WATER
FLOW
THROUGH
TEMPERATE
Andrew G. Fountain•
JosephS. Walder
U.S. GeologicalSurvey
CascadesVolcanoObservatory
Vancouver,Washington
Departmentof Geology
PortlandStateUniversity
Portland,Oregon
Abstract. Understandingwater movementthrough a
glacier is fundamentalto severalcritical issuesin glaciology, including glacier dynamics, glacier-induced
floods, and the prediction of runoff from glacierized
drainage basins. To this end we have synthesizeda
conceptualmodelof water movementthrougha temperate glacier from the surfaceto the outlet stream. Processesthat regulate the rate and distributionof water
input at the glacier surface and that regulate water
movementfrom the surfaceto the bed play important
but commonly neglected roles in glacier hydrology.
Where a glacieris coveredby a layer of porous,permeable firn (the accumulationzone), the flux of water to
the glacierinterior variesslowlybecausethe firn temporarily storeswater and therebysmoothsout variationsin
the supplyrate. In the firn-free ablation zone, in contrast, the flux of water into the glacierdependsdirectly
on the rate
of surface
melt
GLACIERS
or rainfall
and therefore
are usually full of water and flow is pressurized.In
contrast,water flow in englacialconduitssuppliedfrom
the ablation area is pressurizedonly near times of peak
daily flow or during rainstorms;flow is otherwisein an
open-channel configuration. The subglacial drainage
systemtypically consistsof several elements that are
distinctboth morphologicallyand hydrologically.
An upglacier branching,arborescentnetwork of channelsincisedinto the basalice conveyswater rapidly. Much of
the water flux to the bedprobablyentersdirectlyinto the
arborescentchannel network, which coversonly a small
fraction of the glacierbed. More extensivespatiallyis a
nonarborescentnetwork,which commonlyincludescavities (gapsbetweenthe glaciersole and bed), channels
incisedinto the bed, and a layer of permeablesediment.
The nonarborescentnetworkconveyswater slowlyand is
usuallypoorly connectedto the arborescentsystem.The
arborescentchannel network largely collapsesduring
winter but reforms in the spring as the first flush of
varies greatly in time. Water movesfrom the surfaceto
the bed through an upward branchingarborescentnet- meltwater to the bed destabilizes the cavities within the
work consisting of both steeply inclined conduits, nonarborescentnetwork.The volume of water storedby
formed by the enlargementof intergranularveins, and a glaciervariesdiurnallyand seasonally.
Small,tempergently inclined conduits,spawnedby water flow along ate alpine glaciersseem to attain a maximum seasonal
the bottomsof near-surface
fractures(crevasses).
Engla- water storageof---200 mm of water averagedover the
cial drainageconduitsdeliverwater to the glacierbed at area of the glacierbed,with dailyfluctuationsof asmuch
a limited number of points, probably a long distance as 20-30 mm. The likely storagecapacityof subglacial
downglacierof where water entersthe glacier.Englacial cavities is insufficient to account for estimated stored
conduitssuppliedfrom the accumulationzone are quasi water volumes,somostwater storagemay actuallyoccur
steadystatefeaturesthat conveythe slowlyvaryingwater englacially.Stored water may also be releasedabruptly
flux deliveredvia the firn. Their sizeadjustsso that they and catastrophicallyin the form of outburstfloods.
1.
INTRODUCTION
The movementof water throughglaciersis important
for scientificunderstandingand for immediatepractical
applications.Water in glaciersprofoundlyaffectsglacier
movement by influencingthe stressdistribution at the
glacier bed and thereby the rate at which the ice slides
over the bed. This processis important for both alpine
glaciers[e.g.,Iken and Bindschadler,
1986]and polar ice
streams[e.g.,Alleyet al., 1987;Echelmeyer
and Harrison,
1990; Kamb, 1991]. The episodicsurging (orders-ofmagnitudeincreasein speed) of some glaciersis evi-
•Formerlyat U.S. Geological
Survey,Denver,Colorado.
dently due to temporal changesin subglacialhydrology
[Kamb et al., 1985]. Glacial outburstfloods,a common
hazard in mountainousregions,result from the rapid
releaseof large volumesof water stored either within a
glacier or in a glacier-dammedlake [BjOrnsson,1992;
Haeberli, 1983; Walderand Costa, 1996]. Water from
glaciersis becomingincreasinglyimportant for hydroelectricpower generation[Bensonet al., 1986;Lang and
Dyer, 1985].Somehydropowerprojectsin France [Hantz
and Lliboutry,1983], Norway [Hookeet al., 1984], and
Switzerland[B•zinge,1981] have involvedtappingwater
from directlybeneath a glacier.
The purposeof this paper is to presenta conceptual
model of water flow through a glacier based on a syn-
Copyright1998 by the AmericanGeophysicalUnion.
Reviewsof Geophysics,
36, 3 / August1998
pages299-328
8755-1209/98/97 RG-03579 $15.00
Papernumber97RG03579
ß 299
ß
300 ß Fountain and Walder: WATER FLOW THROUGH GLACIERS
•
•
Accumulation
Zone
36, 3 / REVIEWSOF GEOPHYSICS
•.
