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The physics of climate variability and climate change

Michael Ghil and Valerio Lucarini

Michael Ghil

  • Geosciences Department and Laboratoire de Météorologie Dynamique (CNRS and IPSL), Ecole Normale Supérieure and PSL University, F-75231 Paris Cedex 05, France and Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, California 90095-1565, USA

Valerio Lucarini

  • Department of Mathematics and Statistics, University of Reading, Reading RG66AX, United Kingdom, Centre for the Mathematics of Planet Earth, University of Reading, Reading RG66AX, United Kingdom, and CEN—Institute of Meteorology, University of Hamburg, Hamburg 20144, Germany

Rev. Mod. Phys. 92, 035002 – Published 31 July, 2020

DOI: https://doi.org/10.1103/RevModPhys.92.035002

Abstract

The climate is a forced, dissipative, nonlinear, complex, and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject to various external forcings, natural as well as anthropogenic. This review covers the observational evidence on climate phenomena and the governing equations of planetary-scale flow and presents the key concept of a hierarchy of models for use in the climate sciences. Recent advances in the application of dynamical systems theory, on the one hand, and nonequilibrium statistical physics, on the other hand, are brought together for the first time and shown to complement each other in helping understand and predict the system’s behavior. These complementary points of view permit a self-consistent handling of subgrid-scale phenomena as stochastic processes, as well as a unified handling of natural climate variability and forced climate change, along with a treatment of the crucial issues of climate sensitivity, response, and predictability.

Physics Subject Headings (PhySH)

Q&A

The Complex Variability of Climate

Published 31 July, 2020

Climate scientist Michael Ghil describes gaps in our understanding of climate change.  

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Article Text

References (542)

