Climate Dynamics

, Volume 44, Issue 11–12, pp 3187–3210 | Cite as

A voyage through scales, a missing quadrillion and why the climate is not what you expect

Article

Abstract

Using modern climate data and paleodata, we voyage through 17 orders of magnitude in scale explicitly displaying the astounding temporal variability of the atmosphere from fractions of a second to hundreds of millions of years. By combining real space (Haar fluctuation) and Fourier space analysis, we produce composites quantifying the variability. These show that the classical “mental picture” in which quasi periodic processes are taken as the fundamental signals embedded in a spectral continuum of background “noise” is an iconic relic of a nearly 40 year old “educated guess” in which the flatness of the continuum was exaggerated by a factor of ≈1015. Using modern data we show that a more realistic picture is the exact opposite: the quasiperiodic processes are small background perturbations to spectrally continuous wide range scaling foreground processes. We identify five of these: weather, macroweather, climate, macroclimate and megaclimate, with rough transition scales of 10 days, 50 years, 80 kyrs, 0.5 Myr, and we quantify each with scaling exponents. We show that as we move from one regime to the next, that the fluctuation exponent (H) alternates in sign so that fluctuations change sign between growing (H > 0) and diminishing (H < 0) with scale. For example, mean temperature fluctuations increase up to about 5 K at 10 days (the lifetime of planetary structures), then decrease to about 0.2 K at 50 years, and then increase again to about 5 K at glacial-interglacial scales. The pattern then repeats with a minimum RMS fluctuation of 1–2 K at ≈0.5 Myr increasing to ≈20 K at 500 Myrs. We show how this can be understood with the help of the new, pedagogical “H model”. Both deterministic General Circulation Models (GCM’s) with fixed forcings (“control runs”) and stochastic turbulence-based models reproduce weather and macroweather, but not the climate; for this we require “climate forcings” and/or new slow climate processes. Averaging macroweather over periods increasing to ≈30–50 yrs yields apparently converging values: macroweather is “what you expect”. Macroweather averages over ≈30–50 yrs have the lowest variability, they yield well defined climate states and justify the otherwise ad hoc “climate normal” period. However, moving to longer periods, these states increasingly fluctuate: just as with the weather, the climate changes in an apparently unstable manner; the climate is not what you expect. Moving to time scales beyond 100 kyrs, to the macroclimate regime, we find that averaging the varying climate increasingly converges, but ultimately—at scales beyond ≈0.5 Myr in the megaclimate, we discover that the apparent point of convergence itself starts to “wander”, presumably representing shifts from one climate to another.

Keywords

Climate Weather Scaling Variability Paleotemperatures 

References

  1. AchutaRao K, Sperber KR (2006) ENSO simulation in coupled ocean-atmosphere models: are the current models better? Clim Dyn 27:1–15. doi:10.1007/s00382-006-0119-7 CrossRefGoogle Scholar
  2. Ashkenazy Y, Baker D, Gildor H, Havlin S (2003) Nonlinearity and multifractality of climate change in the past 420,000 years. Geophys Res Lett 30:2146. doi:10.1029/2003GL018099 CrossRefGoogle Scholar
