Pacemaking the ice ages by frequency modulation of Earth's orbital eccentricity

Science

Volumn 285, Issue 5427, 1999, Pages 564-568

  Rial, J A ^a  

^a UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CLIMATE FORCING; EARTH ROTATION; MILANKOVITCH CYCLE; ORBITAL FORCING; PALEOCLIMATE;

ARCTIC CLIMATE; ARTICLE; ASTRONOMY; GEOLOGY; PRIORITY JOURNAL;

EID: 0033597831     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.285.5427.564     Document Type: Article

References (29)

1. M. Milankovitch, Canon of Insolation and the Ice-Age Problem, Royal Serbian Academy Spec. Pub., vol. 132 (Israel Program for Scientific Translations, Jerusalem, 1969).
2. J. D. Hays, J. Imbrie, N. J. Shackelton, Science 194, 1121 (1976).
3. A. Berger and M. F. Loutre, Quat. Sci. Rev. 10, 297 (1991); A. Berger, Numercal Values of the Elements of the Earth's Orbit from 5,000,000 YBP to 7,000,000 YAP, Contribution No. 35, Universite Catholique de Louvain, B-1348 Louvain, Belgium (1978).
4. A. Berger and M. F. Loutre, Quat. Sci. Rev. 10, 297 (1991); A. Berger, Numercal Values of the Elements of the Earth's Orbit from 5,000,000 YBP to 7,000,000 YAP, Contribution No. 35, Universite Catholique de Louvain, B-1348 Louvain, Belgium (1978).
5. J. Imbrie et al., in Milankovitch and Climate, A. L. Berger et al., Eds. (Reidel, Hingham, MA, 1984), pp. 269-305.
6. In order of decreasing spectral amplitude, the main periods in the trigonometric expansion of Earth's orbital eccentricity are, approximately, 413, 95, 125, and 100 ky. The 95 and 413 ky spectral peak amplitudes are nearly equal and about twice as strong as the 125 ky amplitude and four times stronger than the 100 ky amplitude (3).
7. J. Imbrie and J. Z. Imbrie, Science 207, 943 (1980).
8. M. E. Raymo, Paleoceanography 12, 577 (1997).
9. W. H. Berger, M. K. Yasuda, T. Bickert, G. Wefer, T. Takayama, Geology 22, 463 (1994); W. H. Berger, T. Bickert, H. Schmidt, C. Wefer, Proc. Ocean Drill. Program Part B Sci. Results 130, 381 (1993).
10. W. H. Berger, M. K. Yasuda, T. Bickert, G. Wefer, T. Takayama, Geology 22, 463 (1994); W. H. Berger, T. Bickert, H. Schmidt, C. Wefer, Proc. Ocean Drill. Program Part B Sci. Results 130, 381 (1993).
11. B. P. Lathi, Modem Digital and Analog Communication Systems (Oxford Univ. Press, New York, 1998).
12. m, n = 1, 2, 3. . . . See, for instance, A. Hund, frequency Modulation (McGraw-Hill, New York, 1942).
13. Frequency modulation of the weaker 125 ky eccentricity component essentially reinforces the 95 ky peak and its sidebands, since 1/95 - 1/413 ∼ 1/125. The contribution of the much weaker 100 ky component is noticeable only in some records (Fig. 4A).
14. D. G., Martinson et al., Quat. Res. 27, 1 (1987).
15. 18O data used in this study are as follows: Site 849 and Site 846 tuning procedures are described in Mix et al. (19). For the construction of the untuned records, the following anchor points between depth (revised composite depth in meters, or rmcd) and age were used. Site 846:0.0 rmcd = 0.00 thousand years before the present (ky B.P.); 65.4 rmcd = 1810 ky B.P. Site 849: 0.0 rmcd = 0.0 ky B.P.; 50.0 rmcd = 1800 ky B.P.; 153.8 rmcd = 5 My B.P. (A. Mix, personal communication). The untuned time scale was then constructed by linear interpolation. Both tuned and raw records are available through anonymous ftp (ftp://oce.orst.edu/ DATA/mix). Site 806: The age model for the tuned record of Site 806 is from (8). Site 677: Tuned and depth-dependent data were obtained from the Delphi project Web site (http://delphi.esc.cam.acuk/). See also N. J. Shackleton, A. Berger, and W. R. Peltier [Tram. R. Soc. Edinburgh Earth Sci. 81, 251 (1990)]. To construct the untuned record, two anchor points at 0 ky B.P. and at 1200 ky B.P. were transferred from the tuned age model. The untuned time scale was then constructed by linear interpolation.
