geothermal energy (coming from the Earth) brings heat
continuously to the base of the ice and the ice acts as an
insulating material preventing this heat from escaping into
the atmosphere. The thicker the ice, the higher the basal
temperature. This temperature also depends on the amount
of geothermal energy, which unfortunately is not well
understood underneath the current ice sheets where it is
difficult to measure directly. The variation in temperature
with depth is not linear (this would be pure diffusion),
because the flow transports cold from the top to the bottom
and from upstream to downstream (advection). Moreover,
the deformation of the ice produces heat (as it does with all
materials). The same is true for the sliding on the bedrock
and for the deformation of the sediment. Areas with rapid
flow have a relatively warm base. If we ignore the phenomena related to flow (diffusive case), temperature would
increase linearly with depth. Because of the flow, the ice is
actually colder overall at the top and warmer at the base.
Finally, if the base is at melting point, the additional heat is
used for melting. It should be noted that the melting point
drops with the ice pressure and therefore the depth. Below
3000 m of ice, the melting point is around −2.2 °C.
It can be seen that the temperature and velocity variables
are connected by several terms. This interdependence is
called ‘thermomechanical coupling’, and this coupling leads
to a positive feedback which can have important effects on
the evolution of the ice sheet. Suppose, for example, that an
ice sheet is growing. Its basal temperature increases due to
the insulating effect of the thickness of the ice, which
reduces its viscosity and favors deformation. This produces
heat which in turn increases the temperature. This positive
feedback loop will quickly bring the base to the melting
point where the water produced introduces a second feedback (the more water there is, the faster the basal velocity
and the more heat is produced which in turn melts the ice).
These feedbacks have been suggested as explanations for
armadas of icebergs recorded as layers of ice rafted debris
(IRD) in marine sediments during glacial periods (see
Chap. 20). It is clear that this mechanism is involved in
triggering a rapid flow. On the other hand, the most realistic
numerical models have difficulties to simulate the return to a
slow phase suggested by observations of rapid climate
variability during glacial periods.
When the ice sheet ends with a marine edge, the ice
streams enter the sea and form ice shelves. If the bay is
sufficiently closed, these ice shelves limit the flow of the
streams from which they originate or which flow into the
same bay. This is called a buttressing effect. This effect
occurs at all levels, from small bays of a few kilometers to
large ice shelves such as the Ross and Ronne (see Fig. 24.2).
The geometry and dynamics of ice streams are balanced by
this buttress but if an ice shelf disintegrates (for example,
through the effect of oceanic heat melting it from below), the
drainage of all the tributary ice streams can be greatly
increased. This phenomenon occurred a few years ago in the
Antarctic Peninsula after the disintegration of the Larsen ice
shelf. The question arises of how much it might have contributed to glacial variations in the past and whether or not it
offers an alternative explanation to the IRD layers found in
marine cores and which testify to the arrival of icebergs.
To mechanically model the floating part, we can use the
shallow shelf approximation to determine a relationship
between the extension rate (variations in speed along the
length of the flow) and the thickness of the ice shelf (at a
specific power determined by the authors). If the ice-shelf is
not confined (if it does not encounter resistance from the
coasts or an island), then its speed increases from the
grounding line to the front where it can exceed one kilometer
per year. Above all, this approximation makes it possible to
demonstrate that the grounding line cannot be stable if the
base is below sea level and with a reverse slope (if it goes
upwards as one goes from the center to the edge of the ice
sheet, Schoof 2007). This instability can be explained
qualitatively as follows: if the ice flow at the grounding line
increases strongly as the ice thickens, any retreat of the
grounding line, caused, for example, by the disintegration of
the corresponding ice shelf, will intensify drainage, leading
to a further retreat of the grounding line. This result is particularly important because it indicates that some ice sheets
are inherently unstable because the location of the grounding
line determines the extent of the cap and its volume. This is
especially the case for Western Antarctica, but also for some
parts of East Antarctica. For ice sheets in previous ice ages,
it is possible that this instability could have contributed to
rapid deglaciation, a process which is not yet fully
understood.
Finally, subglacial isostasy (see Fig. 24.4) is a mechanism which plays an important role because it modulates
many of the others. For example, subsidence of the Earth’s
crust under the weight of the ice does not directly change its
thickness but it alters the altitude of the surface allowing
more intense melting since the surface is lower. Moreover,
the slope of the surface is also decreased, which slows down
the flow and tends to make the ice sheet larger. Since isostasy occurs with a lag, this also leads to highly non-linear
effects. The position of the grounding line is another
example of an element that is very sensitive to isostasy
because it is defined by floating (on the marine side), and
this is determined by the relative sea level, itself affected by
isostasy.