•
AblationZone
.,'."..
*.i,: • "'•.:.•.
Water
saturated
o•
conam•
•
•T..
3
,
Glacier
Bed
Figure 1. Idealized longitudinalcrosssectionof a temperatealpine glaciershowingthe importanthydrologicalcomponents.In the accumulationzone,water percolatesdownwardthroughsnowand firn to form a
perchedwater layer on top of the nearlyimpermeableice, and then flowsfrom the perchedwater layer in
crevasses
(openfractures).In the ablationzone,oncethe seasonalsnowhasmelted,water flowsdirectlyacross
the glaciersurfaceinto crevasses
and moulins(nearlyverticalshafts).Basedon Figure 10.11of R6thlisberger
and Lang [1987];copyrightJohnWiley and SonsLtd.; reproducedwith permission.
thesisof our current understanding.We have extended
the scopeof previousreviews [R6thlisberger
and Lang,
1987; Lawson, 1993] by focusingon waysin which the
variouscomponentsof the drainagesysteminteract. As
part of the conclusions,we outline subjectsthat need
further investigation.This paper emphasizestemperate
alpine glaciers(glaciersat their meltingpoint), but resultsfrom and implicationsfor ice sheetsare included
where appropriate.We do not discussthe hydrological
role of the seasonalsnowpack,as there is a comparative
wealth of literature on the subject[e.g.,Male and Gray,
1981;Balesand Hardngton,1995] and becausethe effect
of snowon glacierhydrologyhasrecentlybeen reviewed
[Fountain,1996].
partially water saturated.The rate of water movement
through unsaturatedfirn dependson the firn's permeability and the degree of saturation [Ambach et al.,
1981], similar to percolationthroughunsaturatedsnow
[Colbeckand Anderson,1982] and soil [e.g., Domenico
and Schwartz,1990]. The near-impermeableglacierice
beneath promotesthe formation of a saturatedwater
layer at the base of the firn. Such water layers are
common in temperate glaciers [Schneider,1994]. The
depth to water generallyincreaseswith distanceupglacier JAmbachet al., 1978; Fountain, 1989], as can be
expectedfrom the general increasein snow accumulation with elevation.High in the accumulationzone, the
water table may be as much as 40 m below the glacier
surface [Lang et al., 1977; Schommer,1977; Fountain,
1989].
2.
HYDROLOGY
OF THE FIRN
The hydrologicalcharacteristics
of firn are fairly uniAND NEAR-SURFACE
ICE
form betweenglaciers.Field testsof the hydraulicconductivity(permeabilitywith respectto water) of the firn
At the end of the melt seasonthe surfaceof a glacier at five different glaciers[Schommer,1978;Behrenset al.,
consistsof ice at lower elevations in the ablation zone,
1979; Oerter and Moser, 1982; Fountain, 1989; Schneider,
where yearlymasslossexceedsmassgain, and snowand
firn at upper elevationsin the accumulationzone,where
yearlymassgain exceedsmassloss(Figure 1). Firn is a
transitionalmaterial in the metamorphosisof seasonal
snowto glacierice. As we will discussin section2.1, the
presenceor absenceof firn has important implications
for subglacialwater flow and for variations in glacial
1994]indicate
a surprisingly
narrowrangeof 1-5 x 10-s
m/s. This may reflect a uniform firn structureresulting
from a common rate of metamorphismof firn to ice.
Firn samplesfrom South CascadeGlacier, Washington
State, had a porosityof 0.08-0.25 with an averageof
0.15 [Fountain,1989].This averagevalue is equalto the
value that Oerter and Moser [1982] found to be most
runoff.
appropriatefor their calculationsof water flow through
the firn. Within the water layer, ---40%of the void space
2.1.
Accumulation
Zone
is occupiedby entrappedair [Fountain,1989].
The accumulationzone typicallycovers---50-80% of
The depth to the water layer dependson the rate of
an alpine glacierin equilibriumwith the local climate water input, the hydrologicalcharacteristicsof the firn,
[Meier and Post, 1962]. The near surfaceof the firn is and the distance between crevasses,which drain the
36 3 / REVIEWS OF GEOPHYSICS
Fountain and Walder: WATER FLOW THROUGH
GLACIERS ß 301
Figure 2. Photomicrographshowingthe veinsin glacierice formed at junctionswhere three grainsof ice are
in contact.The grain at the center is ---1 mm acrossin its longestdimension.The photographis courtesyof
C. F. Raymond.
water from the firn [Lang et al., 1977;Schommer,1977; mondand Harrison,1975], and water passagemay often
Fountain,
1989].Oversmallareas(lengthscales
of----102be blockedby air bubbles[Lliboutry,1971];furthermore,
m) of a glacierboth surfacemelt rate and firn permeability are relativelyuniform, and the depth to water is
controlledprimarilyby crevasse
spacing:Water input to
the firn variesboth seasonallyand daily. Seasonalvariations,rangingfrom no water input in winter to perhaps
as much as severaltens of millimetersper day in summer, causethe thicknessof the water layer to vary up to
severalmeters[Langet al., 1977;Schommer,1977, 1978;
Oerterand Moser, 1982]. Typically,the water table respondsto melt and precipitationwithin a day or two
[Oerter and Moser, 1982; Schommer,1977; Schneider,
1994], althoughdiurnal variationshave been occasionally observed[e.g.,Fountain, 1989].
