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On the use of simple dynamical systems for climate predictions

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Crucifix, Michel [UCL] Rougier, J. [University of Bristol]

Over the last few decades, climate scientists have devoted much effort to the development of large numerical models of the atmosphere and the ocean. While there is no question that such models provide important and useful information on complicated aspects of atmosphere and ocean dynamics, skillful prediction also requires a phenomenological approach, particularly for very slow processes, such as glacial-interglacial cycles. Phenomenological models are often represented as low-order dynamical systems. These are tractable, and a rich source of insights about climate dynamics, but they also ignore large bodies of information on the climate system, and their parameters are generally not operationally defined. Consequently, if they are to be used to predict actual climate system behaviour, then we must take very careful account of the uncertainty introduced by their limitations. In this paper we consider the problem of the timing of the next glacial inception, about which there is on-going debate. Our model is the three-dimensional stochastic system of Saltzman and Maasch (1991), and our inference takes place within a Bayesian framework that allows both for the limitations of the model as a description of the propagation of the climate state vector, and for parametric uncertainty. Our inference takes the form of a data assimilation with unknown static parameters, which we perform with a variant on a Sequential Monte Carlo technique (`particle filter'). Provisional results indicate peak glacial conditions in 60,000 years.

Document type Article de périodique (Journal article) – Synthèse de littérature
Publication date 2009
Language Anglais
Journal information "The European Physical Journal. Special Topics" - Vol. 174, p. 11-31 (2009)
Peer reviewed yes
Publisher Edp Sciences S A (Les Ulis Cedex A)
issn 1951-6355
e-issn 1951-6401
Publication status Publié
Affiliation UCL - SC/PHYS - Département de physique
Links
  1. J. Fourier, Théorie analytique de la chaleur (J. Gabay, Paris, 1822), reproduced in fac-simile in 1988
  2. J. Fourier, Mémoire sur les températures du globe terrestre et des espaces planétaires, in œuvres de Fourier, edited by G. Darboux (Gauthier-Villars et fils, 1890), pp. 97–128
  3. K. Lambeck, Y. Yokoyama, P. Johnston, et al., Earth Planet. Sci. Lett. 181, 513 (2000)
  4. W.F. Ruddiman, Clim. Change 61, 261 (2003)
  5. W.F. Ruddiman, Rev. Geophys. 45, RG4001 (2007)
  6. H. Gallée, J.P. van Ypersele, T. Fichefet, et al., J. Geophys. Res. 96, 13139 (1991)
  7. H. Gallée, J.P. van Ypersele, T. Fichefet, et al., J. Geophys. Res. 97, 15713 (1992)
  8. A. Berger, M.F. Loutre, Science 297, 1287 (2002)
  9. M. Crucifix, A. Berger, Eos, Trans. Am. Geophys. Union 87, 352 (2006)
  10. M. Ghil, Nonlin. Proc. Geophys. 8, 211 (2001)
  11. G. Nicolis, C. Nicolis, Foundations of Complex Systems: Nonlinear Dynamics, Statistical Physics, Information and Prediction (World Scientific, 2007)
  12. B. Saltzman, A.R. Hansen, K.A. Maasch, J. Atmos. Sci. 41, 3380 (1984)
  13. B. Saltzman, Dynamical paleoclimatology: Generalized Theory of Global Climate Change (International Geophysics), Vol. 80 of International Geophysics Series (Academic Press, 2001)
  14. A. Penck, E. Brückner, Die Alpen im Eiszeitalter (Tauchnitz, Leipzig, 1909)
  15. A. Berger, Rev. Geophys. 26, 624 (1988)
