depends on the field temperature, through its effect on
the viscosity and on the melting point threshold at the
base.
The temperature of the ice varies from the surface
where it takes the annual average temperature (down
to −60 °C in Antarctica) to the melting point at the
many points of interface with the bedrock. The temperature thus increases overall with depth and this is
mainly due to the geothermal flux which brings continuous heat to the base of the ice (of around 50
mW/m
2 ). The flow affects temperature by transporting
cold from the top to the bottom and from the center to
the edges (advection). The heat produced by the
deformation and by the sliding also has an impact and
brings the base to melting point in active regions
where speed of movement is high.
This interaction between velocity field and flow is
called thermo-mechanical coupling.
Lastly, it is important to mention isostasy, which is
the sinking of the bedrock under the weight of the ice
(see Fig. 2.4).
Ice sheets have (and have had) different shapes and lifetimes, but they have followed a common pattern. An ice
sheet begins to develop when, as a result of a cooling climate, snow becomes permanent in a region, i.e. when
summer melting fails to eliminate all of the winter snow. It is
usually in areas of high altitude where this process occurs
first. In a mountain region, we see the emergence of glaciers
in places where the slope is not too steep, that is to say,
mainly in the high valleys. If the cooling continues, these
glaciers will grow and descend until they fill up the lower
valleys. When the region concerned is a high plateau,
freezing is more abrupt with a threshold effect when the
snow becomes perennial on the plateau. From this point on,
the flow of ice plays a role by transporting ice to areas where
snow is not permanent, whether by valley glaciers or by
glaciers forming on the periphery of the plateau which bring
ice to the surrounding plain.
From this moment on, two positive feedbacks supporting
the ice expansion and cap formation are established. The first
of these is the altitude-temperature feedback, which is based
on the fact that atmospheric temperature drops with altitude.
Areas where snow would normally not be permanent, freeze
over due to the movement of ice, and this increases the
altitude of their surface. As a result, the temperature at the
surface of the ice drops and summer melting is reduced, so
that eventually the snow becomes perennial. Over the years,
this mechanism gradually causes the ice front to advance
causing the accumulation zone (see Fig. 24.5) to extend
further. The second feedback is the albedo. Because snow
has a very high albedo (of around 0.9), the larger the
accumulation zone, the greater the amount of solar energy
reflected back to space instead of being used to heat the
Earth’s surface. The climate around an area of ice-cover will
therefore change, facilitating the expansion of the permanent
snow zone.
For a given climate, the expansion of an ice sheet will
continue either until it reaches warm regions where melting
prevails over the arriving flow of ice, or until it reaches the
ocean and begins to float on the sea in the form of ice
shelves, producing icebergs (see later the impact of
geography).
It should be noted that we emphasize the impact of
atmospheric temperature which governs the melting of snow
and ice because this climate variable predominates. Precipitation, which governs the amount of snow accumulated,
plays an important but lesser role and explains why, at the
same temperature, certain regions become more easily covered in snow and ice than others. Among these regions are
the glaciers in Norway today, but also the windward faces of
reliefs (mountain or ice) where precipitation is increased by
the orographic effect.
The same mechanisms apply to the retreat and disappearance of the ice caps (deglaciation) operating in the
opposite direction within the context of global warming. The
feedbacks mentioned are still active and they tend to amplify
the retreat of the ice front. There are, however, two important
differences. On the one hand, the growth rate of an ice sheet
is limited by the supply of snow by precipitation, whereas
the rate of decrease is limited by the amount of heat available
to melt the ice. It is easy to understand that the latter limitation will not work well when the ice sheet reaches low
latitudes and that deglaciation in this case can occur much
faster than glaciation. This was the case for the two large ice
sheets that existed during the Ice Age over America and
Eurasia, and this had a strong impact on sea level. This
explains the typical saw-tooth pattern of sea level rise and
fall during a glacial period, with a slow drop followed by an
abrupt rise (Fig. 24.3). On the other hand, the role of ice
flow is not symmetrical between freezing and deglaciation.
Although it helps the advance of the ice front as described,
flow tends to thin the ice layer, so that its impact on the
volume of ice is not uniform. In particular, it may happen
that this flow ‘runs away’ and that the ice sheet then
decreases abruptly (with the help of the altitude-temperature
feedback), which can also lead to a rapid deglaciation phase.
Flow is a fundamental mechanism in the evolution of an
ice sheet, and we explain below that it results from interaction between several processes which are themselves
governed either by the major laws of physics or by laws
(often empirical) describing the properties of the materials
(ice of course but also the bedrock). We won’t go into the
detail of these equations which call upon continuum
24 The Cryosphere and Sea Level
307
the viscosity and on the melting point threshold at the
base.