Nye and Frank [1973]suggested
that significantquan-
the permeabilityof the ice may actuallybe lower near
the ice surfacethan within the body of the glacier [Lliboutry, 1996]. Thus intergranular drainage is probably
negligible,and water drainsfrom the firn into crevasses
that penetrateinto the body of the glacier(Figure 3).
From a hydrologicalperspectivethe firn is a perched,
unconfinedaquifer that drainsinto otherwiseimpermeable ice underneath
via crevasses.
One important differencebetweena firn aquifer and
a typical groundwateraquifer is that the thicknessand
extent of the firn continuallychange,whereasa groundwater aquiferis relativelyconstantovertime. Permeable
firn is lost as metamorphicprocessestransformfirn to
ice, closingthe passagesbetweenthe void spacesand
titiesof meltwater
maydrainfromtheglaciersurface
to renderingthe matrix impermeableto water flow [Shumthe bed throughintergranularveinsin the ice. However, skii, 1964;Kawashimaet al., 1993]. At the same time,
observedveinsare quite small(Figure 2) [seealsoRay- more firn is added as the seasonalsnowagesand snow
-0.5
I
I
I
I
I
I
-1.0
.........
-•.5
Snow surface
,,
-2.0-
..x
[ ',, .
-2.5
-3.0
-3.5
Figure 3. Profile of the depth to the firn water
table on South CascadeGlacier on August26, 1986
[after Fountain, 1989]. The solid curve is the snow
surface,the dotted curve is the top of the perched
water layer, and the dashedvertical lines represent
crevasses.The datum is arbitrary. Reprinted from
Annals of Glaciologywith permission
of the International GladologicalSodety.
: :,;.......•:
-
-4.0
I
0
,',
20
,
,
',:
40
Distance,
:,
60
in meters
• ]
80
100
302 ß Fountainand Walder: WATER FLOW THROUGH GLACIERS
36, 3 / REVIEWSOF GEOPHYSICS
grainssinter together. This processraisesthe baselevel poolsof water and surfacestreamsin the ablation zone
of the water layer relative to its former position[Foun- indicates the relative impermeability of the ice. The
tain, 1989]. Firn thicknesseschangefrom year to year near-surfaceice is not completelyimpermeable,howdependingon the residualsnowthicknessat the end of ever. Water may be transportedalonggrain boundaries
the summer.
in veins, which are enlarged by solar radiation. This
The primary hydrologicaleffectsof the firn on glacier processis limited to the uppermostfew tensof centimehydrology are to temporarily store water, to delay its ters in the ice owingto the limited penetrationof shortpassageto the interior of the glacier,and to smoothout wave solar radiation [Brandt and Warren, 1993]. The
diurnal variationsin meltwater input. Water storagein permeability of the near-surfaceice may account for
the firn water layer delays the onset of spring runoff small(severalcentimeters)fluctuationsof water levelsin
from glaciers and delays the cessationof flow in the boreholesthat do not connectto a subglacialhydraulic
autumn after surface melting has ended. For typical system[Hodge,1979;Fountain, 1994]. However,the wavalues of firn porosityand water saturationthe water ter flux through this near-surfacelayer is almost cercontentof a perchedlayer 1 m thick is equivalentto that tainly negligiblecomparedwith the flow in supraglacial
of a layer of water ---0.09 m thick. Fountain [1989] streams.
showed that at South Cascade Glacier the volume of
Where the ice is moving,melted surfaceice is replenwater stored in the firn is equivalent to ---12% of the ished by ice emerging from the interior of the glacier
maximum volume of water stored seasonallyby the [Meier and Tangborn,1965], and a deeply weathered
glacier [Tangbornet al., 1975]. In comparison,water crust, from the effects of solar radiation, does not destoragein the firn at Storglaci•iren,Sweden[Schneider, velop. In contrast,in regionsof "dead ice," where the ice
1994], accountedfor 44% of the maximum seasonal is not replenished, the near-surface ice can become
waterstorageestimated
by Ostling
andHooke[1986]. weatheredand quite permeable.Observationsof water
Transit time throughthe firn dependson the speedof a level fluctuations in boreholes in dead ice indicate a
wetting front in unsaturatedfirn, ---0.25m/h [Schneider, saturatedwater layer severalmetersthick [Larson,1977,
1994],and the responsetime of the saturatedlayer at the 1978]. On the basisof pump tests the hydraulictransT of thepermeable
surface
layeris ---8x 10-s
base.For example,if the water table is 10 m below the missivity
firn surface, the transit time to the water table is ---40
m2/s[Larson,
1978].If theperched
watertablethickness
hours(longerif a seasonalsnowlayeris present).Transit
time through the saturatedwater layer to crevassesdependson the distancebetweenthe crevasses
and on the
slopeof the water surface.Consideringboth percolation
is b = 2 m, then the hydraulicconductivityK = T/b of
the near-surfaceice is ---4 x 10-s m/s. This value is
withinthe rangegivenfor firn, but the correspondence
is
probablycoincidental.