  1. Abramov, R. V., and A. J. Majda, 2007, “Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems,” Nonlinearity 20, 2793–2821.
  2. Adam, D., 2011, “Climate change in court,” Nat. Clim. Change 1, 127–130.
  3. Allen, M., 2003, “Liability for climate change,” Nature (London) 421, 891–892.
  4. Andersen, K. K., et al. (North Greenland Ice Core Project Collaboration), 2004, “High-resolution record of Northern Hemisphere climate extending into the last interglacial period,” Nature (London) 431, 147–151.
  5. Andronov, A. A., and L. S. Pontryagin, 1937, “Structurally stable systems,” Dokl. Akad. Nauk SSSR 14, 247–251.
  6. Arakawa, A., and W. H. Schubert, 1974, “Interaction of a cumulus cloud ensemble with the large-scale environment. Part I,” J. Atmos. Sci. 31, 674–701.
  7. Arcoya, D., J. I. Diaz, and L. Tello, 1998, “S-shaped bifurcation branch in a quasilinear multivalued model arising in climatology,” J. Differ. Equations 150, 215–225.
  8. Arnold, L., 1998, Random Dynamical Systems (Springer-Verlag, New York).
  9. Arnold, Ludwig, 1988, Random Dynamical Systems (Springer, New York).
  10. Arnold, V., 1983, Geometric Methods in the Theory of Ordinary Differential Equations (Springer, New York).
  11. Arnold, V. I., 2003, Catastrophe Theory (Springer Nature, Berlin).
  12. Ashwin, P., S. Wieczorek, R. Vitolo, and P. Cox, 2012, “Tipping points in open systems: Bifurcation, noise-induced and rate-dependent examples in the climate system,” Phil. Trans. R. Soc. A 370, 1166–1184.
  13. Baladi, V., 2000, Positive Transfer Operators and Decay of Correlations (World Scientific, Singapore).
  14. Baladi, V., 2008, “Linear response despite critical points,” Nonlinearity 21, T81.
  15. Balmaseda, M. A., et al., 2015, “The ocean reanalyses intercomparison project (ORA-IP),” J. Oper. Oceanogr. 8, s80–s97.
  16. Barenblatt, G. L., 1987, Dimensional Analysis (Gordon and Breach, New York).
  17. Barnes, E. A., and J. A. Screen, 2015, “The impact of Arctic warming on the midlatitude jetstream: Can it? Has it? Will it?,” WIREs Clim. Change 6, 277–286.
  18. Barnett, M., W. Brock, and L. P. Hansen, 2020, “Pricing uncertainty induced by climate change,” Rev. Financ. Stud. 33, 1024–1066.
  19. Barnston, A. G., M. K. Tippett, M. L. Heureux, S. Li, and D. G. DeWitt, 2012, “Skill of real-time seasonal ENSO model predictions during 2002–2011—Is our capability improving?,” Bull. Am. Meteorol. Soc. 93, 631–651.
  20. Barrat, A., M. Barthelemy, and A. Vespignani, 2008, Dynamical Processes in Complex Networks (Cambridge University Press, Cambridge, England).
  21. Batchelor, G., 1974, Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, England).
  22. Beck, C., 1990, “Brownian motion from deterministic dynamics,” Physica (Amsterdam) 169A, 324–336.
  23. Bell, T. L., 1980, “Climate sensitivity from fluctuation dissipation: Some simple model tests,” J. Atmos. Sci. 37, 1700–1707.
  24. Bellenger, H., E. Guilyardi, J. Leloup, M. Lengaigne, and J. Vialard, 2014, “Enso representation in climate models: From CMIP3 to CMIP5,” Clim. Dyn. 42, 1999–2018.
  25. Bellman, R. E., and K. L. Cooke, 1963, Differential-Difference Equations (Rand Corporation, Santa Monica, CA).
  26. Bengtsson, L., M. Ghil, and E. Källén, 1981, Dynamic Meteorology: Data Assimilation Methods (Springer, New York).
  27. Bensid, S., and J. I. Diaz, 2019, “On the exact number of monotone solutions of a simplified Budyko climate model and their different stability,” Discrete Contin. Dyn. Syst. B 24, 1033.
  28. Benzi, R., P. Malguzzi, A. Speranza, and A. Sutera, 1986, “The statistical properties of general atmospheric circulation: Observational evidence and a minimal theory of bimodality,” Q. J. R. Meteorol. Soc. 112, 661–674.
  29. Benzi, R., and A. Speranza, 1989, “Statistical properties of low-frequency variability in the Northern Hemisphere,” J. Clim. 2, 367–379.
  30. Berger, A., and S. Siegmund, 2003, “On the gap between random dynamical systems and continuous skew products,” J. Dyn. Differ. Equations 15, 237–279.
  31. Beri, S., R. Mannella, D. G. Luchinsky, A. N. Silchenko, and P. V. E. McClintock, 2005, “Solution of the boundary value problem for optimal escape in continuous stochastic systems and maps,” Phys. Rev. E 72, 036131.
  32. Berloff, P., A. Hogg, and W. K. Dewar, 2007, “The turbulent oscillator: A mechanism of low-frequency variability of the wind-driven ocean gyres,” J. Phys. Oceanogr. 37, 2363–2386.
  33. Berner, J., et al., 2017, “Stochastic parameterization: Toward a new view of weather and climate models,” Bull. Am. Meteorol. Soc. 98, 565–588.
  34. Bhattacharya, K., M. Ghil, and I. L. Vulis, 1982, “Internal variability of an energy-balance model with delayed albedo effects,” J. Atmos. Sci. 39, 1747–1773.
  35. Biggs, R., S. R. Carpenter, and W. A. Brock, 2009, “Turning back from the brink: Detecting an impending regime shift in time to avert it,” Proc. Natl. Acad. Sci. U.S.A. 106, 826–831.
  36. Bisgard, J., 2015, “Mountain passes and saddle points,” SIAM Rev. 57, 275–292.
  37. Bjerknes, J. P., 1969, “Atmospheric teleconnections from the equatorial Pacific,” Mon. Weather Rev. 97, 163–172.
  38. Bjerknes, V., 1904, “Das Problem der Wettervorhersage, betrachtet vom Standpunkte der Mechanik und der Physik,” Meteorol. Z. 21, 1–7 [“The problem of weather prediction, considered from the viewpoints of mechanics and physics,” 18, 663–667 (2009)].
  39. Bódai, T., G. Károlyi, and T. Tél, 2013, “Driving a conceptual model climate by different processes: Snapshot attractors and extreme events,” Phys. Rev. E 87, 022822.
  40. Bódai, T., Gy. Károlyi, and T. Tél, 2011, “A chaotically driven model climate: Extreme events and snapshot attractors,” Nonlinear Processes Geophys. 18, 573–580.
  41. Bódai, T., V. Lucarini, and F. Lunkeit, 2020, “Can we use linear response theory to assess geoengineering strategies?,” Chaos 30, 023124.
  42. Bódai, T., V. Lucarini, F. Lunkeit, and R. Boschi, 2015, “Global instability in the Ghil-Sellers model,” Clim. Dyn. 44, 3361–3381.
  43. Bódai, T., and T. Tél, 2012, “Annual variability in a conceptual climate model: Snapshot attractors, hysteresis in extreme events, and climate sensitivity,” Chaos 22, 023110.
  44. Boers, N., B. Bookhagen, H. M. J. Barbosa, N. Marwan, J. Kurths, and J. A. Marengo, 2014, “Prediction of extreme floods in the Eastern Central Andes based on a complex networks approach,” Nat. Commun. 5, 5199.
  45. Boers, N., M. Ghil, and D.-D. Rousseau, 2018, “Ocean circulation, ice shelf, and sea ice interactions explain Dansgaard-Oeschger cycles,” Proc. Natl. Acad. Sci. U.S.A. 115, E11005–E11014.
  46. Boiseau, M., M. Ghil, and A. Juillet-Leclerc, 1999, “Trends and interdecadal variability from South-Central Pacific coral records,” Geophys. Res. Lett. 26, 2881–2884.
  47. Bond, G., W. Showers, M. Cheseby, R. Lotti, P. Almasi, P. deMenocal, P. Priori, H. Cullen, I. Hajdas, and G. Bonani, 1997, “A pervasive millennial-scale cycle in the North Atlantic Holocene and glacial climates,” Science 278, 1257–1265.
  48. Bony, S., et al., 2015, “Clouds, circulation and climate sensitivity,” Nat. Geosci. 8, 261–268.
  49. Boos, W. R., and J. V. Hurley, 2013, “Thermodynamic bias in the multimodel mean boreal summer monsoon,” J. Clim. 26.
  50. Bouchet, F., J. Laurie, and O. Zaboronski, 2014, “Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations,” J. Stat. Phys. 156, 1066–1092.
  51. Bouchet, F., and J. Sommeria, 2002, “Emergence of intense jets and Jupiter’s Great Red Spot as maximum-entropy structures,” J. Fluid Mech. 464, 165–207.
  52. Bouchet, F., and A. Venaille, 2012, “Statistical mechanics of two-dimensional and geophysical flows,” Phys. Rep. 515, 227–295.
  53. Branstator, G., 1987, “A striking example of the atmosphere’s leading traveling pattern,” J. Atmos. Sci. 44, 2310–2323.
  54. Breiman, L., 2001, “Random forests,” Mach. Learn. 45, 5–32.
  55. Broecker, W. S., 1991, “The great ocean conveyor,” Oceanography 4, 79–89.
  56. Bryan, F. O., 1986, “High-latitude salinity effects and interhemispheric thermohaline circulations,” Nature (London) 323, 301–304.
  57. Budivsić, M., R. Mohr, and I. Mezić, 2012, “Applied Koopmanism,” Chaos 22, 047510.
  58. Budyko, M. I., 1969, “The effect of solar radiation variations on the climate of the Earth,” Tellus 21, 611–619.
  59. Cane, M. A., and S. E. Zebiak, 1985, “A theory for El Nińo and the Southern Oscillation,” Science 228, 1085–1087.
  60. Caraballo, T., and X. Han, 2017, Applied Nonautonomous and Random Dynamical Systems: Applied Dynamical Systems (Springer Science+Business Media, New York).
  61. Carrassi, A., M. Bocquet, L. Bertino, and G. Evensen, 2018, “Data assimilation in the geosciences: An overview of methods, issues, and perspectives,” WIREs Clim. Change 9, e535.
  62. Carton, J. A., and B. S. Giese, 2008, “A reanalysis of ocean climate using Simple Ocean Data Assimilation (SODA),” Mon. Weather Rev. 136, 2999–3017.
  63. Carvalho, A. N., J. Langa, and J. C. Robinson, 2013, “The pullback attractor,” in Attractors for Infinite-Dimensional Non-autonomous Dynamical Systems, Applied Mathematical Sciences Vol. 182 (Springer New York), pp. 3–22.
  64. Cessi, P., 2019, “The global overturning circulation,” Annu. Rev. Mar. Sci. 11, 249–270.
  65. Cessi, P., and G. R. Ierley, 1995, “Symmetry-breaking multiple equilibria in quasi-geostrophic, wind-driven flows,” J. Phys. Oceanogr. 25, 1196–1205.
  66. Cessi, P., and W. R. Young, 1992, “Multiple equilibria in two-dimensional thermohaline circulation,” J. Fluid Mech. 241, 291–309.
  67. Chang, C. P., M. Ghil, M. Latif, and J. M. Wallace, Eds., 2015, Climate Change: Multidecadal and Beyond (World Scientific, Singapore).
  68. Chang, K-Il, M. Ghil, K. Ide, and C-C. A. Lai, 2001, “Transition to aperiodic variability in a wind-driven double-gyre circulation model,” J. Phys. Oceanogr. 31, 1260–1286.
  69. Charney, J. G., 1947, “The dynamics of long waves in a baroclinic westerly current,” J. Meteorol. 4, 136–162.
  70. Charney, J. G., 1971, “Geostrophic turbulence,” J. Atmos. Sci. 28, 1087–1095.
  71. Charney, J. G., A. Arakawa, D. J. Baker, B. Bolin, R. E. Dickinson, R. M. Goody, C. E. Leith, H. M. Stommel, and C. I. Wunsch, 1979, Carbon Dioxide and Climate: A Scientific Assessment (National Academy of Sciences, Washington, DC).
  72. Charney, J. G., and J. G. DeVore, 1979, “Multiple flow equilibria in the atmosphere and blocking,” J. Atmos. Sci. 36, 1205–1216.
  73. Charney, J. G., R. Fjørtoft, and J. von Neumann, 1950, “Numerical integration of the barotropic vorticity equation,” Tellus 2, 237–254.
  74. Charney, J. G., M. Halem, and R. Jastrow, 1969, “Use of incomplete historical data to infer the present state of the atmosphere,” J. Atmos. Sci. 26, 1160–1163.
  75. Charney, J. G., J. Shukla, and K. C. Mo, 1981, “Comparison of a barotropic blocking theory with observation,” J. Atmos. Sci. 38, 762–779.
  76. Chavanis, P. H., and J. Sommeria, 1996, “Classification of self-organized vortices in two-dimensional turbulence: The case of a bounded domain,” J. Fluid Mech. 314, 267–297.
  77. Chekroun, M. D., M. Ghil, and J. D. Neelin, 2018, “Pullback attractor crisis in a delay differential ENSO model,” in Advances in Nonlinear Geosciences, edited by A. Tsonis (Springer, New York), pp. 1–33.
  78. Chekroun, M. D., J. D. Neelin, D. Kondrashov, J. C. McWilliams, and M. Ghil, 2014, “Rough parameter dependence in climate models and the role of Ruelle-Pollicott resonances,” Proc. Natl. Acad. Sci. U.S.A. 111, 1684–1690.
  79. Chekroun, M. D., E. Simonnet, and M. Ghil, 2011, “Stochastic climate dynamics: Random attractors and time-dependent invariant measures,” Physica (Amsterdam) 240D, 1685–1700.
  80. Chen, F., and M. Ghil, 1996, “Interdecadal variability in a hybrid coupled ocean-atmosphere model,” J. Phys. Oceanogr. 26, 1561–1578.
  81. Cheng, X., and J. M. Wallace, 1993, “Cluster analysis of the Northern Hemisphere wintertime 500 pHa heigh field: Spatial patterns,” J. Atmos. Sci. 50, 2674–2696.
