Supporting Online Material
Effects of Basal Debris on Glacier Flow
Neal R. Iverson, Denis Cohen, Thomas S. Hooyer, Urs H. Fischer, Miriam Jackson, Peter
L. Moore, Gaute Lappegard, and Jack Kohler
Materials and Methods
Hard-bed experiment. Figure S1 depicts the panel installed at the mouth of a vertical
shaft that extended three meters downward to an underlying tunnel in the rock bed. The
granite tablet at the upper surface of the panel rested in an aluminum carriage, and the
shear traction on the carriage was measured with two orthogonally-oriented load cells
that pressed on its down-glacier end. The carriage was supported at its bottom by seven,
two-way thrust bearings, each 53 mm in diameter. The bearing friction was measured
under different normal forces in a 2 MN hydraulic press, and the force associated with
this friction was added to the vector sum of the shear force recorded by the two load cells.
Shear force supported by the bearings, F, varied nonlinearly with normal force, N: F = –
(1.120 x 10-3) N + (5.07 x 10-5) N2 – (3.25 x 10-8) N3, where F and N are in kN and values
of N up to 500 kN were considered. Sliding speed was measured with a plastic ball that
was entrained by ice and connected to a cable; the cable was withdrawn from the panel
during glacier slip at a rate recorded by an extensometer in the underlying tunnel. Two
transducers, screened with porous ceramic disks, recorded pressure in the water film at
the upper surface of the tablet.
Thermistors in the panel recorded temperatures used for calculating the upward heat flux
through the panel and the resultant rate of basal melting. Basal melting due to dissipation
of frictional heat was neglected. It was equal to s u / L, where s is the shear traction, u is
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the sliding speed, and L is the volumetric latent heat of fusion of ice (3.1 x 108 J m-3).
Choosing measured values of s (200 kPa) and u (73 m yr-1) that maximize frictional heat
production, yields 0.047 m yr-1, which was less than 18% of the minimum melt rate due
to heat flow through the panel.
To assess the concentration and character of debris in the ice, a cavity was melted in
the base of the glacier above the shaft before installing the panel, and ten 1.0-2.0 l ice
samples were collected from vertical sections of the dirty basal ice layer, which was 1.7
m thick. The volumetric debris concentration of these ice samples was 2-11% (mean,
5.3%), with 32% of the debris gravel-sized or larger, 61% sand, and 7% silt and clay.
Debris particles were primarily feldspar and quartz, and thus were approximately equal in
hardness to the granite tablet. After sampling the basal ice, the panel was winched
upward into position at the bed surface. A period of 1-2 days was then required for the
glacier to come into contact with the panel by sliding and closure of the cavity created for
sampling.
An important consideration is whether ice and debris had access to the up-glacier lateral
edge of the carriage that held the rock tablet (Fig. S1), which could have caused a
horizontal force on the carriage in excess of that due to shear traction on its upper
surface. The carriage, however, was flush to within 0.1 mm with the surrounding smooth
steel plate, and the gap between the carriage and this plate was less than 1.0 mm in width,
with an o-ring at the mouth of the gap to prevent intrusion of fine debris, ice, and water.
Inspection of the panel after experiments revealed accumulation of particles of only silt
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and clay size at the mouth of the gap with no macroscopic wear on the edge of the
carriage. Thus, there was no evidence that debris had pushed on the up-glacier edge of
the carriage.
Soft-bed experiment. With a warm-water melting system, a tunnel was melted through
the ice to a relatively flat location on the bedrock surface, where the bedrock trough was
excavated (Fig. S2). Melting of this tunnel began at a second access point to the base of
the glacier: a horizontal tunnel through the rock bed that intersected the base of the
glacier where the bedrock surface slopes steeply down-glacier (see map in (1)). The ice
tunnel was ~ 15 m long, 2 m high, and 1.5 m wide, except at the site of the trough, where
it was 50-100% higher and wider to accommodate blasting and drilling. The trough was
located 10 m from the mouth of the vertical shaft where the other experiment was
conducted. Three holes, 32 mm in diameter, were drilled from the base of the trough to a
tunnel in the rock 4 m below the bed surface. Two of these holes were used for electrical
cables from instruments, and a sealed pipe was inset into the third hole to conduct water
upward from the tunnel to the base of the trough.