  3. Barras C, Duplessy J-C, Geslin E, Michel E, Jorissen FJ (2010) Calibration of δ18O of cultured benthic foraminiferal calcite as a function of temperature. Biogeosciences 7:1349–1356. doi:10.5194/bg-7-1349-2010 CrossRefGoogle Scholar
  4. Blender R, Fraedrich K, Hunt B (2006) Millennial climate variability: GCMration of δ18O of cultured benthic. Geophys Res Lett 33:L04710. doi:10.1029/2005GL024919 Google Scholar
  5. Bond G, Showers W, Cheseby M, Lotti R, Almasi P, deMenocal P, Priori P, Cullen H, Hajdes I, Bonani G (1997) A pervasive millennial-scale climate cycle in the North Atlantic: the Holocene and late glacial record. Science 278:1257–1266CrossRefGoogle Scholar
  6. Bryson RA (1997) The paradigm of climatology: an essay. Bull Am Meteor Soc 78:450–456Google Scholar
  7. Bunde A, Eichner JF, Kantelhardt JW, Havlin S (2005) Long-term memory: a natural mechanism for the clustering of extreme events and anomalous residual times in climate records. Phys Rev Lett 94:048701CrossRefGoogle Scholar
  8. Charlson RJ, Lovelock JE, Andreae MO, Warren SG (1987) Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate. Nature 326:655–661CrossRefGoogle Scholar
  9. Charney JG (1971) Geostrophic Turbulence. J Atmos Sci 28:1087CrossRefGoogle Scholar
  10. Chekroun MD, Simonnet E, Ghil M (2010) Stochastic climate dynamics: random attractors and time-dependent invariant measures. Phys D 240:1685–1700CrossRefGoogle Scholar
  11. Committee on Radiative Forcing Effects on Climate, N. R. C (2005) Radiative forcing of climate change: expanding the concept and addressing uncertainties. National Academic Press, Washington, 224 pGoogle Scholar
  12. Compo GP et al (2011) The twentieth century reanalysis project. Quart J Roy Meteorol Soc 137:1–28. doi:10.1002/qj.776 CrossRefGoogle Scholar
  13. Delworth T, Manabe S, Stoufer RJ (1993) Interdecadal variations of the thermocline ciruculation in a coupled ocean-atmosphere model. J Clim 6:1993–2011CrossRefGoogle Scholar
  14. Dijkstra H (2013) Nonlinear climate dynamics. Cambridge University Press, Cambridge, p 357CrossRefGoogle Scholar
  15. Dijkstra H, Ghil M (2005) Low frequency variability of the large scale ocean circulations: a dynamical systems approach. Rev Geophys 43(3)Google Scholar
  16. Ditlevsen PD, Svensmark H, Johson S (1996) Contrasting atmospheric and climate dynamics of the last-glacial and Holocene periods. Nature 379:810–812CrossRefGoogle Scholar
  17. Eichner JF, Koscielny-Bunde E, Bunde A, Havlin S, Schellnhuber H-J (2003) Power-law persistance and trends in the atmosphere: a detailed study of long temperature records. Phys Rev E 68:046133. doi:10.1103/PhysRevE.68.046133 CrossRefGoogle Scholar
  18. Fraedrich K, Blender K (2003) Scaling of atmosphere and ocean temperature correlations in observations and climate models. Phys Rev Lett 90:108501–108504CrossRefGoogle Scholar
  19. Fraedrich K, Blender R, Zhu X (2009) Continuum climate variability: long-term memory, scaling, and 1/f-Noise. Int J Mod Phys B 23:5403–5416CrossRefGoogle Scholar
  20. Franzke C (2010) Long-range dependence and climate noise characteristics of Antarctica temperature data. J Clim 23:6074–6081. doi:10.1175/2010JCL13654.1 CrossRefGoogle Scholar
  21. Franzke J, Frank D, Raible CC, Esper J, Brönnimann S (2013) Spectral biases in tree-ring climate proxies. Nat Clim Change 3:360–364. doi:10.1038/Nclimate1816 CrossRefGoogle Scholar
  22. Gagnon J, Lovejoy SS, Schertzer D (2006) Multifractal earth topography. Nonlin Proc Geophys 13:541–570CrossRefGoogle Scholar
  23. Heinlein RA (1973) Time enough for love. GP Putnam’s Sons, New YorkGoogle Scholar
