Links between annual, Milankovitch and continuum temperature variability


Climate variability exists at all timescales—and climatic processes are intimately coupled, so that understanding variability at any one timescale requires some understanding of the whole. Records of the Earth's surface temperature illustrate this interdependence, having a continuum of variability following a power-law scaling1,2,3,4,5,6,7. But although specific modes of interannual variability are relatively well understood8,9, the general controls on continuum variability are uncertain and usually described as purely stochastic processes10,11,12,13. Here we show that power-law relationships of surface temperature variability scale with annual and Milankovitch-period (23,000- and 41,000-year) cycles. The annual cycle corresponds to scaling at monthly to decadal periods, while millennial and longer periods are tied to the Milankovitch cycles. Thus the annual, Milankovitch and continuum temperature variability together represent the response to deterministic insolation forcing. The identification of a deterministic control on the continuum provides insight into the mechanisms governing interannual and longer-period climate variability.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Temperature scaling at instrumental periods from NCEP.
Figure 2: Patch-work spectral estimate using instrumental and proxy records of surface temperature variability, and insolation at 65° N.


  1. 1

    Shackleton, N. J. & Imbrie, J. The δ18O spectrum of oceanic deep water over a five-decade band. Clim. Change 16, 217–230 (1990)

    ADS  Article  Google Scholar 

  2. 2

    Ditlevsen, P., Svensmark, H. & Johnsen, S. Contrasting atmospheric and climate dynamics of the last-glacial and Holocene periods. Nature 379, 810–812 (1996)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Pelletier, J. The power-spectral density of atmospheric temperature from time scales of 10-2 to 106 yr. Earth Planet. Sci. Lett. 158, 157–164 (1998)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Fraedrich, K. & Blender, R. Scaling of atmosphere and ocean temperature correlations in observations and climate models. Phys. Rev. Lett. 90, 108501 (2003)

    ADS  Article  Google Scholar 

  5. 5

    Blender, R. & Fraedrich, K. Long time memory in global warming simulations. Geophys. Res. Lett. 14, doi:10.1029/2003GL017666 (2003)

  6. 6

    Schmitt, F., Lovejoy, S. & Schertzer, D. Multifractal analysis of the Greenland Ice-core Project climate data. Geophys. Res. Lett. 22, 1689–1692 (1995)

    ADS  Article  Google Scholar 

  7. 7

    Ashkenazy, Y., Baker, D., Gildor, H. & Havlin, S. Nonlinearity and multifractality of climate change in the past 420,000 years. Geophys. Res. Lett. 30, doi:10.1029/2003GL018099 (2003)

  8. 8

    Philander, G. El Niño, La Niña, and the Southern Oscillation (Academic, San Diego, California, 1990)

    Google Scholar 

  9. 9

    Hurrell, J. & Van Loon, H. Decadal variations in climate associated with the North Atlantic Oscillation. Clim. Change 36, 301–326 (1997)

    Article  Google Scholar 

  10. 10

    Kominz, M. & Pisias, N. Pleistocene climate—deterministic or stochastic? Science 204, 171–173 (1979)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Pelletier, J. Coherence resonance and ice ages. J. Geophys. Res. 108, doi:10.1029/2002JD003120 (2003)

  12. 12

    Wunsch, C. The spectral description of climate change including the 100 ky energy. Clim. Dyn. 20, 353–363 (2003)

    Article  Google Scholar 

  13. 13

    Fraedrich, K., Luksch, U. & Blender, R. A 1/f-model for long time memory of the ocean surface temperature. Phys. Rev. E 70, 037301 (2003)

    ADS  Article  Google Scholar 

  14. 14

    Hays, J., Imbrie, J. & Shackleton, N. Variations in the earth's orbit: Pacemaker of the ice ages. Science 194, 1121–1132 (1976)

    ADS  CAS  Article  Google Scholar 

  15. 15

    Imbrie, J. et al. On the structure and origin of major glaciation cycles. 1. Linear responses to Milankovitch forcing. Paleoceanography 6, 205–226 (1992)

