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tution of a hard versus a soft bed). The probability Large ice sheets are found only on Greenland and

5 km

(a) (b)
elevations. This positive feedback towards thicker
Fig 1.24 (a) Shaded-relief image of the Algodones Dunes
and thicker ice is limited by the shear strength
located along the California“Arizona border near Yuma,
Arizona. (b) Example output of Werner™s model for eolian of the ice and friction at the base of the ice. Even-
dunes for the transverse-dune case with large sand supply and tually, the thickness and slope of the ice become
constant wind direction.
great enough to overcome the shear strength of
ice or the basal friction (whichever is lower), caus-
ing the ice to surge outward by internal defor-
Antarctica, and alpine glaciers are restricted to el-
mation or basal sliding. Zones of higher eleva-
evations above approximately 5 km a.s.l. in tem-
tion have positive mass balance (i.e. more snow
perate latitudes. In contrast, ice covered nearly
is precipitated on the landscape than melts away)
all of Canada, the northernmost United States,
and areas of lower elevation have negative mass
and most of northern Europe during the LGM.
balance. Ice ¬‚ows from areas of positive mass bal-
Alpine glaciers expanded to cover areas with el-
ance (i.e. accumulation) to areas of negative mass
evations approximately 1 km lower than today
balance (i.e. ablation) when suf¬cient thickness
(Porter et al., 1983). While geomorphology in the
and slope have been built up. Although the me-
southernmost United States means wind and wa-
chanics of ice sheets and glaciers is very complex
ter, geomorphology in Canada and the northern
in detail, at large scales their shapes are often
United States is primarily a story of ice (Flint,
well adjusted to the threshold condition for shear
strength or basal friction. Increases in snow ac-
Ice sheets and glaciers can be thought of as
cumulation cause shear stresses to increase above
conveyor belts of ice. Some of the snow that
the threshold condition, causing rapid surging of
falls at high elevations sticks around through
the ice sheet or glacier in response. Therefore, the
the following summer. Successive years produce
shapes of ice sheets and glaciers on Earth are pri-
more snow that acts as a weight on underlying
marily a function of their shear strength or basal
snow, turning the snow into ¬rn (a state inter-
friction. The speed of these ice bodies is primar-
mediate between snow and ice) and eventually
ily a function of their accumulation and ablation
ice as more snow is deposited above it. As snow
and ice accumulate and the ground surface in-
Ice sheets and glaciers move by a complex
creases in elevation, more snow and ice accumu-
combination of internal ice ¬‚ow, sliding of ice
late because of the cooler temperatures at higher

ice margin

basal velocity
till plane

predominant erosion little or no erosion or deposition
(frozen bed or low velocity)
The erosional potential of ice sheets and
Fig 1.25 The subglacial environment can be broadly divided
into three zones: (1) a zone of little or no erosion or glaciers is not fully understood, but most re-
deposition, located near the divide, where the ice sheet is searchers agree with Hallet (1979; 1996) that the
frozen to the bed or where velocities are too small to erosion rate is proportional to a power-law func-
signi¬cantly modify the surface, (2) a zone of predominant
tion of the basal sliding velocity V :
erosion, where basal velocities and meltwater concentrations
= ’aV b
increase toward the margin, transporting all of the bedrock (1.19)
debris removed from the bed, and (3) a zone of predominant
where a is a coef¬cient that depends primarily
deposition near the ice margin, where basal velocities wane
on the bedrock erodibility, and b is an empirical
and moraines and till plains are commonly formed. Also
exponent equal to ≈ 2 (Figure 1.25).
shown are the zones of accumulation, ablation, internal ¬‚ow
lines, and their relationship to the major subglacial zones. The ability of a warm-based ice sheet or
glacier to erode its bed varies as a function of
on bedrock, and sliding of ice on glacial till. distance along the longitudinal pro¬le. Ice ¬‚ow
Whether an ice sheet or glacier deforms inter- velocities increase with distance downslope in a
nally or slides along its base depends primarily manner very similar to that of ¬‚uvial drainage
on the thermal conditions at the base. In ˜˜cold- networks. In a ¬‚uvial drainage network, water
based™™ ice sheets and glaciers the ice is frozen to ¬‚ows in the direction of the hillslope or chan-
its bed, which precludes basal sliding. In ˜˜warm- nel orientation or aspect. Fluvial channels acco-
based™™ ice sheets and glaciers, motion occurs by modate this continually increasing discharge pri-
a combination of basal sliding and internal ice marily by increasing in width and depth down-
¬‚ow. The frictional force between an ice body and slope. Channel ¬‚ow velocities also increase down-
its bed depends on many factors, but sliding of slope, but at rates typically much lower than
ice over glacial till is generally thought to require changes in width and depth. Flow in an ice sheet
lower basal shear stresses than sliding of ice over or glacier also occurs in the direction of the ice-
bedrock. The distinction between cold and warm- surface gradient. As discharge accumulates with
based ice sheets is very signi¬cant for geomor- distance downslope, the ice velocity is the vari-
phology because only warm-based ice sheets per- able that changes most greatly to accommodate
form signi¬cant glacial erosion. Millions of years the increasing ¬‚ow. The shape of the ice sheet or
of glacial activity have produced little measur- glacier does not vary as greatly as the velocity be-
able glacial erosion in areas dominated by cold- cause a small change in thickness or slope causes
based glaciers (e.g. Dry Valleys of Antarctica). a large change in discharge due to the threshold