  24. Huang S (2004) Merging information from different resources for new insights into climate change in the past and future. Geophys Res Lett 31:L13205. doi:10.1029/2004GL019781 CrossRefGoogle Scholar
  25. Huschke RE (Ed) (1959) Glossary of meteorology, 638 pGoogle Scholar
  26. Huybers P (2007) Glacial variability over the last two million years: an extended depth-derived agemodel, continuous obliquity pacing, and the Pleistocene progression. Quat Sci Rev 26(1–2):37–55CrossRefGoogle Scholar
  27. Huybers P, Curry W (2006) Links between annual, Milankovitch and continuum temperature variability. Nature 441:329–332. doi:10.1038/nature04745 CrossRefGoogle Scholar
  28. Isono D, Yamamoto M, Irino T, Oba T, Murayama M, Nakamura T, Kawahata H (2009) The 1500-year climate oscillation in the midlatitude North Pacific during the Holocene. Geology 37:591–594CrossRefGoogle Scholar
  29. Kantelhardt JW, Zscchegner SA, Koscielny-Bunde K, Havlin S, Bunde A, Stanley HE (2002) Multifractal detrended fluctuation analysis of nonstationary time series. Phys A 316:87–114CrossRefGoogle Scholar
  30. Kolesnikov VN, Monin AS (1965) Spectra of meteorological field fluctuations. Izvestiya Atmos Ocean Phys 1:653–669Google Scholar
  31. Koscielny-Bunde E, Bunde A, Havlin S, Roman HE, Goldreich Y, Schellnhuber HJ (1998) Indication of a universal persistence law governing atmospheric variability. Phys Rev Lett 81:729CrossRefGoogle Scholar
  32. Kraichnan RH (1967) Inertial ranges in two-dimensional turbulence. Phys Fluids 10:1417–1423CrossRefGoogle Scholar
  33. Lamb HH (1972) Climate: past, present, and future. Vol. 1, Fundamentals and climate now. Methuen and Co, LondonGoogle Scholar
  34. Lanfredi M, Simoniello T, Cuomo V, Macchiato M (2009) Discriminating low frequency components from long range persistent fluctuations in daily atmospheric temperature variability. Atmos Chem Phys 9:4537–4544CrossRefGoogle Scholar
  35. Lennartz S, Bunde A (2009) Trend evaluation in records with long term memory: application to global warming. Geophys Res Lett 36:L16706. doi:10.1029/2009GL039516 CrossRefGoogle Scholar
  36. Lindborg E, Tung KK, Nastrom GD, Cho JYN, Gage KS (2010a) Comment on “Reinterpreting aircraft measurement in anisotropic scaling turbulence” by Lovejoy et al. Atmos Chem Phys 10:1401–1402CrossRefGoogle Scholar
  37. Lindborg E, Tung KK, Nastrom GD, Cho JYN, Gage KS et al (2010b) Interactive comment on “Comment on “Reinterpreting aircraft measurements in anisotropic scaling turbulence” by Lovejoy, (2009)”. Atmos Chem Phys Discuss 9:C9797–C9798Google Scholar
  38. Ljungqvist FC (2010) A new reconstruction of temperature variability in the extra—tropical Northern Hemisphere during the last two millennia. Geografiska Annaler: Phys Geograp 92 A(3): 339–351. doi:10.1111/j.1468-0459.2010.00399.x
  39. Lorenz EN (1995) Climate is what you expect, p 55, aps4.mit.edu/research/Lorenz/publications.htm (16 May, 2012)Google Scholar
  40. Lovejoy S (2013) What is climate? EOS 94(1) 1 January, pp 1–2Google Scholar
  41. Lovejoy, S. (2014a), Return periods of global climate fluctuations and the pause. Geophys Res Lett 41. doi:10.1002/2014GL060478
  42. Lovejoy S (2014b) Scaling fluctuation analysis and statistical hypothesis testing of anthropogenic warming. Clim Dyn. doi:10.1007/s00382-014-2128-2 Google Scholar
  43. Lovejoy S, Mandelbrot BB (1985) Fractal properties of rain and a fractal model. Tellus 37(A): 209Google Scholar
