The Physical Basis of Ice Sheet Modelling (Proceedings of the Vancouver Symposium, August
1987). IAHS Publ. no. 170.
Anomalous heat flow and temperatures associated with
subglacial water flow
Keith Echelmeyer
Geophysical Institute
University of Alaska-Fairbanks
Fairbanks, AK 99775-0800, USA
ABSTRACT Recent evidence suggests that many glaciers, ice streams, and ice
sheets are underlain by a layer of till or other permeable, deformable medium.
At some depth in this substratum there may be a flux of groundwater. As initially described by Clarke et al. (1984), such a subglacial water flow will cause
a shift in the melting isotherm below the polar ice mass. Calculations show
that basal temperatures can be strongly elevated and that basal temperature gradients can be increased by more than an order of magnitude when there is a
flux of groundwater through this subglacial aquifer, even though the upper part
of the substratum is frozen. Comparison of calculated profiles with observed
temperature data from cold-based glaciers shows favorable agreement Such
anomalous temperatures and heat flow will have important ramifications in the
motion and dynamics of polar ice masses. Temporalfluctuationsin the flux of
subglacial water may also be an important means of incorporating subglacial
debris into the glacier itself.
Flux de chaleur et températures anormales associés a l'écoulement d'eau
sous-glaciaire
RESUME Des observations récentes suggèrent l'existence, sous de nombreux
glaciers, courants de glace ou nappes de glace, d'une couche de moraine
déposée ou autre milieu perméable de déformable. Il doit y avoir, à une certaine profondeur dans ce substrat, un flux d'eau souterraine. Comme l'ont
décrit Clarke et al. (1984), cet écoulement d'eau sous-glaciaire doit provoquer
une déviation de l'isotherme 0°C sous une calotte polaire. Les calculs montrent que les températures basales peuvent être très augmentées, et les gradients
de température à la base supérieurs d'un order de grandeur, lorsqui'il y a circulation d'eau dans cet aquifère sous-glaciaire, même si la partie supérieure du
substrat est gelée. Des comparaisons de profils de température calculés avec
des températures mesurées sous des glaciers à base froide appuient cette conclusion. Ces températures et flux de chaleur anormaux auront d'importantes
conséquences dans l'écoulement et la dynamique des calottes polaires. Les
fluctuations temporelles du débit d'eau sous-glaciaire pourraient être aussi un
moyen par lequel les débris sous-glaciaires s'incorporent au glacier.
93
94
Keith Echelmeyer
INTRODUCTION
The distribution of temperature in glaciers and ice sheets is important in determining the internal deformation of the ice through the Arrhenius-type temperature dependence of the effective
viscosity. It is also important in determining mechanisms of motion at the glacier bed. If the
base of the glacier is at the pressure melting point, then sliding over a bedrock surface may
occur at a rapid rate, whereas if the bed is at a subfreezing temperature, the rate of sliding,
although nonzero, will be substantially reduced (Shreve, 1984; Fowler, 1986; Echelmeyer &
Wang, 1987). If the ice sheet or glacier is underlain by till or other rock debris, as is typical,
the effective viscosity of this deformable subglacial layer will depend strongly upon the amount
of liquid water present. If the basal material is at the melting point, the pore water pressure is
a controlling factor in the deformation, while if the bed is frozen, the temperature-dependent
thickness of the liquid-like layer surrounding each till particle is important (Echelmeyer &
Wang, 1987).
Calculation of the temperature distribution in these ice masses requires the specification
of various boundary conditions. If the temperature of the basal ice is below the melting point,
one of these boundary conditions is applied on the temperature gradient (and consequently the
heat flow) at the base of the ice. In most calculations of temperature within cold ice sheets or
glaciers, the heat flux at the base is taken to be the regional geothermal flux, qe, which
corresponds to a temperature gradient of approximately 0.02 - 0.03 K m _I .
The assumption of this geothermal heat flow at the base of the ice is valid if the underlying material is relatively impermeable bedrock. However, if the bed material is highly permeable rock or till, then there may be flow of groundwater within the bed material at some depth
below the ice-bed interface. The presence of flowing groundwater in the substratum requires
the melting isotherm to be at the top of the liquid water (the groundwater table). The position
of this water table may be much closer to the base of the ice than that expected from consideration of the geothermal temperature gradient alone. Such a shift in the melting isotherm
will substantially alter the structure of the temperature field in the basal ice, where an accurate
assessment of the temperature is of prime importance. The effects of such a subglacial aquifer
have been put forth by Clarke et al. (1984) as a possible explanation for anomalously large
temperature gradients in the basal ice of Trapridge Glacier, Yukon Territory, Canada. Thus,
even if subglacial till at the ice/bed interface is frozen, the presence of groundwater at some
depth within the till can strongly affect the motion of polar ice masses via the changes in the
temperature field (as well as by the deformation of the frozen substratum).