  82. Chorin, A., and P. Stinis, 2007, “Problem reduction, renormalization, and memory,” Commun. Appl. Math. Comput. Sci. 1, 1–27.
  83. Chorin, A. J., O. H. Hald, and R. Kupferman, 2002, “Optimal prediction with memory,” Physica (Amsterdam) 166D, 239–257.
  84. Chown, M., 2004, “Chaotic heavens,” New Sci. 181, 32–35.
  85. Cionni, I., G. Visconti, and F. Sassi, 2004, “Fluctuation dissipation theorem in a general circulation model,” Geophys. Res. Lett. 31, 10.1029/2004GL019739.
  86. Cohen-Tannoudji, C., J. Dupont-Roc, and G. Grynberg, 2007, Photons and Atoms: Introduction to Quantum Electrodynamics (Wiley, New York).
  87. Coles, S., 2001, An Introduction to Statistical Modeling of Extreme Values (Springer Science+Business Media, New York).
  88. Colon, C., D. Claessen, and M. Ghil, 2015, “Bifurcation analysis of an agent-based model for predator-prey interactions,” Ecol. Modell. 317, 93–106.
  89. Compo, G. P., et al., 2011, “The twentieth century reanalysis project,” Q. J. R. Meteorol. Soc. 137, 1–28.
  90. Cooper, F. C., and P. H. Haynes, 2011, “Climate sensitivity via a nonparametric fluctuation-dissipation theorem,” J. Atmos. Sci. 68, 937–953.
  91. Cox, P. M., C. Huntingford, and M. S. Williamson, 2018, “Emergent constraint on equilibrium climate sensitivity from global temperature variability,” Nature (London) 553, 319–322.
  92. Cronin, T. N., 2010, Paleoclimates: Understanding Climate Change Past and Present (Columbia University Press, New York).
  93. Crowley, T. J., W. T. Hyde, and W. R. Peltier, 2001, “CO2 levels required for deglaciation of a ‘near-snowball’ Earth,” Geophys. Res. Lett. 28, 283–286.
  94. Cushman-Roisin, B., and J.-M. Beckers, 2011, Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects (Academic Press, New York), p. 875.
  95. Cvitanović, Predrag, 1988, “Invariant measurement of strange sets in terms of cycles,” Phys. Rev. Lett. 61, 2729–2732.
  96. Cvitanovíc, P., and B. Eckhardt, 1991, “Periodic orbit expansions for classical smooth flows,” J. Phys. A 24, L237.
  97. Da Costa, E. D., and A. C. Colin de Verdiére, 2002, “The 7.7 year North Atlantic Oscillation,” Q. J. R. Meteorol. Soc. 128, 797–817.
  98. Dansgaard, W., et al., 1993, “Evidence for general instability of past climate from a 250-kyr ice-core record,” Nature (London) 364, 218–220.
  99. Davini, P., and F. D’Andrea, 2016, “Northern Hemisphere atmospheric blocking representation in global climate models: Twenty years of improvements?,” J. Clim. 29, 8823–8840.
  100. De Cruz, L., S. Schubert, J. Demaeyer, V. Lucarini, and S. Vannitsem, 2018, “Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models,” Nonlinear Processes Geophys. 25, 387–412.
  101. Dee, D. P., et al., 2011, “The ERA-Interim reanalysis: Configuration and performance of the data assimilation system,” Q. J. R. Meteorol. Soc. 137, 553–597.
  102. de Groot, S. R., and P. Mazur, 1984, Non-Equilibrium Thermodynamics (Dover, New York).
  103. Dell’Aquila, A., V. Lucarini, P. M. Ruti, and S. Calmanti, 2005, “Hayashi spectra of the Northern Hemisphere mid-latitude atmospheric variability in the NCEP and ERA-40 reanalyses,” Clim. Dyn. 25, 639–652.
  104. Dell’Aquila, A., P. M. Ruti, S. Calmanti, and V. Lucarini, 2007, “Southern Hemisphere midlatitude atmospheric variability of the NCEP-NCAR and ECMWF reanalyses,” J. Geophys. Res. 112, D08106.
  105. Deloncle, A., R. Berk, F. D’Andrea, and M. Ghil, 2007, “Weather regime prediction using statistical learning,” J. Atmos. Sci. 64, 1619–1635.
  106. Delworth, T., S. Manabe, and R. J. Stouffer, 1993, “Interdecadal variations of the thermohaline circulation in a coupled ocean-atmosphere model,” J. Clim. 6, 1993–2011.
  107. Delworth, T. L., and M. E. Mann, 2000, “Observed and simulated multidecadal variability in the Northern Hemisphere,” Clim. Dyn. 16, 661–676.
  108. Demaeyer, J., and S. Vannitsem, 2017, “Stochastic parametrization of subgrid-scale processes in coupled ocean-atmosphere systems: Benefits and limitations of response theory,” Q. J. R. Meteorol. Soc. 143, 881–896.
  109. Dickey, J. O., M. Ghil, and S. L. Marcus, 1991, “Extratropical aspects of the 40–50 day oscillation in length-of-day and atmospheric angular momentum,” J. Geophys. Res. 96, 22643–22658.
  110. Dijkstra, H. A., 2005, Nonlinear Physical Oceanography: A Dynamical Systems Approach to the Large Scale Ocean Circulation and El Niño., 2nd ed. (Springer Science+Business Media., Berlin).
  111. Dijkstra, H. A., 2007, “Characterization of the multiple equilibria regime in a global ocean model,” Tellus A 59, 695–705.
  112. Dijkstra, H. A., 2013, Nonlinear Climate Dynamics (Cambridge University Press, Cambridge, England).
  113. Dijkstra, H. A., and G. Burgers, 2002, “Fluid mechanics of El Niño variability,” Annu. Rev. Fluid Mech. 34, 531–558.
  114. Dijkstra, H. A., and M. Ghil, 2005, “Low-frequency variability of the large-scale ocean circulation: A dynamical systems approach,” Rev. Geophys. 43, RG3002.
  115. Dijkstra, H. A., and C. A. Katsman, 1997, “Temporal variability of the wind-driven quasi-geostrophic double gyre ocean circulation: Basic bifurcation diagrams,” Geophys. Astrophys. Fluid Dyn. 85, 195–232.
  116. Ditlevsen, P. D., and S. J. Johnsen, 2010, “Tipping points: Early warning and wishful thinking,” Geophys. Res. Lett. 37.
  117. Doblas-Reyes, Francisco J., Javier Garcia-Serrano, Fabian Lienert, Aida Pinto Biescas, and Luis R. L. Rodrigues, 2013, “Seasonal climate predictability and forecasting: status and prospects,” WIREs Clim. Change 4, 245–268.
  118. Dobrushin, R., 1970, “Prescribing a system of random variables by conditional distributions,” Theory Probab. Appl. 15, 458–486.
  119. Donges, J. F., Y. Zou, N. Marwan, and J. Kurths, 2009, “Complex networks in climate dynamics,” Eur. Phys. J. Special Topics 174, 157–179.
  120. Driver, R. D., 1977, Ordinary and Delay Differential Equations (Springer-Verlag, New York).
  121. Drótos, G., T. Bódai, and T. Tél, 2015, “Probabilistic concepts in a changing climate: A snapshot attractor picture,” J. Clim. 28, 3275–3288.
  122. Duane, G. S., C. Grabow, F. Selten, and M. Ghil, 2017, “Introduction to focus issue: Synchronization in large networks and continuous media-data, models, and supermodels,” Chaos 27, 126601.
  123. Duplessy, J-C, and N. J. Shackleton, 1985, “Response of global deep-water circulation to Earth’s climatic change 135 000–107 000 years ago,” Nature (London) 316, 500–507.
  124. E, W., and J. Lu, 2011, “Multiscale modeling,” Scholarpedia 6, 11527.
  125. Eade, R., D. Smith, A. Scaife, E. Wallace, N. Dunstone, L. Hermanson, and N. Robinson, 2014, “Do seasonal-to-decadal climate predictions underestimate the predictability of the real world?,” Geophys. Res. Lett. 41, 5620–5628.
  126. Eady, E. T., 1949, “Long waves and cyclone waves,” Tellus 1, 33–52.
  127. Eckmann, J. P., 1981, “Roads to turbulence in disipative dynamical systems,” Rev. Mod. Phys. 53, 643–654.
  128. Eckmann, J. P., and D. Ruelle, 1985, “Ergodic theory of chaos and strange attractors, Rev. Mod. Phys. 57, 617–656.
  129. Edwards, P. N., 2010, A Vast Machine: Computer Models, Climate Data, and the Politics of Global Warming (MIT Press, Cambridge, MA).
  130. Egger, J., 1978, “Dynamics of blocking highs,” J. Atmos. Sci. 35, 1788–1801.
  131. Einstein, A., 1905, “On the movement of small particles suspended in a stationary liquid demanded by the molecular-kinetic theory of heat,” Ann. Phys. (Berlin) 322, 549–560 [reprinted in Investigations on the Theory of the Brownian Movement, edited by R. Furth, and A. D. Cowper (Dover, New York, 1956), p. 122].
  132. Emanuel, K. A., 1994, Atmospheric Convection (Oxford University Press, New York).
  133. Embrechts, P., C. Klüppelberg, and T. Mikosch, 1999, Modelling Extremal Events for Insurance and Finance (Springer-Verlag, New York).
  134. Epstein, E. S., 1988, “Long-range weather prediction: Limits of predictability and beyond,” Weather Forecast. 3, 69–75.
  135. Esper, J., E. R. Cook, and F. H. Schweingruber, 2002, “Low-frequency signals in long tree-ring chronologies and the reconstruction of past temperature variability,” Science 295, 2250–2253.
  136. Eyring, V., S. Bony, G. A. Meehl, C. A. Senior, B. Stevens, R. J. Stouffer, and K. E. Taylor, 2016, “Overview of the Coupled Model Intercomparison Project Phase 6 (CMIP6) experimental design and organization,” Geosci. Model Dev. 9, 1937–1958.
  137. Eyring, V., et al., 2016, “ESMValTool (v1.0)—A community diagnostic and performance metrics tool for routine evaluation of Earth system models in CMIP,” Geosci. Model Dev. 9, 1747–1802.
  138. Eyring, V., et al., 2019, “ESMValTool v2.0—Extended set of large-scale diagnostics for quasi-operational and comprehensive evaluation of earth system models in CMIP,” Geosci. Model Dev. 2019, 1–81.
  139. Faranda, D., G. Messori, and P. Yiou, 2017, “Dynamical proxies of North Atlantic predictability and extremes,” Sci. Rep. 7, 41278.
  140. Farrell, B. F., and P. J. Ioannou, 1996, “Generalized stability theory. I: Autonomous operators,” J. Atmos. Sci. 53, 2025–2040.
  141. Feliks, Y., M. Ghil, and A. W. Robertson, 2010, “Oscillatory climate modes in the Eastern Mediterranean and their synchronization with the North Atlantic Oscillation,” J. Clim. 23, 4060–4079.
  142. Feliks, Y., M. Ghil, and A. W. Robertson, 2011, “The atmospheric circulation over the North Atlantic as induced by the SST field,” J. Clim. 24, 522–542.
  143. Feliks, Y., M. Ghil, and E. Simonnet, 2004, “Low-frequency variability in the mid-latitude atmosphere induced by an oceanic thermal front,” J. Atmos. Sci. 61, 961–981.
  144. Feliks, Y., M. Ghil, and E. Simonnet, 2007, “Low-frequency variability in the mid-latitude baroclinic atmosphere induced by an oceanic thermal front,” J. Atmos. Sci. 64, 97–116.
  145. Fenichel, N., 1979, “Geometric singular perturbation theory for ordinary differential equations,” J. Differ. Equations 31, 53–98.
  146. Ferranti, L., S. Corti, and M. Janousek, 2015, “Flow-dependent verification of the ECMWF ensemble over the Euro-Atlantic sector,” Q. J. R. Meteorol. Soc. 141, 916–924.
  147. Feudel, U., A. N. Pisarchik, and K. Showalter, 2018, “Multistability and tipping: From mathematics and physics to climate and brain—Minireview and preface to the focus issue,” Chaos 28, 033501.
  148. Fraedrich, K., 2012, “A suite of user-friendly global climate models: Hysteresis experiments,” Eur. Phys. J. Plus 127, 53.
  149. Fraedrich, K., and H. Bottger, 1978, “A wavenumber frequency analysis of the 500 mb geopotential at 50° N,” J. Atmos. Sci. 35, 745–750.
  150. Fraedrich, K., H. Jansen, E. Kirk, U. Luksch, and F. Lunkeit, 2005, “The planet simulator: Towards a user friendly mode,” Meteorol. Z. 14, 299–304.
  151. Francis, J. A., and S. J. Vavrus, 2012, “Evidence linking Arctic amplification to extreme weather in mid-latitudes,” Geophys. Res. Lett. 39, L06801.
  152. Franzke, C. L. E., T. J. O’Kane, J. Berner, P. D. Williams, and V. Lucarini, 2015, “Stochastic climate theory and modeling,” WIREs Clim. Change 6, 63–78.
  153. Freidlin, M. I., and A. D. Wentzell, 1984, Random Perturbations of Dynamical Systems (Springer, New York).
  154. Frisius, T., F. Lunkeit, K. Fraedrich, and I. N. James, 1998, “Storm-track organization and variability in a simplified atmospheric global circulation model,” Q. J. R. Meteorol. Soc. 124, 1019–1043.
  155. Gálfi, V. M, V. Lucarini, and J. Wouters, 2019, “A large deviation theory-based analysis of heat waves and cold spells in a simplified model of the general circulation of the atmosphere,” J. Stat. Mech. 033404.
  156. Gallavotti, G., and E. G. D. Cohen, 1995, “Dynamical ensembles in stationary states,” J. Stat. Phys. 80, 931–970.
  157. Ghil, M., 1976, “Climate stability for a Sellers-type model,” J. Atmos. Sci. 33, 3–20.
  158. Ghil, M., 1989, “Meteorological data assimilation for oceanographers. Part I: Description and theoretical framework,” Dyn. Atmos. Oceans 13, 171–218.
  159. Ghil, M., 1994, “Cryothermodynamics: The chaotic dynamics of paleoclimate,” Physica (Amsterdam) 77D, 130–159.