  44. Lovejoy S, Schertzer D (1984) 40,000 years of scaling in climatological temperatures. Meteor Sci Tech 1:51–54Google Scholar
  45. Lovejoy S, Schertzer D (1986) Scale invariance in climatological temperatures and the spectral plateau. Ann Geophys 4B:401–410Google Scholar
  46. Lovejoy S, Schertzer D (1998) Stochastic chaos and multifractal geophysics. In: Guindani FM, Salvadori Chaos G (eds) Fractals and models 96. Italian University Press, ItalyGoogle Scholar
  47. Lovejoy S, Schertzer D (2010) Towards a new synthesis for atmospheric dynamics: space-time cascades. Atmos Res 96:1–52. doi:10.1016/j.atmosres.2010.01.004 CrossRefGoogle Scholar
  48. Lovejoy S, Schertzer D (2011) Space-time cascades and the scaling of ECMWF reanalyses: fluxes and fields. J Geophys Res 116. doi:10.1029/2011JD015654
  49. Lovejoy S, Schertzer D (2012a) Low frequency weather and the emergence of the Climate. In: Sharma AS, Bunde A, Baker D, Dimri VP (eds) Extreme events and natural hazards: the complexity perspective. AGU monographs, Washington, pp 231–254CrossRefGoogle Scholar
  50. Lovejoy S, Schertzer D (2012b) Haar wavelets, fluctuations and structure functions: convenient choices for geophysics. Nonlinear Proc Geophys 19:1–14. doi:10.5194/npg-19-1-2012 CrossRefGoogle Scholar
  51. Lovejoy S, Schertzer D (2012c) Stochastic and scaling climate sensitivities: solar, volcanic and orbital forcings. Geophys Res Lett 39:L11702. doi:10.1029/2012GL051871 Google Scholar
  52. Lovejoy S, Schertzer D (2013) The weather and climate: emergent laws and multifractal cascades. Cambridge University Press, Cambridge, p 496CrossRefGoogle Scholar
  53. Lovejoy S, Tuck AF, Hovde SJ, Schertzer D (2007) Is isotropic turbulence relevant in the atmosphere?. Res Lett, Geophys. doi:10.1029/2007GL029359,L14802 Google Scholar
  54. Lovejoy S, Tuck AF, Schertzer D, Hovde SJ (2009) Reinterpreting aircraft measurements in anisotropic scaling turbulence. Atmos Chem Phys 9:1–19CrossRefGoogle Scholar
  55. Lovejoy S, Schertzer D, Tuck AF (2010) Why anisotropic turbulence matters: another reply to E. Lindborg. Atmos Chem Physics Disc 10:C4689–C4697CrossRefGoogle Scholar
  56. Lovejoy S, Schertzer D, Varon D (2013a) Do GCM’s predict the climate…. or macroweather? Earth Syst Dynam 4:1–16. doi:10.5194/esd-4-1-2013 CrossRefGoogle Scholar
  57. Lovejoy S, Schertzer, D, Tchiguirinskaia I (2013b) Further (monofractal) limitations of climactograms. Hydrol Earth Syst Sci Discuss 10:C3086–C3090. http://www.hydrol-earth-syst-sci-discuss.net/10/C3181/2013/
  58. Lovejoy S, Varotsos C, Efstathiou MN (2014a) Scaling analyses of forcings and outputs of a simplified Last Millennium climate model. J Geophys Res (under review)Google Scholar
  59. Lovejoy S, Muller JP, Boisvert JP (2014b) On Mars too, expect macroweather. Geophys Res Lett (in press)Google Scholar
  60. Mandelbrot B (1981) Scalebound or scaling shapes: a useful distinction in the visual arts and in the natural sciences. Leonardo 14:43–47CrossRefGoogle Scholar
  61. Mann ME, Park J (1994) Global scale modes of surface temperature variaiblity on interannual to century timescales. J Geophys Res 99:819–825Google Scholar
  62. Mann ME, Park J, Bradley RS (1995) Global interdecadal and century scale climate oscillations duering the past five centuries. Nature 378:268–270CrossRefGoogle Scholar
  63. Mann ME, Steinman BA, Miller SK (2014) On forced temperature changes, internal variability, and the AMO. Geophys Res Lett 41:3211–3219. doi:10.1002/2014GL059233 CrossRefGoogle Scholar
