Climate Cycles and Climate Transitions . ..
225
2
The Inclination-Accretion Hypothesis
The astronomical theory of paleoclimates in its traditional form was challenged recently by Muller and MacDonald (1995). They put forward the hypothesis that the 100-ka glacial cycle is based on changes in orbital inclination
rather than eccentricity. Orbital inclination i is the angle between the Earth's
orbital plane and a reference plane. A useful choice of a reference plane is the
invariable plane: the plane perpendicular to the total angular momentum vector of the solar system that is very close to Jupiter's orbital plane. With respect
to the invariable plane, the orbital inclination shows a nearly sinusoidal cycle
with a period of about 100 ka (Muller and MacDonald 1995). Since it has no
direct effect on insolation, a mechanism must be found that could link glacial
cycles to orbital inclination. One such mechanism could be the accretion of
meteoroids and interplanetary dust particles (IDP).
Muller and MacDonald (1997b) have made a spectral reanalysis offour oxygen isotope records: from ODP sites 607 (Ruddiman et al. 1989) and 806 (Berger
et al. 1994), the SPECMAP stack (Imbrie et al. 1984; Imbrie et al. 1992) and the
stack by Hays et al. (1976). Muller and MacDonald note that in previous spectral
analyses, the Blackman-Tukey method was commonly used. This method obtained the power spectral amplitudes by first computing the autocorrelation
function and then performing a fast Fourier transform (FFT). With the lag
parameter set to one-third (the usual value), narrow peaks are artificially broadened by a factor of 3. If the lag parameter is set to two thirds or greater, or if a
direct FFT method is used, a very narrow and unsplit 100-ka peak appears. In
fact, the width of this peak comes close to the width of a peak that results from
calculating the spectral power of a pure 100-ka sine wave of the same duration
as the oxygen isotope record (Muller and MacDonald 1997a).
The narrow width of the 100-ka peak in the oxygen isotope records strongly
suggests that the 100-ka glacial cycle is astronomically driven, but Muller and
MacDonald doubt that it is based on changes in insolation as the Milankovitch
theory states. This is mainly for two reasons. (I) The only orbital parameter that
can cause changes in insolation with a period of about 100 ka is eccentricity;
but eccentricity-induced changes in insolation are very small and need to be
amplified by the climate system. If the climate system were a free oscillator or
a relaxation oscillator that could amplify the small input signal, the output signal would probably be a glacial cycle with a broad spectral peak, due to friction
and phase instability. Such a broad peak would be at variance with the observed
power spectra of oxygen isotope records. (2) The power spectrum of eccentricity does not show a single prominent peak with a period of about 100 ka, but
several peaks, the five largest having periods near 95, 99, 124, 131 and 404 ka. In
the spectra of Late Pleistocene oxygen isotope data, the peak with a period near
100 ka is un split, and there is only a very small peak with a period near 400 ka
(but this peak is larger if the whole Pleistocene is considered - Berger 1992). If
the climate system were a forced oscillator, then a split peak in the input signal
225
2
The Inclination-Accretion Hypothesis
The astronomical theory of paleoclimates in its traditional form was challenged recently by Muller and MacDonald (1995). They put forward the hypothesis that the 100-ka glacial cycle is based on changes in orbital inclination
rather than eccentricity. Orbital inclination i is the angle between the Earth's
orbital plane and a reference plane. A useful choice of a reference plane is the
invariable plane: the plane perpendicular to the total angular momentum vector of the solar system that is very close to Jupiter's orbital plane. With respect
to the invariable plane, the orbital inclination shows a nearly sinusoidal cycle
with a period of about 100 ka (Muller and MacDonald 1995). Since it has no
direct effect on insolation, a mechanism must be found that could link glacial
cycles to orbital inclination. One such mechanism could be the accretion of
meteoroids and interplanetary dust particles (IDP).
Muller and MacDonald (1997b) have made a spectral reanalysis offour oxygen isotope records: from ODP sites 607 (Ruddiman et al. 1989) and 806 (Berger
et al. 1994), the SPECMAP stack (Imbrie et al. 1984; Imbrie et al. 1992) and the
stack by Hays et al. (1976). Muller and MacDonald note that in previous spectral
analyses, the Blackman-Tukey method was commonly used. This method obtained the power spectral amplitudes by first computing the autocorrelation
function and then performing a fast Fourier transform (FFT). With the lag
parameter set to one-third (the usual value), narrow peaks are artificially broadened by a factor of 3. If the lag parameter is set to two thirds or greater, or if a
direct FFT method is used, a very narrow and unsplit 100-ka peak appears. In
fact, the width of this peak comes close to the width of a peak that results from
calculating the spectral power of a pure 100-ka sine wave of the same duration
as the oxygen isotope record (Muller and MacDonald 1997a).
The narrow width of the 100-ka peak in the oxygen isotope records strongly
suggests that the 100-ka glacial cycle is astronomically driven, but Muller and
MacDonald doubt that it is based on changes in insolation as the Milankovitch
theory states. This is mainly for two reasons. (I) The only orbital parameter that
can cause changes in insolation with a period of about 100 ka is eccentricity;
but eccentricity-induced changes in insolation are very small and need to be
amplified by the climate system. If the climate system were a free oscillator or
a relaxation oscillator that could amplify the small input signal, the output signal would probably be a glacial cycle with a broad spectral peak, due to friction
and phase instability. Such a broad peak would be at variance with the observed
power spectra of oxygen isotope records. (2) The power spectrum of eccentricity does not show a single prominent peak with a period of about 100 ka, but
several peaks, the five largest having periods near 95, 99, 124, 131 and 404 ka. In
the spectra of Late Pleistocene oxygen isotope data, the peak with a period near
100 ka is un split, and there is only a very small peak with a period near 400 ka
(but this peak is larger if the whole Pleistocene is considered - Berger 1992). If
the climate system were a forced oscillator, then a split peak in the input signal