  160. Ghil, M., 2001, “Hilbert problems for the geosciences in the 21st century,” Nonlinear Processes Geophys. 8, 211–222.
  161. Ghil, M., 2002, “Natural climate variability,” in Encyclopedia of Global Environmental Change, Vol. 1, edited by T. E. Munn, M. MacCracken, and J. Perry (J. Wiley & Sons, New York), pp. 544–549.
  162. Ghil, M., 2015, “A mathematical theory of climate sensitivity or, How to deal with both anthropogenic forcing and natural variability?” in Climate Change: Multidecadal and Beyond, edited by C. P. Chang, M. Ghil, M. Latif, and J. M. Wallace (World Scientific, Singapore), pp. 31–51.
  163. Ghil, M., 2017, “The wind-driven ocean circulation: Applying dynamical systems theory to a climate problem,” Discrete Contin. Dyn. Syst. A 37, 189–228.
  164. Ghil, M., 2019, “A century of nonlinearity in the geosciences,” Earth Space Sci. 6, 1007–1042.
  165. Ghil, M., 2020, “Hilbert problems for the geosciences in the 21st century—20 years later,” Nonlinear Processes Geophys. (in press), https://doi.org/10.5194/npg-2020-13.
  166. Ghil, M., M. D. Chekroun, and E. Simonnet, 2008, “Climate dynamics and fluid mechanics: Natural variability and related uncertainties,” Physica (Amsterdam) 237D, 2111–2126.
  167. Ghil, M., M. D. Chekroun, and G. Stepan, 2015, “A collection on ’Climate dynamics: Multiple scales and memory effects. Introduction,” Proc. R. Soc. A 471, 20150097.
  168. Ghil, M., and S. Childress, 1987, Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory, and Climate Dynamics (Springer-Verlag, Berlin).
  169. Ghil, M., A. Groth, D. Kondrashov, and A. W. Robertson, 2019, “Extratropical sub-seasonal–to–seasonal oscillations and multiple regimes: The dynamical systems view,” in Sub-seasonal to Seasonal Prediction: The Gap between Weather and Climate Forecasting, edited by A. W. Robertson and F. Vitart (Elsevier, New York), Chap. 6, 119–142.
  170. Ghil, M., M. Halem, and R. Atlas, 1979, “Time-continuous assimilation of remote-sounding data and its effect on weather forecasting,” Mon. Weather Rev. 107, 140–171.
  171. Ghil, M., M. Kimoto, and J. D. Neelin, 1991, “Nonlinear dynamics and predictability in the atmospheric sciences,” Rev. Geophys. 29, 46–55.
  172. Ghil, M., and P. Malanotte-Rizzoli, 1991, “Data assimilation in meteorology and oceanography,” in Advances in Geophysics, Vol. 33 (Academic Press, New York), pp. 141–266.
  173. Ghil, M., and K. C. Mo, 1991, “Intraseasonal oscillations in the global atmosphere. Part 1: Northern Hemisphere and tropics,” J. Atmos. Sci. 48, 752–779.
  174. Ghil, M., A. Mulhaupt, and P. Pestiaux, 1987, “Deep water formation and Quaternary glaciations,” Clim. Dyn. 2, 1–10.
  175. Ghil, M., and A. W. Robertson, 2000, “Solving problems with GCMs: General circulation models and their role in the climate modeling hierarchy,” in General Circulation Model Development: Past, Present and Future, edited by D. A. Randall (Academic Press, New York), pp. 285–325.
  176. Ghil, M., and A. W. Robertson, 2002, ‘Waves’ vs. ‘particles’ in the atmosphere’s phase space: A pathway to long-range forecasting?,” Proc. Natl. Acad. Sci. U.S.A. 99, 2493–2500.
  177. Ghil, M., I. Zaliapin, and S. Thompson, 2008, “A delay differential model of ENSO variability: Parametric instability and the distribution of extremes,” Nonlinear Processes Geophys. 15, 417–433.
  178. Ghil, M., et al., 2002, “Advanced spectral methods for climatic time series,” Rev. Geophys. 40, 3-1–3-41.
  179. Ghil, M., et al., 2011, “Extreme events: Dynamics, statistics and prediction,” Nonlinear Processes Geophys. 18, 295–350.
  180. Gildor, H., and E. Tziperman, 2001, “A sea ice climate switch mechanism for the 100-kyr glacial cycles,” J. Geophys. Res. 106, 9117–9133.
  181. Gill, A. E., 1982, Atmosphere-Ocean Dynamics (Academic Press, New York).
  182. Ginelli, F., P. Poggi, A. Turchi, H. Chaté, R. Livi, and A. Politi, 2007, “Characterizing Dynamics with Covariant Lyapunov Vectors,” Phys. Rev. Lett. 99, 130601.
  183. Gladwell, M., 2000, The Tipping Point: How Little Things Can Make a Big Difference (Little, Brown, Boston).
  184. Gleckler, P. J., C. Doutriaux, P. J. Durack, K. E. Taylor, Y. Zhang, D. N. Williams, E. Mason, and J. Servonnat, 2016, “A more powerful reality test for climate models,” EOS Trans. Am. Geophys. Union 97, https://eos.org/science-updates/a-more-powerful-reality-test-for-climate-models.
  185. Gómez-Leal, I, L. Kaltenegger, V. Lucarini, and F. Lunkeit, 2018, “Climate sensitivity to carbon dioxide and the moist greenhouse threshold of earth-like planets under an increasing solar forcing,” Astrophys. J. 869, 129.
  186. Goody, R., 2000, “Sources and sinks of climate entropy,” Q. J. R. Meteorol. Soc. 126, 1953–1970.
  187. Gottwald, G. A., and I. Melbourne, 2013, “Homogenization for deterministic maps and multiplicative noise,” Proc. R. Soc. A 469, 20130201.
  188. Gozolchiani, A., S. Havlin, and K. Yamasaki, 2011, “Emergence of El Niño as an Autonomous Component in the Climate Network,” Phys. Rev. Lett. 107, 148501.
  189. Graham, R., A. Hamm, and T. Tél, 1991, “Nonequilibrium Potentials for Dynamical Systems with Fractal Attractors or Repellers,” Phys. Rev. Lett. 66, 3089–3092.
  190. Grasman, J., 1987, Asymptotic Methods for Relaxation Oscillations and Applications (Springer Science+Business Media, New York).
  191. Grassberger, P., 1989, “Noise-induced escape from attractors,” J. Phys. A 22, 3283.
  192. Grebogi, C., E. Ott, and J. A. Yorke, 1983, “Fractal Basin Boundaries, Long-Lived Chaotic Transients, and Unstable-Unstable Pair Bifurcation,” Phys. Rev. Lett. 50, 935–938.
  193. Gritsun, A., G. Branstator, and A. J. Majda, 2008, “Climate response of linear and quadratic functionals using the fluctuation-dissipation theorem,” J. Atmos. Sci. 65.
  194. Gritsun, Andrey, and Grant Branstator, 2007, “Climate response using a three-dimensional operator based on the fluctuation-dissipation theorem,” J. Atmos. Sci. 64, 2558–2575.
  195. Gritsun, Andrey, and Valerio Lucarini, 2017, “Fluctuations, response, and resonances in a simple atmospheric model,” Physica (Amsterdam) 349D, 62–76.
  196. Guckenheimer, J., and P. Holmes, 1983, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, 2nd ed. (Springer-Verlag, Berlin).
  197. Guckenheimer, John, Kathleen Hoffman, and Warren Weckesser, 2003, “The forced van der Pol equation I: The slow flow and its bifurcations,” SIAM J. Appl. Dyn. Syst. 2, 1–35.
  198. Haines, K., 1994, “Low-frequency variability in atmospheric middle latitudes,” Surv. Geophys. 15, 1–61.
  199. Hale, J. K., 1977, Theory of Functional Differential Equations (Springer-Verlag, New York).
  200. Hamm, A., T. Tél, and R. Graham, 1994, “Noise-induced attractor explosions near tangent bifurcations,” Phys. Lett. A 185, 313–320.
  201. Hanggi, P., 1986, “Escape from a metastable state,” J. Stat. Phys. 42, 105–148.
  202. Hannart, A., A. Carrassi, M. Bocquet, M. Ghil, P. Naveau, M. Pulido, J. Ruiz, and P. Tandeo, 2016, “DADA: Data assimilation for the detection and attribution of weather and climate-related events,” Clim. Change 136, 155–174.
  203. Hairer, M., and A. J. Majda, 2010, “A simple framework to justify linear response theory,” Nonlinearity 23, 909–922.
  204. Hannart, A., and P. Naveau, 2018, “Probabilities of causation of climate changes,” J. Clim. 31, 5507–5524.
  205. Hannart, A., J. Pearl, F. E. L. Otto, P. Naveau, and M. Ghil, 2016, “Causal counterfactual theory for the attribution of weather and climate-related events,” Bull. Am. Meteorol. Soc. 97, 99–110.
  206. Hassanzadeh, P., Z. Kuang, and B. F. Farrell, 2014, “Responses of midlatitude blocks and wave amplitude to changes in the meridional temperature gradient in an idealized dry GCM,” Geophys. Res. Lett. 41, 5223–5232.
  207. Hasselmann, K., 1976, “Stochastic climate models. I: Theory,” Tellus 28, 473–485.
  208. Hasselmann, K., R. Sausen, E. Maier-Reimer, and R. Voss, 1993, “On the cold start problem in transient simulations with coupled atmosphere-ocean models,” Clim. Dyn. 9, 53–61.
  209. Hasson, S., V. Lucarini, and S. Pascale, 2013, “Hydrological cycle over South and Southeast Asian river basins as simulated by PCMDI/CMIP3 experiments,” Earth Syst. Dyn. 4, 199–217.
  210. Hawkins, E., R. S. Smith, L. C. Allison, J. M. Gregory, T. J. Woollings, H. Pohlmann, and B. Cuevas, 2011, “Bistability of the Atlantic overturning circulation in a global climate model and links to ocean freshwater transport,” Geophys. Res. Lett. 38, L10605.
  211. Hayashi, Y., 1971, “A generalized method for resolving disturbances into progressive and retrogressive waves by space Fourier and time cross-spectral analysis,” J. Meteorol. Soc. Jpn. 49, 125–128.
  212. Heinrich, H., 1988, “Origin and consequences of cyclic ice rafting in the northeast Atlantic Ocean during the past 130 000 years,” Quat. Res. 29, 142–152.
  213. Held, I. M., 2001, “The partitioning of the poleward energy transport between the tropical ocean and atmosphere,” J. Atmos. Sci. 58, 943–948.
  214. Held, I. M., 2005, “The gap between simulation and understanding in climate modeling,” Bull. Am. Meteorol. Soc. 86, 1609–1614.
  215. Held, I. M., and M. J. Suarez, 1974, “Simple albedo feedback models of the ice caps,” Tellus 26, 613–629.
  216. Hochman, A., P. Alpert, T. Harpaz, H. Saaroni, and G. Messori, 2019, “A new dynamical systems perspective on atmospheric predictability: Eastern Mediterranean weather regimes as a case study, Sci. Adv. 5.
  217. Hoffman, P. F., A. J. Kaufman, G. P. Halverson, and D. P. Schrag, 1998, “On the initiation of a snowball Earth,” Science 281, 1342–1346.
  218. Hoffman, P. F., and D. P. Schrag, 2002, “The snowball Earth hypothesis: Testing the limits of global change,” Terra Nova 14, 129.
  219. Holland, Mark P, Renato Vitolo, Pau Rabassa, Alef E. Sterk, and Henk W. Broer, 2012, “Extreme value laws in dynamical systems under physical observables,” Physica (Amsterdam) 241D, 497–513.
  220. Holton, J. R., and G. J. Hakim, 2013, An Introduction to Dynamic Meteorology, 4th ed. (Academic Press, San Diego).
  221. Hoskins, B. J., M. E. McIntyre, and A. W. Robertson, 1985, “On the use and significance of isentropic potential vorticity maps,” Q. J. R. Meteorol. Soc. 111, 877–946.
  222. Hu, G., T. Bódai, and V. Lucarini, 2019, “Effects of stochastic parametrization on extreme value statistics,” Chaos 29, 083102.
  223. Huybers, P., 2005, “Comment on ‘Hockey sticks, principal components, and spurious significance’ by S. McIntyre and R. McKitrick,” Geophys. Res. Lett. 32, L20705.
  224. Imbrie, J., and K. P. Imbrie, 1986, Ice Ages: Solving the Mystery, 2nd ed. (Harvard University Press, Cambridge, MA).
  225. IPCC, 2001, Climate Change 2001: The Scientific Basis. Contribution of Working Group I to the Third Assessment Report of the Intergovernmental Panel on Climate Change, edited by J. T. Houghton et al. (Cambridge University Press, Cambridge, England).
  226. IPCC, 2007, Climate Change 2007—The Physical Science Basis: Working Group I Contribution to the Fourth Assessment Report of the IPCC, edited by S. Solomon et al. (Cambridge University Press, Cambridge, England).
  227. IPCC, 2012, Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation. A Special Report of Working Groups I and II of the Intergovernmental Panel on Climate Change, edited by C. B. Field et al. (Cambridge University Press, Cambridge, England).
  228. IPCC, 2014a, Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by T. Stocker et al. (Cambridge University Press, Cambridge, England).
  229. IPCC, 2014b, Climate Change 2014. Impacts, Adaptation and Vulnerability. Contribution of Working Group II to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by C. B. Field et al. (Cambridge University Press, Cambridge, England).
  230. IPCC, 2014c, Climate Change 2014. Mitigation of Climate Change. Contribution of Working Group III to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, edited by O. Edenhofer et al. (Cambridge University Press, Cambridge, England).