In summary,the near-surfaceprocessesin the snowfree ablationzone introducelittle delayin the routing of
water into the body of the glacier. Moreover, the water
flux into the glacier is greater in the ablation zone,
comparedwith the accumulationzone,becausethe melt
rate is greater owing to both the lower albedo of ice as
comparedwith snowand the warmer air temperaturesat
the lower elevations.Consequently,both the mean daily
flux of meltwater and the variabilityin the flux of meltwater are greater in the ablation zone than in the accu-
to the firn water table and flow in the water table before
exitinginto a crevasse,a parcel of water commonlytakes
---10-160 hours.In comparison,transittimesin the body
of the glacier are commonlyno more than a few hours
for moderate-sizedtemperate glaciers[e.g., Hock and
Hooke, 1993; Fountain, 1993; Nienow, 1994]. Because
the crevasses
are not uniformly spacedand the thickness
of the firn increases with elevation, the transit time
through the firn to the interior is spatiallyvariable with
the net effect of smoothingdiurnal variationsin meltwater input to the glacier.We believethat water passage mulation zone.
through the snowand firn of the accumulationzone is
the sourceof the slowlyvaryingcomponent(baseflow)
3.
WATER" MOVEMENT
of glacial runoff.
THROUGH
THE BODY
OF A GLACIER (ENGLACIAL HYDROLOGY)
2.2.
^blation
Zone
In the ablation zone the seasonalsnowpackretains
meltwater and thus retards runoff during the early part
of the melt season[Fountain,1996].After the seasonal
snowhas melted, revealingglacierice, channelsdevelop
on the glacier surfacethat drain meltwater directly into
crevasses
and moulins(naturallyoccurringverticaltunnels) [Stenborg,1973]. In the absenceof the seasonal
snowpackthe delayfor rainwaterand meltwaterto 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 presenceof
For temperate glaciers,nearly all rain and surface
meltwater enters the body of the glacier through crevassesand moulins [e.g., Stenborg,1973]. As was discussedin section2.2, the flux throughthe veinsin the ice
is probablynegligible.Crevassesare the mostimportant
avenuefor water becausethey are more numerousthan
moulins and are found over the entire glacier,whereas
moulins are generally restricted to the ablation zone.
Water-filled crevassesare not common,indicatingthat
they efficientlyroute water into the body of the glacier.
This conclusionis supportedby Stenborg's[1973] work
36
3 / REVIEWS OF GEOPHYSICS
Fountain and Walder: WATER FLOW THROUGH
GLACIERS ß 303
of numeroustracer injectionsin crevassessupport the
arborescent-network
hypothesis[Fountain,1993].
"•,•'•k/
•) .\ .....
••'•./•
,-Subglacial There are few data bearing on the distributionand
x '• ].-r--• x• xx• xx•
--•
/ tunnel
geometry of englacial conduits or on englacial water
pressuresand flow rates.Most of our information comes
from boreholesdrilled to the glacierbottom usinga jet
of hot water [Taylor,1984].About half of all suchbore-'•
Bedr•k
. x
. •.
_
holesdrain before the glacierbed is reached,indicating
that many.boreholesintersect englacialpassages[EnFigure 4. Fluid equipotentials(dotted curves)and a hypogelhardt, 1978; Hantz and Lliboutry, 1983; Fountain,
thetical network of arborescent englacial channels [after
1994;Hookeand Pohjola,1994].Measurementsof water
Shreve,1985]. Reproducedwith permissionof the publisher,
the GeologicalSocietyof America, Boulder, Colorado USA. level,water quality,andflow directionin boreholes[e.g.,
Sharpet al., 1993b;Meier et al., 1994]and measurements
Copyright@ 1985 GeologicalSocietyof America.
of tracers injected into boreholes[e.g., Hooke et al.,
1988;Hock and Hooke, 1993] stronglysuggestthe presence
of englacialconduits.
showingthat moulins develop from crevasses.Neither
A
number of direct measurementsof englacialpasthe nature of hydrauliclinks betweencrevasses
and the
sages
exist. Hodge [1976] found englacial voids with
bodyof the glaciernor the formationof suchlinksis well
typical
vertical extents of -0.1 m, and Raymond and
understood.We attempt to addressthesetopicsbelow.
Harrison
[1975] found small, arborescent,millimeter
Water flows englacially(through the body of a glascale
passages,
but whetherthesevoidsor passages
were
cier) via ice-walledconduits.The mechanicsof steady
part
of
an
active
hydraulic
system
was
unclear.
(Void
is
flow in englacialconduitshave been describedtheoretused
here
to
mean
a
water-filled
pocket
in
the
ice,
which
icallyby R6thlisberger
[1972] and Shreve[1972].As with
Englacial
conduits
at theglacierbed,discussed
in section
4, en-- mayormaynotbepartoftheenglacial
hydraulic
system.
glacial conduitsexist if the tendencyfor closure,from
the inward creep of ice, isbalancedby the melt enlargement resultingfrom the energy dissipatedby flowing
water. Shreve [1972] argued that englacial conduits
shouldform an upwardbranchingarborescentnetwork,
with the mean flow directionoriented steeplydownglacier, as determinedby the gradientof the total potential
(gravity and ice pressure)driving the flow (Figure 4).