a Newtonian ¬‚uid, strain rate is proportional to
n = 10
n= shear stress. The coef¬cient of proportionality is
the viscosity, a measure of stiffness of the ¬‚uid.
3 In a non-Newtonian ¬‚uid, strain rate and shear
du a
n= 3 stress are nonlinearly related:
2 n

=a (1.20)
n= 1 dz
1 where u is the ¬‚uid velocity, z is the distance
along the pro¬le, „ is the shear stress, „0 is a ref-
erence or yield stress, and a and n are rheological
parameters. The values of a and n can be consid-
1.0 1.5 2.0
t/t0 ered to be constant in some cases, but more of-
ten they depend on the temperature or density of
Fig 1.26 Plot of normalized velocity gradient versus the ¬‚ow. Experiments indicate that ice deforms
normalized shear stress for a Newtonian ¬‚uid (n = 1), a according to Eq. (1.20) with n ≈ 3 (i.e. Glen™s Flow
non-Newtonian ¬‚uid (e.g. n = 3 and n = 10), and a perfectly
Law (Glen, 1955)). Some materials, including rock
plastic material (n = ∞).
in Earth™s upper crust, have highly nonlinear rhe-
ologies characterized by Eq. (1.20) with n = 10 or
nature of ice ¬‚ow. Close to an ice divide, there- greater. Such materials deform very slowly un-
fore, ice-¬‚ow velocities are quite low because the til brittle fracture occurs, after which deforma-
contributing area is small. Ice ¬‚ow velocities are tion can be accommodated relatively easily by
a combination of internal ¬‚ow and basal slid- slippage along fractures. Equation (1.20) does not
ing, so not all of the increased ¬‚ow downstream resolve the detailed structure of fracture zones
occurs as basal sliding. Nevertheless, increasing in such materials, but it can be used to study
ice discharge is usually associated with increased the large-scale behavior of deformation in such
basal sliding velocities. Erosion rates close to an materials.
In the limit n = ∞, the material is called per-
ice divide are, therefore, relatively low according
to Eq. (1.19). Further downslope, ¬‚ow velocities fectly plastic. Perfectly plastic materials are com-
pletely rigid below their yield stress, „0 , but ¬‚ow
and erosion rates increase to accommodate ice
delivered from upslope. Basal sliding velocities entirely without resistance above it. The perfectly
increase with distance downice, usually reach- plastic model is an idealization, but in some
ing a maximum beneath the equilibrium line. cases it is very useful within certain limitations.
Past the equilibrium line, ice-¬‚ow velocities de- Glaciers, ice sheets, lava ¬‚ows, and debris ¬‚ows,
crease due to ablation. This decrease, combined are all examples of ¬‚ows driven by gravity. Flow
with the accumulation of erosional debris from in these systems occurs when the material thick-
further upice, usually causes a zone of sediment ens locally, increasing the shear stress at the base,
deposition beneath the ablation zone of an ice causing the ¬‚ow to surge forward, thereby low-
sheet or glacier. ering the shear stress back below a threshold
value. The dynamics of this type of surge be-
1.3.1 How ice deforms havior depends sensitively on the value of n in
The ¬‚ow of liquid water and air over the Earth™s Eq. (1.20). If one is not interested in resolving
surface are both examples of Newtonian ¬‚ows. the detailed dynamics of individual surge events,
Understanding glacial erosion, however, requires however, then the perfectly plastic model can be
quantifying the behavior of a non-Newtonian very useful. In nature, there is always some ¬-
¬‚uid. The difference between Newtonian and nite time lag between changes in accumulation
non-Newtonian ¬‚uids is illustrated in Figure 1.26, and the associated glacier response. In the per-
where graphs of velocity gradient versus shear fectly plastic model, however, glacier surges start
stress are illustrated for three types of ¬‚uids. In and stop instantly, because any increase in ¬‚ow