The temperature of the ice varies from the surface
where it takes the annual average temperature (down
to −60 °C in Antarctica) to the melting point at the
many points of interface with the bedrock. The temperature thus increases overall with depth and this is
mainly due to the geothermal flux which brings continuous heat to the base of the ice (of around 50
mW/m
2 ). The flow affects temperature by transporting
cold from the top to the bottom and from the center to
the edges (advection). The heat produced by the
deformation and by the sliding also has an impact and
brings the base to melting point in active regions
where speed of movement is high.
This interaction between velocity field and flow is
called thermo-mechanical coupling.
Lastly, it is important to mention isostasy, which is
the sinking of the bedrock under the weight of the ice
(see Fig. 2.4).
Ice sheets have (and have had) different shapes and lifetimes, but they have followed a common pattern. An ice
sheet begins to develop when, as a result of a cooling climate, snow becomes permanent in a region, i.e. when
summer melting fails to eliminate all of the winter snow. It is
usually in areas of high altitude where this process occurs
first. In a mountain region, we see the emergence of glaciers
in places where the slope is not too steep, that is to say,
mainly in the high valleys. If the cooling continues, these
glaciers will grow and descend until they fill up the lower
valleys. When the region concerned is a high plateau,
freezing is more abrupt with a threshold effect when the
snow becomes perennial on the plateau. From this point on,
the flow of ice plays a role by transporting ice to areas where
snow is not permanent, whether by valley glaciers or by
glaciers forming on the periphery of the plateau which bring
ice to the surrounding plain.
From this moment on, two positive feedbacks supporting
the ice expansion and cap formation are established. The first
of these is the altitude-temperature feedback, which is based
on the fact that atmospheric temperature drops with altitude.
Areas where snow would normally not be permanent, freeze
over due to the movement of ice, and this increases the
altitude of their surface. As a result, the temperature at the
surface of the ice drops and summer melting is reduced, so
that eventually the snow becomes perennial. Over the years,
this mechanism gradually causes the ice front to advance
causing the accumulation zone (see Fig. 24.5) to extend
further. The second feedback is the albedo. Because snow
has a very high albedo (of around 0.9), the larger the
accumulation zone, the greater the amount of solar energy
reflected back to space instead of being used to heat the
Earth’s surface. The climate around an area of ice-cover will
therefore change, facilitating the expansion of the permanent
snow zone.
For a given climate, the expansion of an ice sheet will
continue either until it reaches warm regions where melting
prevails over the arriving flow of ice, or until it reaches the
ocean and begins to float on the sea in the form of ice
shelves, producing icebergs (see later the impact of
geography).
It should be noted that we emphasize the impact of
atmospheric temperature which governs the melting of snow
and ice because this climate variable predominates. Precipitation, which governs the amount of snow accumulated,
plays an important but lesser role and explains why, at the
same temperature, certain regions become more easily covered in snow and ice than others. Among these regions are
the glaciers in Norway today, but also the windward faces of
reliefs (mountain or ice) where precipitation is increased by
the orographic effect.
The same mechanisms apply to the retreat and disappearance of the ice caps (deglaciation) operating in the
opposite direction within the context of global warming. The
feedbacks mentioned are still active and they tend to amplify
the retreat of the ice front. There are, however, two important
differences. On the one hand, the growth rate of an ice sheet
is limited by the supply of snow by precipitation, whereas
the rate of decrease is limited by the amount of heat available
to melt the ice. It is easy to understand that the latter limitation will not work well when the ice sheet reaches low
latitudes and that deglaciation in this case can occur much
faster than glaciation. This was the case for the two large ice
sheets that existed during the Ice Age over America and
Eurasia, and this had a strong impact on sea level. This
explains the typical saw-tooth pattern of sea level rise and
fall during a glacial period, with a slow drop followed by an
abrupt rise (Fig. 24.3). On the other hand, the role of ice
flow is not symmetrical between freezing and deglaciation.
Although it helps the advance of the ice front as described,
flow tends to thin the ice layer, so that its impact on the
volume of ice is not uniform. In particular, it may happen
that this flow ‘runs away’ and that the ice sheet then
decreases abruptly (with the help of the altitude-temperature
feedback), which can also lead to a rapid deglaciation phase.
Flow is a fundamental mechanism in the evolution of an
ice sheet, and we explain below that it results from interaction between several processes which are themselves
governed either by the major laws of physics or by laws
(often empirical) describing the properties of the materials
(ice of course but also the bedrock). We won’t go into the
detail of these equations which call upon continuum
24 The Cryosphere and Sea Level
307