Abstract
Climate is a complex dynamical system, whose understanding is a fascinating scientific challenge which has crucial implications on our society. Like any science, the study of climate is based on data, measurements and experiments, and requires the development of analysis and modeling tools to build a coherent view of climate and its variability. In such a framework, the role of Mathematics and of mathematical developments is essential. In the present contribution, I discuss the hierarchy of climate models, mentioning both the progress of the last thirty years, the role of mathematical approaches, and the many open questions which still need to be clarified. The need for a coherent theory of climate is advocated, as a world-wide effort to understand this fascinating manifestation of Planet Earth.
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References
Baudena, M., D’Andrea, F., Provenzale, A.: A model for soil-vegetation-atmosphere interactions in water-limited ecosystems. Water Resour. Res. 44, 1–9 (2008)
Benzi, R., Parisi, G., Sutera, A., Vulpiani, A.: Stochastic resonance in climatic change. Tellus, 34, 10–16 (1982)
Bordi, I., Fraedrich, K., Sutera, A., Zhu, X.: Transient response to well-mixed greenhouse gas changes. Theor. Appl. Climatol., 109, 245–252 (2012)
Brovkin, V., Claussen, M., Petoukhov, V., Ganopolski, A.: On the stability of the atmospherevegetation system in the Sahara/Sahel region. J. Geophys. Res. 103(31), 613–624 (1998)
Charney, J.: Dynamics of deserts and droughts in the Sahel. Q. J. Roy Meteor. Soc. 101, 193–202 (1975)
Claussen, M.: On multiple solutions of the atmosphere-vegetation system in present-day climate. Global Change Biology 4, 549–559 (1998)
Claussen, M. and 18 others: Earth system models of intermediate complexity: closing the gap in the spectrum of climate system models. Climate Dynamics 18, 579–586 (2002)
Cresto Aleina, F., Baudena, M., D’Andrea, F., Provenzale, A.: Multiple equilibria on planet Dune: climate-vegetation dynamics on a sandy planet. Tellus B (2013). doi: 10.3402/tellusb.v65i0.17662
D’Andrea, F., Provenzale, A., Vautard, R., De Noblet-Decoudré, N.: Hot and cool summers: Multiple equilibria of the continental water cycle. Geophys. Res. Lett. (2006). doi: 10.1029/2006GL027972
Dekker, S.C., de Boer, H.J., Brovkin, V., Fraedrich, K., Wassen, M.J., Rietkerk, M.: Biogeophysical feedbacks trigger shifts in the modelled climate system at multiple scales. Biogeosciences 7, 1237–1245 (2010)
Dijkstra, H.A.: Nonlinear Physical Oceanography: A Dynamical Systems Approach to the Large Scale Ocean Circulation and El Nino. Springer, New York, USA (2005)
Dijkstra, H.A.: Nonlinear Climate Dynamics. Cambridge University Press, Cambridge, UK (2013)
Fraedrich, K., Jansen, H., Kirk, E., Luksch, U., Lunkeit, F.: The Planet Simulator: Towards a user friendly model. Meteorologische Zeitschrift 14, 299–304 (2005)
Ghil, M.: Cryothermodynamics: the chaotic dynamics of paleoclimate. Physica D 77, 130–159 (1994)
Ghil, M., Childress, S.: Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory and Climate Dynamics. Springer, New York, USA (1987)
Gildor, H., Tziperman, E.: A sea ice climate switch mechanism for the 100-kyr glacial cycles. J. Geophysical Res. Oceans 106, 9117–9133 (2001)
Hazeleger, W., Bintanja, R.: Studies with the EC-Earth seamless earth system prediction model. Climate Dynamics 39, 2609–2610 (2012)
Jin, F.F., Neelin, J.D., Ghil, M.: El Nino on the Devil’s Staircase: Annual subharmonic steps to chaos. Science 264, 70–72 (1994)
Lovelock, J.E.: Gaia. A new look at life on Earth. Oxford University Press, Oxford, UK (1979)
Milankovitch, M.: Canon of Insolation and the Ice Age Problem. Royal Serbian Academy, Belgrade (1941)
North, G.R., Cahalan, R.F., Coakley, J.A. Jr: Energy Balance ClimateModels. Rev. Geophysics and Space Physics 19, 91–121 (1981)
McGuffie, K., Henderson-Sellers, A.: A Climate Modelling Primer. Wiley, Chichester, UK (2005)
Paillard, D.: Glacial cycles: Toward a new paradigm. Reviews of Geophysics 39, 325–346 (2001)
Peixoto, J.P., Oort, A.H.: Physics of Climate. AIP Press, New York, USA (1992)
Pierrehumbert, R.T.: Principles of Planetary Climate. Cambridge University Press, Cambridge, UK (2010)
Rietkerk, M. and 15 others: Local ecosystem feedbacks and critical transitions in the climate. Ecological Complexity 8, 223–228 (2011)
Spiegel, D.S., Menou, K., Scharf, C.A.: Habitable Climates. The Astrophysical Journal 681, 1609–1623 (2008)
Stommel, H.: Thermohaline Convection with Two Stable Regimes of Flow. Tellus 13, 224–230 (1961)
Tyler, D.R., Catling, D.C.: An analytic radiative-convective model for planetary atmospheres. The Astrophysical Journal (2012). doi:10.1088/0004-637X/757/1/104
Vladilo, G., Murante, G., Silva, L., Provenzale, A., Ferri, G., Ragazzini, G.: The habitable zone of Earth-like planets with different levels of atmospheric pressure. The Astrophysical Journal (2013). doi:10.1088/0004-637X/767/1/65
Washington, W.M., Parkinson, C.L.: An Introduction to Three-Dimensional Climate Modeling. University Science Books, Sausalito, CA, USA (2005)
Williams, D.M., Kasting, J.F.: Habitable Planets with High Obliquities. ICARUS 129, 254–267 (1997)
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Provenzale, A. (2014). Climate as a Complex Dynamical System. In: Celletti, A., Locatelli, U., Ruggeri, T., Strickland, E. (eds) Mathematical Models and Methods for Planet Earth. Springer INdAM Series, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-02657-2_11
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DOI: https://doi.org/10.1007/978-3-319-02657-2_11
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