Water flow through temperate glaciers

Abstract

Understanding water movement through a glacier is fundamental to several critical issues in glaci-ology, including glacier dynamics, glacier-induced floods, and the prediction of runoff from glacierized drainage basins. To this end we have synthesized a conceptual model of water movement through a temper-ate glacier from the surface to the outlet stream. Pro-cesses that regulate the rate and distribution of water input at the glacier surface and that regulate water movement from the surface to the bed play important but commonly neglected roles in glacier hydrology. Where a glacier is covered by a layer of porous, perme-able firn (the accumulation zone), the flux of water to the glacier interior varies slowly because the firn tempo-rarily stores water and thereby smooths out variations in the supply rate. In the firn-free ablation zone, in con-trast, the flux of water into the glacier depends directly on the rate of surface melt or rainfall and therefore varies greatly in time. Water moves from the surface to the bed through an upward branching arborescent net-work consisting of both steeply inclined conduits, formed by the enlargement of intergranular veins, and gently inclined conduits, spawned by water flow along the bottoms of near-surface fractures (crevasses). Engla-cial drainage conduits deliver water to the glacier bed at a limited number of points, probably a long distance downglacier of where water enters the glacier. Englacial conduits supplied from the accumulation zone are quasi steady state features that convey the slowly varying water flux delivered via the firn. Their size adjusts so that they are usually full of water and flow is pressurized. In contrast, water flow in englacial conduits supplied from the ablation area is pressurized only near times of peak daily flow or during rainstorms; flow is otherwise in an open-channel configuration. The subglacial drainage system typically consists of several elements that are distinct both morphologically and hydrologically. An up-glacier branching, arborescent network of channels in-cised into the basal ice conveys water rapidly. Much of the water flux to the bed probably enters directly into the arborescent channel network, which covers only a small fraction of the glacier bed. More extensive spatially is a nonarborescent network, which commonly includes cav-ities (gaps between the glacier sole and bed), channels incised into the bed, and a layer of permeable sediment. The nonarborescent network conveys water slowly and is usually poorly connected to the arborescent system. The arborescent channel network largely collapses during winter but reforms in the spring as the first flush of meltwater to the bed destabilizes the cavities within the nonarborescent network. The volume of water stored by a glacier varies diurnally and seasonally. Small, temper-ate alpine glaciers seem to attain a maximum seasonal water storage of 200 mm of water averaged over the area of the glacier bed, with daily fluctuations of as much as 20 –30 mm. The likely storage capacity of subglacial cavities is insufficient to account for estimated stored water volumes, so most water storage may actually occur englacially. Stored water may also be released abruptly and catastrophically in the form of outburst floods.

Full text

WATER FLOW THROUGH TEMPERATE GLACIERS
Andrew G. Fountain
1
Department of Geology
Portland State University
Portland, Oregon
Joseph S. Walder
U.S. Geological Survey
Cascades Volcano Observatory
Vancouver, Washington
Abstract. Understanding water movement through a
glacier is fundamental to several critical issues in glaci-
ology, including glacier dynamics, glacier-induced
floods, and the prediction of runoff from glacierized
drainage basins. To this end we have synthesized a
conceptual model of water movement through a temper-
ate glacier from the surface to the outlet stream. Pro-
cesses that regulate the rate and distribution of water
input at the glacier surface and that regulate water
movement from the surface to the bed play important
but commonly neglected roles in glacier hydrology.
Where a glacier is covered by a layer of porous, perme-
able firn (the accumulation zone), the flux of water to
the glacier interior varies slowly because the firn tempo-
rarily stores water and thereby smooths out variations in
the supply rate. In the firn-free ablation zone, in con-
trast, the flux of water into the glacier depends directly
on the rate of surface melt or rainfall and therefore
varies greatly in time. Water moves from the surface to
the bed through an upward branching arborescent net-
work consisting of both steeply inclined conduits,
formed by the enlargement of intergranular veins, and
gently inclined conduits, spawned by water flow along
the bottoms of near-surface fractures (crevasses). Engla-
cial drainage conduits deliver water to the glacier bed at
a limited number of points, probably a long distance
downglacier of where water enters the glacier. Englacial
conduits supplied from the accumulation zone are quasi
steady state features that convey the slowly varying water
flux delivered via the firn. Their size adjusts so that they
are usually full of water and flow is pressurized. In
contrast, water flow in englacial conduits supplied from
the ablation area is pressurized only near times of peak
daily flow or during rainstorms; flow is otherwise in an
open-channel configuration. The subglacial drainage
system typically consists of several elements that are
distinct both morphologically and hydrologically. An up-
glacier branching, arborescent network of channels in-
cised into the basal ice conveys water rapidly. Much of
the water flux to the bed probably enters directly into the
arborescent channel network, which covers only a small
fraction of the glacier bed. More extensive spatially is a
nonarborescent network, which commonly includes cav-
ities (gaps between the glacier sole and bed), channels
incised into the bed, and a layer of permeable sediment.
The nonarborescent network conveys water slowly and is
usually poorly connected to the arborescent system. The
arborescent channel network largely collapses during
winter but reforms in the spring as the first flush of
meltwater to the bed destabilizes the cavities within the
nonarborescent network. The volume of water stored by
a glacier varies diurnally and seasonally. Small, temper-
ate alpine glaciers seem to attain a maximum seasonal
water storage of ;200 mm of water averaged over the
area of the glacier bed, with daily fluctuations of as much
as 20–30 mm. The likely storage capacity of subglacial
cavities is insufficient to account for estimated stored
water volumes, so most water storage may actually occur
englacially. Stored water may also be released abruptly
and catastrophically in the form of outburst floods.
1. INTRODUCTION
The movement of water through glaciers is important
for scientific understanding and for immediate practical
applications. Water in glaciers profoundly affects glacier
movement by influencing the stress distribution at the
glacier bed and thereby the rate at which the ice slides
over the bed. This process is important for both alpine
glaciers [e.g., Iken and Bindschadler, 1986] and polar ice
streams [e.g., Alley et al., 1987; Echelmeyer and Harrison,
1990; Kamb, 1991]. The episodic surging (orders-of-
magnitude increase in speed) of some glaciers is evi-
dently due to temporal changes in subglacial hydrology
[Kamb et al., 1985]. Glacial outburst floods, a common
hazard in mountainous regions, result from the rapid
release of large volumes of water stored either within a
glacier or in a glacier-dammed lake [Bjo¨rnsson, 1992;
Haeberli, 1983; Walder and Costa, 1996]. Water from
glaciers is becoming increasingly important for hydro-
electric power generation [Benson et al., 1986; Lang and
Dyer, 1985]. Some hydropower projects in France [Hantz
and Lliboutry, 1983], Norway [Hooke et al., 1984], and
Switzerland [Be´zinge, 1981] have involved tapping water
from directly beneath a glacier.
The purpose of this paper is to present a conceptual
model of water flow through a glacier based on a syn-
1
Formerly at U.S. Geological Survey, Denver, Colorado.
Copyright 1998 by the American Geophysical Union. Reviews of Geophysics, 36, 3 /
August 1998
pages 299–328
8755-1209/98/97RG-03579
$15.00
Paper number 97RG03579
●299 ●

thesis of our current understanding. We have extended
the scope of previous reviews [Ro¨thlisberger and Lang,
1987; Lawson, 1993] by focusing on ways in which the
various components of the drainage system interact. As
part of the conclusions, we outline subjects that need
further investigation. This paper emphasizes temperate
alpine glaciers (glaciers at their melting point), but re-
sults from and implications for ice sheets are included
where appropriate. We do not discuss the hydrological
role of the seasonal snowpack, as there is a comparative
wealth of literature on the subject [e.g., Male and Gray,
1981; Bales and Harrington, 1995] and because the effect
of snow on glacier hydrology has recently been reviewed
[Fountain, 1996].
2. HYDROLOGY OF THE FIRN
AND NEAR-SURFACE ICE
At the end of the melt season the surface of a glacier
consists of ice at lower elevations in the ablation zone,
where yearly mass loss exceeds mass gain, and snow and
firn at upper elevations in the accumulation zone, where
yearly mass gain exceeds mass loss (Figure 1). Firn is a
transitional material in the metamorphosis of seasonal
snow to glacier ice. As we will discuss in section 2.1, the
presence or absence of firn has important implications
for subglacial water flow and for variations in glacial
runoff.
2.1. Accumulation Zone
The accumulation zone typically covers ;50–80% of
an alpine glacier in equilibrium with the local climate
[Meier and Post, 1962]. The near surface of the firn is
partially water saturated. The rate of water movement
through unsaturated firn depends on the firn’s perme-
ability and the degree of saturation [Ambach et al.,
1981], similar to percolation through unsaturated snow
[Colbeck and Anderson, 1982] and soil [e.g., Domenico
and Schwartz, 1990]. The near-impermeable glacier ice
beneath promotes the formation of a saturated water
layer at the base of the firn. Such water layers are
common in temperate glaciers [Schneider, 1994]. The
depth to water generally increases with distance upgla-
cier [Ambach et al., 1978; Fountain, 1989], as can be
expected from the general increase in snow accumula-
tion with elevation. High in the accumulation zone, the
water table may be as much as 40 m below the glacier
surface [Lang et al., 1977; Schommer, 1977; Fountain,
1989].
The hydrological characteristics of firn are fairly uni-
form between glaciers. Field tests of the hydraulic con-
ductivity (permeability with respect to water) of the firn
at five different glaciers [Schommer, 1978; Behrens et al.,
1979; Oerter and Moser, 1982; Fountain, 1989; Schneider,
1994] indicate a surprisingly narrow range of 1–5 310
25
m/s. This may reflect a uniform firn structure resulting
from a common rate of metamorphism of firn to ice.
Firn samples from South Cascade Glacier, Washington
State, had a porosity of 0.08–0.25 with an average of
0.15 [Fountain, 1989]. This average value is equal to the
value that Oerter and Moser [1982] found to be most
appropriate for their calculations of water flow through
the firn. Within the water layer, ;40% of the void space
is occupied by entrapped air [Fountain, 1989].
The depth to the water layer depends on the rate of
water input, the hydrological characteristics of the firn,
and the distance between crevasses, which drain the
Figure 1. Idealized longitudinal cross section of a temperate alpine glacier showing the important hydro-
logical components. In the accumulation zone, water percolates downward through snow and firn to form a
perched water layer on top of the nearly impermeable ice, and then flows from the perched water layer in
crevasses (open fractures). In the ablation zone, once the seasonal snow has melted, water flows directly across
the glacier surface into crevasses and moulins (nearly vertical shafts). Based on Figure 10.11 of Ro¨thlisberger
and Lang [1987]; copyright John Wiley and Sons Ltd.; reproduced with permission.
300 ●Fountain and Walder: WATER FLOW THROUGH GLACIERS 36, 3 / REVIEWS OF GEOPHYSICS

water from the firn [Lang et al., 1977; Schommer, 1977;
Fountain, 1989]. Over small areas (length scales of ;10
2
m) of a glacier both surface melt rate and firn perme-
ability are relatively uniform, and the depth to water is
controlled primarily by crevasse spacing. Water input to
the firn varies both seasonally and daily. Seasonal vari-
ations, ranging from no water input in winter to perhaps
as much as several tens of millimeters per day in sum-
mer, cause the thickness of the water layer to vary up to
several meters [Lang et al., 1977; Schommer, 1977, 1978;
Oerter and Moser, 1982]. Typically, the water table re-
sponds to melt and precipitation within a day or two
[Oerter and Moser, 1982; Schommer, 1977; Schneider,
1994], although diurnal variations have been occasion-
ally observed [e.g., Fountain, 1989].
Nye and Frank [1973] suggested that significant quan-
tities of meltwater may drain from the glacier surface to
the bed through intergranular veins in the ice. However,
observed veins are quite small (Figure 2) [see also Ray-
mond and Harrison, 1975], and water passage may often
be blocked by air bubbles [Lliboutry, 1971]; furthermore,
the permeability of the ice may actually be lower near
the ice surface than within the body of the glacier [Lli-
boutry, 1996]. Thus intergranular drainage is probably
negligible, and water drains from the firn into crevasses
that penetrate into the body of the glacier (Figure 3).
From a hydrological perspective the firn is a perched,
unconfined aquifer that drains into otherwise imperme-
able ice underneath via crevasses.
One important difference between a firn aquifer and
a typical groundwater aquifer is that the thickness and
extent of the firn continually change, whereas a ground-
water aquifer is relatively constant over time. Permeable
firn is lost as metamorphic processes transform firn to
ice, closing the passages between the void spaces and
rendering the matrix impermeable to water flow [Shum-
skii, 1964; Kawashima et al., 1993]. At the same time,
more firn is added as the seasonal snow ages and snow
Figure 2. Photomicrograph showing the veins in glacier ice formed at junctions where three grains of ice are
in contact. The grain at the center is ;1 mm across in its longest dimension. The photograph is courtesy of
C. F. Raymond.
Figure 3. Profile of the depth to the firn water
table on South Cascade Glacier on August 26, 1986
[after Fountain, 1989]. The solid curve is the snow
surface, the dotted curve is the top of the perched
water layer, and the dashed vertical lines represent
crevasses. The datum is arbitrary. Reprinted from
Annals of Glaciology with permission of the Interna-
tional Glaciological Society.
36, 3 / REVIEWS OF GEOPHYSICS Fountain and Walder: WATER FLOW THROUGH GLACIERS ●301