  231. Itoh, H., and M. Kimoto, 1996, “Multiple attractors and chaotic itinerancy in a quasigeostrophic model with realistic topography: Implications for weather regimes and low-frequency variability,” J. Atmos. Sci. 53, 2217–2231.
  232. Itoh, H., and M. Kimoto, 1997, “Chaotic itinerancy with preferred transition routes appearing in an atmospheric model,” Physica (Amsterdam) 109D, 274–292.
  233. Jiang, N., J. D. Neelin, and M. Ghil, 1995, “Quasi-quadrennial and quasi-biennial varibility in the equatorial Pacific,” Clim. Dyn. 12, 101–112.
  234. Jiang, S., F.-F. Jin, and M. Ghil, 1995, “Multiple equilibria and aperiodic solutions in a wind-driven double-gyre, shallow-water model,” J. Phys. Oceanogr. 25, 764–786.
  235. Jin, F-F, and M. Ghil, 1990, “Intraseasonal oscillations in the extratropics: Hopf bifurcation and topographic instabilities,” J. Atmos. Sci. 47, 3007–3022.
  236. Jin, F-F, and J. D. Neelin, 1993, “Modes of interannual tropical ocean-atmosphere interaction—A unified view. I: Numerical results.,” J. Atmos. Sci. 50, 3477–3503.
  237. Jin, F-F, J. D. Neelin, and M. Ghil, 1994, “El Niño on the devil’s staircase: Annual subharmonic steps to chaos,” Science 264, 70–72.
  238. Jin, F-F, J. D. Neelin, and M. Ghil, 1996, “El Niño/Southern Oscillation and the annual cycle: Subharmonic frequency-locking and aperiodicity,” Physica (Amsterdam) 98D, 442–465.
  239. Jones, C. K. R. T., 1995, “Geometric singular perturbation theory,” in Dynamical Systems, Lecture Notes in Mathematics Vol. 1609, edited by R. Johnson (Springer, New York), pp. 44–118.
  240. Jouzel, J., et al., 1993, “Extending the Vostok ice-core record of paleoclimate to the penultimate glacial period,” Nature (London) 364, 407–412.
  241. Just, W., H. Kantz, C. Rödenbeck, and M. Helm, 2001, “Stochastic modelling: Replacing fast degrees of freedom by noise,” J. Phys. A 34, 3199–3213.
  242. Kalnay, E., 2003, Atmospheric Modeling, Data Assimilation and Predictability (Cambridge University Press, Cambridge, England).
  243. Karamperidou, C., P. N. Di Nezio, A. Timmermann, F.-F. Jin, and K. M. Cobb, 2015, “The response of ENSO flavors to mid-Holocene climate: Implications for proxy interpretation,” Paleoceanography 30, 527–547.
  244. Karspeck, Alicia R, et al., 2018, “A global coupled ensemble data assimilation system using the community earth system model and the data assimilation research testbed,” Q. J. R. Meteorol. Soc. 144, 2404–2430.
  245. Katsman, C. A., H. A. Dijkstra, and S. S. Drijfhout, 1998, “The rectification of the wind-driven circulation due to its instabilities,” J. Mar. Res. 56, 559–587.
  246. Katz, R. W., M. B. Parlange, and P. Naveau, 2002, “Statistics of extremes in hydrology,” Adv. Water Res. 25, 1287–1304.
  247. Kautz, R. L., 1987, “Activation energy for thermally induced escape from a basin of attraction,” Phys. Lett. A 125, 315–319.
  248. Kennett, J. P., and L. D. Stott, 1991, “Abrupt deep-sea warming, palaeoceanographic changes and benthic extinctions at the end of the Palaeocene,” Nature (London) 353, 225–229.
  249. Kharin, V. V., F. W. Zwiers, and X. Zhang, 2005, “Intercomparison of near surface temperature and precipitation extremes in AMIP-2 simulations, reanalyses and observations,” J. Clim. 18, 5201–5223.
  250. Kim, Y.-H, and M.-H Kim, 2013, “Examination of the global Lorenz energy cycle using MERRA and NCEP-reanalysis 2,” Clim. Dyn. 40, 1499–1513.
  251. Kimoto, M., and M. Ghil, 1993a, “Multiple flow regimes in the Northern Hemisphere winter. Part I: Methodology and hemispheric regimes,” J. Atmos. Sci. 50, 2625–2643.
  252. Kimoto, M., and M. Ghil, 1993b, “Multiple flow regimes in the Northern Hemisphere winter. Part II: Sectorial regimes and preferred transitions,” J. Atmos. Sci. 50, 2645–2673.
  253. Kistler, R., et al., 2001, “The NCEP-NCAR 50-year reanalysis: Monthly means CD-ROM and documentation,” Bull. Am. Meteorol. Soc. 82, 247–267.
  254. Kleidon, A., 2009, “Non-equilibrium thermodynamics and maximum entropy production,” Naturwissenschaften 96, 653–677.
  255. Kleidon, A., 2010, “Life, hierarchy, and the thermodynamic machinery of planet Earth,” Phys. Life Rev. 7, 424–460.
  256. Kleidon, A., and R. Lorenz, 2005, Eds., Non-equilibrium Thermodynamics and the Production of Entropy (Springer, Berlin).
  257. Klein, R., 2010, “Scale-dependent models for atmospheric flows, Annu. Rev. Fluid Mech. 42, 249–274.
  258. Kloeden, P. E., and M. Rasmussen, 2011, Nonautonomous Dynamical Systems (American Mathematical Society, Providence).
  259. Kondrashov, D., M. D. Chekroun, and M. Ghil, 2015, “Data-driven non-Markovian closure models,” Physica (Amsterdam) 297D, 33–55.
  260. Kondrashov, D., M. D. Chekroun, A. W. Robertson, and M. Ghil, 2013, “Low-order stochastic model and ‘past-noise forecasting’ of the Madden-Julian oscillation,” Geophys. Res. Lett. 40, 5305–5310.
  261. Kondrashov, D., Y. Feliks, and M. Ghil, 2005, “Oscillatory modes of extended Nile River records (A.D. 622–1922),” Geophys. Res. Lett. 32, L10702.
  262. Kondrashov, D., K. Ide, and M. Ghil, 2004, “Weather regimes and preferred transition paths in a three-level quasigeostrophic model,” J. Atmos. Sci. 61, 568–587.
  263. Kondrashov, D., S. Kravtsov, and M. Ghil, 2006, “Empirical mode reduction in a model of extratropical low-frequency variability,” J. Atmos. Sci. 63, 1859–1877.
  264. Kondrashov, D., S. Kravtsov, A. W. Robertson, and M. Ghil, 2005, “A hierarchy of data-based ENSO models,” J. Clim. 18, 4425–4444.
  265. Kondrashov, D., J. Shen, R. Berk, F. DAndrea, and M. Ghil, 2007, “Predicting weather regime transitions in northern hemisphere datasets,” Clim. Dyn. 29, 535–551.
  266. Kramers, H. A., 1940, “Brownian motion in a field of force and the diffusion model of chemical reactions,” Physica (Amsterdam) 7, 284–304.
  267. Kraut, S., and U. Feudel, 2002, “Multistability, noise, and attractor hopping: The crucial role of chaotic saddles, Phys. Rev. E 66, 015207.
  268. Kravtsov, S., P. Berloff, W. K. Dewar, M. Ghil, and J. C. McWilliams, 2006, “Dynamical origin of low-frequency variability in a highly nonlinear mid-latitude coupled model,” J. Clim. 19, 6391–6408.
  269. Kravtsov, S., D. Kondrashov, and M. Ghil, 2005, “Multi-level regression modeling of nonlinear processes: Derivation and applications to climatic variability,” J. Clim. 18, 4404–4424.
  270. Kravtsov, S., D. Kondrashov, and M. Ghil, 2009, “Empirical model reduction and the modeling hierarchy in climate dynamics and the geosciences,” in Stochastic Physics and Climate Modelling, edited by T. N. Palmer and P. Williams (Cambridge University Press, Cambridge, England), pp. 35–72.
  271. Kravtsov, S., D. Kondrashov, Igor Kamenkovich, and M. Ghil, 2011, “An empirical stochastic model of sea-surface temperatures and surface winds over the Southern Ocean,” Ocean Sci. 7, 755–770.
  272. Krishnamurti, T. N., L. Stefanova, and V. Misra, 1979, Tropical Meteorology: An Introduction (Springer, New York).
  273. Kubo, R., 1957, “Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems,” J. Phys. Soc. Jpn. 12, 570–586.
  274. Kubo, R., 1966, “The fluctuation-dissipation theorem,” Rep. Prog. Phys. 29, 255–284.
  275. Kuehn, C., 2011, “A mathematical framework for critical transitions: Bifurcations, fast-slow systems and stochastic dynamics,” Physica (Amsterdam) 240D, 1020–1035.
  276. Kuhlbrodt, T., A. Griesel, M. Montoya, A. Levermann, M. Hofmann, and S. Rahmstorf, 2007, “On the driving processes of the Atlantic meridional overturning circulation,” Rev. Geophys. 45, RG2001.
  277. Kushnir, Y., 1987, “Retrograding wintertime low-frequency disturbances over the North Pacific ocean,” J. Atmos. Sci. 44, 2727–2742.
  278. Kushnir, Y., 1994, “Interdecadal variations in North Atlantic sea surface temperature and associated atmospheric conditions,” J. Phys. Oceanogr. 7, 141–157.
  279. Lagerstrom, P. A., 1988, Matched Asymptotic Expansions: Ideas and Techniques (Springer Science+Business Media, New York).
  280. Lai, Y-C, and T. Tél, 2011, Transient Chaos (Springer, New York).
  281. Laloyaux, P., et al., 2018, “CERA-20C: A coupled reanalysis of the twentieth century,” J. Adv. Model. Earth Syst. 10, 1172–1195.
  282. Lamb, H. H., 1972, Climate: Present, Past and Future (Methuen, London).
  283. Langen, P. L., and V. A. Alexeev, 2005, “Estimating 2X CO2 warming in an aquaplanet GCM using the fluctuation-dissipation theorem,” Geophys. Res. Lett. 32, L23708.
  284. Lawrence, M. G., S. Schäfer, H. Muri, V. Scott, A. Oschlies, N. E. Vaughan, O. Boucher, H. Schmidt, J. Haywood, and J. Scheffran, 2018, “Evaluating climate geoengineering proposals in the context of the Paris Agreement temperature goals,” Nat. Commun. 9, 3734.
  285. /Ledrappier, F., and L.-S. Young, 1988, “Entropy formula for random transformations,” Prob. Theory Relat. Fields 80, 217–240.
  286. Lee, T., T. Awaji, M. A. Balmaseda, E. Greiner, and D. Stammer, 2009, “Ocean state estimation for climate research,” Oceanography 22, 160–167.
  287. Legras, B., and M. Ghil, 1985, “Persistent anomalies, blocking, and variations in atmospheric predictability,” J. Atmos. Sci. 42, 433–471.
  288. Leith, C. E., 1975, “Climate response and fluctuation dissipation,” J. Atmos. Sci. 32, 2022–2026.
  289. Leith, C. E., and R. H. Kraichnan, 1972, “Predictability of turbulent flows,” J. Atmos. Sci. 29, 1041–1058.
  290. Lembo, V., V. Lucarini, and F. Ragone, 2020, “Beyond forcing scenarios: Predicting climate change through response operators in a coupled general circulation model,” Sci. Rep. 10, 8668.
  291. Lembo, V., F. Lunkeit, and V. Lucarini, 2019, “TheDiaTo (v1.0)—A new diagnostic tool for water, energy and entropy budgets in climate models,” Geosci. Model Dev. 12, 3805–3834.
  292. Lenton, T. M., H. Held, E. Kriegler, J. W. Hall, W. Lucht, S. Rahmstorf, and H. J. Schellnhuber, 2008, “Tipping elements in the Earth’s climate system,” Proc. Natl. Acad. Sci. U.S.A. 105, 1786–1793.
  293. Li, Z-X, K. Ide, H. Le Treut, and M. Ghil, 1997, “Atmospheric radiative equilibria in a simple column model,” Clim. Dyn. 13, 429–440.
  294. Lindzen, R. S., 1986, “Stationary planetary waves, blocking, and interannual variability,” in Advances in Geophysics, Vol. 29 (Elsevier, New York), pp. 251–273.
  295. Liu, J., J. A. Curry, H. Wang, M. Song, and R. M. Horton, 2012, “Impact of declining Arctic sea ice on winter snowfall,” Proc. Natl. Acad. Sci. U.S.A. 109, 4074–4079.
  296. Lorenz, E. N., 1955, “Available potential energy and the maintenance of the general circulation,” Tellus 7, 157–167.
  297. Lorenz, E. N., 1963, “Deterministic nonperiodic flow,” J. Atmos. Sci. 20, 130–141.
  298. Lorenz, E. N., 1967, The Nature and Theory of the General Circulation of the Atmosphere (World Meteorological Organization, Geneva).
  299. Lorenz, E. N., 1969a, “The predictability of a flow which possesses many scales of motion,” Tellus 21, 289–307.
  300. Lorenz, E. N., 1969b, “Three approaches to atmospheric predictability,” Bull. Am. Meteorol. Soc. 50, 345–349.
  301. Lorenz, E. N., 1976, “Nondeterministic theories of climatic change,” Quat. Res. 6, 495–506.
  302. Lorenz, E. N., 1979, “Forced and free variations of weather and climate,” J. Atmos. Sci. 36, 1367–1376.
  303. Lorenz, E. N., 1984, “Irregularity: A fundamental property of the atmosphere,” Tellus A 36A, 98–110.
  304. Lorenz, E. N., 1996, “Predictability: A problem partly solved,” in Seminar on Predictability, 4–8 September 1995 (European Centre for Medium-range Weather Forecasts, Reading, England), pp. 1–18.
  305. Lu, Z., Z. Fu, L. Hua, N. Yuan, and L. Chen, 2018, “Evaluation of ENSO simulations in CMIP5 models: A new perspective based on percolation phase transition in complex networks,” Sci. Rep. 8, 14912.
  306. Lucarini, V., 2002, “Towards a definition of climate science,” Intl. J. Environ. Pollution 18, 413–422.
  307. Lucarini, V., 2008a, “Response theory for equilibrium and non-equilibrium statistical mechanics: Causality and generalized kramers-kronig relations,” J. Stat. Phys. 131, 543–558.