Empiricalresultsbasedon the dispersionandtraveltime
:
Isolated voids are known to exist.) Englacial conduits
havebeen observedwhere they debouchinto subglacial
tunnels (Figure 5) and where they intersectboreholes
(Figure 6). Video cameraslowered into boreholesby
Pohjola [1994] and by Harper and Humphrey[1995] revealedmultiple englacialvoidsthroughnearlythe entire
ice thickness.Voids that intersectedopposite sides of
the boreholewall were interpretedas englacialconduits;
typically,one or two suchfeatureswere encounteredin
i
Figure 5. Water pouring from an englacialconduit at the base of South CascadeGlacier. The englacial
conduitintersectsa subglacialtunnel accessiblefrom the glacier margin. Sunglasses
are shownfor scale.
304 ß Fountain and Walder: WATER FLOW THROUGH
GLACIERS
36 3 / REVIEWS OF GEOPHYSICS
Figure 6. An englacialconduit (black triangularvoid at right) intersectinga verticalborehole.Note the
rippleson the water surfacein the boreholecausedby water flowingfrom the conduit,whichhasa diameter
of-0.1 m. This video imagefrom Storglacifiren,Sweden,is courtesyof V. Pohjola.
eachborehole,with diameterstypically•0.1 m. Pohjola
[1994] determinedthat water was flowing in a few englacial conduitsand estimateda flow speed in one of
•0.01-0.1 m/s,the samerangeestimatedby Hookeet al.
[1988]usingdyetracers.Most conduitsseenby borehole
video seemedto be nearly horizontal,althoughHarper
and Humphrey mention one plunging at an angle of
•65 ø.Despiteobvioussamplingproblems,whichinclude
small samplesize, biased samplingof conduit orientationsfrom verticallyorientedboreholes,and a borehole
location largely restrictedto the ablation zone, several
conclusionscan be drawn. First, glaciologistsneed to
considerhowboreholewater levelsand tracer injections,
typicallyu.sed to investigatesubglacialhydraulicconditions,maybe affectedby englacialhydraulicconnections
[Sharpet al., 1993b]. Second,the near-horizontalslope
of many conduitsneedsto be reconciledwith the relatively steepplunge expectedfrom theoreticalconsiderations[Shreve,1972].
We conjecturethat water flowingalongthe baseof a
crevasseeither entersrelativelysteeplysloping,enlarged
veins that form a network of arborescent passages
[Shreve,1972] or entersthe microfracturescreatedduring crevasseformation that connectto other crevasses.
Water flowing along the base of the crevassewill melt
the walls and tend to widen and deepen the crevasse
(Figure 7a). Melting occurswhere water is in contact
with the ice, such that the crevasse surface in contact
with the flowingwater the longest,the crevassebottom,
will melt the most. This scenarioshouldalso apply to
waterflowingalongthe glaciermargin(Figure7b). Typically, water from snowmelt and rainfall on adjacent
slopesflowsunder the edgeof a glacier,exploitinggaps
betweenthe thinner ice alongthe glaciermarginand the
bedrock. Water quickly descendsuntil the gaps no
longer connect and the water forms a stream at the
ice-bedrockinterface.The streammeltsthe ice, causing
the channelto descendalong the slopingbedrock.
The rate of downcuttingby a crevasse-bottom
stream
may be crudely estimated if we assumethat the cross
3.1. Origin of EnglacialPassages
We suggestthat the near-horizontalenglacialcon- section of the crevasse bottom maintains a semicircular
duits encounteredin boreholesmay originatefrom the geometryof radius R (Figure 8). Thus downcutting
action of water flowing along the bottom of crevasses. proceedswithout widening.The local melt rate normal
Some supportfor this notion comesfrom the borehole- to the channelwall is thend cos0, where• is the melt
video observationsof Pohjola [1994], who found that rate at the bottom, that is, the downcuttingrate. The
englacial passageswere usually in close proximity to averagemelt rate (rh) normalto the channelsurfaceis
bandsof blue (i.e., bubblefree) ice and who suggested then givenby
that these bandsoriginatedfrom water freezing in crevasses.Harper and Humphrey[1995] also noticed that
englacialpassagesand blue-ice bands tended to occur
together on the walls of boreholes.
-
cos0 a0 =
J-•r/2
36, 3 / REVIEWSOF GEOPHYSICS
Fountain and Walder: WATER FLOW THROUGH GLACIERS ß 305
Further assumingthat all energydissipatedby the flowing water actuallycausesmelting,we find
QpwgS
(rh) : 'rr
pihiwR
(2)
where Q is the water flux, pwis the densityof water, Pi is
the densityof ice, # is the accelerationdue to gravity,S
is the slopeof the crevassebottom,and hiwis the latent
heat of melting.The hydraulicsare reasonablydescribed
by the empiricalManning equation,whichwe write as Figure 8. Idealized cross-sectionalgeometry of a stream
Q= •-•R8/351/2
(3)
where• isthe roughness.