grains sinter together. This process raises the base level
of the water layer relative to its former position [Foun-
tain, 1989]. Firn thicknesses change from year to year
depending on the residual snow thickness at the end of
the summer.
The primary hydrological effects of the firn on glacier
hydrology are to temporarily store water, to delay its
passage to the interior of the glacier, and to smooth out
diurnal variations in meltwater input. Water storage in
the firn water layer delays the onset of spring runoff
from glaciers and delays the cessation of flow in the
autumn after surface melting has ended. For typical
values of firn porosity and water saturation the water
content of a perched layer 1 m thick is equivalent to that
of a layer of water ;0.09 m thick. Fountain [1989]
showed that at South Cascade Glacier the volume of
water stored in the firn is equivalent to ;12% of the
maximum volume of water stored seasonally by the
glacier [Tangborn et al., 1975]. In comparison, water
storage in the firn at Storglacia¨ren, Sweden [Schneider,
1994], accounted for 44% of the maximum seasonal
water storage estimated by O
¨stling and Hooke [1986].
Transit time through the firn depends on the speed of a
wetting front in unsaturated firn, ;0.25 m/h [Schneider,
1994], and the response time of the saturated layer at the
base. For example, if the water table is 10 m below the
firn surface, the transit time to the water table is ;40
hours (longer if a seasonal snow layer is present). Transit
time through the saturated water layer to crevasses de-
pends on the distance between the crevasses and on the
slope of the water surface. Considering both percolation
to the firn water table and flow in the water table before
exiting into a crevasse, a parcel of water commonly takes
;10–160 hours. In comparison, transit times in the body
of the glacier are commonly no more than a few hours
for moderate-sized temperate glaciers [e.g., Hock and
Hooke, 1993; Fountain, 1993; Nienow, 1994]. Because
the crevasses are not uniformly spaced and the thickness
of the firn increases with elevation, the transit time
through the firn to the interior is spatially variable with
the net effect of smoothing diurnal variations in melt-
water input to the glacier. We believe that water passage
through the snow and firn of the accumulation zone is
the source of the slowly varying component (base flow)
of glacial runoff.
2.2. Ablation Zone
In the ablation zone the seasonal snowpack retains
meltwater and thus retards runoff during the early part
of the melt season [Fountain, 1996]. After the seasonal
snow has melted, revealing glacier ice, channels develop
on the glacier surface that drain meltwater directly into
crevasses and moulins (naturally occurring vertical tun-
nels) [Stenborg, 1973]. In the absence of the seasonal
snowpack the delay for rainwater and meltwater to enter
the body of the glacier is brief, for example, no more
than 40 min at Haut Glacier d’Arolla, Switzerland (M. J.
Sharp, written communication, 1996). The presence of
pools of water and surface streams in the ablation zone
indicates the relative impermeability of the ice. The
near-surface ice is not completely impermeable, how-
ever. Water may be transported along grain boundaries
in veins, which are enlarged by solar radiation. This
process is limited to the uppermost few tens of centime-
ters in the ice owing to the limited penetration of short-
wave solar radiation [Brandt and Warren, 1993]. The
permeability of the near-surface ice may account for
small (several centimeters) fluctuations of water levels in
boreholes that do not connect to a subglacial hydraulic
system [Hodge, 1979; Fountain, 1994]. However, the wa-
ter flux through this near-surface layer is almost cer-
tainly negligible compared with the flow in supraglacial
streams.
Where the ice is moving, melted surface ice is replen-
ished by ice emerging from the interior of the glacier
[Meier and Tangborn, 1965], and a deeply weathered
crust, from the effects of solar radiation, does not de-
velop. In contrast, in regions of “dead ice,” where the ice
is not replenished, the near-surface ice can become
weathered and quite permeable. Observations of water
level fluctuations in boreholes in dead ice indicate a
saturated water layer several meters thick [Larson, 1977,
1978]. On the basis of pump tests the hydraulic trans-
missivity Tof the permeable surface layer is ;8310
25
m
2
/s [Larson, 1978]. If the perched water table thickness
is b52 m, then the hydraulic conductivity k5T/bof
the near-surface ice is ;4310
25
m/s. This value is
within the range given for firn, but the correspondence is
probably coincidental.
In summary, the near-surface processes in the snow-
free ablation zone introduce little delay in the routing of
water into the body of the glacier. Moreover, the water
flux into the glacier is greater in the ablation zone,
compared with the accumulation zone, because the melt
rate is greater owing to both the lower albedo of ice as
compared with snow and the warmer air temperatures at
the lower elevations. Consequently, both the mean daily
flux of meltwater and the variability in the flux of melt-
water are greater in the ablation zone than in the accu-
mulation zone.
3. WATER MOVEMENT THROUGH THE BODY
OF A GLACIER (ENGLACIAL HYDROLOGY)
For temperate glaciers, nearly all rain and surface
meltwater enters the body of the glacier through cre-
vasses and moulins [e.g., Stenborg, 1973]. As was dis-
cussed in section 2.2, the flux through the veins in the ice
is probably negligible. Crevasses are the most important
avenue for water because they are more numerous than
moulins and are found over the entire glacier, whereas
moulins are generally restricted to the ablation zone.
Water-filled crevasses are not common, indicating that
they efficiently route water into the body of the glacier.
This conclusion is supported by Stenborg’s [1973] work
302 ●Fountain and Walder: WATER FLOW THROUGH GLACIERS 36, 3 / REVIEWS OF GEOPHYSICS

showing that moulins develop from crevasses. Neither
the nature of hydraulic links between crevasses and the
body of the glacier nor the formation of such links is well
understood. We attempt to address these topics below.
Water flows englacially (through the body of a gla-
cier) via ice-walled conduits. The mechanics of steady
flow in englacial conduits have been described theoret-
ically by Ro¨thlisberger [1972] and Shreve [1972]. As with
conduits at the glacier bed, discussed in section 4, en-
glacial conduits exist if the tendency for closure, from
the inward creep of ice, is balanced by the melt enlarge-
ment resulting from the energy dissipated by flowing
water. Shreve [1972] argued that englacial conduits
should form an upward branching arborescent network,
with the mean flow direction oriented steeply downgla-
cier, as determined by the gradient of the total potential
(gravity and ice pressure) driving the flow (Figure 4).
Empirical results based on the dispersion and travel time
of numerous tracer injections in crevasses support the
arborescent-network hypothesis [Fountain, 1993].
There are few data bearing on the distribution and
geometry of englacial conduits or on englacial water
pressures and flow rates. Most of our information comes
from boreholes drilled to the glacier bottom using a jet
of hot water [Taylor, 1984]. About half of all such bore-
holes drain before the glacier bed is reached, indicating
that many boreholes intersect englacial passages [En-
gelhardt, 1978; Hantz and Lliboutry, 1983; Fountain,
1994; Hooke and Pohjola, 1994]. Measurements of water
level, water quality, and flow direction in boreholes [e.g.,
Sharp et al., 1993b; Meier et al., 1994] and measurements
of tracers injected into boreholes [e.g., Hooke et al.,
1988; Hock and Hooke, 1993] strongly suggest the pres-
ence of englacial conduits.
A number of direct measurements of englacial pas-
sages exist. Hodge [1976] found englacial voids with
typical vertical extents of ;0.1 m, and Raymond and
Harrison [1975] found small, arborescent, millimeter
scale passages, but whether these voids or passages were
part of an active hydraulic system was unclear. (Void is
used here to mean a water-filled pocket in the ice, which
may or may not be part of the englacial hydraulic system.
Isolated voids are known to exist.) Englacial conduits
have been observed where they debouch into subglacial
tunnels (Figure 5) and where they intersect boreholes
(Figure 6). Video cameras lowered into boreholes by
Pohjola [1994] and by Harper and Humphrey [1995] re-
vealed multiple englacial voids through nearly the entire
ice thickness. Voids that intersected opposite sides of
the borehole wall were interpreted as englacial conduits;
typically, one or two such features were encountered in
Figure 4. Fluid equipotentials (dotted curves) and a hypo-
thetical network of arborescent englacial channels [after
Shreve, 1985]. Reproduced with permission of the publisher,
the Geological Society of America, Boulder, Colorado USA.
Copyright @ 1985 Geological Society of America.
Figure 5. Water pouring from an englacial conduit at the base of South Cascade Glacier. The englacial
conduit intersects a subglacial tunnel accessible from the glacier margin. Sunglasses are shown for scale.
36, 3 / REVIEWS OF GEOPHYSICS Fountain and Walder: WATER FLOW THROUGH GLACIERS ●303

each borehole, with diameters typically ;0.1 m. Pohjola
[1994] determined that water was flowing in a few en-
glacial conduits and estimated a flow speed in one of
;0.01–0.1 m/s, the same range estimated by Hooke et al.
[1988] using dye tracers. Most conduits seen by borehole
video seemed to be nearly horizontal, although Harper
and Humphrey mention one plunging at an angle of
;658. Despite obvious sampling problems, which include
small sample size, biased sampling of conduit orienta-
tions from vertically oriented boreholes, and a borehole
location largely restricted to the ablation zone, several
conclusions can be drawn. First, glaciologists need to
consider how borehole water levels and tracer injections,
typically used to investigate subglacial hydraulic condi-
tions, may be affected by englacial hydraulic connections
[Sharp et al., 1993b]. Second, the near-horizontal slope
of many conduits needs to be reconciled with the rela-
tively steep plunge expected from theoretical consider-
ations [Shreve, 1972].
3.1. Origin of Englacial Passages
We suggest that the near-horizontal englacial con-
duits encountered in boreholes may originate from the
action of water flowing along the bottom of crevasses.
Some support for this notion comes from the borehole-
video observations of Pohjola [1994], who found that
englacial passages were usually in close proximity to
bands of blue (i.e., bubble free) ice and who suggested
that these bands originated from water freezing in cre-
vasses. Harper and Humphrey [1995] also noticed that
englacial passages and blue-ice bands tended to occur
together on the walls of boreholes.
We conjecture that water flowing along the base of a
crevasse either enters relatively steeply sloping, enlarged
veins that form a network of arborescent passages
[Shreve, 1972] or enters the microfractures created dur-
ing crevasse formation that connect to other crevasses.
Water flowing along the base of the crevasse will melt
the walls and tend to widen and deepen the crevasse
(Figure 7a). Melting occurs where water is in contact
with the ice, such that the crevasse surface in contact
with the flowing water the longest, the crevasse bottom,
will melt the most. This scenario should also apply to
water flowing along the glacier margin (Figure 7b). Typ-
ically, water from snowmelt and rainfall on adjacent
slopes flows under the edge of a glacier, exploiting gaps
between the thinner ice along the glacier margin and the
bedrock. Water quickly descends until the gaps no
longer connect and the water forms a stream at the
ice-bedrock interface. The stream melts the ice, causing
the channel to descend along the sloping bedrock.
The rate of downcutting by a crevasse-bottom stream
may be crudely estimated if we assume that the cross
section of the crevasse bottom maintains a semicircular
geometry of radius R(Figure 8). Thus downcutting
proceeds without widening. The local melt rate normal
to the channel wall is then d
˙cos u, where d
˙is the melt
rate at the bottom, that is, the downcutting rate. The
average melt rate ^m˙ &normal to the channel surface is
then given by
^m˙ &51
p
E
2p/2
p/2
d
˙cos udu5
S
2
p
D
d
˙(1)
Figure 6. An englacial conduit (black triangular void at right) intersecting a vertical borehole. Note the
ripples on the water surface in the borehole caused by water flowing from the conduit, which has a diameter
of ;0.1 m. This video image from Storglacia¨ren, Sweden, is courtesy of V. Pohjola.
304 ●Fountain and Walder: WATER FLOW THROUGH GLACIERS 36, 3 / REVIEWS OF GEOPHYSICS

Further assuming that all energy dissipated by the flow-
ing water actually causes melting, we find
^m˙ &5QrwgS
prihiwR(2)
where Qis the water flux, r
w
is the density of water, r
i
is
the density of ice, gis the acceleration due to gravity, S
is the slope of the crevasse bottom, and h
iw
is the latent
heat of melting. The hydraulics are reasonably described
by the empirical Manning equation, which we write as
Q5p
2n
˜
R8/3S1/ 2 (3)
where n
˜
is the roughness. Combining (1) through (3), we
can relate d
˙to Qand Sby
d
˙51
2
S
p
2n
˜
D
3/8
S
rw
ri
DS
g
hiw
D
S19/16Q5/8 (4)
Using r
w
510
3
kg/m
3
,r
i
59310
2
kg/m
3
,g59.8
m/s
2
,h
iw
53.35 310
5
J/kg, and n
˜
50.01 s/m
1/3
(appropriate for a smooth conduit), we have calculated
values of d
˙for the case S50.1 (Table 1). This value of
Sis appropriate for crevasses trending longitudinally
along the glacier and therefore represents a plausible
upper bound.
The values in Table 1 indicate that even very modest
flow rates can cause crevasse-bottom streams to cut
down at a rate of a few to a few tens of meters per year.
(Note that to give downcutting rates relative to the
glacier surface, tabulated rates must be corrected for the
vertical component of ice velocity.) These rates are many
orders of magnitude greater than the rate at which a
water-filled crevasse deepens owing purely to the weight
of the water and the fracture-mechanical properties of
the ice [Weertman, 1971]. Furthermore, the downcutting
rate increases with Q, suggesting a possible mechanism
for stream capture; in regions of complex, crosscutting
crevasses those hosting relatively large water fluxes may
cut down through others hosting small fluxes.
We envisage the following scenario for the evolution
of a crevasse-bottom stream: As the stream cuts down
into the glacier, the creep of ice tends to pinch off the
crevasse above the flowing water. Eventually, the chan-
nel becomes isolated from the crevasse except for rare,
near-vertical passages that convey water from the cre-
vasse to the channel (Figure 7a). The stream ceases to
descend once the rate of closure equals the rate of
melting at the bottom of the channel (downcutting)
because it becomes fully enclosed in ice and melting
occurs equally on all walls.
To estimate the ultimate depth to which a crevasse-
bottom stream can cut down, we idealize the “mature”
channel as having a circular cross section of radius Rand
assume that the melt rate is exactly balanced by the rate
of ice creep. The channel will be flowing full but with
zero pressure head (atmospheric pressure), like the
“gradient conduit” discussed by Ro¨thlisberger [1972]. Us-
ing Nye’s [1953] result for conduit closure, the balance
between melting and closure is given by
rwgQS
2prihiwR2ue5R
S
pi
nA
D
n
(5)
where nand Aare flow-law constants [Nye, 1953], u
e
is
the ice emergence velocity, i.e., the vertical component
of ice velocity, measured positive upwards, and p
i
is the
ice pressure at the depth, D
MAX
at which the channel
ceases to downcut. We take p
i
5r
i
gD
MAX
and rear-
range (5) to write
DMAX 5nA
rig
F
rwgQS
2prihiwR22ue
R
G
1/n
(6)
Using (3) to eliminate R,
Figure 7. Qualitative depiction of the evolution of an engla-
cial conduit from its origin (a) as a crevasse-bottom stream or
(b) as a glacier-margin stream. The stream cuts down because
melting occurs only where water is in contact with ice.
Figure 8. Idealized cross-sectional geometry of a stream
flowing at the base of a crevasse. The rate at which the stream
melts its way downward into the ice is calculated assuming that
the crevasse “tip” is semicircular and that the stream cuts
vertically downward.
36, 3 / REVIEWS OF GEOPHYSICS Fountain and Walder: WATER FLOW THROUGH GLACIERS ●305