24 The Cryosphere and Sea Level
309
continuously to the base of the ice and the ice acts as an
insulating material preventing this heat from escaping into
the atmosphere. The thicker the ice, the higher the basal
temperature. This temperature also depends on the amount
of geothermal energy, which unfortunately is not well
understood underneath the current ice sheets where it is
difficult to measure directly. The variation in temperature
with depth is not linear (this would be pure diffusion),
because the flow transports cold from the top to the bottom
and from upstream to downstream (advection). Moreover,
the deformation of the ice produces heat (as it does with all
materials). The same is true for the sliding on the bedrock
and for the deformation of the sediment. Areas with rapid
flow have a relatively warm base. If we ignore the phenomena related to flow (diffusive case), temperature would
increase linearly with depth. Because of the flow, the ice is
actually colder overall at the top and warmer at the base.
Finally, if the base is at melting point, the additional heat is
used for melting. It should be noted that the melting point
drops with the ice pressure and therefore the depth. Below
3000 m of ice, the melting point is around −2.2 °C.
It can be seen that the temperature and velocity variables
are connected by several terms. This interdependence is
called ‘thermomechanical coupling’, and this coupling leads
to a positive feedback which can have important effects on
the evolution of the ice sheet. Suppose, for example, that an
ice sheet is growing. Its basal temperature increases due to
the insulating effect of the thickness of the ice, which
reduces its viscosity and favors deformation. This produces
heat which in turn increases the temperature. This positive
feedback loop will quickly bring the base to the melting
point where the water produced introduces a second feedback (the more water there is, the faster the basal velocity
and the more heat is produced which in turn melts the ice).
These feedbacks have been suggested as explanations for
armadas of icebergs recorded as layers of ice rafted debris
(IRD) in marine sediments during glacial periods (see
Chap. 20). It is clear that this mechanism is involved in
triggering a rapid flow. On the other hand, the most realistic
numerical models have difficulties to simulate the return to a
slow phase suggested by observations of rapid climate
variability during glacial periods.
When the ice sheet ends with a marine edge, the ice
streams enter the sea and form ice shelves. If the bay is
sufficiently closed, these ice shelves limit the flow of the
streams from which they originate or which flow into the
same bay. This is called a buttressing effect. This effect
occurs at all levels, from small bays of a few kilometers to
large ice shelves such as the Ross and Ronne (see Fig. 24.2).
The geometry and dynamics of ice streams are balanced by
this buttress but if an ice shelf disintegrates (for example,
through the effect of oceanic heat melting it from below), the
drainage of all the tributary ice streams can be greatly
increased. This phenomenon occurred a few years ago in the
Antarctic Peninsula after the disintegration of the Larsen ice
shelf. The question arises of how much it might have contributed to glacial variations in the past and whether or not it
offers an alternative explanation to the IRD layers found in
marine cores and which testify to the arrival of icebergs.
To mechanically model the floating part, we can use the
shallow shelf approximation to determine a relationship
between the extension rate (variations in speed along the
length of the flow) and the thickness of the ice shelf (at a
specific power determined by the authors). If the ice-shelf is
not confined (if it does not encounter resistance from the
coasts or an island), then its speed increases from the
grounding line to the front where it can exceed one kilometer
per year. Above all, this approximation makes it possible to
demonstrate that the grounding line cannot be stable if the
base is below sea level and with a reverse slope (if it goes
upwards as one goes from the center to the edge of the ice
sheet, Schoof 2007). This instability can be explained
qualitatively as follows: if the ice flow at the grounding line
increases strongly as the ice thickens, any retreat of the
grounding line, caused, for example, by the disintegration of
the corresponding ice shelf, will intensify drainage, leading
to a further retreat of the grounding line. This result is particularly important because it indicates that some ice sheets
are inherently unstable because the location of the grounding
line determines the extent of the cap and its volume. This is
especially the case for Western Antarctica, but also for some
parts of East Antarctica. For ice sheets in previous ice ages,
it is possible that this instability could have contributed to
rapid deglaciation, a process which is not yet fully
understood.
Finally, subglacial isostasy (see Fig. 24.4) is a mechanism which plays an important role because it modulates
many of the others. For example, subsidence of the Earth’s
crust under the weight of the ice does not directly change its
thickness but it alters the altitude of the surface allowing
more intense melting since the surface is lower. Moreover,
the slope of the surface is also decreased, which slows down
the flow and tends to make the ice sheet larger. Since isostasy occurs with a lag, this also leads to highly non-linear
effects. The position of the grounding line is another
example of an element that is very sensitive to isostasy
because it is defined by floating (on the marine side), and
this is determined by the relative sea level, itself affected by
isostasy.
24 The Cryosphere and Sea Level
309