242
A. Paul· W. H. Berger
later than observed in the 8 18 0 data (at 2 Ma B. P. as compared to 2.6 to 2.4 Ma
B. P.), the second earlier (at about 1.1 Ma B. P. - as compared to about 900 ka
B. P. if the time domain is considered). Our set of parameters is designed to give
a reasonable fit to the benthic 8 18 0 record from ODP site 806B. A different
choice of parameters places these transitions closer to the observed dates
(Saltzman and Verbitsky 1993). In any case, the PCM can qualitatively account
for the abrupt climate transitions in the late Cenozoic as well as the major 100ka climate cycles of the late Pleistocene. We note that the earlier climate transition is difficult to detect in the benthic 8 18 0 record shown in Fig. 13a. It indicates a more gradual rise in ice mass than the PCM predicts, and there is only a
slight temporary increase in ice mass variance shortly after 2.5 Ma B. P.
We acknowledge that the conclusions that we draw from our results are
semi-quantitative in nature since they are based on a comparison of simulated
and observed time series by visual inspection. This method seems to be appropriate because the questions we have addressed are, in a sense, also semi-quantitative in nature. Thus, we are satisfied that there is no reason to abandon the
traditional astronomical theory for the inclination-accretion hypothesis ..
Finally, we wish to point out that the model of Saltzman and Verbitsky
(1993) also yields the following result: if the anthropogenically induced level
of atmospheric CO2 were maintained over a long period of time, the climate
system would be driven toward a stable state devoid of the natural ice age cycles (Saltzman and Maasch 1993). Berger and Loutre (1996) use a much more
complex model to make a forecast for the next 130 ka, driven only by the astronomically induced changes in insolation and prescribed variations in atmospheric CO2• In their experiments, the human burst of atmospheric CO2 seems
to be sufficient to lead to a melting of the Greenland ice sheet after 6 to 10 ka.
They find that it takes at least 40 ka for the climate system to recover from what
could happen over the next few centuries.
8
Conclusions
Our previous experiments with the Milankovitch template (Paul and Berger
1997), as well as our present experiments with the «reduced PCM" and the «full
PCM", lead us to the following conclusions:
1 The 100-ka climate cycle may be explained in terms of either a conditional
or an unconditional instability that admits free or «quasi-free" oscillations.
2 A simple parameterization of the elevation-temperature feedback does not
result in an improved simulation of the observed 8 18 0 record.
3 Inclination forcing can help to achieve nearly complete terminations and
increase the spectral power in the 100-ka band of the ice mass response.
However, the ice-calving mechanism is still required to melt all ice and let
the 100-ka peak dominate the power spectrum.
4 If the ice-calving mechanism is invoked, the actual timing of the terminations appears to be less satisfactory with inclination forcing than without it.
A. Paul· W. H. Berger
later than observed in the 8 18 0 data (at 2 Ma B. P. as compared to 2.6 to 2.4 Ma
B. P.), the second earlier (at about 1.1 Ma B. P. - as compared to about 900 ka
B. P. if the time domain is considered). Our set of parameters is designed to give
a reasonable fit to the benthic 8 18 0 record from ODP site 806B. A different
choice of parameters places these transitions closer to the observed dates
(Saltzman and Verbitsky 1993). In any case, the PCM can qualitatively account
for the abrupt climate transitions in the late Cenozoic as well as the major 100ka climate cycles of the late Pleistocene. We note that the earlier climate transition is difficult to detect in the benthic 8 18 0 record shown in Fig. 13a. It indicates a more gradual rise in ice mass than the PCM predicts, and there is only a
slight temporary increase in ice mass variance shortly after 2.5 Ma B. P.
We acknowledge that the conclusions that we draw from our results are
semi-quantitative in nature since they are based on a comparison of simulated
and observed time series by visual inspection. This method seems to be appropriate because the questions we have addressed are, in a sense, also semi-quantitative in nature. Thus, we are satisfied that there is no reason to abandon the
traditional astronomical theory for the inclination-accretion hypothesis ..
Finally, we wish to point out that the model of Saltzman and Verbitsky
(1993) also yields the following result: if the anthropogenically induced level
of atmospheric CO2 were maintained over a long period of time, the climate
system would be driven toward a stable state devoid of the natural ice age cycles (Saltzman and Maasch 1993). Berger and Loutre (1996) use a much more
complex model to make a forecast for the next 130 ka, driven only by the astronomically induced changes in insolation and prescribed variations in atmospheric CO2• In their experiments, the human burst of atmospheric CO2 seems
to be sufficient to lead to a melting of the Greenland ice sheet after 6 to 10 ka.
They find that it takes at least 40 ka for the climate system to recover from what
could happen over the next few centuries.
8
Conclusions
Our previous experiments with the Milankovitch template (Paul and Berger
1997), as well as our present experiments with the «reduced PCM" and the «full
PCM", lead us to the following conclusions:
1 The 100-ka climate cycle may be explained in terms of either a conditional
or an unconditional instability that admits free or «quasi-free" oscillations.
2 A simple parameterization of the elevation-temperature feedback does not
result in an improved simulation of the observed 8 18 0 record.
3 Inclination forcing can help to achieve nearly complete terminations and
increase the spectral power in the 100-ka band of the ice mass response.
However, the ice-calving mechanism is still required to melt all ice and let
the 100-ka peak dominate the power spectrum.
4 If the ice-calving mechanism is invoked, the actual timing of the terminations appears to be less satisfactory with inclination forcing than without it.