DMAX 5
S
nA
rig
DFS
rwg
2prihiw
DS
p
2n
˜
D
3/4
Q1/4S11/8
2
S
p
2n
˜
D
3/8
ueS3/16Q23/8
G
1/n
(7)
The “equilibrium” depth D
MAX
is weakly dependent on
Q, although, of course, the time required for the channel
to cut to this depth decreases as Qincreases. For very
small discharges the apparent value of D
MAX
is negative.
Physically, this means that a very small crevasse-bottom
stream cannot cut down and simply remain at the base of
the crevasse, the depth of which is governed by the
rheological properties of ice [Paterson, 1994]. Calculated
values of D
MAX
given in Table 1 are quite large, perhaps
reflecting an overestimate of A(which decreases as the
water content of the ice increases [Lliboutry, 1983], un-
derestimate of n
˜
, overestimate of S, or some effect of a
possibly noncircular channel cross section [cf. Hooke,
1984; Hooke and Pohjola, 1994].
In arriving at the expression in (7) for D
MAX
we
assumed steady flow in the channel. However, for an
alpine glacier a constant or slowly varying discharge
cannot exist unless there is a storage mechanism that can
maintain a supply of water. We conjecture that channels
supplied with water from the ablation zone may be able
to descend deeper than those in the accumulation zone
because of the large daily variability in water flux. For
channels supplied from the accumulation zone they
come closer to the ideal case (equation (7)) because the
firn filters out daily water fluctuations and provides a
water storage reservoir, reducing longer-term variations.
In neither case, however, do the channels reach a true
equilibrium position because of the variations in water
supply.
3.2. Synopsis and Implications
Our view of the englacial drainage system is shown in
Figure 9. Subhorizontal channels, spawned by the water
flow in crevasse bottoms, are connected by either steeply
plunging passages, formed by the enlargement of inter-
granular passages [Shreve, 1972], or microfractures be-
tween crevasses. Marginal channels also form under the
edge of the glacier where water collects from the valley
walls; these channels may eventually connect to channels
spawned from crevasses. We infer that surface water
reaching the bed is generally shifted downglacier so that
it extends the influence of the firn over a larger subgla-
cial area than it covers at the surface. This view is
supported by the observations of Iken and Bindschadler
[1986] at Findelengletscher, Switzerland, where glacier-
surface streams, which exhibited marked diurnal varia-
tions, flowed into crevasses near boreholes drilled to the
bottom of the glacier. Subglacial water pressure varia-
tions, as indicated by fluctuations in water level, did not
correlate with the diurnal streamflow variations but
rather correlated with the slower variation of meltwater
input from a snow cover upglacier. Lateral shifts in
surface to bed water routing are supported by the results
of an experiment whereby a tracer injected at the bottom
of a borehole drained to one outlet stream while a tracer
injected into a crevasse adjacent to the borehole ap-
peared in a different outlet stream [Fountain, 1993].
The englacial hydraulic system supplied from the
ablation zone should develop more quickly and to a
much greater extent than that supplied from the accu-
mulation zone. As the snow line moves up the glacier
Figure 9. Geometry of hypothetical englacial drainage sys-
tem, comprising both gently plunging conduits spawned by
crevasse-bottom streams and steeply plunging “Shrevian” con-
duits formed where water exploits veins in the ice.
TABLE 1. Calculated Values of the Rate of Downcutting and Equilibrium Depth for Englacial Conduits for Several Values
of Vertical Ice Velocity u
e
Water Flux,
10
23
m
3
/s Rate of Channel
Incision, m/yr
Equilibrium Channel Depth D
MAX
,m
u
e
521 m/yr u
e
50u
e
51 m/yr u
e
55 m/yr
1 2.9 268 210 zzz zzz
5 8.1 268 240 204 zzz
10 12 275 255 231 zzz
50 34 300 291 283 238
100 52 317 308 304 276
The value u
e
is positive in the ablation zone. The tabulated downcutting rate does not take into account ice creep and therefore applies strictly
only near the glacier surface.
306 ●Fountain and Walder: WATER FLOW THROUGH GLACIERS 36, 3 / REVIEWS OF GEOPHYSICS

during the summer, ice is exposed in the ablation zone.
The combination of lower albedo for ice, compared with
snow, and warmer air temperatures lower on the glacier
increases the water flux into the ablation zone compared
to the accumulation zone. We therefore expect englacial
conduits receiving water from the ablation zone to be
more developed compared to the conduits receiving
water from the accumulation zone. The common occur-
rence of moulins in the ablation zone rather than in the
accumulation zone probably reflects the difference in
drainage development between the two zones. The en-
glacial drainage system must be highly dynamic, with
channels being continuously reoriented by differential
shear as ice is advected downstream or severed in ice-
falls. Channel segments must frequently close off be-
cause their water supply is lost to other channels by
drainage capture or because their connection to the
glacier surface is interrupted neither by refreezing dur-
ing the winter or by ice creep.
Table 1 indicates that for ice thicknesses of 200 m or
less, descending englacial channels may reach the bot-
tom of the glacier to become subglacial conduits. This
process provides a mechanism to route water from the
glacier surface to the bed and a process by which new
subglacial conduits are formed. We do not expect the
englacial conduits to descend much below 300 m except
in unusual circumstances; therefore subglacial conduits
found below 300 m are probably formed from some
other mechanism.
Our conception of the englacial drainage system has
significant implications for overdeepened regions of al-
pine glaciers. An overdeepening is a topographic feature
that would form a closed depression, and likely host a
lake, if the glacier were removed [e.g., Hooke, 1991].
Three borehole studies at Glacier d’Argentie`re, France
[Hantz and Lliboutry, 1983], Storglacia¨ren [Hooke and
Pohjola, 1994], and South Cascade Glacier [Hodge, 1976,
1979; Fountain, 1994] have involved drilling to the gla-
cier bed in overdeepened areas. In all three cases the
drilling was done in the ablation zone, and certain qual-
itative features were common:
1. Many boreholes encountered englacial conduits.
2. Once boreholes reached the bed, water levels
remained close to the ice overburden pressure and did
not exhibit diurnal fluctuations; thus there was no indi-
cation of low-pressure conduits within the overdeepen-
ing.
3. Low-pressure conduits seemed to exist near the
valley sides.
These observations seem to contradict our conclusion
that englacial conduits in the ablation zone should nor-
mally be efficient at conducting water to the bed. A
resolution of this apparent contradiction is possible,
however, if we consider the peculiar effect of the over-
deepening on the englacial conduits.
Figure 10 shows a section of a subhorizontal conduit,
one that has developed from a crevasse-bottom stream,
that has cut down to the lip of an overdeepening. The
conduit is now “pinned” at the downstream end and will
evolve into a conduit approximately paralleling the ice
surface. In that configuration the conduit is full of water,
so melting occurs equally on all surfaces, and downcut-
ting ceases. This conclusion holds for a single continuous
conduit or for a network of conduits. We therefore
suggest that in overdeepened areas the movement of
water from the glacier surface to the bed will be re-
stricted, as will the development of conduits at the
glacier bed. Subglacial conduits can be developed from
water percolating under the glacier margins, but such
conduits will also be pinned by the lip of the overdeep-
ening. We expect that subglacial conduits will be most
commonly observed to pass around overdeepenings near
the valley walls, as was suggested by Lliboutry [1983].
4. SUBGLACIAL HYDROLOGY
The modern study of subglacial hydrology can plau-
sibly be traced to Mathews [1964], who measured water
pressure at the end of a shaft that reached the base of
South Leduc Glacier, Canada, from a mine beneath the
glacier. Mathews observed that water pressure was gen-
erally higher in winter than in summer, a situation that
turns out to be common, and that abrupt increases in
water pressure were correlated with periods of rapid
ablation or heavy rain, reflecting the efficient hydraulic
connections between the glacier surface and bed. These
general conclusions were supported by investigators who
reached the bed of Gornergletscher, Switzerland [Be´z-
Figure 10. Longitudinal cross section of a glacier showing a
hypothetical englacial conduit descending into an overdeep-
ened region of a glacier. The conduit becomes pinned once it
reaches the bed at the downstream margin of the overdeepen-
ing. Deepening upstream of this point continues until the
channel becomes water filled.
36, 3 / REVIEWS OF GEOPHYSICS Fountain and Walder: WATER FLOW THROUGH GLACIERS ●307

inge et al., 1973] and Glacier d’Argentie`re [Vivian and
Zumstein, 1973] in connection with hydropower devel-
opments. Vivian and Zumstein [1973] also showed that
the strong diurnal pressure fluctuations observed during
the melt season were absent during winter.
Iken [1972] measured water pressure in moulins in the
subpolar White Glacier and observed large diurnal vari-
ations. Subsequently, various investigators developed
techniques to drill to the glacier bed and used the water
level in boreholes as a piezometric measure of subglacial
water pressure. The first systematic borehole studies of
the subglacial drainage system were done at South Cas-
cade Glacier [Hodge, 1976, 1979], Blue Glacier, Wash-
ington State, United States [Engelhardt, 1978; Engelhardt
et al., 1978], and several Swiss glaciers [Ro¨thlisberger et
al., 1979]. In a minority of the boreholes in all of these
glaciers, the water level dropped as soon as the drill
reached the glacier bed. Water levels in these boreholes
fluctuated diurnally but were usually not closely corre-
lated. In a majority of the boreholes the water level
remained high and nearly constant, commonly at a level
corresponding to a water pressure greater than local ice
overburden pressure, even after the drill reached the
bed; a drop in the water level, if it occurred at all, was
delayed for several days to a few weeks. Such experi-
ences with borehole water levels seem to be ubiquitous.
Glaciologists commonly describe the first sort of bore-
hole as “connected” to the subglacial drainage system
and, assuming that the borehole volume is small com-
pared with the volume of accessible subglacial water,
treat borehole water level as a manometric measure of
water pressure at the bed. The second sort of borehole is
termed “unconnected” and cannot be used as a manom-
eter, as the hole volume is probably large compared with
the volume of accessible subglacial water. Recently,
Waddington and Clarke [1995] and Murray and Clarke
[1995] have shown that valuable information can be
collected from unconnected boreholes when the top of
the borehole can be sealed, in their case, by freezing, and
water pressure is measured directly at the bed, without
relying on the manometric principle.
4.1. Components of the Subglacial Drainage System
Water emerges at the glacier terminus in a small
number of conduits incised into the basal ice, and it is
tempting to suppose that these conditions prevail sub-
glacially as well. Reality is probably much more compli-
cated. There is presently broad agreement among glaci-
ologists that water flows at the glacier bed in one or both
of two qualitatively different flow systems (Figure 11),
commonly termed “channelized” and “distributed.” This
terminology is problematic because, as we shall point
out, the distributed system often consists in part of what
common sense dictates be called channels. We suggest
that it makes more sense to refer to “fast” and “slow”
drainage systems [Raymond et al., 1995]. In the fast
system, relatively small changes in total system volume
produce relatively large changes in discharge. The fast
system has a relatively low surface-to-volume ratio, cov-
ers a very small fraction of the glacier bed, and com-
prises an arborescent (converging flow) network of con-
duits, similar to a subaerial stream network. In the slow
system, in contrast, relatively large changes in total sys-
tem volume produce only small changes in discharge.
The slow system has a relatively large surface-to-volume
ratio, covers a relatively large fraction of the glacier bed,
is nonarborescent, and may involve a variety of compli-
cated flow paths at the glacier bed.
The distinction between fast and slow flow systems
has been inferred from variations in borehole water
levels, from the travel time and dispersion of tracers
injected into glaciers, and from measurements of water
flux and chemistry in streams flowing from glaciers.
Under any particular glacier, part of the bed may host a
fast drainage system while the rest hosts a slow drainage
system, with transitional zones linking the two. Further-
more, the basal drainage system in any particular region
may switch from one configuration to the other in re-
sponse to perturbations in meltwater input.
4.1.1. Fast drainage system (Ro¨ thlisberger chan-
nels). An isolated, water-filled void in a glacier will
tend to be closed by inward ice flow unless the water
pressure p
w
equals the ice overburden pressure p
i
[Nye,
1953]. Englacial or subglacial channels may exist with
p
w
,p
i
if the flowing water dissipates enough energy as
heat to melt the ice and thereby keep the channel open
(Figure 12a). Ro¨thlisberger [1972] presented the first
reasonably complete analysis of the hydraulics and ther-
modynamics of steady flow in a subglacial channel, and
glaciologists now commonly refer to such channels as
“Ro¨thlisberger” or “R” channels. Ro¨thlisberger as-
sumed that subglacial channels have a semicircular cross
section and that the flowing water must gain or lose
energy so as to remain at the pressure-melting temper-
ature. He derived the following differential equation for
steady flow in a channel:
Figure 11. Idealized plan view of (a) an arborescent hydrau-
lic (fast) system composed of channels and (b) a nonarbores-
cent hydraulic (slow) system.
308 ●Fountain and Walder: WATER FLOW THROUGH GLACIERS 36, 3 / REVIEWS OF GEOPHYSICS

