Global instability in the Ghil–Sellers model

详细信息    查看全文

• 作者：Tamás Bódai ; Valerio Lucarini ; Frank Lunkeit ; Robert Boschi
• 关键词：Edge tracking ; Global instability ; Tipping point ; Nonequilibrium thermodynamics ; Energy balance model
• 刊名：Climate Dynamics
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：44
• 期：11-12
• 页码：3361-3381
• 全文大小：1,221 KB
• 参考文献：Ashwin P, Wieczorek S, Vitolo R, Cox P (2012) Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system. Philos Trans R Soc A 371(1962):1166-184View Article
  Berry FAJ, Bollay E, Beers NRe (1945) Handbook of meteorology. McGraw-Hill, New York
  Bódai T, Károlyi G, Tél T (2011) Fractal snapshot components in chaos induced by strong noise. Phys Rev E 83(046):201. doi:10.-103/?PhysRevE.-3.-46201
  Bódai T, Altmann EG, Endler A (2013) Stochastic perturbations in open chaotic systems: random versus noisy maps. Phys Rev E 87(042):902. doi:10.-103/?PhysRevE.-7.-42902
  Bordi I, Fraedrich K, Sutera A, Zhu X (2013) On the effect of decreasing \(\text{ CO}_2\) concentration in the atmosphere. Clim Dyn 40(3-):651-62. doi: 10.-007/?s00382-012-1581-z View Article
  Boschi R, Lucarini V, Pascale S (2013) Bistability of the climate around the habitable zone: a thermodynamic investigation. Icarus 226(2):1724-742, doi:10.-016/?j.?icarus.-013.-3.-17
  Budyko MI (1969) The effect of solar radiation variations on the climate of the earth. Tellus 21(5):611-19. doi:10.-111/?j.-153-3490.-969.?tb00466.?x View Article
  Dakos V, Scheffer M, van Nes EH, Brovkin V, Petoukhov V, Held H (2008) Slowing down as an early warning signal for abrupt climate change. In: Proceedings of the National Academy of Sciences 105(38):14308-4312. doi:10.-073/?pnas.-802430105
  Dijkstra HA (2005) Nonlinear physical oceanography. Springer, Dordrecht
  Dijkstra HA, Weijer W (2005) Stability of the global ocean circulation: basic bifurcation diagrams. J Phys Oceanogr 35(6):933-48. doi:10.-175/?JPO2726.- View Article
  Dijkstra HA, Wubs FW, Cliffe AK, Doedel E, Dragomirescu IF, Eckhardt B, Gelfgat AY, Hazel AL, Lucarini V, Salinger AG, Phipps ET, Sanchez-Umbria J, Schuttelaars H, Tuckerman LS, Thiele U (2014) Numerical bifurcation methods and their application to fluid dynamics: analysis beyond simulation. Commun Comput Phys 15:1-5
  Ditlevsen PD, Johnsen SJ (2010) Tipping points: early warning and wishful thinking. Geophys Res Lett 37(19). doi:10.-029/-010GL044486
  Donnadieu Y, Ramstein G, Fluteau F, Roche D, Ganopolski A (2004) The impact of atmospheric and oceanic heat transports on the sea-ice-albedo instability during the neoproterozoic. Clim Dyn 22(2-):293-06. doi:10.-007/?s00382-003-0378-5
  Dwyer HA, Pettersen (1973) Time-dependent global energy modeling. J Appl Meteor 12:36-2View Article
  Faranda D, Lucarini V, Manneville P, Wouters J (2012) On using extreme values to detect global stability thresholds in multi-stable systems: the case of transitional plane Couette flow. arXiv:-2110510 [mathDS]
  Fraedrich K (2012) A suite of user-friendly global climate models: hysteresis experiments. Eur Phys J Plus 127(5):1-. doi:10.-140/?epjp/?i2012-12053-7 View Article
  Freidlin MI, Wentzell AD (1984) Random perturbations of dynamical systems. Springer, New YorkView Article
  Ghil M (1976) Climate stability for a Sellers-type model. J Atmos Sci 33:3-0View Article
  Ghil M (2001) Hilbert problems for the geosciences in the 21st century. Nonlinear processes in geophysics 8(4/5):211. doi:10.-194/?npg-8-211-2001
  Ghil M, Childress S (1987) Topics in geophysical fluid dynamics: atmospheric dynamics, dynamo theory, and climate dynamics. Springer, New YorkView Article
  Grassl H (1981) The climate at maximum entropy production by meridional atmospheric and oceanic heat fluxes. Q J R Meteorol Soc 107(451):153-66. doi:10.-002/?qj.-9710745110 View Article
  de Groot SR, Mazur P (1969) Non-equilibrium thermodynamics. North-Holland Publishing Company, Amsterdam
  Hoffman PF, Kaufman AJ, Halverson GP, Schrag DP (1998) A neoproterozoic snowball earth. Science 281(5381):1342-346. doi:10.-126/?science.-81.-381.-342
  Iansiti M, Hu Q, Westervelt RM, Tinkham M (1985) Noise and chaos in a fractal basin boundary regime of a Josephson junction. Phys Rev Lett 55:746-49. doi:10.-103/?PhysRevLett.-5.-46 View Article
  Jabri Y (2003) The Mountain Pass theorem, variants, generalizations and some applications. Cambridge University Press, CambridgeView Article
  Lai YC, Tél T (2011) Transient chaos. Springer, New YorkView Article
  Lenton TM, Held H, Kriegler E, Hall JW, Lucht W, Rahmstorf S, Schellnhuber HJ (2008) Tipping elements in the Earth’s climate system. In: Proceedings of the National Academy of Sciences 105(6):1786-793. doi:10.-073/?pnas.-705414105
  Lucarini V (2009a) Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system. J Stat Phys 134(2):381-00. doi:10.-007/?s10955-008-9675-z View Article
  Lucarini V (2009b) Thermodynamic efficiency and entropy production in the climate system. Phys Rev E 80(021):118. doi:10.-103/?PhysRevE.-0.-21118
  Lucarini V, Sarno S (2011) A statistical mechanical approach for the computation of the climatic response to general forcings. Nonlinear Process Geo
• 作者单位：Tamás Bódai (1)
  Valerio Lucarini (1) (2)
  Frank Lunkeit (1)
  Robert Boschi (1)
  