That such groundwater flow is present beneath polar or sub-polar glaciers is shown by
the non-zero winter discharge of the streams emanating downvalley from such glaciers as the
Urumqi Glaciers in the Tien Shan Mountains of China (Wang Zhongxiang, personal communication) and Trapridge Glacier (Clarke et al, 1984). These glaciers are of the subpolar
category, with subfreezing temperatures at some locations along the bed. The recent work of
Blankenship et al. (in press) on Ice Stream B, Antarctica, shows that at least under the small
area investigated, there may be a layer of water-saturated till. It is likely that this groundwater
may exist at some depth within the bed (which may be frozen till) upstream of the location
investigated by Blankenship et al. (in press). Calculations of temperature profiles within these
glaciers, based on the assumption of a geothermal temperature gradient only, may be in error if
such groundwater is present. In this paper, the effects of a groundwater table beneath a cold
glacier on the basal temperature gradient (and thus the basal heat flux) are calculated and compared with the commonly considered case in which the only heat flux at the bed is geothermal.
Significant and important differences in temperature profiles are described. The effects of flow
in a subglacial aquifer are used to explain the anomalous temperature distribution found at the
base of such glaciers as Urumqi Glacier No. 1, Trapridge Glacier (following Clarke et al,
Anomalous heatflowand temperatures
95
1984) and Matanuska Glacier, Alaska (Lawson, 1986).
THEORETICAL DISCUSSION
As a simple model, consider a horizontal, planar glacier of thickness H overlying a half-space
of permeable bedrock or till which to some depth h is below freezing, as shown in Fig. 1. Let
the thermal conductivity and diffusivity be denoted by K and K, respectively. Subscript i
denotes ice while subscript d denotes the frozen subglacial till or permeable bedrock. The
coordinate system is chosen with the origin at the base of the subfreezing till, where temperature T = 0°C. The vertical coordinate is denoted Ç.
T = Tfe^.
S
Ç=H
+h
Ice
rm
I =
Frozen
Till,
or Bedrock •
vi'*
-rrr-
V t- i £
Unfrozen
Till r v r A * •
•, or Bedrock
* +r *W<A Ar- * *"* "*
'»" vi't'ji
>'V'
r=o<^v;
v
r
-
•
.
.
*
*
IIMIH
ft
*
-*
^
i . A "7
v * - ^
v
r 7 '
v
' \ A * ' >
•
•*•
i
*
F/G. i Geometry of the model ice sheet and coordinate system.
At the surface of the glacier, the net mass balance is b (m a-1), with accumulation being
positive. If the ice thickness is to remain constant in time, a nonzero balance will impart a
nonzero vertical velocity, v(z), which is taken to be a linear function of depth.
The temperature T varies with depth in the ice and is a prescribed value Ts at the surface.
In order to investigate the effects of groundwater flow at depth in the substratum, we note that
the top of the groundwater layer will define the melting point isotherm, here taken to be 0°C.
(This neglects pressure and solute effects, which will only shift the melting isotherm a small
amount and make the temperature difference between the surface and the melting isotherm
slightly larger in magnitude. This can easily be accounted for by changing Ts.) This 0°C
isotherm will be at Ç = 0. At this depth, the flowing groundwater provides a steady heat
source, mamtaining 0°C at Ç = 0. Along with a constant surface temperature (i.e., neglecting
seasonal and climatic variations), the problem then becomes one of determining the steady-state
96
Keith Echelmeyer
temperature profile in the layered system shown in Fig. 1. This temperature distribution is
governed by the one-dimensional conduction/advection equation
dz1
dz
where horizontal advection and deformational heating are neglected. (These two factors may
be included in the manner used in a moving column model (Paterson, 1983, p. 206), but they
have been neglected here in order to clearly illuminate the effects of groundwater.)
Different assumptions about the vertical velocity distribution in the subglacial material
give rise to different solutions. Two models are proposed. In the first, the vertical velocity in
the frozen till or bedrock (v^) is taken to be zero. The bed does not deform and the glacier
may slide over this undeformable bed. In the second, the frozen subglacial debris (ice-saturated
till) does deform, and thus is actually part of the glacier, differing only in thermal and mechanical properties. Under this assumption, vd is taken to be nonzero down to the 0°C isotherm.
