Global instability in the Ghil–Sellers model

Climate Dynamics

Volumn 44, Issue 11-12, 2015, Pages 3361-3381

  Bódai, Tamás ^a   Lucarini, Valerio ^a,b   Lunkeit, Frank ^a   Boschi, Robert ^a  

^a UNIVERSITY OF HAMBURG   (Germany)

^b UNIVERSITY OF READING   (United Kingdom)

Author keywords

Edge tracking; Energy balance model; Global instability; Nonequilibrium thermodynamics; Tipping point

Indexed keywords

EID: 84939897858     PISSN: 09307575     EISSN: 14320894     Source Type: Journal    
DOI: 10.1007/s00382-014-2206-5     Document Type: Article

References (54)

1. 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):1166–1184
2. Berry FAJ, Bollay E, Beers NRe (1945) Handbook of meteorology. McGraw-Hill, New York
3. Bódai T, Károlyi G, Tél T (2011) Fractal snapshot components in chaos induced by strong noise. Phys Rev E 83(046):201. doi:10.1103/PhysRevE.83.046201
4. Bódai T, Altmann EG, Endler A (2013) Stochastic perturbations in open chaotic systems: random versus noisy maps. Phys Rev E 87(042):902. doi:10.1103/PhysRevE.87.042902
5. Bordi I, Fraedrich K, Sutera A, Zhu X (2013) On the effect of decreasing $$\text{ CO}_2$$CO2 concentration in the atmosphere. Clim Dyn 40(3–4):651–662. doi: 10.1007/s00382-012-1581-z
6. Boschi R, Lucarini V, Pascale S (2013) Bistability of the climate around the habitable zone: a thermodynamic investigation. Icarus 226(2):1724–1742, doi:10.1016/j.icarus.2013.03.017
7. Budyko MI (1969) The effect of solar radiation variations on the climate of the earth. Tellus 21(5):611–619. doi:10.1111/j.2153-3490.1969.tb00466.x
8. 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):14308–14312. doi:10.1073/pnas.0802430105
9. Dijkstra HA (2005) Nonlinear physical oceanography. Springer, Dordrecht
10. Dijkstra HA, Weijer W (2005) Stability of the global ocean circulation: basic bifurcation diagrams. J Phys Oceanogr 35(6):933–948. doi:10.1175/JPO2726.1
11. 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 15:1–45
12. Ditlevsen PD, Johnsen SJ (2010) Tipping points: early warning and wishful thinking. Geophys Res Lett 37(19). doi:10.1029/2010GL044486
13. 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(2–3):293–306. doi:10.1007/s00382-003-0378-5
14. Dwyer HA, Pettersen (1973) Time-dependent global energy modeling. J Appl Meteor 12:36–42
15. 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:12110510 [mathDS]
16. Fraedrich K (2012) A suite of user-friendly global climate models: hysteresis experiments. Eur Phys J Plus 127(5):1–9. doi:10.1140/epjp/i2012-12053-7
17. Freidlin MI, Wentzell AD (1984) Random perturbations of dynamical systems. Springer, New York
18. Ghil M (1976) Climate stability for a Sellers-type model. J Atmos Sci 33:3–20
19. Ghil M (2001) Hilbert problems for the geosciences in the 21st century. Nonlinear processes in geophysics 8(4/5):211. doi:10.5194/npg-8-211-2001
20. Ghil M, Childress S (1987) Topics in geophysical fluid dynamics: atmospheric dynamics, dynamo theory, and climate dynamics. Springer, New York
21. Grassl H (1981) The climate at maximum entropy production by meridional atmospheric and oceanic heat fluxes. Q J R Meteorol Soc 107(451):153–166. doi:10.1002/qj.49710745110
22. de Groot SR, Mazur P (1969) Non-equilibrium thermodynamics. North-Holland Publishing Company, Amsterdam
23. Hoffman PF, Kaufman AJ, Halverson GP, Schrag DP (1998) A neoproterozoic snowball earth. Science 281(5381):1342–1346. doi:10.1126/science.281.5381.1342
24. 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 55:746–749. doi:10.1103/PhysRevLett.55.746
25. Jabri Y (2003) The Mountain Pass theorem, variants, generalizations and some applications. Cambridge University Press, Cambridge
26. Lai YC, Tél T (2011) Transient chaos. Springer, New York
27. 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):1786–1793. doi:10.1073/pnas.0705414105
28. Lucarini V (2009a) Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system. J Stat Phys 134(2):381–400. doi:10.1007/s10955-008-9675-z