  64. Markonis Y, Koutsoyiannis D (2013) Climatic variability over time scales spanning nine orders of magnitude: connecting milankovitch cycles with Hurst-Kolmogorov dynamics. Surv Geophys 34(2):181–207CrossRefGoogle Scholar
  65. Mitchell JM (1976) An overview of climatic variability and its causal mechanisms. Quat Res 6:481–493CrossRefGoogle Scholar
  66. Moberg A, Sonnechkin DM, Holmgren K, Datsenko NM, Karlén W (2005) Highly variable Northern Hemisphere temperatures reconstructed from low- and high—resolution proxy data. Nature 433(7026):613–617CrossRefGoogle Scholar
  67. Monetti RA, Havlin S, Bunde A (2003) Long-term persistance in the sea surface temperature fluctuations. Phys A 320:581–589CrossRefGoogle Scholar
  68. Monin AS (1972) Weather forecasting as a problem in physics. MIT press, BostonGoogle Scholar
  69. Palmer T (2005) Global warming in a nonlinear climate—Can we be sure?, Europhysics news March/April 2005, pp 42–46. doi: 10.1051/epn:2005202
  70. Palmer TN (2012) Towards the probabilistic Earth-system simulator: a vision for the future of climate and weather prediction. Q J R Meteorol Soc (in press)Google Scholar
  71. Palmer TN, Doblas-Reyes FJ, Weisheimer A, Rodwell MJ (2008) Toward seamless prediction: calibration of climate change projections using seasonal forecasts. Bull Am Meteor Soc 89:459–470. doi:10.1175/BAMS-89-4-459 CrossRefGoogle Scholar
  72. Panofsky HA (1969) The spectrum of temperature. J Radio Sci 4:1101–1109CrossRefGoogle Scholar
  73. Pelletier JD (1998) The power spectral density of atmospheric temperature from scales of 10**-2 to 10**6 yr. EPSL 158:157–164CrossRefGoogle Scholar
  74. Peng C-K, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL (1994) Mosaic organisation of DNA nucleotides. Phys Rev E 49:1685–1689CrossRefGoogle Scholar
  75. Pielke R (1998) Climate prediction as an initial value problem. Bull Am Meteor Soc 79:2743–2746Google Scholar
  76. Pielke RAS, Wilby R, Niyogi D, Hossain F, Dairuku K, Adegoke J, Kallos G, Seastedt T, Suding K (2012) Dealing with complexity and extreme events using a bottom-up, resource-based vulnerability perspective. In: Sharma AS, Bunde A, Baker D, Dimri VP (eds) Complexity and Extreme Events in Geosciences. AGU, WashingtonGoogle Scholar
  77. Pinel J, Lovejoy S, Schertzer D, Tuck AF (2012) Joint horizontal—vertical anisotropic scaling, isobaric and isoheight wind statistics from aircraft data. Geophys Res Lett 39:L11803. doi:10.1029/2012GL051698 Google Scholar
  78. Pinel J, Lovejoy S, Schertzer D (2014) The horizontal space-time scaling and cascade structure of the atmosphere inferred from satellite radiances. Atmos Res 140–141:95–114. doi:10.1016/j.atmosres.2013.11.022 CrossRefGoogle Scholar
  79. Radkevitch, A., S. Lovejoy, K. B. Strawbridge, D. Schertzer, and M. Lilley (2008), Scaling turbulent atmospheric stratification, Part III: empIrical study of Space-time stratification of passive scalars using lidar data. Quart J Roy Meteor Soc doi: 10.1002/qj.1203
  80. Rohde R, Muller RA, Jacobsen R, Muller E, Perlmutter S, Rosenfeld A, Wurtele J, Groom D, Wickham C (2013) A new estimate of the average earth surface land temperature spanning 1753 to 2011. Geoinfor Geostat An Overv 1:1. doi:10.4172/2327-4581.1000101
  81. Rybski D, Bunde A, von Storch H (2008) Long-term memory in 1000- year simulated temperature records. J Geophys Res 113:D02106-02101–D02106-02109. doi:10.1029/2007JD008568 Google Scholar
  82. Rypdal M, Rypdal K (2014) Long-memory effects in linear-response models of Earth’s temperature and implications for future global warming. Clim Dyn (in press)Google Scholar