From the observations of Echelmeyer & Wang (1987), the second case will probably apply to
any ice mass underlain by ice-saturated rock debris that is at subfreezing temperature. Echelmeyer & Wang observed substantial deformation of frozen ice-laden till at temperatures down
to -5°C; in fact, most of the motion of the glacier in the observed region was accommodated
by the deformation of this frozen till. The second case is therefore likely to apply to Trapridge
Glacier (Clarke et al, 1984) and also to Ice Stream B in Antarctica, at least at some location
upstream from that at which Blankenship et al. (in press) have made their isolated measurements, where the groundwater table was presumably at the ice-bed interface.
The solutions for both models have been developed by the author. The differences in the
resulting temperature profiles and basal temperature gradients are very small (less than 1%).
Therefore, only the more realistic case of a deformable, frozen substratum is treated here.
The boundary conditions imposed are T(0) = 0, T(H + h) = Ts, and
[mi* = 0
(2a)
[[•f 1 ]]* = 0
(2b)
dz
where the double brackets denote the jump in the enclosed quantity as the boundary is
approached from above and below (e.g., T(h+) - T{h~)).
In the frozen debris, v(0 * 0 and we assume that a linear velocity profile extends through
the deformable substratum to Ç = 0:
H+h
Ç e [OJf]
(3)
Thus, in the frozen till,
Ts
-je
Vit k! O
d
dz
(4a)
and, in the ice,
where a and c are constants to be determined from the boundary conditions. Characteristic
length scales in both the till and the ice must be defined:
l
H+h
L = 2Kd
b
(5a)
Anomalous heat flow and
temperatures
97
and
>-, i
H+h
/,= 2K,-
(5b)
From Equation (2b) a relation between the constants a and c is obtained:
a = c~— exp -h?
il
H
(6)
,2
d
l
Using this relation and the boundary condition at the surface, Equations (4a) and (4b) give
V V i
H+h
+ p erf
c = ^erf
-erf
(7)
where
1
P = Ki r y e x p -h
d h
1}
Il
and the error function is defined as
erf(r|) = -2= \e*dx
With c so defined, the temperature distribution for a positive balance (b > 0) is
r(Q
js
fpc erfTO
=
£<&
|c[erf(C//,) - erf(M;) + p erf(Mi)] Ç>/Î
(8)
and the temperature gradient in the basal ice is
dT,
+
_ 2
T
s -h2/(f
C
(9)
k6
dC» - ^
In the ablation zone b < 0 and the error functions must be replaced by a modified
Dawson's integral £)(•), where
£>(n) s e* D(n)
and
(10)
n
e^jefdx
D(r\) s
(11)
is Dawson's integral as defined and tabulated by Abramowitz & Stegun (1965). Letting
c =• D
H+h
l/;l
£>
h
+ p'D
V V1
(12)
where
p =
exn
Kd I/.-I
J
1_
l/,l2
I//
the resulting temperature distribution for b < 0 is
p'c 'D(Ç/I/J)
no J c '[5(C/I/,I) - b(hMf)
r
C<A
+ p'D(h/\ld\)]
>h
(13)
Keith Echelmeyer
98
and
dT,
^
=C
Js h2/\if
lJe
(14)
Examples of the temperature profiles in a thin (25 m) glacier, a somewhat thicker (100
m) glacier, and a 1000 m thick ice sheet with frozen, deformable beds are shown in Fig. 2,
using the thermal properties listed in Table 1. The thermal properties of the frozen till were
assumed to follow those of permafrost. Temperature profiles as determined for the case when
no groundwater is present, with a basal heat flux of 0.05 W m -2 , are also shown. These are
derived from Paterson (1983, Equation 10.20).
T/T s
T'T,
T/T s
FIG. 2 Temperature profiles with a non-zero vertical velocity in the frozen bed
down to the T = 0°C isotherm. Ts = -10°C in no-groundwater model.
The calculated profiles show a much stronger gradient at depth than the usual nogroundwater model. This is, of course, to be expected, since the 0°C isotherm is much closer
to the ice-bed interface than would be predicted for geothermal heating alone, given the low
surface temperature assumed. The effects of subglacial groundwater flow are most pronounced
for thin glaciers, where the basal temperature would normally be well below 0°C for
Ts < -10°C. For ice sheets, the thermal effects of groundwater can be negligible if the surface
is not cold (Ts > -10°C.)