  308. Lucarini, V., 2008b, “Validation of climate models,” in Encyclopedia of Global Warming and Climate Change, edited by G. Philander (SAGEThousand Oaks, CA), pp. 1053–1057.
  309. Lucarini, V., 2009a, “Evidence of dispersion relations for the nonlinear response of the Lorenz 63 system,” J. Stat. Phys. 134, 381–400.
  310. Lucarini, V., 2009b, “Thermodynamic efficiency and entropy production in the climate system, Phys. Rev. E 80, 021118.
  311. Lucarini, V., 2012, “Stochastic perturbations to dynamical systems: A response theory approach,” J. Stat. Phys. 146, 774–786.
  312. Lucarini, V., 2013, “Modeling complexity: The case of climate science,” in Models, Simulations, and the Reduction of Complexity, edited by U. Gähde, S. Hartmann, and J. H Wolf (De Gruyter, Berlin), pp. 229–254.
  313. Lucarini, V., 2016, “Response operators for Markov processes in a finite state space: Radius of convergence and link to the response theory for Axiom A systems,” J. Stat. Phys. 162, 312–333.
  314. Lucarini, V., 2018, “Revising and extending the linear response theory for statistical mechanical systems: Evaluating observables as predictors and predictands,” J. Stat. Phys. 173, 1698–1721.
  315. Lucarini, V., R. Blender, C. Herbert, F. Ragone, S. Pascale, and J. Wouters, 2014, “Mathematical and physical ideas for climate science,” Rev. Geophys. 52, 809–859.
  316. Lucarini, V., and T. Bódai, 2017, “Edge states in the climate system: Exploring global instabilities and critical transitions,” Nonlinearity 30, R32.
  317. Lucarini, V., and T. Bódai, 2019, “Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View, Phys. Rev. Lett. 122, 158701.
  318. Lucarini, V., and T. Bódai, 2020, “Global stability properties of the climate: Melancholia states, invariant measures, and phase transitions,” Nonlinearity (to be published), 10.1088/1361-6544/ab86cc.
  319. Lucarini, V., S. Calmanti, and V. Artale, 2005, “Destabilization of the thermohaline circulation by transient changes in the hydrological cycle,” Clim. Dyn. 24, 253–262.
  320. Lucarini, V., S. Calmanti, and V. Artale, 2007, “Experimental mathematics: Dependence of the stability properties of a two-dimensional model of the Atlantic Ocean circulation on the boundary conditions,” Russ. J. Math. Phys. 14, 224–231.
  321. Lucarini, V., and M. Colangeli, 2012, “Beyond the linear fluctuation-dissipation theorem: The role of causality,” J. Stat. Mech. P05013.
  322. Lucarini, V., D. Faranda, A. C. G. M. M. de Freitas, J. M. M. de Freitas, M. Holland, T. Kuna, M. Nicol, M. Todd, and S. Vaienti, 2016, Extremes and Recurrence in Dynamical Systems (Wiley, New York).
  323. Lucarini, V., K. Fraedrich, and F. Lunkeit, 2010a, “Thermodynamic analysis of snowball Earth hysteresis experiment: Efficiency, entropy production, and irreversibility,” Q. J. R. Meteorol. Soc. 136, 2–11.
  324. Lucarini, V., K. Fraedrich, and F. Lunkeit, 2010b, “Thermodynamics of climate change: Generalized sensitivities,” Atmos. Chem. Phys. 10, 9729–9737.
  325. Lucarini, V., and A. Gritsun, 2020, “A new mathematical framework for atmospheric blocking events,” Clim. Dyn. 54, 575–598.
  326. Lucarini, V., T. Kuna, D. Faranda, and J. Wouters, 2014, “Towards a general theory of extremes for observables of chaotic dynamical systems,” J. Stat. Phys. 154.
  327. Lucarini, V., S. Pascale, V. Boschi, E. Kirk, and N. Iro, 2013, “Habitability and multistability in Earth-like planets,” Astron. Nachr. 334, 576–588.
  328. Lucarini, V., and F. Ragone, 2011, “Energetics of climate models: Net energy balance and meridional enthalpy transport,” Rev. Geophys. 49, RG1001.
  329. Lucarini, V., F. Ragone, and F. Lunkeit, 2017, “Predicting climate change using response theory: Global averages and spatial patterns,” J. Stat. Phys. 166, 1036–1064.
  330. Lucarini, V., J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, 2005, Kramers-Kronig relations in Optical Materials Research (Springer, New York).
  331. Lucarini, V., and S. Sarno, 2011, “A statistical mechanical approach for the computation of the climatic response to general forcings,” Nonlinear Processes Geophys. 18, 7–28.
  332. Lucarini, Valerio, and Peter H. Stone, 2005, “Thermohaline circulation stability: A box model study. Part I: Uncoupled model,” J. Clim. 18, 501–513.
  333. Lynch, P., 2008, “The ENIAC forecasts: A re-creation,” Bull. Am. Meteorol. Soc. 89, 45–55.
  334. Madden, R. A., and P. R. Julian, 1971, “Detection of a 40–50 day oscillation in the zonal wind in the tropical Pacific,” J. Atmos. Sci. 28, 702–708.
  335. Majda, A. J., B. Gershgorin, and Y. Yuan, 2010, “Low-frequency climate response and fluctuation–Dissipation theorems: Theory and practice,” J. Atmos. Sci. 67, 1186–1201.
  336. Majda, A. J., and X. Wang, 2006, Nonlinear Dynamics and Statistical Theories for Basic Geophysical Flows (Cambridge University Press, Cambridge, England).
  337. Maloney, E. D., and D. L. Hartmann, 2000, “Modulation of hurricane activity in the Gulf of Mexico by the Madden-Julian oscillation,” Science 287, 2002–2004.
  338. Manabe, Syukuro, and Robert F. Strickler, 1964, “Thermal equilibrium of the atmosphere with a convective adjustment,” J. Atmos. Sci. 21, 361–385.
  339. Mann, M. E., R. S. Bradley, and M. K. Hughes, 1998, “Global-scale temperature patterns and climate forcing over the past six centuries,” Nature (London) 392, 779–787.
  340. Mann, M. E., R. S. Bradley, and M. K. Hughes, 1999, “Northern Hemisphere temperatures during the past millennium: Inferences, uncertainties, and limitations,” Geophys. Res. Lett. 26, 759–762.
  341. Mann, M. E., Z. Zhang, M. K. Hughes, R. S. Bradley, S. K. Miller, F. Rutherford, and S. Ni, 2008, “Proxy-based reconstructions of hemispheric and global surface temperature variations over the past two millennia,” Proc. Natl. Acad. Sci. U.S.A. 105, 13252–13257.
  342. Marangio, L., J. Sedro, S. Galatolo, A. Di Garbo, and M. Ghil, 2019, “Arnold maps with noise: Differentiability and non-monotonicity of the rotation number,” arXiv:1904.11744.
  343. Marconi, U Marini Bettolo, A. Puglisi, L. Rondoni, and A. Vulpiani, 2008, “Fluctuation-dissipation: Response theory in statistical physics,” Phys. Rep. 461, 111.
  344. Marotzke, J., 2000, “Abrupt climate change and thermohaline circulation: Mechanisms and predictability,” Proc. Natl. Acad. Sci. U.S.A. 97, 1347–1350.
  345. Marques, C. A. F., A. Rocha, and J Corte-Real, 2010, “Comparative energetic of ERA-40, JRA-25 and NCEP-R2 reanalysis, in the wave number domain,” Dyn. Atmos. Oceans 50, 375–399.
  346. Marques, C. A. F., A. Rocha, J. Corte-Real, J. M. Castanheira, J. Ferreira, and P. Melo-Goncalves, 2009, “Global atmospheric energetic from NCEP-reanalysis 2 and ECMWF-ERA40 reanalysis,” Int. J. Climatol. 29, 159–174.
  347. Marshall, J., C. Hill, L. Perelman, and A.. Adcroft, 1997, “Hydrostatic, quasi-hydrostatic, and non-hydrostatic ocean modelling,” J. Geophys. Res. 102, 5733–5752.
  348. Marshall, J., and F. Molteni, 1993, “Toward a dynamical understanding of atmospheric weather regimes,” J. Atmos. Sci. 50, 1792.
  349. Martinson, D. G., K. Bryan, M. Ghil, M. M. Hall, T. R. Karl, E. S. Sarachik, S. Sorooshian, and L. D. Talley, 1995, Eds., Natural Climate Variability on Decade-to-Century Time Scales (National Academies Press, Washington, DC).
  350. McIntyre, S., and R. McKitrick, 2005, “Hockey sticks, principal components, and spurious significance,” Geophys. Res. Lett. 32, L03710.
  351. McWilliams, J. C., 2006, Fundamentals of Geophysical Fluids (Cambridge University Press, Cambridge, England).
  352. McWilliams, J. C., 2019, “A perspective on the legacy of Edward Lorenz,” Earth Space Sci. (in press).
  353. Meacham, S. P., 2000, “Low frequency variability of the wind-driven circulation,” J. Phys. Oceanogr. 30, 269–293.
  354. Meehl, G. A., et al., 2014, “Decadal climate prediction: An update from the trenches,” Bull. Am. Meteorol. Soc. 95, 243–267.
  355. Melbourne, I., and A. M. Stuart, 2011, “A note on diffusion limits of chaotic skew-product flows,” Nonlinearity 24, 1361–1367.
  356. Merkin, V. G., D. Kondrashov, M. Ghil, and B. J. Anderson, 2016, “Data assimilation of low-altitude magnetic perturbations into a global magnetosphere model,” Space Weather 14, 165–184.
  357. Merryfield, William J et al., 2020, “Current and emerging developments in subseasonal to decadal prediction,” Bull. Am. Meteorol. Soc. (in press).
  358. Mitchell, J. M., 1976, “An overview of climate variability and its causal mechanisms,” Quat. Res. 6, 481–493.
  359. Mo, K. C., and M. Ghil, 1987, “Statistics and dynamics of persistent anomalies,” J. Atmos. Sci. 44, 877–902.
  360. Molteni, F. M., 2002, “Weather regimes and multiple equilibria,” in Encyclopedia of Atmospheric Sciences, edited by J. R. Holton (Academic Press, New York), pp. 2577–2586.
  361. Monge, G., 1781, “An essay on the theory of excavation and embankment,” Hist. Acad. R. Sci. 1, 666–704.
  362. Mori, H., 1965, “Transport, collective motion, and Brownian motion,” Prog. Theor. Phys. 33, 423–455.
  363. Moron, V., R. Vautard, and M. Ghil, 1998, “Trends, interdecadal and interannual oscillations in global sea-surace temperature,” Clim. Dyn. 14, 545–569.
  364. Mukhin, D., D. Kondrashov, E. Loskutov, A. Gavrilov, A. Feigin, and M. Ghil, 2015, “Predicting critical transitions in ENSO models. Part II: Spatially dependent models,” J. Clim. 28, 1962–1976.
  365. Mukhin, D., E. Loskutov, A. Mukhina, A. Feigin, I. Zaliapin, and M. Ghil, 2015, “Predicting critical transitions in ENSO Models. Part I: Methodology and simple models with memory,” J. Clim. 28, 1940–1961.
  366. Munk, W., and C. Wunsch, 1982, “Observing the ocean in the 1990s,” Phil. Trans. R. Soc. A 307, 439–464.
  367. NAC, 1986, NASA Advisory Council: Earth System Science Overview, edited by F. Bretherton et al. (National Aeronautics and Space Administration, Washington, DC).
  368. Nadiga, B. T., and B. Luce, 2001, “Global bifurcation of Shilñikov type in a double-gyre model,” J. Phys. Oceanogr. 31, 2669–2690.
  369. Namias, J., 1968, “Long-range weather forecasting: History, current status and outlook,” Bull. Am. Meteorol. Soc. 49, 438–470.
  370. Neelin, J. D., D. S. Battisti, A. C. Hirst, F.-F. Jin, Y. Wakata, T. Yamagata, and S. E. Zebiak, 1998, “ENSO Theory,” J. Geophys. Res. 103, 14261.
  371. Neelin, J. D., M. Latif, and F.-F. Jin, 1994, “Dynamics of coupled ocean-atmosphere models: The tropical problem,” Annu. Rev. Fluid Mech. 26, 617–659.
  372. Newman, Mark, 2010, Networks: An Introduction (Oxford University Press, Oxford).
  373. North, G. R., 1975, “Analytical solution to a simple climate model with diffusive heat transport,” J. Atmos. Sci. 32, 1301–1307.
  374. North, G. R., R. E. Bell, and J. W. Hardin, 1993, “Fluctuation dissipation in a general circulation model,” Clim. Dyn. 8, 259–264.
  375. North, G. R., R. F. Cahalan, and J. A. Coakley, 1981, “Energy balance climate models,” Rev. Geophys. Space Phys. 19, 91.
  376. North, G. R., L. Howard, D. Pollard, and B. Wielicki, 1979, “Variational formulation of Budyko-Sellers climate models,” J. Atmos. Sci. 36, 255–259.
  377. NRC, 2006, National Research Council: Surface Temperature Reconstructions for the Last 2000 Years (National Academies Press, Washington, DC).
  378. Onogi, K., et al., 2007, “The JRA-25 reanalysis,” J. Meteorol. Soc. Jpn. 85, 369–432.
  379. Onsager, L., 1931, “Reciprocal relations in irreversible processes. I,” Phys. Rev. 37, 405–426.
  380. Ott, E., 2002, Chaos in Dynamical Systems (Cambridge University Press, Cambridge, England).
  381. Otto, A., et al., 2013, “Energy budget constraints on climate response,” Nat. Geosci. 6, 415–416.
  382. PAGES 2k Consortium, 2013, “Continental-scale temperature variability during the past two millennia,” Nat. Geosci. 6, 339–346.
  383. Palmer, C. E., 1951, “Tropical meteorology,” in Compendium of Meteorology (Springer, New York), pp. 859–880.
  384. Palmer, T., 2017, “The primacy of doubt: Evolution of numerical weather prediction from determinism to probability,” J. Adv. Model. Earth Syst. 9, 730–734.