29. Lucarini V (2009b) Thermodynamic efficiency and entropy production in the climate system. Phys Rev E 80(021):118. doi:10.1103/PhysRevE.80.021118
30. Lucarini V, Sarno S (2011) A statistical mechanical approach for the computation of the climatic response to general forcings. Nonlinear Process Geophys 18(1):7–28. doi:10.5194/npg-18-7-2011
31. Lucarini V, Fraedrich K, Lunkeit F (2010) Thermodynamic analysis of snowball Earth hysteresis experiment: efficiency, entropy production and irreversibility. Q J R Meteorol Soc 136(646):2–11. doi:10.1002/qj.543
32. Lucarini V, Fraedrich K, Ragone F (2011) New results on the thermodynamic properties of the climate system. J Atmos Sci 68:2438–2458
33. Lucarini V, Pascale S, Boschi R, Kirk E, Iro N (2013) Habitability and multistability in Earth-like planets. Astronomische Nachrichten 334(6):576–588. doi:10.1002/asna.201311903
34. Madré TK (2011) Turbulence transition in the asymptotic suction boundary layer, diplomarbeit. Philipps-Universität, Marburg
35. Marotzke J, Botzet M (2007) Present-day and ice-covered equilibrium states in a comprehensive climate model. Geophys Res Lett 34(16). doi:10.1029/2006GL028880
36. North GR, Cahalan RF, Coakley JA (1981) Energy balance climate models. Rev Geophys 19(1):91–121. doi:10.1029/RG019i001p00091
37. Nusse HE, Yorke JA (1989) A procedure for finding numerical trajectories on chaotic saddles. Phys D: Nonlinear Phenom 36(1–2):137–156. doi:10.1016/0167-2789(89)90253-4
38. Paltridge GW (1978) The steady-state format of global climate. Q J R Meteorol Soc 104(442):927–945. doi:10.1002/qj.49710444206
39. Pascale S, Gregory JM, Ambaum MHP, Tailleux R, Lucarini V (2012) Vertical and horizontal processes in the global atmosphere and the maximum entropy production conjecture. Earth Syst Dyn 3(1):19–32. doi:10.5194/esd-3-19-2012
40. Pierrehumbert RT (2005) Climate dynamics of a hard snowball earth. J Geophys Res: Atmos 110(D1). doi:10.1029/2004JD005162
41. Pierrehumbert RT, Abbot DS, Voigt A, Koll D (2011) Climate of the Neoproterozoic. Annu Rev Earth Planet Sci 39:417–460. doi:10.1146/annurev-earth-040809-152447
42. Saltzman B (2002) Dynamical paleoclimatology: generalized theory of global climate change. Academic Press, New York
43. Schneider TM, Eckhardt B (2009) Edge states intermediate between laminar and turbulent dynamics in pipe flow. Philos Trans R Soc A 367(1888):577–587. doi:10.1098/rsta.2008.0216
44. Schneider TM, Gibson JF, Lagha M, De Lillo F, Eckhardt B (2008) Laminar-turbulent boundary in plane couette flow. Phys Rev E 78:037301. doi:10.1103/PhysRevE.78.037301
45. Sellers WD (1969) A global climatic model based on the energy balance of the earth-atmosphere system. J Appl Meteorol 8(3):392–400
46. Sieber J, Thompson JMT (2012) Nonlinear softening as a predictive precursor to climate tipping. Philos Trans R Soc A 370(1962):1205–1227. doi:10.1098/rsta.2011.0372
47. Skufca JD, Yorke JA, Eckhardt B (2006) Edge of chaos in a parallel shear flow. Phys Rev Lett 96:174101. doi:10.1103/PhysRevLett.96.174101
48. Stommel H (1961) Thermohaline convection with two stable regimes of flow. Tellus 13:224–230
49. Stone PH (1978) Baroclinic adjustment. J Atmos Sci 35(4):561–571. doi:10.1175/1520-0469(1978)0350561:BA2.0.CO;2
50. Tél T, Gruiz M (2006) Chaotic dynamics. Cambridge University Press, Cambridge
51. Tél T, Lai YC, Gruiz M (2008) Noise-induced chaos: a consequence of long deterministic transients. Int J Bifurc Chaos 18(02):509–520. doi:10.1142/S0218127408020422
52. Voigt A, Marotzke J (2010) The transition from the present-day climate to a modern snowball Earth. Clim Dyn 35(5):887–905. doi:10.1007/s00382-009-0633-5
53. Wetherald RT, Manabe S (1975) The effect of changing the solar constant on the climate of a general circulation model. J Atmos Sci 32:2044–2059
54. Zaliapin I, Ghil M (2010) Another look at climate sensitivity. Nonlinear Process Geophys 17(2):113–122. doi:10.5194/npg-17-113-2010