Basal temperature gradients calculated for several different values of ice thickness are
given in Table 2, along with the ratio of these gradients to that expected when no groundwater
is present. There is a strong dependence on overall thickness and surface temperature, but only
a small variation with balance and thickness of the.frozen aquifer. For a thin glacier, the basal
gradient is 15 to 20 times larger than that usually assumed, while for a thick ice sheet resting
on a nondeformable, permeable bed, the basal gradient may be only slightly larger than that
assumed in a model with only geothermal heat flow at the base.
Anomalous heatflowand temperatures
99
TABLE 1 Thermal properties (from Lunardini, 1981)
Ice
Frozen Saturated Soils
Frozen Urumqi Glacier 'Till'*
Sandstone
K(Wm-1 KT1)
2.1
1.9-2.7
2.5
2.5
K(m2 a - 1 )
36
35-44
40
31
*Urumqi Glacier 'Till' : bulk density 1.62 g cm 3, moisture content 0.47, fine grained,
T~ -3°C.
TABLE 2 Ratio of basal temperature gradient to geothermal heating value Ts = -10°C. Ratio
scales linearly with Ts. Kd = 2.5 W m~l K~l. There is no significant variation with Kd in
range shown in Table 1. (dT/dz)e = 0.023 K m'1. M = melting
d7.
h, m
1
5
25
b,m a
-2
-1
+0.1
+1
+2
-2
-1
+1
+2
-2
-1
+1
+2
l
H = 25 m
12.5
14.3
15.6
18.0
19.6
11.4
12.9
15.8
16.9
7.8
8.5
9.6
10.0
Â7.
100 m
1.1
2.2
4.5
6.0
7.9
1.1
2.2
5.8
7.4
1.1
2.1
4.7
5.7
1000 m
M
M
M
1.8
2.5
M
M
1.8
2.4
M
M
1.6
2.2
Because the thermal properties of permafrost do not differ greatly from those of ice, and
because the thickness of the frozen bed is small in comparison with the ice thickness in many
cases, the basal temperature gradients calculated above will not differ appreciably from those
obtained by assuming an effective ice thickness equal to H+h and setting Kd = Kt and Kd = K;.
Then /,- = ld, p = p' = 1 and c = [erfC////,)]-1, c ' = [DQmif)]-1 in Equations (8), (9), (13) and
(14).
WATER FLOW IN THE SUBGLACIAL AQUIFER
The large values of heat flow (q = -K,{dT/dz)) at the basal interface (Table 2), being an order
of magnitude larger than the geothermal heat flow, require a substantial source of heat in the
substratum. This heat source is the groundwater reservoir. But just how large a water flux
distributed in the subglacial aquifer is needed to provide this heat?
The loss of potential energy per unit volume of a fluid flowing down an elevation drop
Az over a distance Ax is -pg Az/Ax, where p is the density and g the acceleration of gravity.
Given a total flux of water in the aquifer Qw and a total width of the aquifer equal to the width
of the glacier, W, the rate of energy loss per unit area in the aquifer is equal to the heat flux, q,
where
100
Keith Echelmeyer
?=
^1F^
(l5)
(This assumes there is no other drop in pressure, as might be due to thinning of the ice above.)
This result is similar to that given by Clarke et al (1984).
For a relatively steep glacier (and valley) such as Urumqi Glacier No. I (slope = .3) and
a subglacial heat flow equal to 0.63 W m -2 (observed dTldz = 0.3 K m-1), the required flux of
water is about 0.1 m3 s over the 400 m width, which is a very reasonable value. A similar
water flow under Trapridge Glacier is predicted by Clarke et al. (1984) based on the temperature gradient they observed there. Clarke et al. (1984) showed that the hydraulic conductivity
of the subglacial aquifer is close to that expected for sand.
For the range of heat flux shown in Table 2 {qe = 0.05 W m-2), a subglacial water flux of
0.05-100 m3 s_1 are required for small steep glaciers to large ice streams, respectively. The
values are again well within the range of probable (but largely unmeasured) subglacial water
fluxes.
COMPARISON WITH OBSERVATIONS
Large temperature gradients have been observed at the ice-bed interface of some subpolar glaciers. Clarke et al. (1984) have measured basal gradients in several boreholes through the
surge-type Trapridge Glacier that are an order of magnitude larger than the geothermal gradient
qJKi. Lawson (1986) reported anomalously high gradients at cold-based regions of Matanuska
Glacier, Alaska. Finally, in a tunnel excavated along the bed of Urumqi Glacier No. 1 in
China, Echelmeyer & Wang (1987) have measured a temperature gradient which is more than
an order of magnitude greater than geothermal. This last measurement was made at the interface with actively deforming yet still frozen till.