  1. Meteorological Institute, University of Hamburg, Hamburg, Germany
  2. Department of Mathematics and Statistics, University of Reading, Reading, UK
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Geophysics and Geodesy
  Meteorology and Climatology
  Oceanography
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0894

文摘

The Ghil–Sellers model, a diffusive one-dimensional energy balance model of Earth’s climate, features—for a considerable range of the parameter descriptive of the intensity of the incoming radiation—two stable climate states, where the bistability results from the celebrated ice-albedo feedback. The warm state is qualitatively similar to the present climate, while the cold state corresponds to snowball conditions. Additionally, in the region of bistability, one can find unstable climate states. We find such unstable states by applying for the first time in a geophysical context the so-called edge tracking method, which has been used for studying multiple coexisting states in shear flows. This method has a great potential for studying the global instabilities in multistable systems, and for providing crucial information on the possibility of transitions when forcing is present. We examine robustness, efficiency, and accuracy properties of the edge tracking algorithm. We find that the procedure is the most efficient when taking a single bisection per cycle. Due to the strong diffusivity of the system, the transient dynamics, is approximately confined to the heteroclininc trajectory, connecting the fixed unstable and stable states, after relatively short transient times. Such a constraint dictates a functional relationship between observables. We characterize such a relationship between the global average temperature and a descriptor of nonequilibrium thermodynamics, the large scale temperature gradient between low and high latitudes. We find that a maximum of the temperature gradient is realized at the same value of the average temperature, about 270?K, largely independent of the strength of incoming solar radiation. Due to this maximum, a transient increase and nonmonotonic evolution of the temperature gradient is possible and not untypical. We also examine the structural properties of the system defined by bifurcation diagrams describing the equilibria depending on a system parameter of interest, here the solar strength. We construct new bifurcation diagrams in terms of quantities relevant for describing thermodynamic properties such as the temperature gradient and the material entropy production due to heat transport. We compare our results for the energy balance model to results for the intermediate complexity general circulation model the Planet Simulator and find an interesting qualitative agreement.