  16. S. Elias (ed.), Encyclopedia of Quaternary Science, 1st edn. (Elsevier, 2007)
  17. H.C. Urey, Science 108, 489 (1948)
  18. D.L. Buchanan, A. Nakao, G. Edwards, Science 117, 541 (1953)
  19. W. Dansgaard, Tellus 26, 436 (1964)
  20. C. Emiliani, J. Geol. 63, 538 (1955)
  21. J. Jouzel, V. Masson-Delmotte, O. Cattani, et al., Science 317, 793 (2007)
  22. D. Luethi, M. Le Floch, B. Bereiter, et al., Nature 453, 379 (2008)
  23. CLIMAP Project Members, Geol. Soc. Am. 36, (1981)
  24. J.J. Imbrie, J.D. Hays, D.G. Martinson, et al., The orbital theory of Pleistocene climate: Support from a revised chronology of the marine δO18record, in Milankovitch and Climate, Part I, edited by A. Berger, J. Imbrie, J. Hays, et al. (D. Reidel, Norwell, Mass., 1984), pp. 269–305
  25. M.E. Raymo, B. Grant, M. Horowitz, et al., Mar. Micropaleont. 27, 313 (1996)
  26. L.E. Lisiecki, M.E. Raymo, Paleoceanogr. 20, PA1003 (2005)
  27. M.E. Raymo, Paleoceanogr. 12, 577 (1997)
  28. A. Grossman, J. Morlet, SIAM J. Math. Anal. 15, 723 (1984)
  29. C. Torrence, G.P. Compo, Bull. Am. Meteorol. Soc. 79, 61 (1998)
  30. P. Grassberger, I. Procaccia, Phys. Rev. Lett. 50, 346 (1983)
  31. C. Nicolis, G. Nicolis, Proc. Natl. Acad. Sci. USA 83, 536 (1986)
  32. K.A. Maasch, Clim. Dyn. 4, 45 (1989)
  33. P. Huybers, C. Wunsch, Paleoceanogr. 19, PA1028 (2004)
  34. W. Constantine, D.B. Percival, Fractal: Insightful Fractal Time Series Modeling and Analysis, Insightful Corporation and Applied Physics Laboratory, University of Washington (2007), R package version 1.0-2
  35. P. Grassberger, Nature 323, 609 (1986)
  36. P. Pestiaux, Approche spectrale en modélisation climatique, Ph.D. thesis, Université Catholique de Louvain (1984)
  37. R. Vautard, M. Ghil, Physica D 35, 395 (1989)
  38. P. Yiou, M. Ghil, J. Jouzel, D. Paillard, et al., Clim. Dyn. 9, 371 (1994)
  39. M. Ghil, M.R. Allen, M.D. Dettinger, et al., Rev. Geophys. 40, 769 (2002)
  40. T. Shun, C.J. Duffy, Water Resour. Res. 35, 191 (1999)
  41. L. Gudmundsson, Simsalabim: A collection of Methods for time Series Analysis and Signal Detection (2008), package version 0.1-3, http://simsalabim.r-forge.r-project.org/
  42. P. Huybers, Quaternary Sci. Rev. 26, 37 (2007)
  43. E. Haam, P. Huybers, J. Geophys. Res. (in review)
  44. J.D. Hays, J. Imbrie, N.J. Shackleton, Science 194, 1121 (1976)
  45. N.J. Shackleton, A. Berger, W.R. Peltier, Trans. Roy. Soc. Edinburgh-Earth Sci. 81, 251 (1990)
  46. B. Saltzman, M. Verbitsky, Nature 367, 419 (1994)
  47. J.M. Barnola, D. Raynaud, Y.S. Korotkevich, C. Lorius, Nature 329, 408 (1987)
  48. J. Jouzel, N. Barkov, J. Barnola, et al., Nature 364, 407 (1993)
  49. K. Kawamura, F. Parrenin, L. Lisiecki, et al., Nature 448, 912 (2007)
  50. W.F. Ruddiman, Quat. Sci. Rev. 22, 1597 (2003)
  51. N.J. Shackleton, Science 289, 1897 (2000)
  52. Y. Yokoyama, K. Lambeck, P. de Deckker, et al., Nature 406, 713 (2000)
  53. J.R. Petit, J. Jouzel, D. Raynaud, N.I. Barkov, J.M. Barnola, I. Basile, M. Bender, J. Chappellaz, M. Davis, G. Delaygue, et al., Nature 399, 429 (1999)
  54. J. Adhémar, Révolutions de la mer : déluges périodiques (Carillan-Goeury et V. Dalmont, Paris, 1842)
  55. J.J. Murphy, Q. J. Geol. Soc. London 32, 400 (1876)
  56. J. Croll, Climate and Time in their Geological Relations: A theory of Secular Changes of the Earth’s Climate (Appleton, New York, 1875)
  57. M. Milankovitch, Canon of Insolation and the Ice-Age Problem (Narodna Biblioteka Srbije, Beograd, 1998), (English translation of the original 1941 publication)