In none of the cases mentioned above are the stress and the velocity gradient at the bed
large enough to produce sufficient deformational heating to account for the large temperature
gradients (even though, in the case of Urumqi Glacier No. 1, nearly 70% of the overall motion
is accommodated by deformation of the frozen till just below the ice).
These glaciers are of the subpolar category, with meltwater produced at the surface during the ablation season, and regions of cold (subfreezing) ice, which locally extend to the bed
to make a partially cold-based ice mass. In the case of Trapridge Glacier, the cold-based terminal region may be important in determining the surge mechanism of this glacier (Clarke et
al, 1984). Melt produced at the surface and at temperate regions of the bed may flow into the
permeable bed which underlies each of these glaciers, and percolate beneath the regions of
subglacial permafrost, as in the models described earlier in this paper.
A comparison of predicted and observed temperatures for Trapridge and Urumqi glaciers
is given in Table 3 and Figs. 3 and 4. Since the bed appears to be actively deforming on
Trapridge Glacier (Clarke et al., 1984) and has been observed to deform on Urumqi Glacier
(Echelmeyer & Wang, 1987), and each site considered is in the ablation zone, Equations (13)
and (14) are used to calculate the model temperatures.
Figure 3 and the first part of Table 3 shows the comparison for Trapridge Glacier. Net
mass balance was estimated by the present author, but as shown in Table 2, results are relatively insensitive to errors in b. Ten-meter temperature at each site is approximately -6°C. If
this represents the mean annual surface temperature, then each of the predicted profiles is too
warm. If, instead, a somewhat lower surface temperature of -7.5 to -9°C is assumed, then the
model profile and basal gradient agree extremely well with those observed at each site. (The
Anomalous heatflowand temperatures
101
uppermost measurement at site 6 appears anomalous.) Thus groundwater flow at shallow depth
(5-10 m) beneath this glacier can explain the large temperature gradients and anomalous temperature profiles, although the reason for the lower-than-expected surface temperatures^ required
in the model remains unclear.
Figure 4 and the second part of Table 3 shows the comparison between a temperature
profile measured at a location 40 m into the ice tunnel on Urumqi Glacier No. 1 and the
predicted profile. This profile extends from the frozen subglacial till upward through one-half
of the total ice thickness (22 m), in the wall of a vertical drift. The mean annual temperature
at a station 300 m below the glacier is -5.5°C (Shi & Zhang, 1984). Thus a surface temperature of approximately -7.5°C is to be expected above the tunnel. Calculated temperatures for
this value of Ts and a somewhat lower value (-10°C) do not show as good correlation with the
measured values as on Trapridge Glacier. The agreement is particularly poor at the shallowest
depths.
TABLE 3 Observed versus calculated temperature profiles. The observed profiles are from (I)
Clarke et al. (1984, Fig. 5) and (II) Echelmeyer & Wang (1987)
dT.
Site
b(m a~x)
3
3
3
6
6
6
9
9
9
-1
-1
-1
-1
-1
-1
-0.5
-0.5
-0.5
-1.5
-1.5
-1.5
-1.5
~d7lb
Him)
h(m)
TfC)
Observed
f. Trapridge Glacier
21
8
-0.26
-6.0
21
8
-0.26
-7.5
21
-0.26
8
-9.0
-0.22
30
5
-6.0
-0.22
5
30
-7.5
5
-0.22
30
-9.0
-0.11
50
5
-6.0
50
5
-7.5
-0.11
-0.11
50
5
-9.0
II. Urumqi Glacier No. 1
22
5
-7.5
-0.35
22
-0.35
5
-9.0
22
-0.34
10
-7.5
-0.34
22
10
-9.0
(K m~l)
Calculated
-0.19
-0.24
-0.29
-0.15
-0.19
-0.22
-0.10
-0.12
-0.15
-0.24
-0.32
-0.21
-0.27
Each of the measured profiles on Trapridge Glacier appears to be smooth, slowly varying and
monotonie. Therefore, these profiles may be assumed to be in steady state. The observed
profile on Urumqi Glacier, however, is not monotonie. The depth of the upper points of the
profile precludes their being affected by seasonal variations at the surface, and yet this profile
is clearly not in steady state. Because the tunnel is open to the atmosphere, which was at
approximately -6 to -8°C during the .months when the profile was measured, and much
activity (physical work, electric lighting) was occurring in the tunnel during this time, it is
likely that the actual ice temperatures (measured approximately 10 to 20 cm in from the wall)
were disturbed. Undisturbed temperature measurements in 10 m boreholes nearby show lower
temperatures (-3.5 to -4°C) at depths corresponding to the upper points shown in Fig. 4, and,
thus, the actual profile may be more realistic in shape.