Combining(1) through(3), we
flowingat the baseof a crevasse.The rate at whichthe stream
meltsitsway downwardinto the ice is calculatedassumingthat
the crevasse"tip" is semicircularand that the stream cuts
vertically downward.
canrelate• to Q andS by
1
,r
3/8
verticalcomponentof icevelocity.)Theseratesare many
orders of magnitude greater than the rate at which a
water-filledcrevassedeepensowingpurelyto the weight
of the water and the fracture-mechanicalpropertiesof
the ice [Weenman,1971].Furthermore,the downcutting
rate increaseswith Q, suggesting
a possiblemechanism
for stream capture;in regionsof complex,crosscutting
crevasses
thosehostingrelativelylarge water fluxesmay
cut down through othershostingsmall fluxes.
We envisagethe followingscenariofor the evolution
•=• (•--•)(P•w.)(•--•.w)S19/laQS/8
(4)
UsingPw- 103kg/m3,Pi = 9 x 102kg/m3,g = 9.8
m/s2, hiw = 3.35 x 10s J/kg,and h = 0.01 s/m1/3
(appropriatefor a smoothconduit),we have calculated
valuesof d for the caseS - 0.1 (Table 1). This value of
S is appropriate for crevassestrending longitudinally
along the glacier and therefore representsa plausible
upper bound.
The valuesin Table 1 indicatethat evenvery modest
flow' rates can cause crevasse-bottom
streams
to cut
down at a rate of a few to a few tensof metersper year.
(Note that to give downcuttingrates relative to the
glaciersurface,tabulatedratesmustbe correctedfor the
of a crevasse-bottom
stream:
As the stream
cuts down
into the glacier,the creep of ice tends to pinch off the
crevasseabovethe flowingwater. Eventually,the channel becomesisolatedfrom the crevasseexceptfor rare,
near-verticalpassagesthat conveywater from the crevasseto the channel(Figure 7a). The streamceasesto
descendonce the rate of closure equals the rate of
melting at the bottom of the channel (downcutting)
becauseit becomesfully enclosedin ice and melting
occursequallyon all walls.
To estimatethe ultimate depth to which a crevassebottom stream can cut down, we idealize the "mature"
channelashavinga circularcrosssectionof radiusR and
assumethat the melt rate is exactlybalancedby the rate
of ice creep. The channelwill be flowing full but with
zero pressurehead (atmosphericpressure),like the
"gradientconduit"discussed
byROthlisberger
[1972].Using Nye's [1953] result for conduitclosure,the balance
betweenmelting and closureis given by
2xrpihiw
R--Ue--'R
(5)
where n andA are flow-law constants[Nye, 1953],ue is
the ice emergencevelocity,i.e., the vertical component
of ice velocity,measuredpositiveupwards,andPi is the
ice pressureat the depth, D•aAX at which the channel
ceasesto downcut.We take Pi - 9i#D•tAX and rearrange (5) to write
Figure 7. Qualitativedepictionof the evolutionof an englaD^x =
cial conduitfrom its origin (a) as a crevasse-bottom
streamor
Pig 2'rrpihiwR2
(b) as a glacier-margin
stream.The streamcutsdownbecause
melting occursonly where water is in contactwith ice.
Using (3) to eliminateR,
(6)
306 ß Fountain and Walder: WATER FLOW THROUGH GLACIERS
36, 3 / REVIEWSOF GEOPHYSICS
TABLE 1. Calculated Values of the Rate of Downcutting and Equilibrium Depth for Englacial Conduits for Several Values
of Vertical Ice Velocity Ue
Water
Flux,
Rate
ofChannel
Equilibrium
Channel
Depth
D•t•orn
10-• rn•/s
Incision,rn/yr
ue = -1 rn/yr
ue= 0
1
5
10
50
100
2.9
268
210
8.1
12
34
52
268
275
300
317
240
255
291
308
u• = 1 rn/yr
......
204
231
283
304
u• = 5 m/yr
.....
238
276
The valueu• is positivein the ablationzone.The tabulateddowncuttingrate doesnot take into accounticecreepandthereforeappliesstrictly
only near the glacier surface.
spawnedfrom crevasses.We infer that surface water
reachingthe bed is generallyshifteddownglaciersothat
it extendsthe influenceof the firn over a larger subglacial area than it covers at the surface. This view is
__'iT3/8HeS3/16Q
(7) supportedby the observationsof Iken and Bindschadler
[1986] at Findelengletscher,
Switzerland,where glacierThe "equilibrium"depthDMAX is weakly dependenton surface streams, which exhibited marked diurnal variaQ, although,of course,the time requiredfor the channel tions, flowed into crevassesnear boreholes drilled to the
to cut to this depth decreasesas Q increases.For very bottom of the glacier.Subglacialwater pressurevariasmalldischarges
the apparentvalue of DMAx is negative. tions, as indicatedby fluctuationsin water level, did not
Physically,this meansthat a very smallcrevasse-bottom correlate with the diurnal streamflow variations but
streamcannotcut downand simplyremain at the baseof rather correlated with the slower variation of meltwater
the crevasse,the depth of which is governed by the input from a snow cover upglacier.Lateral shifts in
rheologicalpropertiesof ice [Paterson,1994].Calculated surfaceto bed water routingare supportedby the results
valuesof DMAX givenin Table 1 are quite large,perhaps of an experimentwherebya tracer injectedat the bottom
reflectingan overestimateof ,4 (whichdecreases
as the of a borehole drained to one outlet stream while a tracer
water contentof the ice increases[Lliboutry,1983], un- injected into a crevasseadjacent to the borehole ap-
derestimate of h, overestimate of S, or some effect of a
peared in a different outlet stream [Fountain,1993].
