redistribution of insolation with latitude and time of
the year, with a negligible impact on global annual
mean insolation. Therefore, annual mean models are
not adequate when investigating the impact of orbital
insolation on climate, as they cannot capture the
parts of the insolation variations which are seasonal
and translate them into long-term climate change.
The second type of models includes a representation
of the seasonal cycle, and has been used to investigate
the orbital theory of Milankovitch. In this case, the
seasonal variations in orbital insolation are resolved.
However, as for the first type of models, past changes
in ice cover are assumed to follow the simulated
variations in the extent of perennial snow. This approach assumes that ice cover and the powerful ice
albedo feedback are governed only by temperature, as
the extent of snow in these models is fixed to the
latitude with a temperature of 0 1C. In reality, the
growth and decay of land-based ice sheets are governed by the balance of accumulation and ablation.
Therefore, when investigating changes in ice cover, it is
necessary to include an appropriate representation of
the dynamics and mass balance of ice sheets in the
model.
The third type of models improves upon this by
focusing on modeling past changes in mass balance
and size of typical Northern Hemisphere ice sheets,
such as the Laurentide. This type of studies was
initiated by Weertman in the 1960s who used simple
ice sheet models, forced by a prescribed distribution
of accumulation minus ablation, to predict ice
thickness versus latitude. These models do not calculate the atmospheric energy balance in order to
estimate snowfall and surface melt; instead, changes
to the prescribed distribution of net accumulation
follow variations in mean summer insolation.
The fourth type of models include zonal mean
seasonal climate models coupled to the simple
Weertman-type ice sheet model, as well as earth
models of intermediate complexity (EMICs) coupled
to a dynamic ice sheet. These models give a more
realistic representation of the climate as compared
with the simpler models.
Partly due to the lack of good data on variations in
global ice volume older than about half a million
years, most model studies have focused on understanding the more recent records dominated by the
B100 000 years glacial cycles. All of these models
respond with periods close to the precession and obliquity periods of the insolation forcing. However, the
amplitude of the response is in most cases significantly
smaller than what is observed in the proxy records. At
the same time, the dominant B100 000 year cycles of
the ice volume record, characterized by rapid deglaciations, are only found when including a time lag in
the response of the model. Such an internal time lag
can be produced by taking into account bedrock depression under the load of the ice, or by adding a
parametrization of ice calving into proglacial lakes, or
marine incursions at the margin of the ice sheet. Alternatively, the B100 000-year cycles have been explained as free, self-sustained oscillations, which might
be phase-locked to oscillations in orbital insolation.
One of the very few model studies that have investigated variations in ice volume before the late
Pleistocene transition (B800 000 years ago) used a
two-dimensional climate model developed at
Louvain-la-Neuve in Belgium. It falls within the definition of an EMIC and includes a simple atmosphere
coupled to a mixed layer ocean, sea ice and ice sheets.
By forcing this model with insolation and steadily
decreasing atmospheric CO 2 concentrations, the
model reproduces some of the characteristics of the
ice volume record. The 41 000-year periodicity is
present in the simulated ice volume for most of the
past 3 My and the strength of the 100 000-year signal
increases after about 1 My. However, a longer
400 000-year year period is also present and often
dominates the simulated Northern Hemisphere ice
volume record.
This nicely illustrates the remaining questions in the
field. It is expected that models responding to the
100 000-year period will also respond to the longer
400 000-year period of eccentricity. However, this later
period is not present in the ice volume record. At the
same time, the late Pleistocene transition from a
dominance of 41 to B100 000-year period oscillations
in ice volume is not well understood. Explanations for
the transition which have been tested in models are: a
steady decrease in CO 2 forcing and its associated slow
global cooling; or a shift from a soft to a hard sediment bed underlying the North American ice sheet
through glacial erosion and exposure of unweathered
bedrock. Neither of these changes are in themselves
abrupt, but could cause a transition in the response of
the ice sheets to insolation as the ice sheets grew to a
sufficiently large size.
In addition to the challenge of modeling the midPleistocene transition, no model has successfully reproduced the relatively clean 41 000-year cycles
preceding the transition. Following the transition,
the models only exhibit a good match with the observed glacial cycles when forced with reconstructed
CO 2 from Antarctic ice cores together with orbital
insolation.