Keith Echelmeyer
102
TRAPRIDGE GLACIER
-6
TEMPERATURE (°C)
-4
-2
0
-6
TEMPERATURE (°C)
-4
-2
0
-8
TEMPERATURE <°C)
-6
-4
-2
0
FIG. 3
Observed (Clarke et al, 1984) and computed temperature profiles
at three different sites on lower Trapridge Glacier. Parameters used in calculations are listed in Tables 1 and 3.
For an aquifer depth of 10 m, the lower part of the predicted profile in Urumqi Glacier
agrees well with that observed, but again, the surface temperature must be colder than that
expected from measured values or 10 m temperatures (-9°C versus -7.5°C).
CONCLUSIONS
Groundwater flowing beneath a cold-based glacier or ice sheet can cause a substantial change
in the temperature distribution within the ice. The top of the unfrozen groundwater-saturated
bed material (till or bedrock) corresponds to the melting isotherm. If this groundwater table is
relatively shallow, then the temperature of basal ice will be significantly larger than that
predicted using the assumption of a basal heat flux equal to the geothermal flux. For a realistic
choice of model parameters (ice thickness, surface temperature, net mass balance, groundwater
table depth), the basal temperature gradient can easily be more than an order of magnitude
greater than the value of qJK, the temperature gradient usually assumed in cold-based ice temperature models.
Anomalous heatflowand temperatures
103
URUMQI GLACIER
5
TEMPERATURE ( C)
-4
-3
-2
1
\ \ I
TEMPERATURE ( C)
-4
-3
-2
-5
13
1
\
\
\
\
\
15-
15-
\
\
\
17-
1 1-
I
l0.
LU
Q
\V
i\
\
19"
*
\
19-
\
h = 5m
\
\
\p
h = 10m
\
A
\\
\\
\
\
21-
21-
(a)
OBSERVED
\
\
\ \ \\
<».
Ts = -7.5 C
\ \ \
\\\
Ts = -10 C
FIG. 4
Observed (Echelmeyer & Wang, 1987) and computed temperature
profiles at tunnel location in Urumqi Glacier No. 1.
The presence of subglacial groundwater is of key importance. As the models presented
above have shown, thermal properties of the basal material are usually close in magnitude to
those of the overlying ice and, therefore, the exact choice of these parameters does not alter the
conclusion of high basal ice temperatures and large temperature gradients. Similarly, the
choice of the vertical velocity at the surface (b) and within the bed material does not strongly
influence the temperature profiles. This relatively weak sensitivity to model parameters is to be
expected, since the position of a shallow depth for the melting isotherm requires the high basal
gradients and temperatures. Models with only a geothermal heat flux at the base place no such
restrictions on the depth of the 0°C isotherm.
Recent observations on the basal conditions of cold (polar or subpolar) glaciers and ice
sheets indicate that such groundwater-induced temperature effects will be important in determining the overall temperature field in the ice, and thus will strongly influence the deformation
rate within the basal ice and basal sliding rates.
The incorporation of debris into cold-based glaciers may also be facilitated by the motion
of groundwater in a subglacial aquifer. Temporal variations in groundwater discharge will
104
Keith Echelmeyer
cause variations in the basal heat flux and migration of the melting isotherm. As the freezing
front moves to greater depths, the newly formed ice-rich debris may become part of the glacier
sole, and thus add new rock material to the glacier for transport downvalley. Motion of the
freezing front in relation to groundwater variations may also lead to sub-sole ice lens formation
in much the same manner as happens in permafrost (T. Osterkamp, personal communication).
Long-term temporal ice temperature variations observed by Clarke et al. (1984) may be
related to fluctuations in groundwater discharge as the surge bulge grows and propagates
downvalley on Trapridge Glacier.
ACKNOWLEDGEMENTS I thank Will Harrison for helpful comments on an earlier version
of this paper and the Lanzhou Institute of Glaciology and Cryopedology for help in the field.
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