S
dF
ds
D
p11
2a
S
dF
ds
D
pdpw
ds 5bQ2qpe
n(8)
where (Figure 12b) the coordinate sincreases in an
upglacier direction along the water flow path, zis the
bed elevation relative to an arbitrary datum, F5p
w
1
r
w
gzis the total hydraulic potential, Qis the discharge,
r
w
is the density of water, gis the acceleration due to
gravity, and p
e
5p
i
2p
w
is the effective pressure in the
channel. The term multiplied by areflects the pressure-
melting effect, and binvolves channel roughness and ice
rheology. The exponents pand qare both positive and
depend weakly on the empiricism chosen to describe
turbulent flow in the channel [Lliboutry, 1983]. The
exponent n'3 follows from empirical ice rheology.
Ro¨thlisberger [1972] showed that the form of (8) im-
mediately leads to an important conclusion, most easily
seen for the case in which the local channel inclination
(u5sin
21
(dz/ds)) equals 0, in which case, F5p
w
and
(8) becomes
dpw
ds 5
S
b
12a
D
1/~11p!
Q2q/~11p!pe
n/~11p!(9)
The greater the discharge, the smaller the pressure gra-
dient; accordingly, if we envisage two nearby channels
and integrate (9) over some finite distance x, the channel
carrying the greater discharge will be at a lower pressure
than the other. Ro¨thlisberger concluded that if hydraulic
connections between channels exist, the largest channels
should capture the drainage of the smaller ones and an
arborescent drainage network should develop. Shreve
[1972] reached the same conclusion by a slightly differ-
ent line of reasoning.
Ro¨thlisberger’s [1972] analysis applies strictly only for
steady flow. This is certainly a poor approximation for
channels fed from the ablation area, in which case,
temporal variations of discharge are commonly large,
and channels probably flow full of water only a small
fraction of the time. The steady flow approximation is
probably reasonable for channels fed from the accumu-
lation area, but even in this case, channels may not be
full of water. Weertman [1972] and Hooke [1984] both
assessed theoretically the likely extent of open-channel
flow in semicircular channels and predicted that open-
channel flow under a constant discharge will occur if the
ice thickness H
i
is less than a critical value H
crit
5const
Q
a
(dF/ds)
b
, with a'0.07–0.08 and b'0.46. Hooke
concluded that open-channel flow should be common
beneath steeply sloping alpine glaciers less than a few
hundred meters thick. Data to assess this conclusion are
sparse. Fountain [1993] and Kohler [1995] inferred from
analysis of tracer injections that while open-channel flow
probably did occur, it was restricted to very thin ice near
the glacier terminus (i.e., in the ablation area) and thus
not nearly as extensive as Hooke’s calculations would
have predicted.
Application of (8) to predict measured subglacial
water pressures (as indicated by the water level in bore-
holes drilled to the bed) has been problematic. Predicted
values of p
w
are commonly much less than measured
values [Engelhardt, 1978; Hooke et al., 1990; Fountain,
1994]. Lliboutry [1983] argued that this primarily re-
flected an inadequate description of the channel-closure
physics and that the correction entailed considering the
complicated stress state created by glacier sliding past
bedrock obstacles, as well as a proper choice of ice
rheology parameters. Hooke et al. [1990] suggested that
the discrepancy between measured and predicted p
w
could be resolved if R channels are actually broad, and
they proposed an ad hoc modification to Ro¨thlisberger’s
[1972] analysis in line with their idea about channel
shape. Predicted water pressures for the modified chan-
nel shape were in good agreement with the observed
borehole water pressures at Storglacia¨ren. Finite ele-
ment modeling of R channel evolution in response to
variable water input [Cutler, 1998] supports Hooke et
al.’s conjecture about channel shape.
In considering the discrepancy between predicted and
measured p
w
it is worth reflecting on whether borehole
water level should even be considered as a piezometric
Figure 12. Schematic of a Ro¨thlisberger channel [after
Ro¨thlisberger, 1972]. (a) The channel tends to close by creep
of ice at overburden pressure p
i
but tends to be opened by
melting as the flowing water (pressure p
w
) dissipates energy.
(b) In general, the channel is inclined at some angle to the
horizontal (the xaxis). Reprinted from the Journal of Gla-
ciology with permission of the International Glaciological
Society.
36, 3 / REVIEWS OF GEOPHYSICS Fountain and Walder: WATER FLOW THROUGH GLACIERS ●309

measurement of water pressure in an R channel. Bore-
hole water level does not reflect basal water pressure if
water enters the borehole either at the glacier surface or
englacially. Surface runoff can be diverted from a bore-
hole, but the same is not true for water entering engla-
cially, and there is a substantial body of evidence that
boreholes do commonly intersect englacial channels
during drilling. Moreover, although R channels have
certainly been seen at the margins of glaciers (Figure
13), there is no unequivocal evidence that a borehole has
ever intersected an R channel. If a borehole intersects a
part of the basal hydraulic system that drains to a sub-
glacial channel, then borehole water levels will necessar-
ily reflect p
w
greater than that in the channel [cf. En-
gelhardt, 1978]. Until a borehole can be drilled that
unambiguously intersects a subglacial channel and that is
not adversely affected by englacial water input, it is
perhaps premature to discount the quantitative accuracy
of (8). Several investigators seem to have drilled bore-
holes that came tantalizingly close to basal channels.
Water level in borehole U of Engelhardt et al. [1978] fell
to the glacier bed a few days after the borehole was
completed, and a sounding float lowered into the bore-
hole did not stop at the bottom of the borehole but ran
out along some sort of basal passage as far as it was
allowed to go. Hantz and Lliboutry [1983], Fountain
[1994], and Hubbard et al. [1995] found that in a few
boreholes, there were large diurnal pressure fluctua-
tions, with minimum values of p
w
close to atmospheric
pressure, and concluded that these boreholes were effi-
ciently connected to R channels.
Studies by Fountain [1994] and by Hubbard et al.
[1995] at two different glaciers yielded intriguingly sim-
ilar results bearing on the hydraulic connection between
subglacial channels and the surrounding, presumably
slow basal drainage system. At both glaciers, water level
measurements in arrays of boreholes in the ablation area
indicated the existence of a zone, elongated along the ice
flow direction but only a few tens of meters wide, in
which basal water pressure fluctuated greatly and com-
monly fell to atmospheric values. To either side of this
zone, basal water pressure was generally high and fluc-
tuated relatively little. A plausible interpretation is that
an R channel existed and was efficiently connected to
the ablation-zone input, whereas the adjacent (slow)
hydraulic system was poorly connected to the channel
and was fed from farther upglacier. We will elaborate on
this idea in our discussion of the temporal evolution of
the basal drainage system in section 5.
4.1.2. Slow drainage system. The slow drainage
system comprises several morphologically distinct flow
pathways. Most of the discharge in the slow system
moves through cavities and subglacial sediment. A wide-
spread, thin water film also forms part of the slow
system; this film accommodates little water flux but may
affect the glacier sliding speed as well as water chemistry
[Hallet, 1976, 1979].
4.1.2.1. Subglacial cavities: A subglacial cavity
forms where sliding ice separates from the glacier bed
(Figure 14). Large cavities beneath thin ice are some-
times accessible from the glacier margin [e.g., Anderson
et al., 1982]. Cavity formation is favored by rapid sliding
and high bed roughness [Nye, 1970]. Lliboutry [1965,
1968] was the first to propose that cavitation played a
critical role in glacier sliding. In later papers [Lliboutry,
1976, 1978, 1979] he argued that there were two types of
Figure 13. Subglacial conduit incised into ice near the margin of South Cascade Glacier. The height of the
conduit is ;1.5 m. Note three important features: The ice is resting on unconsolidated sediments, the channel
is not full of water, and the cross-sectional shape is flattened instead of semicircular.
310 ●Fountain and Walder: WATER FLOW THROUGH GLACIERS 36, 3 / REVIEWS OF GEOPHYSICS

cavities: “autonomous” cavities containing stagnant
meltwater hydraulically isolated from the subglacial
drainage system and “interconnected” cavities linked to
R channels. Lliboutry [1976] also proposed that sliding
speed should depend on the effective pressure p
e
in a
network of R channels and interconnected cavities.
Walder and Hallet [1979], Hallet and Anderson [1980],
and Sharp et al. [1989] mapped small-scale geomorphic
features on recently deglaciated carbonate bedrock sur-
faces and concluded that widespread cavitation must
have occurred beneath some small alpine glaciers. Steep
concavities downglacier of local bedrock knobs or ledges
were often deeply scalloped and similar in appearance to
the surfaces created by turbulent water flow over lime-
stone in caves and subaerial environments. Because
these concavities, which covered 20–50% of the degla-
ciated surfaces, could not hold water subaerially, they
could have experienced extensive dissolution only if wa-
ter had been confined over them, as in subglacial cavi-
ties. In every one of the mapped examples the overall
basal drainage system was nonarborescent.
The hydraulics of steady flow through a cavity system
was investigated theoretically by Walder [1986] and more
completely by Kamb [1987]. A subglacial cavity opens as
ice separates from the bed at the upglacier margin of the
cavity and closes by the creep of ice into the cavity.
Energy dissipated by flowing water also enlarges the
cavity, but this effect is minor except in the orifices that
link large cavities because nearly all of the head loss
occurs in the orifices. Analyses by Walder and Kamb
lead to the result
Q,ub
m~dF/ds!1/ 2pe
23(10)
where u
b
is the sliding speed and m50.5–1. The key
feature of (10) is that water flux increases as p
e
falls, that
is, as p
w
rises. Thus there is no tendency for many
smaller cavities to drain into fewer, larger cavities, con-
trary to the situation with R channels. Another key
feature of a cavity drainage system, shown particularly
clearly by Kamb [1987], is that for a given discharge the
water pressure in the cavity system must be much greater
than in an R channel system.
Considering again Figure 14, it seems apparent that
an arborescent R channel network should be much more
efficient at evacuating meltwater than a nonarborescent
cavity network. The channel network has shorter aver-
age flow paths, thus shorter travel times, than the cavity
network. We also expect the behavior of tracers injected
into the subglacial drainage system to be very different
for the two cases: Tracers injected into a cavity network
should tend to become highly dispersed, with multiple
concentration peaks resulting from comparatively long
travel times and multiple flow paths, whereas in a chan-
nelized system the travel times should be shorter, and
dispersion should be much less. Field data such as those
from Variegated Glacier, Alaska [Brugman, 1986; Hum-
phrey et al., 1986], support this conclusion.
4.1.2.2. Subglacial water film: Weertman [1962,
1964, 1966, 1969, 1972] argued that meltwater drainage
involved a widespread, thin water layer at the glacier bed
(Figure 15). He argued [Weertman, 1972] that basal
channels were inefficient at capturing meltwater gener-
ated at the glacier bed (by geothermal heat and energy
dissipated by basal sliding) and that basally generated
water must flow in a thin layer, typically ;1 mm thick.
Weertman’s [1972] argument for the inability of channels
to capture meltwater generated at the glacier bed relied
on peculiarities of the stress distribution near a channel
Figure 14. Idealized subglacial cavity network in (a) plan
view and (b) cross section [after Kamb, 1987]. Unshaded areas
are regions of ice-rock contact; shaded areas are regions of
ice-rock separation (cavities). Flow directions in the cavities
are indicated by arrows. Orifices are the most constricted parts
of the cavity network and account for most of the energy losses.
36, 3 / REVIEWS OF GEOPHYSICS Fountain and Walder: WATER FLOW THROUGH GLACIERS ●311

in a material with the rheological properties of glacier
ice; he concluded that except near the margins of a
channel the pressure gradient at the glacier bed would
drive water away from the channel and that water layer
drainage was the only plausible alternative. Weertman’s
[1972] argument was formulated with the implicit as-
sumptions that (1) the glacier-bedrock interface is pla-
nar and free of rock debris and (2) the bedrock is
impermeable. Actual glacier beds are rough on a range
of length scales, and it is probable that there would
always be flow paths through the zone of supposedly
adverse pressure gradient. Moreover, if there is a per-
meable layer of rock debris at the glacier bed, and this
seems to be typically the case, then meltwater can flow to
a channel through the permeable rock debris. The water
layer concept has two other problems. Nye [1973]
pointed out a fundamental inconsistency in postulating a
widespread water layer that provides both a path for
local redistribution of meltwater involved in the regela-
tion-sliding process, which requires a layer thickness of
;1mm, and a path for basally generated, through-
flowing meltwater, with a characteristic layer thickness
of ;1 mm. Some other paths must exist to allow for the
net downglacier flow of meltwater. Finally, a water layer
at the glacier bed is not stable against perturbations in
layer thickness. The instability, proposed by Nye [1976]
and analyzed by Walder [1982], arises because the
thicker the layer, the more energy is dissipated by vis-
cous forces and thus the greater is the melt rate. Vari-
ations in water layer thickness are therefore magnified,
and protochannels tend to develop.
4.1.2.3. Nye channels: Nye [1973] suggested that
R channels must be transient features, being squeezed
shut as they are advected against the upglacier sides of
bumps on the glacier bed, and that the maintenance of
continuous subglacial meltwater drainage requires the
presence of channels incised into the bed (Figure 16).
Studies of recently deglaciated bedrock surfaces cited in
section 4.1.2.1 in connection with the distribution of
cavities [Walder and Hallet, 1979; Hallet and Anderson,
1980; Sharp et al., 1989] also revealed large numbers of
Nye channels, typically ;0.1 m deep, preferentially ori-
ented along the former ice flow direction and commonly
connecting cavities to one another. Because these obser-
vations were all made on highly soluble carbonate bed-
rock, it is uncertain how representative they are of
glacier beds in general. However, it seems clear that
beneath at least some small alpine glaciers, Nye channels
constitute a morphologically distinct part of the slow
drainage system. Within the context of present-day the-
ory, however, their hydraulic behavior, at least on the
mapped glacier beds mentioned above, is simply that of
elongated orifices in a cavity network.
4.1.2.4. Subglacial sediments: Recently deglaci-
ated bedrock surfaces nearly devoid of unconsolidated
sediment are rare, and it is likely that most glaciers are
in fact underlain by a spatially variable, perhaps discon-
tinuous layer of rock debris (Figure 17), which for sim-
plicity (and without sedimentological connotations) we
will call glacial till. The till acts as a confined aquifer as
long as it is much more permeable than the underlying
bedrock (Figure 18); this seems to have been first rec-
ognized by Mathews and Mackay [1960], although it was
not widely appreciated by glaciologists until the work of
Boulton and Jones [1979]. Even a pervasive basal till
layer, however, can evacuate only a small fraction of the
total water flux through the glacier. Consider, for exam-
ple, a till layer with a thickness B50.1 m and a
hydraulic conductivity kin the range of 10
28
–10
24
m/s,
values that are plausible in light of the field evidence
discussed below. Assuming that this layer covers the
entire glacier bed, of width Wtransverse to the ice flow
direction, the net meltwater flux through the layer is
QDarcy 5
S
kBW
rwg
DS
dF
ds
D
(11)
The gradient (1/r
w
g)(dF/ds), determined largely by the
ice-surface slope [e.g., Shreve, 1972], is typically ;0.1 for
alpine glaciers. Taking W51 km, we find Q
Darcy
'
10
27
–10
23
m
3
/s, as compared with typical melt-season
discharges of ;1–10 m
3
/s and winter discharges of per-
haps 0.01–0.1 m
3
/s [cf. Lliboutry, 1983]. Analogous cal-
culations with similar conclusions have been presented
for till aquifers beneath ice sheets [Boulton and Jones,
1979] and ice streams [Alley, 1989]. We conclude that
most of the water draining from a till-floored glacier
either avoids the bed altogether and simply flows engla-
Figure 15. Regelation film of water at the ice-rock interface.
Figure 16. Nye channels (channels incised into subglacial
bedrock). A Nye channel may be accompanied by a Ro¨thlis-
berger channel incised into the overlying ice.
312 ●Fountain and Walder: WATER FLOW THROUGH GLACIERS 36, 3 / REVIEWS OF GEOPHYSICS

