240
A. Paul· W. H. Berger
power in the 100-ka band. A notoriously difficult problem is the simulation of
Termination V, which occurs at the base of isotope stage 11 at a time when
eccentricity is very low (at about 400 ka BP; Imbrie and Imbrie 1980). The free
and "quasi-free" oscillations underlying the solutions of the Milankovitch template (Paul and Berger 1997; Fig. 3) and the "reduced PCM" (Fig. 5b) can overcome this problem.
The first question that arises is what actually is the source of the large inertia inherent to the climate system? A good fit of the Milankovitch template to
the target time series requires the "memory" of the climate system to cover a
period of 57 ka (Berger et al. 1996; Paul and Berger 1997). The "reduced PCM"
can only yield an oscillation of near-100 ka period with a long time constant
for bedrock depression, E Z I = 30 ka. For a probably more realistic time constant of E Z
I = 3 ka, the same model admits a free oscillation with a period
closer to 40ka than to 100ka (Saltzman and Verbitsky 1992, 1993). The orbital
inclination curve must be shifted by 33 ± 3 ka to give the best least-squares fit
to the SPECMAP stack (Muller and MacDonald 1995). In this respect, we note
that Eq. (6) does not allow for a mere shift of the orbital inclination curve.
Rather it integrates the applied forcing over the elapsed time t with an exponential factor exp( -0(3[t - t'D. It is the damping constant 0(3 that must be set to
the large value of 1/100 ka- l in order to reduce the difference in phase between
the PCM output and SPECMAP. Hence, in all these cases a time constant is
assigned a value that is unrealistically large.
The answer to the above question may be that the large inertia inherent to
the climate system results from a delicate balance of positive and negative feedbacks, and that either more spatial complexity or additional feedback mechanisms must be included to achieve such a balance. In contrast to the zero-dimensional "reduced PCM", the one-dimensional ice sheet-bedrock models of
Pollard (1983) and Deblonde and Peltier (1991) yield realistic 100-ka climate
cycles for a time constant of E Z I = 5 ka, if the ice sheet -calving mechanism or a
related generalized meltwater parameterization is used. In this connection Pollard mentions that it is necessary to tune the crustal topography, such that
calving is not initiated too easily - something that is possible in a one-dimensional model but cannot be done in a zero-dimensional model. In his model,
calving affects only the outermost 50 to 150 km of the ice sheet, while in the
"reduced PCM" the ice sheet becomes submerged completely below sea level
and vanishes instantaneously (Saltzman and Verbitsky 1993).
Additional feedback mechanisms are provided by Eq. (7) and (8) of Saltzman and Verbitsky (1993) that govern the changes in atmospheric CO2 concentration and mean ocean temperature in the "full PCM". The equation that
represents the global carbon cycle contains five relatively unconstrained or
"free" parameters. It is very difficult to judge whether the values assigend to
these parameters are realistic or not. They are much more uncertain than those
in the ice sheet-bedrock system, because at present it is impossible to calculate
the fundamental fluxes leading to net changes of atmospheric CO2 concentration on long time scales (Saltzman and Maasch 1991).
A. Paul· W. H. Berger
power in the 100-ka band. A notoriously difficult problem is the simulation of
Termination V, which occurs at the base of isotope stage 11 at a time when
eccentricity is very low (at about 400 ka BP; Imbrie and Imbrie 1980). The free
and "quasi-free" oscillations underlying the solutions of the Milankovitch template (Paul and Berger 1997; Fig. 3) and the "reduced PCM" (Fig. 5b) can overcome this problem.
The first question that arises is what actually is the source of the large inertia inherent to the climate system? A good fit of the Milankovitch template to
the target time series requires the "memory" of the climate system to cover a
period of 57 ka (Berger et al. 1996; Paul and Berger 1997). The "reduced PCM"
can only yield an oscillation of near-100 ka period with a long time constant
for bedrock depression, E Z I = 30 ka. For a probably more realistic time constant of E Z
I = 3 ka, the same model admits a free oscillation with a period
closer to 40ka than to 100ka (Saltzman and Verbitsky 1992, 1993). The orbital
inclination curve must be shifted by 33 ± 3 ka to give the best least-squares fit
to the SPECMAP stack (Muller and MacDonald 1995). In this respect, we note
that Eq. (6) does not allow for a mere shift of the orbital inclination curve.
Rather it integrates the applied forcing over the elapsed time t with an exponential factor exp( -0(3[t - t'D. It is the damping constant 0(3 that must be set to
the large value of 1/100 ka- l in order to reduce the difference in phase between
the PCM output and SPECMAP. Hence, in all these cases a time constant is
assigned a value that is unrealistically large.
The answer to the above question may be that the large inertia inherent to
the climate system results from a delicate balance of positive and negative feedbacks, and that either more spatial complexity or additional feedback mechanisms must be included to achieve such a balance. In contrast to the zero-dimensional "reduced PCM", the one-dimensional ice sheet-bedrock models of
Pollard (1983) and Deblonde and Peltier (1991) yield realistic 100-ka climate
cycles for a time constant of E Z I = 5 ka, if the ice sheet -calving mechanism or a
related generalized meltwater parameterization is used. In this connection Pollard mentions that it is necessary to tune the crustal topography, such that
calving is not initiated too easily - something that is possible in a one-dimensional model but cannot be done in a zero-dimensional model. In his model,
calving affects only the outermost 50 to 150 km of the ice sheet, while in the
"reduced PCM" the ice sheet becomes submerged completely below sea level
and vanishes instantaneously (Saltzman and Verbitsky 1993).
Additional feedback mechanisms are provided by Eq. (7) and (8) of Saltzman and Verbitsky (1993) that govern the changes in atmospheric CO2 concentration and mean ocean temperature in the "full PCM". The equation that
represents the global carbon cycle contains five relatively unconstrained or
"free" parameters. It is very difficult to judge whether the values assigend to
these parameters are realistic or not. They are much more uncertain than those
in the ice sheet-bedrock system, because at present it is impossible to calculate
the fundamental fluxes leading to net changes of atmospheric CO2 concentration on long time scales (Saltzman and Maasch 1991).