The simulated till that was added to the trough was mixed from sediment excavated from
tunnels beneath the glacier. Till is sediment deposited directly from glacier ice and
contains a wide range of grain sizes. The simulated till consisted of 75% gravel and sand,
20% silt, and 5% clay, by weight, comparable to the grain-size distributions of some
natural tills deposited subglacially (2).
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Approximately 3 tons of simulated till were added to the trough in layers. To measure
shear deformation, vertical columns of four tiltmeters were placed in the till spanning its
thickness at two locations, and vertical columns of beads were positioned for excavation
after the experiment (Fig. S2). One or two earth-pressure cells recorded the total normal
stress on the till, and three piezometers recorded pore-water pressure. A strain meter,
initially oriented vertically, recorded contraction or dilation of till in a direction parallel
to the instrument’s length as it rotated during till shear. Dataloggers in the underlying
tunnel excited the instruments and recorded their signals.
After ice had contacted the till and normal stress on the till had become relatively steady,
water was pumped at a constant discharge to the base of the till wedge. Pump tests
differed in 2001 and 2002. In 2001, water was pumped to the wedge until a hydraulic
connection along the ice-rock interface was established with the mouth of the horizontal
access tunnel. A hydraulic connection was indicated by turbid water flowing into the
tunnel. Pumping was then stopped to minimize erosion of the till wedge by water. In
2002, this hydraulic connection was not established. Instead, water flowed away from the
till wedge along an unknown drainage path. This drainage path was apparently far less
conductive than that of 2001 because higher pore-water pressure was sustained during
pump tests and the rate of decrease in pore-water pressure after pumping was two orders
of magnitude smaller. Pump tests lasted several hours.
In 2001, after completion of pump tests, a tunnel was melted through the glacier to the till
wedge, which was carefully dissected. Beads were displaced by shear an amount
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commensurate with tiltmeter rotation, indicating that the tiltmeters, despite being rigid
inclusions in the till, recorded shear strain reliably. Some marked cobbles at the ice-till
interface had plowed through the till surface, as indicated by accumulations of sediment
bulldozed on their down-glacier sides (3). Bulk densities of the till before and after the
experiment were 1.83 ± 0.05 gm cm-3 and 2.19 ± 0.03 gm cm-3, respectively.
Supporting Online Text
Shear traction due to clean, temperate ice. Results of laboratory experiments, in which
clean ice at its melting temperature was slid across flat concrete with a cement finish (4),
indicate that shear traction exerted on the rock tablet by ice was likely a minor fraction of
the measured shear traction. Sliding ice exerted a shear traction of ~ 5 kPa on a cement
finish at an effective normal stress of 100 kPa. Even smaller shear tractions would be
expected on the granite tablet of this study, since its largest roughness elements (0.1 mm)
were an order of magnitude smaller than those of the cement. Moreover, boundary
conditions of the laboratory experiments likely resulted in a water film between the ice
and cement that was thinner than that expected subglacially, such that measured shear
tractions may have been unrealistically large.
Shear traction due to debris. The shear traction on the rock tablet exerted by debris
particles, sp, is approximated by
sp =
µp
A
n
∑ N i Fi ,
i =1
where Fi is the effective contact force exerted normal to the tablet by particles of size
class i, Ni is the number of particles of that size class in contact with the tablet, n is the
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(1)
number of size classes, µp is a coefficient of sliding friction between debris particles in
ice and the tablet, and A is the area of the tablet. This equation assumes that particle
rotations in ice, which may reduce shear traction, are negligible (5). If ice regelates and
creeps viscously around particles on the bed that are sparse enough to be considered
isolated, then
Fi =
4πfη Ri3
4
3
V N + πg ( ρ r − ρ )Ri ,
3
R + Ri
2
*
2
(2)
where VN is the component of ice velocity toward the bed, η is the effective ice viscosity,
Ri is mean radius of particle size class i, R* is the transition particle size for which drags
due to ice regelation and creep are equal, f is an empirical factor that accounts for
chemical effects and the bed as a heat source and rigid boundary, g is the gravitational
acceleration, ρr and ρ are the densities of rock (2600 kg m-3) and ice (910 kg m-3),
respectively, and L is the volumetric latent heat of fusion of ice (3.1 x 108 J m-3) (6, 7).