mer ice sheets. These mantle-¬‚ow patterns are
dif¬cult to interpret uniquely in terms of ice-
sheet size and shape, however, because the re-
sponse is a function of lithospheric rigidity and
2 km
the mantle-viscosity pro¬le in addition to the size
and shape of the ice sheet. Therefore, many dif-
3 km
ferent ice-sheet sizes and shapes may be equally
consistent with the observed data pattern of sea-
level change. Landforms such as drumlins, ¬‚utes,
and mega-scale lineations can also be used to re-
construct ice-¬‚ow directions and provide infor-
mation on the locations of ice domes (Clarke
et al., 2000). While these geomorphic markers pro-
vide solid evidence that ice once ¬‚owed in a cer-
tain direction, it is often dif¬cult to reconstruct
Fig 1.27 Model reconstruction of the Laurentide Ice Sheet
a spatially complete ¬‚ow ¬eld or to determine
at 18 ka constructed using a perfectly plastic ice sheet model
the time that the observed ¬‚ow directions were
and assuming isostatic balance.
imprinted on the landscape.

1.3.2 Glacial landforms
thickness that causes the shear stress to increase
above a threshold value instantaneously triggers Upstate New York provides some of the most
¬‚ow to correct the imbalance. Perfectly plastic striking examples of erosional and depositional
glaciers and ice sheets, therefore, are constantly glacial landforms on Earth. Figure 1.28a illus-
in balance with the pattern of accumulation and trates the topography of a portion of upstate New
ablation. York immediately south of Lake Ontario. This On-
Figure 1.27 illustrates a model reconstruction tario Lowlands region has the largest drumlin
of the Laurentide Ice Sheet over North America ¬eld in North America, with nearly 10 000 drum-
at 18 ka. This reconstruction was developed us- lins. Drumlins are subglacial bedforms elongated
ing the perfectly plastic model with basal shear parallel to the ice-¬‚ow direction and composed
stresses similar to modern ice sheets (e.g. Green- primarily of subglacial till or sediment. Drum-
land, East Antarctica) and assuming isostatic bal- lins in the New York State drumlin ¬eld come in
ance. Isostatic balance in this context means that a wide variety of shapes and sizes. The controls
the weight of the ice sheet causes the crust to on drumlin size and shape are not well under-
subside into the mantle until the point where stood, but we will explore a possible model for
the additional load is balanced by the buoyancy drumlin formation in Chapter 7. Subsurface bed-
associated with the displaced mantle material. ding in drumlins often parallels the topographic
Despite decades of research, the shape and thick- surface, suggesting that they form by localized,
ness of the Laurentide Ice Sheet (LIS) is still a upward ¬‚ow of sediment into low pressure zones
subject of active research and debate. Sophis- beneath the ice sheet.
ticated mass-balance thermomechanical models Along the southern portion of Figure 1.28a,
are used to reconstruct the ice sheet, but un- the elevation rises up to the Allegheny Plateau
certainty in paleoclimatic, rheological, and basal- and the Finger Lakes Region. The Finger Lakes
¬‚ow parameters results in uncertainty in the re- Region is characterized by ¬ve major elongated
sulting reconstructions (Marshall et al., 2000). In- lakes that fan out like the ¬ngers of a hand.
terpretation of past sea-level changes is another More generally, ¬nger lakes are any kind of elon-
method by which the shape of the former ice gated glacial lake formed near the margin of a
sheet can be inferred. In this method, the past former ice sheet. Figure 1.28b illustrates the to-
≈100 yr of sea-level records are used to determine pography in the vicinity of the town of Ithaca,
the present pattern of mantle ¬‚ow beneath for- located near the southern tip of Cayuga Lake (the