possiblynoncircularchannel crosssection [cf. Hooke,
The englacial hydraulic system supplied from the
1984;Hooke and ?ohjola, 1994].
ablation zone should develop more quickly and to a
In arriving at the expressionin (7) for DMAX we much greater extent than that suppliedfrom the accuassumedsteadyflow in the channel. However, for an mulation zone. As the snowline movesup the glacier
alpine glacier a constantor slowlyvarying discharge
cannotexistunlessthere is a storagemechanismthat can
maintain a supplyof water. We conjecturethat channels
.................
Plan View
suppliedwith water from the ablationzone may be able
to descenddeeper than thosein the accumulationzone
•r----$urface
crevasse
becauseof the large daily variability in water flux. For
channels supplied from the accumulationzone they
Engl.
acial_.
ff
•------"•..._.•
conduits
comecloserto the ideal case(equation(7)) becausethe
conduits
••
'•'•-•-"- •Subglac'•d
conduit
firn filters out daily water fluctuationsand providesa
water storagereservoir,reducinglonger-termvariations.
In neither case, however, do the channels reach a true
equilibrium position becauseof the variationsin water
supply.
3.2. Synopsisand Implications
Our view of the englacialdrainagesystemis shownin
Figure 9. Subhorizontalchannels,spawnedby the water
flow in crevasse
bottoms,are connectedby either steeply
plungingpassages,
formed by the enlargementof intergranular passages[Shreve,1972], or microfracturesbetweencrevasses.
Marginal channelsalsoform under the
edge of the glacierwhere water collectsfrom the valley
walls;thesechannelsmay eventuallyconnectto channels
Side
V-}
• •'"•..
View ............
Glacie
r surface
•'x--Passage
from
c-i;'--evasse•
Figure 9. Geometry of hypotheticalenglacialdrainagesystem, comprisingboth gently plunging conduitsspawnedby
crevasse-bottom
streamsand steeplyplunging"Shrevian"conduitsformedwhere water exploitsveinsin the ice.
36, 3 / REVIEWS OF GEOPHYSICS
Fountain and Walder: WATER FLOW THROUGH GLACIERS ß 307
duringthe summer,ice is exposedin the ablationzone.
The combination
of loweralbedofor ice,compared
with
snow,andwarmerair temperatures
loweron the glacier
increases
thewaterfluxintothe ablationzonecompared
to the accumulation
zone.We thereforeexpectenglacial
filled
conduit /
conduitsreceivingwater from the ablation zone to be
more developedcomparedto the conduitsreceiving
water from the accumulation zone. The common occurrence of moulins in the ablation zone rather than in the
accumulationzone probablyreflectsthe differencein
drainagedevelopmentbetweenthe two zones.The englacialdrainagesystemmust be highly dynamic,with
channelsbeing continuously
reorientedby differential
shear as ice is advected downstream or severed in ice-
falls. Channel segmentsmust frequentlycloseoff becausetheir water supplyis lost to other channelsby
drainage capture or becausetheir connectionto the
glaciersurfaceis interruptedneitherby refreezingduring the winter or by ice creep.
Table 1 indicates that for ice thicknesses of 200 m or
less,descendingenglacialchannelsmay reach the bottom of the glacierto becomesubglacialconduits.This
processprovidesa mechanismto route water from the
glaciersurfaceto the bed and a processby whichnew
subglacialconduitsare formed.We do not expectthe
englacialconduitsto descend
muchbelow300m except
in unusualcircumstances;
thereforesubglacialconduits
found below 300 m are probablyformed from some
Figure 10. Longitudinalcrosssectionof a glaciershowinga
hypothetical
englacialconduitdescending
into an overdeepenedregionof a glacier.The conduitbecomespinnedonceit
reachesthe bed at the downstream
marginof the overdeepening. Deepening upstreamof this point continuesuntil the
channel becomes water filled.
conduitis now "pinned"at the downstreamend andwill
evolveinto a conduitapproximately
parallelingthe ice
Our conceptionof the englacialdrainagesystemhas surface.In that configurationthe conduitis full of water,
significantimplicationsfor overdeepened
regionsof al- so melting occursequallyon all surfaces,and downcutpineglaciers.An overdeepening
is a topographic
feature tingceases.
