Department of Physics and Lawrence Berkeley Laboratory University of California Berkeley CA and International Institute for Applied Systems Analysis A Laxenburg Austria

600-kyr length. A re-analysis of the original pacemaker core stack with full resolution also produces a single narrow peak (FWHM = 0.0019), which is the theoretically minimum width for a record of 464 kyr length. Likewise, the spectral analysis of data from site 806 (19) shows a single narrow peak.

Fig. 1. 518O for past 800 kyr. (a) Data of site 607 from Ruddiman et al. (15). (b) Specmap stack of Imbrie et al. (16). (c) Spectral power of site 607. (d) Spectral power of Specmap. In the Milankovitch theory, the peak near 0.01 (100-kyr period) is attributed to eccentricity, the peak near 0.024 (41-kyr period) to obliquity, and the peak near 0.043 (23-kyr period) to precession.

Fig. 1. 518O for past 800 kyr. (a) Data of site 607 from Ruddiman et al. (15). (b) Specmap stack of Imbrie et al. (16). (c) Spectral power of site 607. (d) Spectral power of Specmap. In the Milankovitch theory, the peak near 0.01 (100-kyr period) is attributed to eccentricity, the peak near 0.024 (41-kyr period) to obliquity, and the peak near 0.043 (23-kyr period) to precession.

The narrow width of the 100-kyr peak strongly suggests a driven oscillation of astronomical origin. In contrast to dynamical astronomy, where dissipative processes are almost nonexistent, all known resonances within the earth-atmosphere system have energy transfer mechanisms that cause loss of phase stability. Narrowness of the 41-kyr and 23-kyr cycles is not necessarily significant, since the time scale of the data was tuned by adjusting the sedimentation rate to match the expected orbital cycles. The 100-kyr peak is incoherent with these other two cycles, there is no phase relationship. The fact that an unrelated peak is sharp can be considered as an a posteriori evidence that the tuning procedure yielded a basically correct time scale, although it could be incorrect by an overall stretch factor and delay. We did not anticipate the narrowness of the 100-kyr peak, assuming, as others have done, that it was due to forcing by variations in eccentricity. However, it is not easily reconciled with any published theory. The narrowness of the peak was missed in previous spectral analysis of isotopic data because of the common use of the Blackman-Tukey algorithm (20), which, as usually applied (lag parameter = 1/3), artificially broadens narrow peaks by a factor of 3. The Blackman-Tukey algorithm gained wide use in the 1950s because of Tukey's admonition that analysts could be misled by using classical periodograms in analyzing spectra having a continuous spectrum. For analysis of glacial cycles, these considerations did not arise, because the spectra are mixed spectra with very strong quasi-periodic peaks. Spectra of glacial cycles, as Tukey recognized, lend themselves to the use of conventional Fourier transforms.

The region of the 100-kyr peak for the S18O data is replotted in Fig. 2 a and Fig. 2 b with an expanded frequency scale. These plots can be compared with the spectral power of the eccentricity variations, shown in Fig. 2c, calculated from the detailed computations of Quinn et al. (5). Three strong peaks are present in the eccentricity spectrum: near 0.0025 cycles per kyr (400-kyr period), near 0.08 cycles per kyr (125-kyr period), and near 0.0105 cycles per kyr (95-kyr period). The disagreement between the spectrum of climate and that of eccentricity is evident. The absence of the 400-kyr peak in the climate data has long been recognized (for a review, see Imbrie et al. (6), and numerous models have been devised that attempt to suppress that peak.

We note that the 100-kyr peak is split into 95- and 125-kyr components, in serious conflict with the single narrow line seen in the climate data. The splitting of this peak into a doublet is well known theoretically (22), and results from the phase-coherent modulation by the 400-kyr peak. But in comparisons with data, the two peaks in eccentricity were made into a single broad peak by the enforced poor resolution of the Blackman-Tukey algorithm. The single narrow peak in the climate data was likewise broadened and the resulting comparisons led to the belief that the theoretical eccentricity and the observed climate data were very much alike.

The disagreement between the data (Fig. 2 a and Fig. 2 b) and the theory (Fig. 2 c and Fig. 2 d), cannot be accounted for by experimental error uncertainty. Tuning of the time scale to a specific peak (by adjusting the unknown sedimentation rates) can artificially narrow that peak as other peaks that are coherent with it [see, for example, Neeman (23)]. However, the data in Fig. 2 a and Fig 2 b were tuned only to peaks obliquity and precession that are incoherent with the 100-kyr eccentricity cycle, so that tuning cannot account for the narrow width. Likewise, chatter (errors in the time scale from mis-estimated sedimentation rates) cannot reconcile the disagreement, since although chatter can smear a doublet into a single broad peak, it will not turn a doublet into a single narrow peak. Could a physical mechanism convert a 95- to 125-kyr doublet into a single narrow peak? Dissipative mechanisms could obscure the doublet, but (like chatter) they yield a single broad peak or a cluster of doublets. Resonances used to suppress the 400-kyr peak are not sharp enough to suppress one element of the narrow doublet. In principle, a strong nonlinear process could turn a doublet into a single peak, as it does (for example) in a laser; however, no such mechanism has been identified in the lossy, friction-filled environment of the earth and its atmosphere.

Fig. 2. Spectral fingerprints in the vicinity of the 100-kyr peak for data from site 607 (a); for data of the Specmap stack (b); for a model with linear response to eccentricity, calculated from the results of Quinn et al. (5) (c); for the nonlinear icesheet model of Imbrie and Imbrie (21) (d); and for a model with linear response to the inclination of the Earth's orbit (measured with respect to the invariable plane) (e). All calculations are for the period 0-600 ka. The 100-kyr peak in the data in a and b do not fit the fingerprints from the theories c and d, but are a good match to the prediction from inclination in e.

Several nonlinear models reviewed by Imbrie et al. (6) derive the 100 kyr cycle from the envelope of the precession cycle. However, this envelope also has a split peak, since it derives ultimately from eccentricity (the envelope of the precession is the eccentricity). As an example, we show the spectrum of the ice sheet model of Imbrie and Imbrie (21) in Fig. 2d. As expected, it too shows the 95- to 125-kyr doublet, in disagreement with the data. None of the nonlinear models in the recent comprehensive review by Imbrie et al. (6) have the required laser-like mechanism, and they all predict a split peak. This is a fundamental disagreement, not fixed by adjusting parameters. Unlike the 400-kyr cycle, which is far enough mismatched from the 100 kyr to be suppressed (at least in principle) by the models, the lines in the 95-125 doublet are too close. We draw a remarkably strong conclusion that variations in the earth's eccentricity cannot be responsible for the 100-kyr cycle.

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