  58. A. Berger, Nature 268, 44 (1977)
  59. A. Berger, Celes. Mech. 15, 53 (1977)
  60. A.L. Berger, J. Atmos. Sci. 35, 2362 (1978)
  61. A.D. Vernekar, Meteor. Monogr. 34 (1972)
  62. W.S. Broecker, J. van Donk, Rev. Geophys. 8, 169 (1970)
  63. J. Weertman, Nature 261, 17 (1976)
  64. D.A. Randall (ed.), General Circulation Model Development: Past, Present and Future, Vol. 70 of International Geophysics Series (Academic Press, San Diego, 2000)
  65. A.J. Broccoli, S. Manabe, Clim. Dyn. 1, 87 (1987)
  66. J.E. Kutzbach, Science 214, 59 (1981)
  67. J.F.B. Mitchell, Phil. Trans. Roy. Lond. B 341, 267 (1993)
  68. M.R. Allen, P.A. Stott, J.F.B. Mitchell, et al., Nature 407, 617 (2000)
  69. J.M. Murphy, D.M.H. Sexton, D.N. Barnett, et al., Nature 430, 768 (2004)
  70. J. Imbrie, E.A. Boyle, S.C. Clemens, et al., Paleoceanogr. 7, 701 (1992)
  71. E. Källén, C. Crafoord, M. Ghil, J. Clim. 36, 2292 (1979)
  72. M. Ghil, H. Le Treut, J. Geophys. Res. 86, 5262 (1981)
  73. H. Le Treut, M. Ghil, J. Geophys. Res. 88, 5167 (1983)
  74. H. Gildor, E. Tziperman, J. Geoph. Res. Oceans 106, 9117 (2001)
  75. I.M. Held, Bull. Am. Meteorol. Soc. 86, 1609 (2005)
  76. J. Imbrie, A. Berger, E.A. Boyle, et al., Paleoceanogr. 8, 699 (1993)
  77. W.F. Ruddiman, Clim. Past 2, 43 (2006)
  78. E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)
  79. B. Saltzman, Tellus 34, 97 (1982)
  80. B. Saltzman, K.A. Maasch, Trans. R. Soc. Edinburgh Earth Sci. 81, 315 (1990)
  81. B. Saltzman, K.A. Maasch, Clim. Dyn. 5, 201 (1991)
  82. B. Saltzman, M.Y. Verbitsky, Clim. Dyn. 9, 1 (1993)
  83. H. Haken, Synergetics: An Introduction (Springer, 2004)
  84. J.E. Kutzbach, Quat. Res. 6, 471 (1976), ISSN 0033-5894
  85. N.J. Shackleton, J. Imbrie, Clim. Change 16, 217 (1990)
  86. P. Ditlevsen, H. Svensmark, S. Johnsen, Nature 379, 810 (1996)
  87. J.D. Pelletier, Earth Plan. Sci. Lett. 158, 157 (1998)
  88. P. Huybers, W. Curry, Nature 441, 329 (2006)
  89. B. Saltzman, K.A. Maasch, Glob. Biogeochem. Cycl. 2, 117 (1988)
  90. I. Marsiat, A. Berger, Clim. Dyn. 4, 81 (1992)
  91. G.H. Roe, M.R. Allen, Geoph. Res. Lett. 26, 2259 (1999)
  92. E. Tziperman, M.E. Raymo, P. Huybers, C. Wunsch, Paleoceanography 21, PA4206 (2006)
  93. C.D. Jones, J.M. Gregory, R.B. Thorpe, et al., Clim. Dyn. 25, 189 (2005)
  94. C. Hitchcock, E. Sober, Brit. J. Phil. Sci. 55, 1 (2004)
  95. P. Lipton, Science 307(5707), 219 (2005)
  96. E.T. Jaynes, Where do we stand on maximum entropy, in The maximum entropy formalism, edited by R.D. Levine, M. Tribus (MIT press, 1979), p. 17 http://bayes.wustl.edu/etj/articles/stand.on.entropy.pdf
  97. J. Rougier, Clim. Change 81, 247 (2007)
  98. J.C. Hargreaves, J.D. Annan, Clim. Dyn. 19, 371 (2002)
  99. R.N. Miller, Physica 230, 17 (2007)
  100. K.A. Maasch, B. Saltzman, J. Geoph. Res. Atmospheres 95, 1955 (1990)
  101. K. Hasselmann, Tellus 28, 473 (1976)
  102. J. Liu, M. West, in Sequential Monte Carlo Methods in Practice, edited by A. Doucet, N. de Freitas, N. Gordon (Springer, 2001)
  103. M. Siddall, E. Rohling, A. Almogi-Labin, et al., Nature 423, 853 (2003)
  104. R Development Core Team, R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria (2004), 3-900051-07-0, http://www.R-project.org
Bibliographic reference Crucifix, Michel ; Rougier, J.. On the use of simple dynamical systems for climate predictions. In: The European Physical Journal. Special Topics, Vol. 174, p. 11-31 (2009)
Permanent URL http://hdl.handle.net/2078.1/35446