  83. Schertzer D, Lovejoy S (1985) The dimension and intermittency of atmospheric dynamics. In: Launder B (ed) Turbulent shear flow 4. Springer, Berlin, pp 7–33CrossRefGoogle Scholar
  84. Schertzer D, Lovejoy S (1987) Physical modeling and analysis of rain and clouds by anisotropic scaling of multiplicative processes. J Geophys Res 92:9693–9714CrossRefGoogle Scholar
  85. Schertzer D, Tchiguirinskaia I, Lovejoy S, Tuck AF (2011) Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply to Lindborg. Atmos Chem Phys Discus 11:3301–3320CrossRefGoogle Scholar
  86. Schertzer D, Tchiguirinskaia I, Lovejoy S, Tuck AF (2012) Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply. Atmos Chem Phys 12:327–336. doi:10.5194/acp-12-327-2012 CrossRefGoogle Scholar
  87. Schlesinger ME, Ramankutty N (1994) An oscillation in the global climate system of period 65–70 Years. Nature 367:723–726CrossRefGoogle Scholar
  88. Schmitt F, Lovejoy S, Schertzer D (1995) Multifractal analysis of the Greenland Ice-core project climate data. Geophys Res Lett 22:1689–1692CrossRefGoogle Scholar
  89. Schwander J, Jouzel J, Hammer CU, Petit J-R, Udisti R, Wolff EW (2001) A tentative chronology for the EPICA Dome Concordia ice core. Geophys Res Lett 28:4243–4246CrossRefGoogle Scholar
  90. Shackleton NJ, Imbrie J (1990) The δ18O spectrum of oceanic deep water over a five-decade band. Clim Change 16:217–230CrossRefGoogle Scholar
  91. Shaviv NJ, Veizer J (2003) Celestial driver of Phanerozoic climate? GSA Today, July 2003, pp 4–10Google Scholar
  92. Stolle J, Lovejoy S, Schertzer D (2009) The stochastic cascade structure of deterministic numerical models of the atmosphere. Nonlin Proc Geophys 16:1–15CrossRefGoogle Scholar
  93. Stolle J, Lovejoy S, Schertzer D (2012) The temporal cascade structure and space-time relations for reanalyses and Global Circulation models. Quart J Roy Meteor Soc (in press)Google Scholar
  94. Talkner P, Weber RO (2000) Power spectrum and detrended fluctuation analysis: application to daily temperatures. Phys Rev E 62:150–160CrossRefGoogle Scholar
  95. Vallis G (2010) Mechanisms of climate variaiblity from years to decades. In: Palmer PWT (ed) Stochstic Physics and Climate Modelliing. Cambridge University Press, Cambridge, pp 1–34Google Scholar
  96. Van der Hoven I (1957) Power spectrum of horizontal wind speed in the frequency range from 0007 to 900 cycles per hour. J Meteorol 14:160–164CrossRefGoogle Scholar
  97. Veizer J et al (1999) 87Sr/86Sr, d18O and d13C evolution of phanerozoic seawater. Chem Geol 161:59–88CrossRefGoogle Scholar
  98. Veizer J, Godderis Y, Francois LM (2000) Evidence for decoupling of atmospheric CO2 and global climate during the Phanerozoic eon. Nature 408:698–701CrossRefGoogle Scholar
  99. Wunsch C (2003) The spectral energy description of climate change including the 100 ky energy. Clim Dyn 20:353–363Google Scholar
  100. Yano J (2009) Interactive comment on “Reinterpreting aircraft measurements in anisotropic scaling turbulence” by S. Lovejoy et al. Atmos Chem Phys Discuss 9: S162–S166. http://www.atmos-chem-phys-discuss.net/9/S162/2009/
  101. Zachos J, Pagani M, Sloan L, Thomas E, Billups K (2001) Trends, rhythms, and aberrations in global climate 65 Ma to Present. Science 292(5517):686–693. doi:10.1126/science.1059412 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of PhysicsMcGill UniversityMontrealCanada

Personalised recommendations