cially or else passes directly from englacial conduits into
basal conduits.
The characteristics of subglacial channels coexisting
with a till aquifer (Figure 19) were analyzed by Walder
and Fowler [1994]. The geometry of a sediment-floored
channel develops in response to flow interactions with
both the ice roof and the sediment floor. As in the case
of a rock-floored R channel, the channel is enlarged by
melting of the ice and shrunken by inward creep of the
ice. In addition, the channel may be enlarged by fluvial
erosion and closed by inward creep of the till [Boulton
and Hindmarsh, 1987]. Walder and Fowler showed that
a network of sediment-floored channels may exist in two
asymptotically distinct conditions: either an arborescent
network of sediment-floored R channels at p
e
.p
˜
or a
nonarborescent network of wide, shallow, ice-roofed ca-
nals eroded into the sediment at p
e
,p
˜
, where p
˜
is a
“critical” effective pressure. Which drainage network is
stable depends on the magnitude of p
˜
(determined pri-
marily by the creep properties of the ice and sediment)
and the hydraulic gradient, which is approximated by the
ice-surface slope. For very low hydraulic gradients typi-
cal of ice streams and ice sheets the drainage network
should comprise nonarborescent canals. For large hy-
draulic gradients typical of alpine glaciers the drainage
system should comprise arborescent R channels over
relatively “stiff” till, with properties like those of the
Breidamerkurjo¨kull till in Iceland [Boulton and Hind-
marsh, 1987]; however, as was pointed out by Fountain
and Walder [1993], for alpine glaciers floored by rela-
tively “soft” till [e.g., Humphrey et al., 1993] the stable
drainage system would consist of nonarborescent canals.
Figure 17. Basal ice resting on unconsolidated sediments at South Cascade Glacier. The photograph was
taken in a Ro¨thlisberger channel near the glacier margin. The tape measure at the right shows the scale in both
inches (numbers in front) and centimeters (numbers in rear).
Figure 18. Drainage through subglacial till. Beneath most
temperate alpine glaciers a thin layer of unconsolidated till lies
between the base of the glacier and the underlying bedrock.
Figure 19. Subglacial “canals” coexisting with subglacial till.
Canals tend to be enlarged as the flowing water removes
sediment as both bed load and suspended load. Enlargement is
counteracted by the tendency for canals to be closed by inward
movement of sediment by creep or mass failures from the canal
walls. Energy dissipated by the flowing water also melts the
overlying ice and counteracts the tendency for ice creep to
close off the canal.
36, 3 / REVIEWS OF GEOPHYSICS Fountain and Walder: WATER FLOW THROUGH GLACIERS ●313

Basal drainage over a till bed may also involve linked
cavities, even if all of the bedrock irregularities are
smothered by till. The cavities in this case would simply
be gaps on the downglacier side of clasts protruding up
into the ice (Figure 20), as was pointed out by Kamb
[1987].
Clearly, there must be important interactions be-
tween the subglacial till layer and the basal conduits,
regardless of the exact geometry of the latter. Although
the amount of water actually exchanged between the till
and the basal conduits may be small, the till provides a
pathway for smoothing out water pressure differences
between distinct conduits. Depending on the efficiency
of the subglacial conduits, the pore pressure p
p
within
the till aquifer may be close to p
i
, with potentially
important implications for the mechanical properties of
the till.
A consistent set of measurements is beginning to
emerge for the hydrological characteristics of subglacial
till. For tills that seem to be dilated owing to active shear
deformation the porosity is typically near 0.4; nonde-
forming tills have a porosity more commonly of ;0.25–
0.3 (Table 2). There is considerably more variability in
the apparent hydraulic conductivity (Table 3), as one
might expect from the 6-order-of-magnitude range
(10
212
–10
26
m/s) reported for subaerial till aquifers
[Domenico and Schwartz, 1990, p. 48]. Laboratory mea-
surements of tills from beneath Breidamerkurjo¨kull
[Boulton et al., 1974], ice stream B, Antarctica [En-
gelhardt et al., 1990], and Storglacia¨ren [Iverson et al.,
1994] yield values in the range of 10
29
–10
26
m/s. It is
difficult to compare these values without knowledge of
(1) the till grain-size distribution, which was given for the
Breidamerkurjo¨kull till [Boulton and Dent, 1974] but for
neither of the other two samples, and (2) the p
e
value
during testing, considering the strong dependence of k
on p
e
at low p
e
[cf. Boulton et al., 1974]. The measured k
values probably all correspond to very low values of p
e
.
Estimated hydraulic conductivity values of till in-
ferred from in situ measurements vary substantially.
Several in situ measurements yield values broadly con-
sistent with laboratory data and values for subaerial till
aquifers. For South Cascade Glacier, Fountain [1994]
estimated the hydraulic conductivity range from k5
10
27
to 10
24
m/s on the basis of the migration rate (as
observed in several boreholes) of diurnal water pressure
fluctuations. The boreholes intersected a region where
dye-tracer tests and water level measurements suggested
that a basal till layer probably provided hydraulic com-
munication to a low-pressure basal channel. Using the
same approach, Hubbard et al. [1995] inferred the same
range of kfor till at the base of Haut Glacier d’Arolla
and also inferred that kdecreased with distance away
from a subglacial conduit. A much larger value of hy-
draulic conductivity for till beneath Gornergletscher has
been inferred from borehole-response tests by Iken et al.
[1996]: 0.02 m/s, a conductivity value typical of medium
to coarse gravel [Domenico and Schwartz, 1990, p. 48].
Similarly large (or even larger) values were originally
inferred by Stone and Clarke [1993] from Trapridge
Glacier, Canada, borehole-response tests, but more re-
cent work by Stone et al. [1997] involving the detailed
application of inverse theory has yielded a revised esti-
mate of 5 310
24
m/s in the connected part of the
drainage system. Much smaller values (k'10
29
–10
28
m/s) have been inferred by Waddington and Clarke
[1995] for till in unconnected regions of the bed of
Trapridge Glacier on the basis of long-term borehole
water level variations. The situation at Trapridge Glacier
is somewhat unusual because of several factors: (1) the
glacier is probably on the verge of surging, (2) the highly
correlated behavior of water levels in connected bore-
holes, with water pressures commonly near (or greater
than) the ice overburden pressure, suggests that locally,
the glacier is nearly floating on a layer of water, and (3)
the glacier margins are frozen to their bed, forcing all
meltwater to drain downward through the subglacial till
and underlying bedrock.
Another estimate of in situ kfor basal till is wildly at
variance with all other data discussed above. This
“anomalous” kvalue follows from our interpretation of
a tracer test at the bottom of a borehole in ice stream B
[Engelhardt et al., 1990]. The flow rate of subglacial water
Figure 20. Hypothetical microcavity network at the ice-till
interface. Small cavities may form at the lee of relatively large
clasts that protrude above the mean surface of the till into the
flowing ice.
TABLE 2. Porosity of Subglacial Till
Location Porosity Reference
Trapridge Glacier, Yukon Territory, Canada 0.35–0.40 Stone and Clarke [1993]
Ice stream B, West Antarctica 0.32–0.40 Blankenship et al. [1987]
Ice stream B, West Antarctica 0.40 Engelhardt et al. [1990]
314 ●Fountain and Walder: WATER FLOW THROUGH GLACIERS 36, 3 / REVIEWS OF GEOPHYSICS

between two boreholes, inferred from tracer injection,
was 30 m/h. Assuming the validity of Darcy’s law and
estimating the hydraulic gradient from the surface slope
of the ice stream (3.5 310
24
to 1.25 310
23
, according
to Shabtaie et al. [1987]), we estimate k56.6–24 m/s,
about an order of magnitude greater than for coarse
gravel [Domenico and Schwartz, 1990].
It is not entirely clear how to interpret the various in
situ values of kcited above. The values were all based on
simple models that assumed a homogeneous, isotropic
till layer of constant thickness. Furthermore, one must
be careful in comparing the derived kvalues with those
for subaerial till aquifers, which may have been affected
by consolidation [e.g., Boulton and Dent, 1974] or diage-
netic processes subsequent to being exposed by retreat-
ing ice. Even with these caveats, however, it seems likely
that the exceptionally large value of kfor ice stream B
represents something other than Darcian flow through
the till; for one thing, the Reynolds number is too high
for Darcy’s law to be valid [cf. Stone and Clarke, 1993, p.
332]. In line with Kamb’s [1991] analysis the large ap-
parent kprobably reflects the flow through a network of
connected “microcavities” at the ice-till interface. This
situation is analogous to water movement through frac-
tured rock, in which case, flow through fractures domi-
nates flow through the rock’s pore space [Domenico and
Schwartz, 1990].
As a simple illustration of the relative conductivities
of a till layer and a microcavity network, consider the
situation sketched in Figure 20 with the microcavities
idealized for simplicity as gaps of uniform width hcov-
ering a fraction fof the bed. The effective hydraulic
conductivity k
eff
of a slit of width his r
w
gh
2
/12m
w
,
where m
w
is the viscosity of water; correcting for the
fraction of the bed covered by microcavities gives k
eff
5
fr
w
gh
2
/12m
w
. For f50.1–0.5 we find k
eff
50.1–10 m/s
for h50.3–15 mm. If we account for the tortuosity of
the actual flow paths along the ice-till interface, the
estimates of hwould be perhaps a factor of 2 greater.
For comparison, Kamb [1991] suggested that the micro-
cavity gaps have a characteristic width of ;1 mm. (We
again note that the Reynolds number may be great
enough that flow is actually turbulent.) The microcavity
concept seems better grounded physically than Alley’s
[1989] suggestion that flow takes place in a nonuniform
“Weertman” water layer. On theoretical grounds it
seems plausible that drainage at the bed may also in-
volve wide, shallow, nonarborescent canals incised into
the till [Walder and Fowler, 1994], particularly if water
reaches the bed from the glacier surface. Realistically,
the hydraulics of these various scenarios are probably
indistinguishable. The precise geometry of the flow
paths is less important than the conclusion that a high-
conductivity, nonarborescent flow path probably does
exist.
In closing our discussion of the subglacial till layer we
should emphasize that the hydraulic properties of the
subglacial till, and perhaps the till itself, seem to be
patchy, with a characteristic length scale of ;10–100 m
beneath alpine glaciers [Engelhardt et al., 1978; Stone et
al., 1994; Fountain, 1994; Harper and Humphrey, 1995]
and ;100–10
4
m under ice sheets [Alley, 1993]. Until
more is learned, categorical statements about the prop-
erties of subglacial till should be regarded with skepti-
cism.
4.2. Synopsis and Implications
Until about the mid-1980s, subglacial water flow was
almost invariably interpreted within the context of an
assumed R channel dominated drainage system. The R
channel concept had successfully formed the basis for a
quantitative theory of outburst floods from glacier-
dammed lakes [Nye, 1976; Clarke, 1982] and was widely
applied; for example, Bindschadler [1983] discussed the
link between basal hydrology and ice dynamics of an
Antarctic ice stream and a surging glacier within the
context of classic R channel theory. It was known both
theoretically [e.g., Lliboutry, 1968; Nye, 1970] and from
studies of exhumed glacier beds [Walder and Hallet,
1979; Hallet and Anderson, 1980] that cavitation was
probably common, but the hydrologic significance of
cavities had barely been explored. An analogous state-
ment could be made about the hydrologic significance of
TABLE 3. Apparent Hydraulic Conductivity of Subglacial Till
Location Hydraulic Conductivity, m/s Reference
In Situ Estimates
Trapridge Glacier 5 310
24
Stone et al. [1997]
Trapridge Glacier 10
29
Waddington and Clarke [1995]
South Cascade Glacier 10
27
–10
24
Fountain [1994]
Haut Glacier d’Arolla 10
27
–10
24
Hubbard et al. [1995]
Breidamerkurjo¨kull 10
26
Boulton et al. [1974]
Laboratory Measurements
Storglacia¨ren 10
27
Iverson et al. [1994]
Ice stream B 10
29
Engelhardt et al. [1990]
Subaerial Till Aquifers
Various tills 10
212
–10
26
Domenico and Schwartz [1990]
36, 3 / REVIEWS OF GEOPHYSICS Fountain and Walder: WATER FLOW THROUGH GLACIERS ●315