16. R. A. Muller and C. J. MacDonald, Science 277, 215 (1997).
17. -1, or 0.00167 cycles/ky, so that the spectrum entirely washes out the gap between the eccentricity's 95-ky carrier and the important 107-ky sideband, separated by a 1/826 = 0.00121 cycles/ky interval, and barely resolves sidebands produced by the 413-ky modulation, separated by multiple integers of 0.00242 cycles/ky. A possible reason for the presence of a strong 100-ky peak in the short window spectra is found in the spectrogram of Fig. 1B, which shows that the highest power in the eccentricity band is associated with a transient event about 400 ka (well within the 0 to 600 ky window), which lasted for about 100 ky and had most of its power between 90 and 110 ky. Low spectral resolution of this transient event can certainly contribute to make the 100-ky peak (14) as prominent as shown in Fig. 3C.
18. 18O records is unlikely to be an artifact of time scaling techniques, because different time series treated with different tuning schemes contain the two eccentricity peaks prominently, even for times before 1 Ma.
19. Increase in the modulation index ε increases the number of sidebands and hence the bandwidth. Its increase also increases the power of the sidebands relative to the carrier's (Fig. 4).
20. 22t]. An interesting point is then that Eq. 3 represents a climate response that is both linear and nonlinear, since it allows for the linear superposition of the spectra of each individual modulated carrier and its sidebands, while the FM process acting on each carrier is itself nonlinear. In fact, having more than one modulating frequency creates an infinite number of combination tones (this distinguishes FM from AM, or amplitude modulation), and so Eq. 3 predicts that the spectral peak at 107 ky is strong because it is both a sideband of the 95-ky carrier modulated by the 826-ky subharmonic and a nonlinearly produced combination tone, which probably explains why it appears to have its own sidebands (Fig. 4).
21. A. C. Mix et al., Proc. Ocean Drill. Program Part B Sci. Results 138, 371 (1995); A. C. Mix, J. Le, N. J. Shackleton, ibid., p. 839.
22. A. C. Mix et al., Proc. Ocean Drill. Program Part B Sci. Results 138, 371 (1995); A. C. Mix, J. Le, N. J. Shackleton, ibid., p. 839.
23. M. Chil and S. Childress, Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory and Climate Dynamics (Springer-Verlag, Berlin, 1987).
24. The capacitor of a resonating circuit is analogous to the ice sheet in that it stores energy in proportion to its area. An FM signal is created, for instance, by sinusoidalty varying the circuit's capacitance.
25. E. Kallén, C. Crafoord, M. Ghil, J. Atmos. Dyn. 36. 2292 (1980).
26. Mathieu's equation is a particular case of Hill's equation, arising in many practical applications and in the theory of astronomical perturbations.
27. L. A. Pipes and L. R. Harvill, Applied Mathematics for Engineers and Physicists (McCraw-Hill, NewYork. 1970).
28. T. Mulin, Ed., The Nature of Chaos (Clarendon, Oxford, 1993).
29. L. Hinnov, A. Mix, F. Schmieder, J. Park, and B. Bills provided useful comments, data, and continuous encouragement, for which I will always be grateful. Reaction to a critical anonymous review made this paper publishable. The research was supported in part by grants from NSF, U.S. Department of Energy, and the University of North Carolina Research Council.