  385. Palmer, T. N., F. J. Doblas-Reyes, A. Weisheimer, and M. J. Rodwell, 2008, “Toward seamless prediction: Calibration of climate change projections using seasonal forecasts,” Bull. Am. Meteorol. Soc. 89, 459–470.
  386. Palmer, T. N., and P. Williams, 2009, Eds., Stochastic Physics and Climate Modelling (Cambridge University Press, Cambridge, England).
  387. Pan, D-M, and D. A. Randall, 1998, “A cumulus parameterization with a prognostic closure,” Q. J. R. Meteorol. Soc. 124, 949–981.
  388. Papanicolaou, G. C., and W. Kohler, 1974, “Asymptotic theory of mixing stochastic ordinary differential equations,” Commun. Pure Appl. Math. 27, 641–668.
  389. Parker, W. S., 2010, “Whose probabilities? Predicting climate change with ensembles of models,” Philos. Sci. 77, 985–997.
  390. Paterson, W. S. B., 1981, The Physics of Glaciers, 2nd ed. (Pergamon Press, Oxford).
  391. Pauluis, O., and I M. Held, 2002, “Entropy budget of an atmosphere in radiative-convective equilibrium. Part I: Maximum work and frictional dissipation,” J. Atmos. Sci. 59, 125–139.
  392. Pavliotis, G. A., 2014, Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations, Texts in Applied Mathematics (Springer, New York).
  393. Pavliotis, G. A., and A. M. Stuart, 2008, Multiscale Methods (Springer, New York).
  394. Pearl, J., 2009, Causality: Models, Reasoning, and Inference (Cambridge University Press, Cambridge, England).
  395. Pedlosky, J., 1987, Geophysical Fluid Dynamics, 2nd ed. (Springer-Verlag, New York).
  396. Pedlosky, J., 1996, Ocean Circulation Theory (Springer, New York).
  397. Peixoto, J. P., and A. H. Oort, 1992, Physics of Climate (AIP Press, New York).
  398. Penland, C., 1989, “Random forcing and forecasting using principal oscillation pattern analysis,” Mon. Weather Rev. 117, 2165–2185.
  399. Penland, C., 1996, “A stochastic model of IndoPacific sea surface temperature anomalies,” Physica (Amsterdam) 98D, 534–558.
  400. Penland, C., and M. Ghil, 1993, “Forecasting Northern Hemisphere 700-mb geopotential height anomalies using empirical normal modes,” Mon. Weather Rev. 121, 2355–2372.
  401. Penland, C., and P. D. Sardeshmukh, 1995, “The optimal growth of tropical sea surface temperature anomalies,” J. Clim. 8, 1999–2024.
  402. Penny, S. G., and T. M. Hamill, 2017, “Coupled data assimilation for integrated Earth system analysis and prediction,” Bull. Am. Meteorol. Soc. 98, ES169–ES172.
  403. Pfeffer, R. L., 1960, Ed., Dynamics of Climate (Pergamon Press, New York).
  404. Pfister, P. L., and T. F. Stocker, 2017, “State-dependence of the climate sensitivity in earth system models of intermediate complexity,” Geophys. Res. Lett. 44, 10 643–10 653.
  405. Philander, S. G. H., 1990, El Niño and the Southern Oscillation. (Academic Press, New York).
  406. Pierini, S., M. D. Chekroun, and M. Ghil, 2018, “The onset of chaos in nonautonomous dissipative dynamical systems: A low-order ocean-model case study,” Nonlinear Processes Geophys. 25, 671–692.
  407. Pierini, S., M. Ghil, and M. D. Chekroun, 2016, “Exploring the pullback attractors of a low-order quasigeostrophic ocean model: The deterministic case,” J. Clim. 29, 4185–4202.
  408. Pierrehumbert, R. T., 2004, “High levels of atmospheric carbon dioxide necessary for the termination of global glaciation,” Nature (London) 429, 646.
  409. Plant, R. S., and J. I. Yano, 2016, Parameterization of Atmospheric Convection, Vol. 1(Imperial College Press, London).
  410. Plaut, G., M. Ghil, and R. Vautard, 1995, “Interannual and interdecadal variability in 335 years of Central England temperature,” Science 268, 710–713.
  411. Poincaré, H., 1902, La Science et l’Hypothèse, translated in 1905 into English as Science and Hypothesis; versions of this translation are (i) downloadable for free as Gutenberg Project EBook No. 37157, published in 2011, and (ii) available online as a Wikisource book, https://en.wikisource.org/wiki/Science_and_Hypothesis, published in 2017.
  412. Poincaré, H., 1908, Science et Méthode (Ernest Flammarion, Paris).
  413. Poli, P., et al., 2016, “ERA-20C: An atmospheric reanalysis of the twentieth century,” J. Clim. 29, 4083–4097.
  414. Pollicott, M., 1985, “On the rate of mixing of Axiom A flows,” Invent. Math. 81, 413–426.
  415. Pratt, R. W., 1976, “The interpretation of space-time spectral quantities,” J. Atmos. Sci. 33, 1060–1066.
  416. Preisendorfer, R. W., 1988, Principal Component Analysis in Meteorology and Oceanography (Elsevier, Amsterdam).
  417. Prigogine, I., 1961, Thermodynamics of Irreversible Processes (Interscience, New York).
  418. Proctor, J., S. Hsiang, J. Burney, M. Burke, and W. Schlenker, 2018, “Estimating global agricultural effects of geoengineering using volcanic eruptions,” Nature (London) 560, 480–483.
  419. Quon, C., and M. Ghil, 1992, “Multiple equilibria in thermosolutal convection due to salt-flux boundary conditions,” J. Fluid Mech. 245, 449–484.
  420. Ragone, F., V. Lucarini, and F. Lunkeit, 2016, “A new framework for climate sensitivity and prediction: A modelling perspective,” Clim. Dyn. 46, 1459–1471.
  421. Ragone, F., J. Wouters, and F. Bouchet, 2018, “Computation of extreme heat waves in climate models using a large deviation algorithm,” Proc. Natl. Acad. Sci. U.S.A. 115, 24–29.
  422. Rahmstorf, Stefan, et al., 2005, “Thermohaline circulation hysteresis: A model intercomparison,” Geophys. Res. Lett. 32, 10.1029/2005GL023655.
  423. Ramanathan, V., and J. A. Coakley, 1978, “Climate modeling through radiative-convective models,” Rev. Geophys. 16, 465–489.
  424. Randall, D. A., 2000, Ed., General Circulation Model Development: Past, Present and Future (Academic Press, New York).
  425. Rasmusson, E., X. Wang, and C. Ropelewski, 1990, “The biennial component of ENSO variability,” J. Mar. Syst. 1, 71–96.
  426. Richardson, L. F., 1922, Weather Prediction by Numerical Process (Cambridge University Press, Cambridge, England).
  427. Riehl, H., 1954, Tropical Meteorology (McGraw-Hill, New York).
  428. Robert, C., K. T. Alligood, E. Ott, and J. A. Yorke, 2000, “Explosions of chaotic sets,” Physica (Amsterdam) 144D, 44–61.
  429. Robert, R., and J. Sommeria, 1991, “Statistical equilibrium states for two-dimensional flows, J. Fluid Mech. 229, 291–310.
  430. Robertson, A. W., and F. Vitart, Eds., 2018, The Gap Between Weather and Climate Forecasting: Sub-seasonal to Seasonal Prediction (Elsevier, Amsterdam).
  431. Robin, Y., P. Yiou, and P. Naveau, 2017, “Detecting changes in forced climate attractors with Wasserstein distance,” Nonlinear Processes Geophys. 24, 393–405.
  432. Robinson, I. S., 2010, Discovering the Ocean From Space: The Unique Applications of Satellite Oceanography (Praxis Publishing, Chichester, England).
  433. Roe, G. H., and M. B. Baker, 2007, “Why is climate sensitivity so unpredictable?,” Science 318, 629–632.
  434. Rohling, E. J., et al. (PALAEOSENS Project Collaboration), 2012, “Making sense of palaeoclimate sensitivity,” Nature (London) 491, 683.
  435. Rombouts, J., and M. Ghil, 2015, “Oscillations in a simple climate–vegetation model,” Nonlinear Processes Geophys. 22, 275–288.
  436. Romeiras, F. J., C. Grebogi, and E. Ott, 1990, “Multifractal properties of snapshot attractors of random maps,” Phys. Rev. A 41, 784.
  437. Rooth, C., 1982, “Hydrology and ocean circulation,” Prog. Oceanogr. 11, 131–149.
  438. Roques, L., M. D. Chekroun, M. Cristofol, S. Soubeyrand, and M. Ghil, 2014, “Parameter estimation for energy balance models with memory,” Proc. R. Soc. A 470, 20140349.
  439. Rossby, C.-G., 1939, “Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action,” J. Mar. Res. 2, 38–55.
  440. Rothman, D. H., J. M. Hayes, and R. E. Summons, 2003, “Dynamics of the Neoproterozoic carbon cycle,” Proc. Natl. Acad. Sci. U.S.A. 100, 8124–8129.
  441. Ruelle, D., 1986, “Resonances of Chaotic Dynamical Systems,” Phys. Rev. Lett. 56, 405–407.
  442. Ruelle, D., 1998, “General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium,” Phys. Lett. A 245, 220–224.
  443. Ruelle, D., 1999, “Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics,” J. Stat. Phys. 95, 393–468.
  444. Ruelle, D., 2009, “A review of linear response theory for general differentiable dynamical systems,” Nonlinearity 22, 855–870.
  445. Ruti, P. M., V. Lucarini, A. Dell’Aquila, S. Calmanti, and A. Speranza, 2006, “Does the subtropical jet catalyze the midlatitude atmospheric regimes?,” Geophys. Res. Lett. 33, L06814.
  446. Salmon, Rick, 1998, Lectures on Geophysical Fluid Dynamics (Oxford University Press, Oxford).
  447. Saltzman, B., 2001, Dynamical Paleoclimatology: Generalized Theory of Global Climate Change (Academic Press, New York).
  448. Sardeshmukh, P. D., and C. Penland, 2015, “Understanding the distinctively skewed and heavy tailed character of atmospheric and oceanic probability distributions,” Chaos 25, 036410.
  449. Satoh, M., A. T. Noda, T. Seiki, Y.-W. Chen, C. Kodama, Y. Yamada, N. Kuba, and Y. Sato, 2018, “Toward reduction of the uncertainties in climate sensitivity due to cloud processes using a global non-hydrostatic atmospheric model,” Prog. Earth Planet. Sci. 5, 67.
  450. Scheffer, M., J. Bascompte, W. A. Brock, V. Brovkin, S. R. Carpenter, V. Dakos, H. Held, Egbert H. Van Nes, M. Rietkerk, and G. Sugihara, 2009, “Early-warning signals for critical transitions,” Nature (London) 461, 53–59.
  451. Schneider, S. H., and R. E. Dickinson, 1974, “Climate modelling,” Rev. Geophys. 12, 447–493.
  452. Schneider, T., J. Teixeira, C. S. Bretherton, F. Brient, K. G. Pressel, C. Schär, and A. P. Siebesma, 2017, “Climate goals and computing the future of clouds,” Nat. Clim. Change 7, 10.1038/nclimate3190.
  453. Schneider, T. M., B. Eckhardt, and J. A. Yorke, 2007, “Turbulence Transition and the Edge of Chaos in Pipe Flow,” Phys. Rev. Lett. 99, 034502.
  454. Schneider, Tapio, Colleen M. Kaul, and Kyle G. Pressel, 2019, “Possible climate transitions from breakup of stratocumulus decks under greenhouse warming,” Nat. Geosci. 12, 163–167.
  455. Schubert, Sebastian, and Valerio Lucarini, 2016, “Dynamical analysis of blocking events: Spatial and temporal fluctuations of covariant Lyapunov vectors,” Q. J. R. Meteorol. Soc. 142, 2143–2158.
  456. Scott, J. R., J. Marotzke, and P. H. Stone, 1999, “Interhemispheric thermohaline circulation in a coupled box model,” J. Phys. Oceanogr. 29, 351–365.
  457. Sell, G. R., 1967, “Nonautonomous differential equations and topological dynamics. I. The basic theory,” Trans. Am. Math. Soc. 127, 241–262.
  458. Sell, G. R., 1971, Topological Dynamics and Ordinary Differential Equations (Van Nostrand Reinhold, New York).
  459. Sellers, W. D., 1969, “A global climatic model based on the energy balance of the earth atmosphere,” J. Appl. Meteorol. 8, 392–400.
  460. Sevellec, F., and A. V. Fedorov, 2015, “Unstable AMOC during glacial intervals and millennial variability: The role of mean sea ice extent,” Earth Planet. Sci. Lett. 429, 60–68.
  461. Sheremet, V. A., G. R. Ierley, and V. M. Kamenkovich, 1997, “Eigenanalysis of the two-dimensional wind-driven ocean circulation problem,” J. Mar. Res. 55, 57–92.
  462. Simonnet, E., 2005, “Quantization of the low-frequency variability of the double-gyre circulation,” J. Phys. Oceanogr. 35, 2268–2290.
  463. Simonnet, E., and H. A. Dijkstra, 2002, “Spontaneous generation of low-frequency modes of variability in the wind-driven ocean circulation,” J. Phys. Oceanogr. 32, 1747–1762.
  464. Simonnet, E., M. Ghil, and H. A. Dijkstra, 2005, “Homoclinc bifurcations in the quasi-geostrophic double-gyre circulation,” J. Mar. Res. 63, 931–956.
  465. Simonnet, E., M. Ghil, K. Ide, R. Temam, and S. Wang, 2003a, “Low-frequency variability in shallow-water models of the wind-driven ocean circulation. Part I: Steady-state solutions,” J. Phys. Oceanogr. 33, 712–728.
  466. Simonnet, E., M. Ghil, K. Ide, R. Temam, and S. Wang, 2003b, “Low-frequency variability in shallow-water models of the wind-driven ocean circulation. Part II: Time dependent solutions,” J. Phys. Oceanogr. 33, 729–752.