unconsolidated sediment at the glacier bed [Engelhardt
et al., 1978].
By about 1990 the way that glaciologists envisaged
basal water flow had greatly changed, largely owing to
the realization that R channels could not form the basis
for an explanation of observations from surging Varie-
gated Glacier [Kamb et al., 1985] and rapidly moving ice
stream B in Antarctica [Blankenship et al., 1987]. Theo-
ries were developed to elucidate the hydraulics of water
flow through linked cavities [Walder, 1986; Kamb, 1987],
deformable till [Alley et al., 1987], and till-floored chan-
nels [Walder and Fowler, 1994]. The interpretive frame-
work shifted to one in which glaciologists usually tried to
explain field data from any particular glacier in terms of
a basal drainage system presumed to be dominated by
one or another of three morphologically distinct compo-
nents: R channel, cavity, or till.
We believe that the most significant general conclu-
sion to be drawn from the last 3 decades of investigations
is that the basal drainage system is highly heterogeneous
in both space and time. It is probable that the various
components of the subglacial drainage system have now
all been identified, and their hydraulics have been rea-
sonably well described. However, the distribution, spa-
tial extent, and seasonal evolution of each drainage-
system component under any particular glacier are still
uncertain. The way in which the drainage-system com-
ponents interact also remains poorly understood. These
issues need to be addressed to improve our understand-
ing of both glacier dynamics and hydrology. The link
between the subglacial drainage system and groundwa-
ter flow also remains unexplored aside from gross gen-
eralizations [cf. Lliboutry, 1983].
To summarize, the drainage system under any given
glacier comprises several or all of the morphologically
distinct components described in this section. A slow,
nonarborescent drainage system, comprising a mixture
of elements including cavities, permeable till, and con-
duits incised into the bed (i.e., Nye channels and canals),
probably covers most of the glacier bed and is nearly
fixed relative to the bed. The water pressure in the slow
drainage system is commonly close to the ice-overbur-
den pressure. A fast drainage system consisting of arbo-
rescent R channels may also exist. The fast drainage
system, being incised into the base of the glacier, is
advected by glacier movement and probably undergoes
continuous rearrangement as the sliding ice interacts
with the rough bed beneath. The water pressure in the
fast drainage system is commonly much less than the ice
overburden pressure; indeed, the fast drainage channels
may be only partly full most of the time, in which case
the flow is unpressurized except at times of peak diurnal
discharge. Both the fast and slow components of the
basal drainage system probably undergo major temporal
changes, particularly at the beginning and end of the
melt season, as discussed in section 5.
5. TEMPORAL EVOLUTION OF
THE DRAINAGE SYSTEM
Meltwater discharge from temperate alpine glaciers
varies typically by about 2 orders of magnitude from
winter to summer, so it seems plausible that the subgla-
cial drainage system must also undergo seasonal
changes. Data bearing on this question are sparse, as
little information is available except for the ablation
season. Moreover, there is not much of a theoretical
foundation for understanding time-dependent dis-
charge.
It is very unlikely that a robust system of R channels
can survive from year to year except perhaps beneath ice
only a few tens of meters thick. This is readily seen by
considering the fate of a channel of radius Rthat be-
comes empty of water at the end of the melt season. The
channel will tend to be closed by inward creep of ice,
with the channel radius as a function of time given by
[Weertman, 1972]
R~t!5R0exp ~2t/t! (12)
where R
0
is the radius at the end of the melt season. The
characteristic time tis proportional to p
i
2n
, where n'
3. For ice thicknesses $150 m a channel that has sur-
vived the winter will have a radius at the beginning of the
melt season of #10
23
R
0
, probably no more than a few
millimeters for even the main trunk channels. A similar
argument can be made for the closure of Nye channels
and sediment-floored canals. In contrast, a cavity net-
work ought to be able to survive from 1 year to the next
because cavities are maintained open primarily by basal
sliding and only secondarily by melting. As long as slid-
ing does not cease in winter and the accumulation of
sediment is not too great, cavities stay open, although
some of the links between the cavities may become quite
constricted. Thus we suggest that the subglacial drainage
system beneath the entire glacier at the beginning of the
melt season should typically be cavity dominated, with
the cavities probably poorly connected. A similar sce-
nario has been discussed by Raymond [1987] in connec-
tion with glacier-surge initiation, which we will discuss in
section 8. In the case of a sediment-floored glacier the
cavities will be located at the downglacier sides of iso-
lated bedrock protuberances or relatively large boulders
that protrude above the mean local till surface [Kamb,
1987].
At the beginning of the melt season, once meltwater
penetrates the winter snowpack, it flows into crevasses
and preexisting englacial channels linked to the cre-
vasses. In the event that such links were severed during
winter, water will pond in the crevasses while slowly
escaping through intergranular passages or microfrac-
tures in the ice; the escaping water eventually enlarges
these flow paths by melting, and the cycle of englacial
channel development starts anew. The englacial network
of channels begins to fill again, and water makes its way
316 ●Fountain and Walder: WATER FLOW THROUGH GLACIERS 36, 3 / REVIEWS OF GEOPHYSICS

to the glacier bed. Initially, the basal drainage system is
unable to cope with the increased meltwater flux. The
initial response will essentially be like that proposed by
Iken et al. [1983], who measured vertical uplift of the
surface of Unteraargletscher, Switzerland, at the begin-
ning of the melt season: Water pressure will increase,
and cavities will enlarge. During this period of time the
glacier will store large volumes of water, consistent with
the observations of Tangborn et al. [1975] and Willis et al.
[1991/1992]. The rate of water input to the glacier varies
slowly in time as long as the available storage in the firn
and the seasonal snowpack are great enough. Therefore,
in the ablation zone the water flux into the glacier
interior must begin to exhibit large diurnal variations
once the seasonal snow has melted [Nienow, 1994]. Once
this happens, englacial channels fed from the ablation
zone enlarge and cut down rapidly, and the parts of the
basal hydraulic system fed by these channels become
subjected to large daily variations in water pressure. The
transient increase in water pressures, as well as in the
melting caused by the increase in flow, enlarges the
orifices in the basal cavity system. If the englacial water
flux, and thus the pressure perturbation, is great enough,
cavity orifices will enlarge unstably and spawn an R
channel system [Kamb, 1987]. However, if the flux reach-
ing the bed through an englacial conduit is sufficiently
small, the local cavity system will remain stable. Thus we
envisage that both the fast and slow components of the
basal drainage system receive water directly from the
glacier surface and that R channels represent the con-
tinuation at the glacier bed of the largest englacial con-
duits. These R channels probably endure throughout the
melt season [Sharp et al., 1993a] as long as the water
supply from the glacier surface is sufficient to melt the
ice walls and thus counteract creep closure.
Because the hypothetical process of R channel devel-
opment described above is driven by water input from
the surface, it seems reasonable that this sort of devel-
opment in the basal drainage system should progress
upglacier as the melt season progresses. Evidence for
such a spatial progression has been presented by Nienow
[1994], who inferred from dye-tracer studies at Haut
Glacier d’Arolla that the boundary between a slow,
nonarborescent, wintertime drainage system and a fast
R channel system moved upglacier through time as the
snow line on the glacier surface retreated.
Data bearing on the seasonal evolution of the basal
drainage system are sparse. Seaberg et al. [1988] and
Hock and Hooke [1993] injected dye into moulins in the
lower part of the ablation area of Storglacia¨ren. They
calculated subglacial flow speeds mostly in the range of
0.1–0.2 m/s and also found that the dispersivity progres-
sively decreased. They inferred that the basal drainage
system included shallow but very wide conduits (Figure
21), not at all like the classic conception of an R channel
but similar to the predicted geometry of canals on a
sediment bed (Figure 19). Seaberg et al. [1988] and Hock
and Hooke [1993] suggested that the conduits were es-
sentially ice-roofed braided streams and interpreted the
progressive decrease in dispersivity as reflecting a de-
crease in the degree of braiding. Fountain [1993] in-
jected dye mostly into crevasses at South Cascade Gla-
cier and compared the measured travel time of tracers
with that derived from calculations based on a model of
turbulent flow in conduits. He also concluded that the
subglacial conduits were shallow and broad and that they
were pressurized early in the melt season but evolved
toward open-channel flow as the season progressed.
6. WATER STORAGE
Glaciers store and release large volumes of water on
daily to seasonal timescales [Tangborn et al., 1975], mak-
ing short-term runoff prediction difficult. Outburst
floods, resulting from englacial and subglacial water
storage and release, are probably common to most gla-
ciers; small floods, with a peak discharge not much
larger than the typical maximum daily flow, probably
occur frequently but are rarely detected [cf. Warburton
and Fenn, 1994], whereas large, destructive floods are
rare. Water storage also affects glacier movement. Surg-
ing glaciers store large volumes of water, and major
surge slowdowns as well as surge terminations are cor-
related with the release of stored water [Kamb et al.,
1985; Humphrey and Raymond, 1994]. The rapid flow of
Columbia Glacier, Alaska, seems to be controlled by the
volume of stored water [Meier et al., 1994; Kamb et al.,
1994]. More generally, the ability of glaciers to store
water modulates rapid changes in the basal water pres-
sure and may help to increase and sustain glacier motion
by distributing high water pressure over large bed re-
gions [Humphrey, 1987; Alley, 1996].
Small, temperate alpine glaciers seem to attain a
maximum seasonal water storage of ;200 mm of water
averaged over the area of the glacier bed, with daily
fluctuations of as much as 20–30 mm [Tangborn et al.,
1975; Willis et al., 1991/1992]. It is tempting to assume
that subglacial cavities provide the capacity for most of
Figure 21. Hypothetical broad, shallow conduit incised into
the basal ice, a variant of the standard concept of a semicir-
cular Ro¨thlisberger channel. Basal channels may be broad and
shallow because ice creeps inwardly more quickly at the top of
the channel (which is not full at times of low flow) than at the
sides of the channel (where the creep rate is reduced by the
effect of drag at the ice-rock interface).
36, 3 / REVIEWS OF GEOPHYSICS Fountain and Walder: WATER FLOW THROUGH GLACIERS ●317

the storage, but this is questionable. The volume of the
former linked cavity system beneath Castleguard Gla-
cier, Alberta, was inferred to be equivalent to an average
water layer thickness of only ;27 mm [Hallet and Ander-
son, 1980], and this figure is within a factor of 2 for
exhumed cavity systems at Blackfoot Glacier, Montana,
United States [Walder and Hallet, 1979] and Glacier de
Tsanfleuron, Switzerland [Sharp et al., 1989]. The dis-
crepancy between the estimated stored volume and the
likely storage capacity of subglacial cavities is also evi-
dent when we consider the situation at Variegated Gla-
cier, where the volume of water stored during the glacier
surge of 1982–1983 was equivalent to a layer of water ;1
m thick [Humphrey and Raymond, 1994]. This seems like
an implausibly large amount of water to store in subgla-
cial cavities, even if a majority of the glacier was sepa-
rated from the bed, unless the glacier bed was extraor-
dinarily rough.
Subglacial till may play an important, although not
predominant, role in seasonal water storage. An uncon-
solidated till layer covering the entire glacier bed, a
questionable scenario, and having a thickness of, say,
0.25 m and a porosity of 0.30 would provide a storage
volume equivalent to a 75-mm-thick layer of water.
Accommodating as much as 200 mm of stored water in
a basal till layer would require that the till be substan-
tially thicker than that suggested by the limited borehole
data from alpine glaciers [e.g., Engelhardt et al., 1978;
Stone et al., 1997]. Furthermore, diurnal variations in
water storage probably cannot be explained with refer-
ence to basal till. The fractional change in storage in a
saturated till layer is given approximately by S
s
Dh,
where S
s
is the specific storage, a measure of the water
volume stored or released as the till layer is strained, and
Dhis the variation in hydraulic head. With S
s
;10
24
/m
for sandy or gravelly till [cf. Stone et al., 1997; Domenico
and Schwartz, 1990] and Dh;100 m (at most) the
fractional change in storage is ;0.01 or ;1 mm. By
process of elimination we conclude that a substantial
fraction of the water storage, both short- and long-term,
is probably englacial [cf. Jacobel and Raymond, 1984;
Humphrey and Raymond, 1994].
Borehole-video studies [Pohjola, 1994; Harper and
Humphrey, 1995] suggest that englacial voids and con-
duits in small temperate glaciers constitute a macropo-
rosity of ;0.4–1.3%, although some of this probably
comprises isolated, water-filled voids. Fountain [1992]
estimated a macroporosity of 1% to maintain reasonable
calculated subglacial water pressures. Englacial water
storage is an attractive hypothesis because a macropo-
rosity of only 0.1% in hydraulic communication with the
bed would be equivalent to a 100-mm-thick water layer
for a glacier with an average thickness of only 100 m.
Filling and draining of englacial passages have been
detected by radar [Jacobel and Raymond, 1984], and the
filling of moulins has been measured [Iken, 1972]. Thus
it seems both qualitatively and quantitatively likely that
englacial storage may exceed subglacial storage in many
cases. Water storage in surging glaciers also involves
water-filled surface potholes [Sturm, 1987] and crevasses
[Kamb et al., 1985]. Near-surface storage of this sort
implies that water is in fact backed up in englacial
passages.
7. OUTBURST FLOODS
A glacial outburst flood, sometimes called by the
Icelandic term “jo¨kulhlaup,” may be broadly defined as
the sudden, rapid release of water either stored within a
glacier or dammed by a glacier. Although outburst
floods are perhaps best known for the hazards they pose
in alpine regions, they are not limited to such glaciers
but are also associated with large tidewater glaciers in
Alaska [Mayo, 1989] and Icelandic ice caps [Bjo¨rnsson,
1992]. The Pleistocene Missoula floods, the largest
known terrestrial floods, were caused by periodic drain-
age of an enormous lake dammed by the Cordilleran ice
sheet in western North America. Floodwaters swept
across an area of ;3310
4
km
2
in present-day Wash-
ington State, creating the unique landscape known as the
Channeled Scabland [Waitt, 1985].
Most observed outburst floods involve drainage of
glacier-dammed lakes. The water either drains through a
subglacial tunnel and appears at the glacier terminus, or
drains through a breach between the glacier and valley
wall. For drainage through subglacial tunnels, drainage
occurs, to a first approximation, when the lake level rises
sufficiently to nearly float the ice dam [Bjo¨rnsson, 1974].
As water begins to leak under the dam, frictional energy
dissipation causes flow to localize in a channel. Initially,
the channel enlarges rapidly by melting, but as the lake
level drops, water pressure in the channel falls, the rate
of inward ice creep increases, and the channel closes,
thereby terminating the flood. The flood hydrograph
commonly has a long, gentle ascending limb and a steep,
abrupt falling limb, with the flood lasting a few days to
weeks (Figure 22a). Details of the physics have been
elucidated by Nye [1976], Glazyrin and Sokolov [1976],
Spring and Hutter [1981], and Clarke [1982]. Clarke’s
analysis has the greatest utilitarian value. He showed
that the exit hydrograph is determined primarily by (1)
the temperature u
LAKE
, volume V, and hypsometry of
the lake, (2) the ice overburden pressure p
i
where the
tunnel meets the lake, and (3) the tunnel roughness n
˜
and mean hydraulic gradient G. These factors are incor-
porated into two dimensionless parameters, a “tunnel
closure parameter” aand a “lake temperature parame-
ter” b. Exit hydrographs can be calculated if plausible
bounds on aand bcan be estimated. For many alpine
glaciers, ais relatively small, and plausible bounds can
be placed on peak discharge Q
MAX
even without calcu-
lating the complete exit hydrograph. The lower bound
corresponds to the case in which u
LAKE
508C; the upper
bound corresponds to the case in which tunnel enlarge-
318 ●Fountain and Walder: WATER FLOW THROUGH GLACIERS 36, 3 / REVIEWS OF GEOPHYSICS