    Google Scholar 

  16. 16

    Wunsch, C. The spectrum from two years to two minutes of temperature fluctuations in the main thermocline at Bermuda. Deep-Sea Res. 19, 577–593 (1972)

    Google Scholar 

  17. 17

    Garrett, C. & Munk, W. Internal waves in the ocean. Annu. Rev. Fluid Mech. 80, 291–297 (1979)

    MATH  Google Scholar 

  18. 18

    Percival, D. & Walden, A. Spectral Analysis for Physical Applications (Cambridge Univ. Press, Cambridge, UK, 1993)

    Google Scholar 

  19. 19

    Kalnay, E. et al. The NCEP/NCAR 40-year reanalysis project. Bull. Am. Meteorol. Soc. 77, 437–471 (1996)

    ADS  Article  Google Scholar 

  20. 20

    DeWitt, D. G. & Schneider, E. K. The processes determining the annual cycle of equatorial sea surface temperature: A coupled general circulation model perspective. Mon. Weath. Rev. 127, 381–395 (1999)

    ADS  Article  Google Scholar 

  21. 21

    Jones, P., New, M., Parker, D., Martin, S. & Rigor, I. Surface air temperature and its variations over the last 150 years. Rev. Geophys. 37, 173–199 (1999)

    ADS  Article  Google Scholar 

  22. 22

    Elgar, S. & Sebert, G. Statistics of bicoherence and biphase. J. Geophys. Res. 94, 10993–10998 (1989)

    ADS  Article  Google Scholar 

  23. 23

    Hasselmann, K. Stochastic climate models. Part I. Theory. Tellus 6, 473–485 (1976)

    ADS  Google Scholar 

  24. 24

    Serreze, M. C. et al. Observational evidence of recent change in the northern high-latitude environment. Clim. Change 46, 159–207 (2000)

    Article  Google Scholar 

  25. 25

    Delworth, T. L. et al. Review of simulations of climate variability and change with the GFDL R30 coupled climate model. J. Clim. 19, 555–574 (2002)

    Google Scholar 

  26. 26

    McCoy, E., Walden, A. & Percival, D. Multitaper spectral estimation of power law processes. IEEE Trans. Signal Process. 46, 655–668 (1998)

    ADS  Article  Google Scholar 

  27. 27

    Wilson, K., Francis, D., Wensel, R., Coats, A. & Parker, K. Relationship between detrended fluctuation analysis and spectral analysis of heart-rate variability. Physiol. Meas. 23, 385–401 (2002)

    Article  Google Scholar 

  28. 28

    Briffa, K. et al. Low-frequency temperature variations from a northern tree-ring density network. J. Geophys. Res. 106, 2929–2941 (2001)

    ADS  Article  Google Scholar 

  29. 29

    Wunsch, C. & Gunn, D. A densely sampled core and climate variable aliasing. Geo-mar. Lett. 29, doi:10.1007/s00367-003-0125-2 (2003)

  30. 30

    Huybers, P. & Wunsch, C. A depth-derived Pleistocene age-model: Uncertainty estimates, sedimentation variability, and nonlinear climate change. Paleoceanography 19, doi:10.1029/2002PA000857 (2004)

Download references


P.H. was supported by the NOAA Postdoctoral Program in Climate and Global Change. Funding for W.C. was provided by the National Science Foundation, Division of Ocean Sciences. T. Crowley, R. Ferrari, O. Marchal, J. Sachs, D. Steele and C. Wunsch provided useful comments.

Author information



Corresponding author

Correspondence to Peter Huybers.

Ethics declarations

Competing interests

Reprints and permissions information is available at The authors declare no competing financial interests.

Supplementary information

Supplementary Notes

This file contains Supplementary Table, Supplementary Figures 1 and 2 and additional references. (PDF 699 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Huybers, P., Curry, W. Links between annual, Milankovitch and continuum temperature variability. Nature 441, 329–332 (2006).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing