Climate Cycles and Climate Transitions . ..
229
the spirit of Muller and Macdonald (1997a, b), who advocate a spectral method
that maximizes the frequency resolution or, equivalently, minimizes the resolution bandwidth. The second set of parameters means that the time series is
split into nso segments that overlap each other by 50 %. In order to suppress
spurious peaks and side lobes, each segment is multiplied by a Hanning window. Then the nso windowed segments are Fourier transformed separately.
Averaging the resulting raw spectra yields a consistent estimate of an autospectrum with an increased resolution bandwidth, but a decreased standard error
in the power spectral amplitudes. We refer to the power spectra corresponding
to the two sets of parameters as the raw and the smoothed spectrum. In all
figures that represent spectral analyses, we use a logarithmic decibel (dB)
scale:
dB = 10 10glO Gxx(j),
(5)
where Gxx(j) denotes the power spectral amplitude. A horizontal line marks
the 6 dB-bandwith, and a vertical line marks the standard error (see, e.g.,
Fig. 2).
5
The 100000-Year Glacial Cycle in the Late Pleistocene
In our first series of experiments, we assume that to a first order the waxing
and waning of the continental ice sheets is not affected by variations in atmospheric carbon dioxide concentration and mean ocean temperature (see Table
2, cases 1-3). Thus in Eq. (2) we set k(J = 0 and B = 0 and obtain the "reduced
PCM", a pure ice sheet-bedrock model in the spirit of, e.g., Birchfield et al.
(1981), Pollard (1982, 1983) and Deblonde and Peltier (1991).
We focus on the time period between 600 ka B. P. and the last deglaciation,
after the onset of the 100-ka glacial cycle. In Fig. 1, we present three 8 18 0 records, which we wish to compare with our model results: the SPECMAP stack
(Imbrie et al. 1984; Imbrie et al. 1992) and the benthic 8 18 0 records from ODP
sites 659 (Tiedemann et al. 1994) and 806B (Berger et al. 1995). The SPECMAP
time scale has been tuned to the precessional and obliquity cycles. For the data
from ODP sites 659 and 806B, we use the following chronology: in order to
minimize any bias by using a time scale that is tuned to the astronomical frequencies, we adopt the untuned time scale developed by Raymo (1997). This
time scale uses three radiometric age constraints: the midpoints of the last two
de glaciations (Terminations I and II) and the midpoint of stage 19, with constant sedimentation rates inbetween. The ages of Terminations I and II are assigned to be l3.5 and 128 ka B. P., and the midpoint of stage 19 is taken to be
772 ka old, 6 ka younger than the Brunhes-Matuyama boundary radiometrically dated at 778 ± 3.5 ka by Tauxe et al. (1996). In the time domain, looking
at the ages of the remaining terminations, we find from Fig. 1 that the agreement between the tuned SPECMAP time series and the untuned time series is
rather good for ODP site 659, but mediocre for ODP site 806B. In the frequency
229
the spirit of Muller and Macdonald (1997a, b), who advocate a spectral method
that maximizes the frequency resolution or, equivalently, minimizes the resolution bandwidth. The second set of parameters means that the time series is
split into nso segments that overlap each other by 50 %. In order to suppress
spurious peaks and side lobes, each segment is multiplied by a Hanning window. Then the nso windowed segments are Fourier transformed separately.
Averaging the resulting raw spectra yields a consistent estimate of an autospectrum with an increased resolution bandwidth, but a decreased standard error
in the power spectral amplitudes. We refer to the power spectra corresponding
to the two sets of parameters as the raw and the smoothed spectrum. In all
figures that represent spectral analyses, we use a logarithmic decibel (dB)
scale:
dB = 10 10glO Gxx(j),
(5)
where Gxx(j) denotes the power spectral amplitude. A horizontal line marks
the 6 dB-bandwith, and a vertical line marks the standard error (see, e.g.,
Fig. 2).
5
The 100000-Year Glacial Cycle in the Late Pleistocene
In our first series of experiments, we assume that to a first order the waxing
and waning of the continental ice sheets is not affected by variations in atmospheric carbon dioxide concentration and mean ocean temperature (see Table
2, cases 1-3). Thus in Eq. (2) we set k(J = 0 and B = 0 and obtain the "reduced
PCM", a pure ice sheet-bedrock model in the spirit of, e.g., Birchfield et al.
(1981), Pollard (1982, 1983) and Deblonde and Peltier (1991).
We focus on the time period between 600 ka B. P. and the last deglaciation,
after the onset of the 100-ka glacial cycle. In Fig. 1, we present three 8 18 0 records, which we wish to compare with our model results: the SPECMAP stack
(Imbrie et al. 1984; Imbrie et al. 1992) and the benthic 8 18 0 records from ODP
sites 659 (Tiedemann et al. 1994) and 806B (Berger et al. 1995). The SPECMAP
time scale has been tuned to the precessional and obliquity cycles. For the data
from ODP sites 659 and 806B, we use the following chronology: in order to
minimize any bias by using a time scale that is tuned to the astronomical frequencies, we adopt the untuned time scale developed by Raymo (1997). This
time scale uses three radiometric age constraints: the midpoints of the last two
de glaciations (Terminations I and II) and the midpoint of stage 19, with constant sedimentation rates inbetween. The ages of Terminations I and II are assigned to be l3.5 and 128 ka B. P., and the midpoint of stage 19 is taken to be
772 ka old, 6 ka younger than the Brunhes-Matuyama boundary radiometrically dated at 778 ± 3.5 ka by Tauxe et al. (1996). In the time domain, looking
at the ages of the remaining terminations, we find from Fig. 1 that the agreement between the tuned SPECMAP time series and the untuned time series is
rather good for ODP site 659, but mediocre for ODP site 806B. In the frequency