ment is dominated by the lake’s thermal energy and
frictional dissipation is negligible.
Where a valley is blocked by a glacier advancing from
a tributary valley (Figure 23), the glacier-dammed lake
commonly drains through a breach between the ice dam
and an adjacent rock wall [Walder and Costa, 1996]. The
way in which drainage begins is enigmatic. In some
cases, drainage may begin through a subglacial tunnel
near the valley wall because the ice is normally thinnest
at that point. Tunnels formed in this way seem to be
prone to roof collapse, and marginal breaches develop
[e.g., Liss, 1970]. Alternatively, because the ice-wall con-
tact is typically irregular, seepage through the gaps erodes
the ice through frictional heating, thereby initiating a
breach (M. F. Meier, personal communication, 1994). A
theoretical description of breach-drainage outburst
floods has been given by Walder and Costa [1996]. Their
analysis parallels Clarke’s [1982] analysis of tunnel-
drainage outbursts in many important respects, particu-
larly in the assumption that breach enlargement pro-
ceeds by melting of the ice. Calving also widens the
breach [Liss, 1970] but is not hydraulically important
unless calved ice actually blocks the breach. Breach
closure resulting from ice movement is negligible. The
flood hydrograph commonly exhibits a steep rising limb
(Figure 22b), similar to floods caused by the failure of
constructed dams [MacDonald and Langridge-Monopo-
lis, 1984]. The hydrograph depends primarily on lake
hypsometry and two dimensionless parameters, a
“breach roughness parameter” gand a lake temperature
parameter d. Both gand ddepend on the initial lake
volume and depth. Again, approximate bounds can be
placed on Q
MAX
for cases in which the effect of the
lake’s thermal energy on breach erosion is either negli-
gible or dominant.
Simple empiricisms have also been useful for estimat-
ing Q
MAX
from lake drainage. Clague and Mathews
[1973] were the first to present a regression relation
between Q
MAX
and V:
QMAX 5bVa(13)
where Q
MAX
is given in cubic meters per second and V
is given in millions of cubic meters and with values of
b575 and a50.67. Walder and Costa [1996] updated
the Clague-Mathews relation by developing separate
regressions for tunnel drainage (b546 and a50.66)
and breach drainage (b51100 and a50.44). For a
given value of V,Q
MAX
for a breach-drainage flood is
commonly much greater than for a tunnel-drainage
flood. The values of the constants for a breach drainage
are quite similar to the regression developed by Costa
[1988] for floods from constructed earthen dams (b5
1200 and a50.48). The similarity of constants is
probably not fortuitous but rather reflective of the fact
that both were developed for floods that drained
through rapidly formed subaerial breaches. The differ-
ences in material properties of the dams and in erosion
mechanisms are evidently less important than the flow
hydraulics, which are the same in both cases.
Another class of outburst floods involves the abrupt
release of water from subglacial or englacial storage
[Haeberli, 1983; Driedger and Fountain, 1989]. Outburst
Figure 22. Outburst-flood hydrographs for two distinct
types of water release: (a) flood caused by lake water tun-
neling under a glacier and (b) flood caused by release of
subglacially stored water or by subaerial breaching of an ice
dam [after Haeberli, 1983]. Reprinted from Annals of Gla-
ciology with permission of the International Glaciological
Society.
Figure 23. Contrasting modes of gla-
cier-dammed lake formation. A lake im-
pounded by the advance of a glacier
across the mouth of a tributary valley
(left side of figure) drains through a
subglacial channel, but a lake formed by
the advance of a glacier from a tributary
valley typically drains through a sub-
aerial breach, usually at the terminus.
Based on Figure 3 of Walder and Costa
[1996]; copyright John Wiley and Sons
Ltd.; reproduced with permission.
36, 3 / REVIEWS OF GEOPHYSICS Fountain and Walder: WATER FLOW THROUGH GLACIERS ●319

floods of this type, which are by their nature unantici-
pated and poorly described, seem to be triggered by
rapid input of rain or meltwater to the glacier. Walder
and Driedger [1995] suggested that the release mecha-
nism probably involves unstable enlargement of the or-
ifices in a basal cavity network that transforms into one
that drains water rapidly. This mechanism, initially pro-
posed in connection with glacier-surge termination
[Kamb, 1987], is also considered important to the annual
reestablishment of an R channel network [cf. Nienow,
1994; M. J. Sharp, personal communication, 1996]. Bore-
hole measurements showing an abrupt reorganization of
the basal drainage system, consistent with the scenario
discussed here, have been collected at Trapridge Glacier
[Stone and Clarke, 1996]. Alternatively, water could be
stored englacially in passages temporarily isolated from the
subglacial drainage system, then released when rapid input
of water to the glacier forces reconnection with the bed.
Floods from internally stored water are largely unpre-
dictable. Walder and Driedger [1995] used statistical
methods to show that for South Tahoma Glacier (Mount
Rainier, Washington State), which released 14 or 15
floods during a 6-year period, the probability of a flood
increased as the input rate of water to the glacier (as rain
or meltwater) increased. These results agree with the
observations of Warburton and Fenn [1994]. Unfortu-
nately, a relationship of this sort developed for a partic-
ular glacier is unlikely to be applicable elsewhere. A
physically plausible, albeit crude, estimate of Q
MAX
is
nonetheless possible. Glaciological experience [e.g.,
Haeberli, 1983; Walder and Driedger, 1995] suggests that
the water volume released from storage during an out-
burst flood is likely to be of a magnitude corresponding
to a water layer ;10–100 mm thick over the entire
glacier bed and that the release typically occurs during a
period tequal to ;15–60 min, although sometimes as
long as a day [Warburton and Fenn, 1994]. Estimating the
released water volume as the product of the glacier-bed
area Aand equivalent water layer thickness dand as-
suming a triangular exit hydrograph, we estimate
QMAX <2Ad
t(14)
As an example, consider a small alpine glacier with A5
1km
2
. The base flow from such a glacier is probably ;1
m
3
/s [e.g., Fountain, 1993]. From (14) we estimate an
upper bound for Q
MAX
of ;100 m
3
/s. Flood peaks of
this magnitude can be extremely destructive in small
alpine drainage basins, particularly if the water floods
transform to debris flows [Driedger and Fountain, 1989;
Walder and Driedger, 1995].
8. LINKS BETWEEN HYDROLOGY
AND GLACIER DYNAMICS
8.1. Effect of Glacier-Surface Morphology
Variations in water input to a glacier should affect
basal water pressure. If water moves rapidly from the
glacier surface to the bed, a proposition that we examine
in section 9, the water pressure in bed areas supplied
from the ablation zone should respond rapidly (probably
within a few minutes to a few hours) to variations in the
water input at the surface. In contrast, water pressure in
bed areas supplied from the accumulation zone should
respond slowly (probably on a timescale of days to a
week or more) to varying water input at the surface,
owing to delayed transport through snow and firn. A
change in supply region from accumulation to ablation
zone should therefore be reflected at the base of the
glacier by a relatively sharp gradient in variations of
subglacial water pressure. This may have important im-
plications for glacier dynamics because the rate of gla-
cier sliding is, in part, related to the effective pressure
(ice pressure minus water pressure) at the base of the
glacier [Iken and Bindschadler, 1986; Jansson, 1995]. We
expect the sliding speed in the ablation zone to be
greater than that in the accumulation zone during peak
diurnal melt periods but less when the melt rate is at a
minimum. The ablation zone would then “pull” the
accumulation during midday, and the accumulation zone
would “push” the ablation zone during the night. Simi-
larly, the ablation zone would move fastest during the
first few days of a rainy period before the water perco-
lated through the accumulation zone and slowest just
after the rain stopped. This scenario would be somewhat
modified if most of the surface water input were routed
directly to subglacial channels. Not only do the channels
only pressurize a small part of the bed, but during their
largest development in midsummer the conduits may
only be pressurized during a short time each day. Under
these conditions the accumulation zone may more or
less constantly push the ablation zone. Because spatial
variations in glacier movement are smoothed by longi-
tudinal stress-gradient coupling over a distance related
to the glacier thickness [Kamb and Echelmeyer, 1986],
differences in flow speed between the accumulation and
ablation zones caused by variations in water input should
tend to increase with the length of the glacier.
8.2. Subglacial Hydrology
A large body of data has accumulated suggesting a
link between variations in the basal drainage system and
perturbations in glacier movement, but the physical na-
ture of the coupling remains elusive. The best known
evidence suggesting the hydrology-dynamics link in-
volves seasonal variations in glacier-surface velocity, first
observed by Forbes [1846] at Mer de Glace, France.
Generally, the surface velocity peaks in late spring to
early summer in the ablation area; in the accumulation
area the seasonal variation may be of the opposite phase.
The usual interpretation [e.g., Hodge, 1974] is that
changes in surface velocity are too large to be explained
by mass balance induced changes in applied stress and
that changes in surface velocity therefore reflect changes
in sliding velocity. Such an interpretation requires cau-
tion. Balise and Raymond [1985] showed theoretically
320 ●Fountain and Walder: WATER FLOW THROUGH GLACIERS 36, 3 / REVIEWS OF GEOPHYSICS

that the transfer of basal-velocity variations to the gla-
cier surface is sensitively dependent on the length scale
of such variations. They concluded that broad-scale vari-
ations in basal sliding should be reflected by similarly
broad-scale variations in surface speed but that very
localized basal-velocity variations cannot be unambigu-
ously resolved by glacier-surface observations.
A key point of contention has been whether sliding
speed is controlled primarily by the volume of stored
water or by basal water pressure. Hodge [1974] showed
that the surface speed of Nisqually Glacier, Washington
State, peaked before the meltwater discharge from the
glacier and also that the speed actually increased
throughout the winter, even while meltwater discharge
was falling. He interpreted this to mean that sliding
speed was controlled by the amount of water stored at
the glacier bed, with the maximum storage occurring
early in the melt season before an efficient basal drain-
age system had developed (in line with our discussion in
section 5). In contrast, Iken et al. [1983] found that the
maximum sliding speed coincided with times when the
glacier surface was rising most rapidly, the surface rise
being thought to indicate water going into storage,
rather than with the time of maximum surface elevation;
they interpreted this to mean that sliding speed was a
function of subglacial water pressure rather than stor-
age. Iken and Bindschadler [1986] subsequently showed a
correlation between velocity fluctuations and borehole
water pressures at Findelengletscher, and similar measure-
ments have been made at Storglacia¨ren [Jansson, 1995].
Probably, the most detailed observations dealing with
the link between basal hydrology and glacier dynamics
are those from Columbia Glacier, a rapidly moving
tidewater glacier [Meier et al., 1994; Kamb et al., 1994].
Surface-velocity fluctuations at two sites 7 km apart were
strongly correlated with each other and fairly well cor-
related with the borehole water level at the upglacier of
the two sites but not with the borehole water level at the
lower site. Using estimates for recharge to and discharge
from the basal drainage system, Kamb et al. [1994] con-
cluded that variations in ice velocity were best correlated
with variations in the amount of water stored at the
glacier bed.
We appear to be faced with a conundrum. Models of
the basal-cavitation process [Lliboutry, 1968; Iken, 1981;
Fowler, 1986, 1987; Kamb, 1987] predict an increase in
basal storage with an increase in basal water pressure,
yet glacier movement seems sometimes to correlate with
storage, sometimes with water pressure, but not with
both. Kamb et al. [1994] suggested a resolution of this
conundrum, as follows: Glacier sliding speed u
b
and
basal storage are controlled by ^p
w
&, the basal water
pressure averaged over the distance l, the length scale
over which the basal shear stress is effectively averaged
by glacier dynamics [Kamb and Echelmeyer, 1986]. The
basal water pressure p
w
measured at a point, however, is
the sum of the spatial mean value ^p
w
&and a local
fluctuating value p9
w
, where p9
w
is controlled by rapid,
local reorganization of the basal drainage system. Thus
one expects u
b
to correlate with storage but not neces-
sarily with local p
w
.
8.3. Glacier Surging
Surging glaciers exhibit [Raymond, 1987, p. 9121] “a
multi-year, quasi-periodic oscillation between extended
periods of normal motion and brief periods of compar-
atively fast motion.” A thorough review of glacier surg-
ing is beyond the scope of this paper (we refer the reader
to the review by Raymond [1987]), but we do want to
highlight recent developments related to the study of the
1982–1983 surge of Variegated Glacier [Kamb et al.,
1985; Humphrey et al., 1986; Kamb, 1987; Humphrey and
Raymond, 1994] that point to regulation of the surge
process by basal water flow.
Kamb [1987] noted the following observations from
Variegated Glacier as the basis for his surge model:
1. Borehole measurements demonstrate directly
that rapid glacier motion during the surge is due to basal
sliding.
2. Basal water pressure during the surge was close
to the overburden pressure and notably higher than
during the nonsurging state. Peaks in water pressure
corresponded with peaks in sliding motion in both surg-
ing and nonsurging states.
3. Major decreases in surge motion, as well as surge
termination, were accompanied by large flood peaks in
outlet streams and a lowering of the glacier surface,
indicating that the high sliding speed and water pressure
during the surge are coupled with water storage within
and at the bed of the glacier.
4. Dye-tracing experiments [Brugman, 1986] showed
that the mean flow of water in the basal drainage system
was ;25–30 times faster after surge termination than
during the surge. Moreover, dye appeared at a number
of locations across the width of the glacier during the
surge, but in only a single stream after surge termina-
tion.
5. Water discharged from the glacier during the
surge was extremely turbid; suspended-sediment con-
centration was much higher, and the average grain size
of suspended sediment was finer during the surge than in
the nonsurging phase [Humphrey and Raymond, 1994].
A physical model of surging that accounts for these
observations was developed by Kamb [1987], who pro-
posed that the basal drainage system during surge com-
prised a linked-cavity network, whereas the drainage
system during the nonsurging phase consisted of arbo-
rescent R channels. The cavity system is associated with
high water pressure and multiple, tortuous flow paths
leading to prolonged, highly dispersed dye returns.
Surge slowdowns and surge termination result from
large transient increases in basal water pressure that
destabilize part of the cavity system, thereby releasing
water from storage. Sediment concentration in the melt-
water discharged from the glacier increased during the
surge because a linked-cavity drainage system brought a
36, 3 / REVIEWS OF GEOPHYSICS Fountain and Walder: WATER FLOW THROUGH GLACIERS ●321