  467. Simonnet, E., R. Temam, S. Wang, M. Ghil, and K. Ide, 1998, “Successive bifurcations in a shallow-water ocean model,” Lect. Notes Phys. 515, 225–230.
  468. Simonnet, S., H. A. Dijkstra, and M. Ghil, 2009, “Bifurcation analysis of ocean, atmosphere and climate models,” in Computational Methods for the Ocean and the Atmosphere, edited by R. Temam and J. J. Tribbia (North-Holland, Amsterdam), pp. 187–229.
  469. Skufca, J. D., J. A. Yorke, and B. Eckhardt, 2006, “Edge of Chaos in a Parallel Shear Flow,” Phys. Rev. Lett. 96, 174101.
  470. Slingo, J., and T. N. Palmer, 2011, “Uncertainty in weather and climate prediction,” Phil. Trans. R. Soc. A 369, 4751–4767.
  471. Smith, W., and G. Wagner, 2018, “Stratospheric aerosol injection tactics and costs in the first 15 years of deployment,” Environ. Res. Lett. 13, 124001.
  472. Smyth, P., K. Ide, and M. Ghil, 1999, “Multiple regimes in Northern Hemisphere height fields via mixture model clustering,” J. Atmos. Sci. 56, 3704–3723.
  473. Speich, S., H. A. Dijkstra, and M. Ghil, 1995a, “Successive bifurcations in a shallow-water model applied to the wind-driven ocean circulation,” Nonlinear Processes Geophys. 2, 241–268.
  474. Speich, S., H. A. Dijkstra, and M. Ghil, 1995b, “Successive bifurcations of a shallow-water model with applications to the wind driven circulation,” Nonlinear Processes Geophys. 2, 241–268.
  475. Speranza, A., 1983, “Deterministic and statistical properties of the westerlies,” Pure Appl. Geophys. 121, 511–562
  476. Stommel, H., 1961, “Thermohaline convection with two stable regimes of flow,” Tellus 13, 224–230.
  477. Stommel, H., 1963, “Varieties of oceanographic experience, Science 139, 572–576.
  478. Sushama, L., M. Ghil, and K. Ide, 2007, “Spatio-temporal variability in a mid-latitude ocean basin subject to periodic wind forcing,” Atmosphere-Ocean 45, 227–250.
  479. Sverdrup, H. U., 1947, “Wind-driven currents in a baroclinic ocean with application to the equatorial current in the eastern Pacific,” Proc. Natl. Acad. Sci. U.S.A. 33, 318–326.
  480. Sverdrup, H. U., M. W. Johnson, and R. H. Fleming, 1946, The Oceans: Their Physics, Chemistry and General Biology (Prentice-Hall, Englewood Cliffs, NJ).
  481. Swinbank, R., P. Friederichs, and S. Wahl, 2016, “Forecasting high-impact weather using ensemble prediction systems,” in Dynamics and Predictability of Large-Scale, High-Impact Weather and Climate Events, Special Publications of the International Union of Geodesy and Geophysics, edited by J. Li, R. Swinbank, R. Grotjahn, and H. Volkert (Cambridge University Press, Cambridge, England), pp. 95–112.
  482. Tantet, A., V. Lucarini, F. Lunkeit, and H. A. Dijkstra, 2018, “Crisis of the chaotic attractor of a climate model: A transfer operator approach,” Nonlinearity 31, 2221–2251.
  483. Taricco, C., M. Ghil, S. Alessio, and G. Vivaldo, 2009, “Two millennia of climate variability in the Central Mediterranean,” Clim. Past 5, 171–181.
  484. Taylor, G. I., 1921, “Diffusion by continuous movements,” Proc. London Math. Soc. s2-20, 196–212.
  485. Tebaldi, C., and R. Knutti, 2007, “The use of the multi-model ensemble in probabilistic climate projections,” Phil. Trans. R. Soc. A 365, 2053–2075.
  486. Teisserenc de Bort, L., 1881, “Study of the winter of 1879-80 and investigations on the position of atmospheric centers of action in abnormal winters,” Ann. Bur. Cent. Météor. France 4, 17–62.
  487. Temam, R., 1984, Navier-Stokes Equations: Theory and Numerical Analysis (North-Holland, Amsterdam).
  488. Temam, R., 1997, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, 2nd ed. (Springer Nature, New York).
  489. Thompson, P. D., 1957, “Uncertainty of initial state as a factor in the predictability of large scale atmospheric flow patterns,” Tellus 9, 275–295.
  490. Thual, O., and J. C. McWilliams, 1992, “The catastrophe structure of thermohaline convection in a two-dimensional fluid model and a comparison with low-order box models,” Geophys. Astrophys. Fluid Dyn. 64, 67–95.
  491. Titz, S., T. Kuhlbrodt, S. Rahmstorf, and U. Feudel, 2002, “On freshwater-dependent bifurcations in box models of the interhemispheric thermohaline circulation,” Tellus A 54, 89–98.
  492. Torralba, V., F. J. Doblas-Reyes, D. MacLeod, I. Christel, and M. Davis, 2017, “Seasonal climate prediction: A new source of information for the management of wind energy resources,” J. Appl. Meteorol. Climatol. 56, 1231–1247.
  493. Touchette, H., 2009, “The large deviation approach to statistical mechanics,” Phys. Rep. 478, 1–69.
  494. Trenberth, K. E., and J. M. Caron, 2001, “Estimates of meridional atmosphere and ocean heat transports,” J. Clim. 14, 3433–3443.
  495. Trenberth, Kevin E, John T. Fasullo, and Jeffrey Kiehl, 2009, “Earth’s global energy budget,” Bull. Am. Meteorol. Soc. 90, 311–324.
  496. Trevisan, A., and A. Buzzi, 1980, “Stationary response of barotropic weakly non-linear Rossby waves to quasi-resonant orographic forcing,” J. Atmos. Sci. 37, 947–957.
  497. Tribbia, J. J., and R. A. Anthes, 1987, “Scientific basis of modern weather prediction,” Science 237, 493–499.
  498. Tsonis, A. A., and P. J. Roebber, 2004, “The architecture of the climate network,” Physica (Amsterdam) 333A, 497–504.
  499. Tsonis, A. A., K. L. Swanson, and P. J. Roebber, 2006, “What do networks have to do with climate?,” Bull. Am. Meteorol. Soc. 87, 585–595.
  500. Turco, R. P., O. B. Toon, T. P. Ackerman, J. B. Pollack, and C. Sagan, 1983, “Nuclear winter: Global consequences of multiple nuclear explosions,” Science 222, 1283–1292.
  501. Turner, A. G., and H. Annamalai, 2012, “Climate change and the South Asian summer monsoon,” Nat. Clim. Change 2, 587–595.
  502. Tziperman, E., L. Stone, M. A. Cane, and H. Jarosh, 1994a, “El Niño chaos: Overlapping of resonances between the seasonal cycle and the Pacific ocean-atmosphere oscillator,” Science 264, 72–74.
  503. Tziperman, E., L. Stone, M. A. Cane, and H. Jarosh, 1994b, “El Niño chaos: Overlapping of resonances between the seasonal cycle and the Pacific ocean-atmosphere oscillator,” Science 264, 72–74.
  504. Vallis, G. K., 2006, Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation (Cambridge University Press, Cambridge, England).
  505. Vannitsem, S., J. Demaeyer, L. De Cruz, and M. Ghil, 2015, “Low-frequency variability and heat transport in a low-order nonlinear coupled ocean-atmosphere model,” Physica (Amsterdam) 309D, 71–85.
  506. Vannitsem, S., and V. Lucarini, 2016, “Statistical and dynamical properties of covariant Lyapunov vectors in a coupled atmosphere-ocean model—Multiscale effects, geometric degeneracy, and error dynamics,” J. Phys. A 49, 224001.
  507. Varadhan, S. R. S., 1966, “Asymptotic probabilities and differential equations,” Commun. Pure Appl. Math. 19, 261–286.
  508. Varadhan, S. R. S., 1984, Large Deviations and Applications (SIAM, Philadelphia).
  509. Veronis, G., 1963, “An analysis of the wind-driven ocean circulation with a limited number of Fourier components,” J. Atmos. Sci. 20, 577–593.
  510. Villani, C., 2009, Optimal Transport: Old and New (Springer Science+Business Media, New York).
  511. Vissio, G., and V. Lucarini, 2018a, “A proof of concept for scale-adaptive parametrizations: The case of the Lorenz ’96 model,” Q. J. R. Meteorol. Soc. 144, 63–75.
  512. Vissio, G., and V. Lucarini, 2018b, “Evaluating a stochastic parametrization for a fast-slow system using the Wasserstein distance,” Nonlinear Processes Geophys. 25, 413–427.
  513. Vollmer, J., T. M. Schneider, and B. Eckhardt, 2009, “Basin boundary, edge of chaos and edge state in a two-dimensional model,” New J. Phys. 11, 013040.
  514. von der Heydt, Anna S., et al., 2016, “Lessons on climate sensitivity from past climate changes,” Curr. Clim. Change Rep. 2, 148–158.
  515. Von Neumann, J., 1960, “Some remarks on the problem of forecasting climatic fluctuations,” in Dynamics of Climate, edited by R. L. Pfeffer (Pergamon Press, New York), pp. 9–11.
  516. Wallace, J. M., and D. S. Gutzler, 1981, “Teleconnections in the geopotential height field during the Northern Hemisphere winter,” Mon. Weather Rev. 109, 784–812.
  517. Walsh, J. E., 2014, “Intensified warming of the Arctic: Causes and impacts on middle latitudes,” Global Planet. Change 117, 52–63.
  518. Wang, Q., 2013, “Forward and adjoint sensitivity computation of chaotic dynamical systems,” J. Comput. Phys. 235, 1–13.
  519. Wang, Y., A. Gozolchiani, Y. Ashkenazy, Y. Berezin, O. Guez, and S. Havlin, 2013, “Dominant Imprint of Rossby Waves in the Climate Network,” Phys. Rev. Lett. 111, 138501.
  520. Washington, W. M., and C. L. Parkinson, 2005, An Introduction to Three-dimensional Climate Modeling (University Science Books, Sausalito, CA).
  521. Watson, A. J., and J. E. Lovelock, 1983, “Biological homeostasis of the global environment: The parable of Daisyworld,” Tellus B 35B, 284–289.
  522. Weeks, E. R., Y. Tian, J. S. Urbach, K. Ide, H. L. Swinney, and M. Ghil, 1997, “Transitions between blocked and zonal flows in a rotating annulus with topography,” Science 278, 1598–1601.
  523. Wester, P., A. Mishra, A. Mukherji, and A. B. Shrestha., Eds, 2019, The Hindu Kush Himalaya Assessment—Mountains, Climate Change, Sustainability and People (Springer Nature, Cham, Switzerland).
  524. Wetherald, R. T., and S. Manabe, 1975, “The effect of changing the solar constant on the climate of a general circulation model,” J. Atmos. Sci. 32, 2044–2059.
  525. Wiener, N., 1949, Extrapolation, Interpolation and Smoothing of Stationary Time Series, with Engineering Applications (MIT Press, Cambridge, MA).
  526. Wolf, E. T., J. Haqq-Misra, and O. B. Toon, 2018, “Evaluating climate sensitivity to CO2 across Earth’s history,” J. Geophys. Res. 123, 11 861–11 874.
  527. Woollings, T., D. Barriopedro, J. Methven, S.-W. Son, O. Martius, B. Harvey, J. Sillmann, A. R. Lupo, and S. Seneviratne, 2018, “Blocking and its response to climate change,” Curr. Clim. Change Rep. 4, 287–300.
  528. Wormell, C. L., and G. A. Gottwald, 2019, “Linear response for macroscopic observables in high-dimensional systems,” Chaos 29, 113127.
  529. , 2019a, “Edgeworth expansions for slow-fast systems with finite time-scale separation,” Proc. R. Soc. A 475, 20180358.
  530. , 2019b, “Stochastic model reduction for slow-fast systems with moderate time scale separation,” Multiscale Model. Simul. 17, 1172–1188.
  531. Wouters, J., and V. Lucarini, 2012, “Disentangling multi-level systems: Averaging, correlations and memory,” J. Stat. Mech. P03003.
  532. Wouters, J., and V. Lucarini, 2013, “Multi-level dynamical systems: Connecting the Ruelle response theory and the Mori-Zwanzig approach,” J. Stat. Phys. 151, 850–860.
  533. Wunsch, C., 1999, “The interpretation of short climate records, with comments on the North Atlantic and Southern Oscillations,” Bull. Am. Meteorol. Soc. 80, 245–255.
  534. Wunsch, C., 2002, “What is the thermohaline circulation?,” Science 298, 1179–1180.
  535. Wunsch, C., 2013, “The past and future ocean circulation from a contemporary perspective,” in Ocean Circulation: Mechanisms and Impacts—Past and Future Changes of Meridional Overturning (American Geophysical Union, Washington, DC), pp. 53–74.
  536. Yanai, M., 1975, “Tropical meteorology,” Rev. Geophys. 13, 685–710.
  537. Young, L-S, 2002, “What are SRB measures, and which dynamical systems have them?” J. Stat. Phys. 108, 733–754.
  538. Zaliapin, I., and M. Ghil, 2010, “Another look at climate sensitivity,” Nonlinear Processes Geophys. 17, 113–122.
  539. Zeng, N., and J. D. Neelin, 2000, “The role of vegetation–climate interaction and interannual variability in shaping the African savanna,” J. Clim. 13, 2665–2670.
  540. Zhang, C., 2005, “Madden-Julian oscillation,” Rev. Geophys. 43, RG2003.
  541. Zilitinkevich, S. S., 1975, “Resistance laws and prediction equations for depth of planetary boundary-layer,” J. Atmos. Sci. 32, 741–752.
  542. Zwanzig, R., 1961, “Memory effects in irreversible thermodynamics,” Phys. Rev. 124, 983–992.

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