(b) resolution limit

N (>A) N (>A) ∝ A

102 uncompensated,
"great" lakes
compensated lakes

104 105
100 101
A (km 2)
Fig 1.28 Shaded relief images of two portions of upstate
New York. (a) Drumlin ¬eld of the Ontario Lowlands. (b) Fig 1.29 Analysis of lakes in central Canada. (a) Radarsat
Southern Cayuga Lake (one of the ¬ve Finger Lakes) in the mosaic image of central Canada (resolution 250 m), including
vicinity of the town of Ithaca. a closeup of Dubawnt Lake region to illustrate the full
resolution of the image. (b) Cumulative frequency-size
distribution of lakes extracted from (a). Also included in this
largest of the Finger Lakes). The topography of the plot are the Great Lakes, even though they are not included
in (a). A power-law relationship N(>A ) ∝ A ’1 is observed
Ithaca area is characterized by wide (>1 km), deep
from A = 100 to A ≈ 104 km2 . Above A ≈ 104 km2 , the
(>100 m), glacially scoured valleys cut into the
largest lakes do not ¬t the power-law relationship. The larger,
broad, low-relief Allegheny Plateau (von Engeln,
more uniform size of the great lakes is consistent with the
1961). Fluvial channels in the region are said to
in¬‚uence of lithospheric ¬‚exure on their formation.
be under¬t because channels occupy only a small
portion of the broad valley ¬‚oors that were once
occupied by ice up to 1 km in thickness. Flu-
vial drainage density is low, re¬‚ecting the short cumulative frequency-size distribution of lakes is
period of geologic time since small-scale land- the number of lakes larger than a given area. Con-
forms were last smoothed by glacial processes. sider Figure 1.29b, which illustrates the cumula-
The deeply scoured valleys and smooth uplands tive frequency-size distribution of all the lakes in
illustrate that glacial processes smooth the land- Canada resolvable in a 250 m-resolution Radarsat
scape at small (<5 km) scales, while increasing mosaic of the country. Certainly not all Cana-
relief through trough formation at larger scales. dian lakes are erosional in origin; some of the
In addition to elongated ¬nger lakes, the smaller lakes occur in kettles and hummocky
northern US and Canada contain innumerable moraine, for example. Nonetheless, the majority
glacially carved lakes that come in a wide range of Canadian lakes, particularly the largest lakes,
of sizes (Figure 1.29a). The cumulative frequency- are erosional in origin. Figure 1.29a shows a sub-
size distribution is one tool for quantifying set of the Radarsat mosaic, illustrating the mo-
the population of lakes in a given region. The saic image data at both small and large scales.




largest lakes in North America may be controlled
Fig 1.30 Sur¬cial geologic map of eastern Canada,
by some additional process not involved in the
illustrating moraines (thick curves oriented perpendicular to
erosion of smaller lakes. In Chapter 6, we will
ice ¬‚ow), eskers (long, thin curves oriented parallel to ice
propose that the bending of the lithosphere be-
¬‚ow) and drumlins (short, thin curves parallel to ice ¬‚ow).
neath the ice is that additional process that con-
trols the formation of the largest North American
glacial lakes.
Lakes were extracted from the image by scanning
Depositional landforms beneath ice sheets in-
the grid for pixels with water coverage. Once a
clude moraines, eskers, drumlins, kettles, and
water-covered pixel was identi¬ed, all neighbor-
kames. Figure 1.30 includes a map of deposi-
ing pixels were searched recursively, calculating
tional landforms in eastern Canada. As ice sheets
the number of pixels in the connected lake ˜˜do-
have waxed and waned, nearly all glaciated ar-
main.™™ In this way, the size of each lake in the im-
eas have experienced a combination of erosion
age was determined. We have also included the
and deposition. As such, glacial landscapes are
¬ve Great Lakes in this population, even though
classic palimpsests. This poses a problem for the
they are not included in the mosaic image. The
interpretation of formerly glaciated topography.
distribution of Figure 1.29b includes two dis-
tinct lake types. Lakes smaller than ≈ 104 km2 in For example, predominantly erosional topogra-
phy may be covered with till of varying thickness,
area follow a simple power-law distribution char-
acterized by N (> A) ∝ A ’1 . Above 104 km2 , the obscuring the bedrock erosional surface.
Alpine glaciers differ from ice sheets primar-
largest lakes do not follow the trend of smaller
ily in their size and the extent to which ice ¬‚ow
lakes. Instead, these lakes are larger than the size
is controlled by subglacial topography. In an ice
predicted by an extrapolation of the trend for
sheet, the thickness of the ice is often several
smaller lakes. This distribution suggests that the

high peaks

plateau surface
U-shaped valley

hanging valley glacial

Fig 1.32 Oblique virtual aerial photograph of the Wind
River Range, illustrating the three distinct topographic levels
Fig 1.31 U-shaped and hanging valley of the Beartooth
characteristic of many glaciated mountain ranges of the
Mountains, Montana.
western US.

times greater than the relief of the bed topog-
raphy (except near the margins). As a result, the a main valley takes place much faster than ero-
pattern of ice ¬‚ow is controlled principally by sion of a side tributary, leaving the side trib-
the planform shape of the ice sheet with valleys utary ˜˜hung™™ above the ¬‚oor of the main val-
and ridges beneath the ice sheet playing a rel- ley. Hanging valleys are, therefore, a consequence
atively minor role. In contrast, ice thickness in of the more spatially discontinuous nature of
a glacier is typically much less than the relief of glacial erosion compared with ¬‚uvial erosion. It

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