large fraction of the glacier bed into contact with flowing
water, but the mean suspended-sediment size dropped
during the surge because the sluggishly flowing water in
the cavity system could not suspend as much coarse
sediment as could rapidly flowing, channelized water
[Humphrey and Raymond, 1994].
The conditions that cause surge initiation can also be
explained, at least qualitatively, in the context of the
channel-cavity dichotomy. Raymond [1987] and Kamb
[1987] suggested that during winter, R channels collapse
and a high-p
w
linked-cavity network develops. Usually,
as the melt season begins, the flux of meltwater to the
bed causes water pressure transients that destabilize
parts of the linked-cavity network, and an R channel
network reforms. (We have suggested in section 5 that
this scenario is probably common to all temperate gla-
ciers, not just those that surge.) The stability of the cavity
network to pressure perturbations is controlled by a
parameter J[Kamb, 1987] that depends on roughness
characteristics of the glacier bed, ice rheology, and gla-
cier geometry; in a surging glacier, as the glacier geom-
etry (primarily the thickness) changes with time during
the nonsurging phase, a point is reached at which J
attains a small enough value to stabilize the wintertime
cavity network against early melt-season water pressure
perturbations. When this occurs, the high-pressure
linked-cavity system persists and enlarges, and surging
begins. Complications in this scenario have been dis-
cussed by Humphrey and Raymond [1994].
9. UNIFIED MODEL OF WATER FLOW
THROUGH A TEMPERATE GLACIER
Water enters the body of a glacier primarily through
crevasses and moulins. The englacial drainage system
comprises a complex combination of gently inclined pas-
sages spawned by water flow along crevasse bottoms and
steeply inclined passages formed by water enlarging in-
tergranular veins. In general, water flows englacially for
long distances, perhaps equal to several times the glacier
thickness, before reaching the bed, although the com-
mon presence of moulins in the ablation zone indicates
that water can sometimes descend vertically through a
significant fraction of the ice thickness.
The englacial conduit system supplied from the accu-
mulation zone is of relatively limited extent compared
with the system supplied from the ablation zone because
of the role of the firn in damping diurnal variations in
water input. Much of the water that enters the glacier in
the accumulation zone probably reaches the bed in the
ablation zone. Thus the subglacial area of influence of
each zone is shifted downglacier, and the firn influences
a subglacial area greater than the area it actually covers.
The supply of surface water to the bed is inhibited in
overdeepened parts of the glacier because the gently
inclined parts of the englacial conduit system become
pinned by the downglacier margin of the overdeepening.
Basal water flow in an overdeepening is essentially re-
stricted to the water already in the basal drainage system
upglacier of the overdeepening; basal conduits may tend
to freeze shut where they encounter the adverse slope
coming out of the overdeepening. Basal conduits should
be most frequently located along the margins of the
overdeepening.
The morphology of the subglacial drainage system is
controlled by a number of factors, including the distri-
bution of englacial conduits reaching the bed, ice thick-
ness, glacier sliding speed, bed lithology, and bed rough-
ness. Any one of these factors may be of relatively
greater or lesser importance at any particular glacier.
Generally speaking, the morphology of the basal drain-
age system is heterogeneous. Slow drainage systems,
involving linked cavities, permeable till, and channel
segments incised into the bed and trending along the ice
flow direction, cover most of the bed. The slow drainage
system is in poor hydraulic communication with a fast
system of R channels incised into the basal ice. The R
channel system largely collapses during winter and is
reformed in the spring as a flush of water reaches the
bed and destabilizes parts of the linked-cavity network.
In relatively thick ice, say, 200 m or more, there is
probably ample opportunity for englacial drainage to
become concentrated into a relatively small number of
trunk conduits, each carrying a large water flux, whereas
in thin ice, say, 50 m or less, the englacial flow is
relatively more diffuse, with a large number of englacial
conduits, each carrying a small flux of water, reaching
the bed.
10. DIRECTIONS FOR FUTURE RESEARCH
Glaciologists need to adopt a holistic perspective in
studying glacier hydrology. Indeed, although we have
written separately about near-surface, englacial, and
subglacial water flow, the three phenomena are obvi-
ously coupled. Influences in the glacier drainage system
nearly always move from the glacier surface downward.
Forcings imposed on the englacial and subglacial pas-
sages are distinctly different, depending on whether wa-
ter is supplied from the accumulation zone or the abla-
tion zone.
Coupling between the near-surface and englacial
drainage systems needs to be investigated much more
thoroughly. There are almost no data available showing
how water flux to crevasses and moulins is distributed
over the glacier surface and how this distribution evolves
temporally. These flux data constitute a fundamental
boundary condition for the englacial part of the drainage
system.
The water flux delivered to the bed at the points of
coupling between the englacial and subglacial drainage
systems constitutes the “upstream” boundary condition
on the subglacial drainage system. This flux distribution
obviously cannot be directly measured, but it may still be
322 ●Fountain and Walder: WATER FLOW THROUGH GLACIERS 36, 3 / REVIEWS OF GEOPHYSICS

investigated once we recognize that surface water sup-
plied to the englacial drainage system almost certainly
becomes concentrated into a relatively limited number
of trunk conduits by the time it reaches the glacier bed
[Shreve, 1972]. It may be possible to use tracers to
delineate the “drainage basins” of the englacial trunk
conduits (i.e., the ones that reach the bed) and thereby
to estimate the distribution of recharge to the subglacial
drainage system, much as tracers have been used to
delineate the gross drainage-basin structure of entire
glaciers [e.g., Stenborg, 1973; Fountain, 1992, 1993;
Fountain and Vaughn, 1995].
Some of the theoretical foundations of glacier hydrol-
ogy theory need to be revisited. Clarke [1994] has re-
cently begun doing this for the case of Ro¨thlisberger
channels by critically examining one of the key simplify-
ing assumptions (the neglect of heat advection by the
water) in Ro¨thlisberger’s [1972] analysis. (At the time of
writing, Clarke’s recent work has appeared only as an
abstract, and we cannot assess it critically.) There is also
a distinct need to understand how the drainage system
should respond to time-varying water input. This topic
has been touched upon by Spring [1980], who explored
the pressure-discharge relation for sinusoidally varying
flow in R channels, and by Kamb [1987] in his analysis of
the stability of cavities to pressure transients.
The time seems to be ripe for constructing theoretical
models that fully couple glacier sliding and basal hydrol-
ogy, accounting properly for both the long-range spatial
averaging imposed by ice dynamics and the complex,
time- and space-dependent variations within the basal
drainage system. Some important studies that we believe
can jointly serve as a springboard are those of Humphrey
[1987], Murray and Clarke [1995], and Clarke [1996].
Humphrey [1987] presented the only analysis to date
of the dynamic coupling between a glacier and its basal
drainage system, albeit within the context of a highly
idealized view of glacier-bed geometry. He argued that a
complete description of the coupling between subglacial
water flow and glacier dynamics requires one to specify
the following: (1) a force balance at the bed, (2) the
coupling between the basal shear stress and the stresses
in the body of the glacier, with careful attention to
longitudinal stress gradients, (3) a relation between cav-
ity size, sliding speed, and basal water pressure, and (4)
a description of the hydraulics of water flow in the linked
cavities. The mathematical model is complicated, and its
consequences have not yet been fully elucidated, but the
results are tantalizing. Most importantly, from the per-
spective of glaciologically meaningful measurements,
Humphrey showed that the model predicts no simple
relation between the variation in sliding speed and the
variation in water pressure as a function of distance
along the glacier, although variations in sliding speed are
predicted to correlate with basal water storage. These
model predictions are in line with field data and inter-
pretation from Columbia Glacier [Meier et al., 1994;
Kamb et al., 1994].
Murray and Clarke [1995] developed a “black-box”
model of the subglacial drainage system to explain pe-
culiarities of the borehole water level data from Tra-
pridge Glacier, but the concepts they developed are
more widely applicable. Murray and Clarke showed that
observed, time-dependent coupling between connected
and unconnected boreholes could be modeled by think-
ing of water pressure in a connected borehole as a
forcing function to which water pressure in an uncon-
nected borehole must respond. Although their mathe-
matical formulation was somewhat ad hoc, they argued
plausibly that their model coefficients could be inter-
preted in terms of physical processes at the glacier bed,
namely, dilation/compaction of porous subglacial sedi-
ment, diffusion of water pressure disturbances through
the sediment, and uplift of the glacier from its bed.
Subsequently, Clarke [1996] has shown that conceiving
of the subglacial drainage system as consisting of linked
“lumped elements,” analogous to an electrical circuit,
provides a powerful basis for explaining many of the
complicated data collected during ;25 years of borehole
studies. This approach seems to have great potential for
elucidating the details of basal hydrology at relatively
small spatial scales and short time periods. In this sense
it complements Humphrey’s [1987] approach, which is
directed at explaining large-scale, long time period be-
havior.
A key issue that needs much more thorough investi-
gation is how the various components of the glacial
drainage system interact in space and time. The system
components (snow, firn, and surface streams; crevasses,
moulins, and other englacial passages; and basal chan-
nels, cavities, and till) are in a state of flux throughout
the year and are unevenly distributed.
GLOSSARY
Ablation: All forms of mass loss including sublima-
tion, evaporation, melting, and calving. For alpine gla-
ciers, the term “ablation” is often used, incorrectly, to
mean melt because that is the dominant means of mass
loss.
Ablation zone: The part of the glacier where yearly
mass loss exceeds that gained by snow accumulation and
the surface exposed in the late summer is ice.
Accumulation zone: The part of the glacier where
yearly mass gain generally exceeds that lost by ablation
and the surface consists of either snow or firn.
Albedo: The ratio of reflected energy flux to inci-
dent energy flux from solar radiation.
Arborescent: Tree like, used to describe a network
of channels that converge as the branches of a tree
converge to a trunk.
Confined aquifer: A water-bearing formation con-
fined on the top and bottom by nearly impermeable
formations.
36, 3 / REVIEWS OF GEOPHYSICS Fountain and Walder: WATER FLOW THROUGH GLACIERS ●323

Crevasse: A gaping crack in a glacier formed by
tensile stresses resulting from glacier movement.
Englacial: Within the body of a glacier.
Equilibrium line: Line dividing the ablation and
accumulation zones, where net annual mass change is
zero.
Firn: A metamorphic transition stage between snow
and ice. By definition, firn is seasonal snow that has
survived the summer melt season.
Glacierized: Landscape currently covered by gla-
ciers.
Glaciated: Landscape once acted upon by glaciers.
Hydraulic conductivity: A measure of the ability of
a porous medium to transmit fluids.
Ice stream: Fast-moving (hundreds of meters per
year) river of ice within an otherwise slow-moving (tens
of meters per year) ice sheet. Ice streams are found in
Antarctica and Greenland.
Intergranular: Between the grains. Used here in
connection with veins to indicate small passages between
the grains (crystals) of ice, specifically at the boundary
where three or more grains meet.
Moulin: A natural vertical shaft in the glacier
formed from the heat of meltwater flowing into the body
of the glacier.
Nonarborescent: Refers to a network that does not
converge from many flow paths to a few flow paths.
Paths will converge and diverge with little or no change
in the number of paths.
Overdeepening: A large depression in the bedrock
under a glacier. If the glacier receded, water would fill
the overdeepening to form a lake.
Subglacial: At the base of the glacier.
Supraglacial: On the glacier surface.
Surging glacier: A glacier that rapidly accelerates
its motion. These glaciers typically exhibit a cycle lasting
decades with quiescent “normal” flow (;0.1 m/d) inter-
rupted by one or two seasons of rapid flow (tens of
meters per day).
Temperate glacier: A glacier in which the temper-
ature at the bed and within most of the body of the ice
is at its melting point. Most glaciers in the temperate
zones of the Earth are temperate glaciers. A polar gla-
cier is one that is frozen to the bed and in which
meltwater does not penetrate to significant depths.
Till: Unconsolidated sediment composed of silt,
sand, and cobbles, formed by glacial erosion. As used in
this paper, the term does not have any sedimentological
connotations.
ACKNOWLEDGMENTS. This manuscript would not
have been possible without the insightful, candid discussions
we have had with many glaciologists over the years. We par-
ticularly wish to thank M. Tranter, who originally motivated
this project; M. J. Sharp and D. B. Stone, who carefully
reviewed an early version of this manuscript and helped us
focus our efforts; and G. K. C. Clarke and N. F. Humphrey,
who provided thoughtful reviews at a later stage. L. Faust
assisted with the illustrations.
The Editor thanks Neil Humphrey and Garry Clarke for
technical reviews.
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A. G. Fountain, Department of Geology, Portland State
University, 17 Cramer Hall, 1721 Southwest Broadway, Port-
land, OR 97207-0751. (e-mail: fountaina@pdx.edu)
J. S. Walder, U.S. Geological Survey, Cascades Volcano
Observatory, 5400 MacArthur Boulevard, Vancouver, WA
98661. (e-mail: jswalder@usgs.gov)
328 ●Fountain and Walder: WATER FLOW THROUGH GLACIERS 36, 3 / REVIEWS OF GEOPHYSICS