The left-hand term is the drag on particles that results from ice movement toward the bed,
and the right-hand term is the particle buoyant weight in ice. Zero shear traction is
assumed between ice and particles. The non-linear flow relation of ice (dependence of
η on VN) can be accounted for approximately using a solution for the drag on a sphere in
which non-linear ice creep is considered in the absence of regelation (8). This solution
indicates that
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 SKB  4 − 12
 VN
R* = 13.3
 fL 
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and
R*2 L
η =
,
9 SK
(3)
where B is the viscosity parameter for ice (9), S is the reduction in melting temperature
with pressure (7.4 x 10-8 °C Pa-1), and K is the mean thermal conductivity of ice and rock
(2.5 J m-1 °C-1 s-1).
Combining Eqs. 1-3 yields the shear stress on the tablet due to debris-bed friction as a
function of VN. The measured size distribution was divided into 17 size classes from silt
to cobbles 0.20 m in diameter, which were approximately the largest particles observed in
the basal ice above the shaft. Assuming a volumetric debris concentration near the upper
bound of the range measured (0.10), values of B and f near the upper limits of their
uncertainties (B = 2.6 x 105 Pa s1/3, f = 50), and that the measured basal melt rate (1.6 x
10-8 m s-1) equaled VN, yields sp ~ 60 kPa. Larger values of sp are possible depending
upon how the measured distribution of particle sizes is extrapolated to include the largest
particle sizes observed.
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Supporting Figures
Ice flow
Plastic ball
Tablet
Bed
Bed
Load
cell
(1 of 2)
Bearings
(3 of 7)
0.20 m
Water
pressure
sensors
Supports
(2 of 4)
Wire rope to
extensometer
0.60 m
Top of vertical shaft
Fig. S1. Panel for measuring shear traction exerted by the glacier on smooth rock at the bed
of the Svartisen ice cap, Norway. A profilometer dragged across the surface of the granite
tablet prior to experiments indicated no roughness elements in excess of 100 microns.
Load cells were vibrating-wire sensors (Geokon, model 4900X-5-0). The precision of the
measured shear traction, which was limited by the uncertainty of the bearing-friction
estimation (see Materials and Methods), was 10 kPa. Water-pressure sensors (Geokon,
model 4500SH-500) were contained in ports filled with water in hydraulic communication
with the upper surface of the tablet. Porous ceramic disks (50 kPa air entry pressure)
screened the ports. The extensometer (Unimeasure, model HX-PA-60) that recorded
displacement of the ball was mounted near the floor of the tunnel. The panel frame was
aluminum and filled with foam insulation to minimize upward heat flow from the tunnel to
the tablet surface. Plastic (Dupont Delrin) spacers in vertical members of the aluminum
frame minimized upward heat flow through the aluminum. Fenwal glass probe NTC
thermistors (series 121) with a precision of 0.02 °C were mounted in both the frame and
rock tablet. Supports extended 5 m downward to the tunnel floor.
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Ice
Tiltmeters
E.P.
cell
Beads Strain
meter
Till
Piezometer
Rock
Water conduit
Holes for electrical
cable
0.50 m
Fig. S2. Flow-parallel cross-section through the till wedge with instruments. Lateral
walls of the bedrock trough were irregular and sloped more gently than the headwall.
Tiltmeters consisted of biaxial, electrolytic cells (Fredericks Company, model 07172201) mounted in plastic cylinders, 16 mm in diameter and 50 mm long. Piezometers,
earth pressure cells, and strain meters were vibrating-wire sensors (Geokon models
4500S-500, 4800X-1-500, and 4430-X, respectively). Earth pressure cells had circular
sensing faces 102 mm in diameter, and strain meters were 0.33 m long. Beads for
measuring bed-parallel till displacement with depth were 18 mm in diameter.
References
1. D. Cohen, R. LeB. Hooke, N. R. Iverson, J. Kohler, J. Glaciol. 46, 599 (2000).
2. S. Haldorsen, Boreas 10, 91 (1981).
3. P. U. Clark and A. K. Hansel, Boreas 18, 201 (1989).
4. W. F. Budd, P. L. Kleage, N. A. Blundy, J. Glaciol. 23, 157 (1979).
5. N. R. Iverson, Geol. Soc. Am. Bull. 103, 1308 (1991)
6. B. Hallet, J. Glaciol. 23, 39 (1979).
7. B. Hallet, Ann. Glaciol. 2, 23 (1981).
8. L. Liboutry, C. Ritz, Ann. Géophys. 34, 133 (1978)
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9. D. Cohen, J. Glaciol. 46, 611 (2000).
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