Summary
The Plio-Pleistocene glacial cycles represent some of
the largest and most significant changes in past
PLIO-PLEISTOCENE GLACIAL CYCLES AND MILANKOVITCH VARIABILITY 441
the year, with a negligible impact on global annual
mean insolation. Therefore, annual mean models are
not adequate when investigating the impact of orbital
insolation on climate, as they cannot capture the
parts of the insolation variations which are seasonal
and translate them into long-term climate change.
The second type of models includes a representation
of the seasonal cycle, and has been used to investigate
the orbital theory of Milankovitch. In this case, the
seasonal variations in orbital insolation are resolved.
However, as for the first type of models, past changes
in ice cover are assumed to follow the simulated
variations in the extent of perennial snow. This approach assumes that ice cover and the powerful ice
albedo feedback are governed only by temperature, as
the extent of snow in these models is fixed to the
latitude with a temperature of 0 1C. In reality, the
growth and decay of land-based ice sheets are governed by the balance of accumulation and ablation.
Therefore, when investigating changes in ice cover, it is
necessary to include an appropriate representation of
the dynamics and mass balance of ice sheets in the
model.
The third type of models improves upon this by
focusing on modeling past changes in mass balance
and size of typical Northern Hemisphere ice sheets,
such as the Laurentide. This type of studies was
initiated by Weertman in the 1960s who used simple
ice sheet models, forced by a prescribed distribution
of accumulation minus ablation, to predict ice
thickness versus latitude. These models do not calculate the atmospheric energy balance in order to
estimate snowfall and surface melt; instead, changes
to the prescribed distribution of net accumulation
follow variations in mean summer insolation.
The fourth type of models include zonal mean
seasonal climate models coupled to the simple
Weertman-type ice sheet model, as well as earth
models of intermediate complexity (EMICs) coupled
to a dynamic ice sheet. These models give a more
realistic representation of the climate as compared
with the simpler models.
Partly due to the lack of good data on variations in
global ice volume older than about half a million
years, most model studies have focused on understanding the more recent records dominated by the
B100 000 years glacial cycles. All of these models
respond with periods close to the precession and obliquity periods of the insolation forcing. However, the
amplitude of the response is in most cases significantly
smaller than what is observed in the proxy records. At
the same time, the dominant B100 000 year cycles of
the ice volume record, characterized by rapid deglaciations, are only found when including a time lag in
the response of the model. Such an internal time lag
can be produced by taking into account bedrock depression under the load of the ice, or by adding a
parametrization of ice calving into proglacial lakes, or
marine incursions at the margin of the ice sheet. Alternatively, the B100 000-year cycles have been explained as free, self-sustained oscillations, which might
be phase-locked to oscillations in orbital insolation.
One of the very few model studies that have investigated variations in ice volume before the late
Pleistocene transition (B800 000 years ago) used a
two-dimensional climate model developed at
Louvain-la-Neuve in Belgium. It falls within the definition of an EMIC and includes a simple atmosphere
coupled to a mixed layer ocean, sea ice and ice sheets.
By forcing this model with insolation and steadily
decreasing atmospheric CO 2 concentrations, the
model reproduces some of the characteristics of the
ice volume record. The 41 000-year periodicity is
present in the simulated ice volume for most of the
past 3 My and the strength of the 100 000-year signal
increases after about 1 My. However, a longer
400 000-year year period is also present and often
dominates the simulated Northern Hemisphere ice
volume record.
This nicely illustrates the remaining questions in the
field. It is expected that models responding to the
100 000-year period will also respond to the longer
400 000-year period of eccentricity. However, this later
period is not present in the ice volume record. At the
same time, the late Pleistocene transition from a
dominance of 41 to B100 000-year period oscillations
in ice volume is not well understood. Explanations for
the transition which have been tested in models are: a
steady decrease in CO 2 forcing and its associated slow
global cooling; or a shift from a soft to a hard sediment bed underlying the North American ice sheet
through glacial erosion and exposure of unweathered
bedrock. Neither of these changes are in themselves
abrupt, but could cause a transition in the response of
the ice sheets to insolation as the ice sheets grew to a
sufficiently large size.
In addition to the challenge of modeling the midPleistocene transition, no model has successfully reproduced the relatively clean 41 000-year cycles
preceding the transition. Following the transition,
the models only exhibit a good match with the observed glacial cycles when forced with reconstructed
CO 2 from Antarctic ice cores together with orbital
insolation.
Summary
The Plio-Pleistocene glacial cycles represent some of
the largest and most significant changes in past
PLIO-PLEISTOCENE GLACIAL CYCLES AND MILANKOVITCH VARIABILITY 441