelle, D.: General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium, Phys. Lett. A, 245, 220–224, 1998. Ruelle, D.: A review of linear response theory for general differentiable dynamical systems, Nonlinearity, 22, 855–870, 2009. Yin, J. F.: A consistent poleward shift of the storm tracks in simulations of 21st century climate, Geophys. Res. Lett., 32, L18701, doi:10.1029/2005GL02368, 2005.