Thisconclusion
holdsfor a singlecontinuous
that wouldform a closeddepression,
and likely hosta conduit or for a network of conduits. We therefore
lake, if the glacierwere removed[e.g.,Hooke, 1991]. suggestthat in overdeepenedareas the movementof
Three boreholestudiesat Glacierd'Argenti•re,France water from the glacier surface to the bed will be re[Hantzand Lliboutry,1983],Storglaci/firen
[Hookeand stricted, as will the developmentof conduitsat the
Pohjola,1994],andSouthCascadeGlacier[Hodge,1976, glacierbed. Subglacialconduitscanbe developedfrom
1979;Fountain,1994]haveinvolveddrillingto the gla- water percolatingunder the glaciermargins,but such
cier bed in overdeepenedareas.In all three casesthe conduits
will alsobe pinnedby the lip of the overdeepdrillingwasdonein the ablationzone,andcertainqual- ening. We expectthat subglacialconduitswill be most
itative features were common:
commonlyobservedto passaroundoverdeepenings
near
1. Many boreholesencounteredenglacialconduits. the valleywalls,aswassuggested
by Lliboutry[1983].
2. Once boreholes reached the bed, water levels
remainedcloseto the ice overburdenpressureand did
not exhibit diurnal fluctuations;thus there was no indi- 4. SUBGLACIAL HYDROLOGY
cationof low-pressure
conduitswithin the overdeepening.
The modernstudyof subglacial
hydrologycanplau3. Low-pressureconduitsseemedto exist near the siblybe tracedto Mathews[1964],who measuredwater
valley sides.
pressureat the end of a shaft that reached the base of
These observations seem. to contradict our conclusion
South Leduc Glacier, Canada, from a mine beneath the
that englacialconduitsin the ablationzone shouldnor- glacier.Mathewsobservedthat waterpressurewasgenmally be efficient at conductingwater to the bed. A erally higher in winter than in summer,a situationthat
resolutionof this apparentcontradictionis possible, turns out to be common,and that abrupt increasesin
however,if we considerthe peculiareffectof the over- water pressurewere correlatedwith periodsof rapid
deepeningon the englacialconduits.
ablationor heavyrain, reflectingthe efficienthydraulic
Figure 10 showsa sectionof a subhorizontalconduit, connectionsbetweenthe glaciersurfaceand bed. These
one that hasdevelopedfrom a crevasse-bottom
stream, generalconclusions
weresupportedby investigators
who
that hascut downto the lip of an overdeepening.
The reachedthe bed of Gornergletscher,
Switzerland[B•zother mechanism.
308 ß Fountain and Walder: WATER FLOW THROUGH GLACIERS
36, 3 / REVIEWSOF GEOPHYSICS
water pressureis measureddirectly at the bed, without
relyingon the manometricprinciple.
4.1. Components
of the SubglacialDrainageSystem
Water emerges at the glacier terminus in a small
number of conduits incised into the basal ice, and it is
tempting to supposethat these conditionsprevail subglaciallyaswell. Reality is probablymuch more complicated.There is presentlybroad agreementamongglaciologiststhat water flowsat the glacierbed in one or both
of two qualitativelydifferent flow systems(Figure 11),
commonlytermed "channelized"and "distributed."This
terminologyis problematicbecause,as we shall point
out, the distributedsystemoften consistsin part of what
Figure 11. Idealizedplan view of (a) an arborescenthydraulic (fast) systemcomposedof channelsand (b) a nonarbores- commonsensedictatesbe called channels.We suggest
cent hydraulic(slow) system.
that it makes more
sense to refer
to "fast"
and "slow"
drainage systems[Raymondet al., 1995]. In the fast
system,relatively small changesin total systemvolume
ingeet al., 1973] and Glacier d'Argenti•re [Vivian and producerelatively large changesin discharge.The fast
Zumstein,1973] in connectionwith hydropowerdevel- systemhas a relativelylow surface-to-volumeratio, covopments.Vivian and Zumstein [1973] also showedthat ers a very small fraction of the glacier bed, and comthe strongdiurnalpressurefluctuationsobservedduring prisesan arborescent(convergingflow) networkof conduits, similar to a subaerial stream network. In the slow
the melt seasonwere absentduringwinter.
Iken [1972]measuredwater pressurein moulinsin the system,in contrast,relativelylarge changesin total syssubpolarWhite Glacier and observedlarge diurnalvari- tem volume produce only small changesin discharge.
ations. Subsequently,various investigatorsdeveloped The slowsystemhasa relativelylarge surface-to-volume
techniquesto drill to the glacierbed and usedthe water ratio, coversa relativelylargefractionof the glacierbed,
level in boreholesasa piezometricmeasureof subglacial is nonarborescent,and may involvea variety of compliwater pressure.The first systematicboreholestudiesof catedflow pathsat the glacierbed.
the subglacialdrainagesystemwere done at South CasThe distinctionbetweenfast and slow flow systems
cade Glacier [Hodge,1976, 1979], Blue Glacier, Wash- has been inferred from variations in borehole water
ingtonState,United States[Engelhardt,1978;Engelhardt levels, from the travel time and dispersionof tracers
et al., 1978], and severalSwissglaciers[R6thlisberger
et injected into glaciers,and from measurementsof water
al., 1979]. In a minority of the boreholesin all of these flux and chemistryin streamsflowing from glaciers.
glaciers,the water level dropped as soon as the drill Under any particularglacier,part of the bed may hosta
reachedthe glacierbed. Water levelsin theseboreholes fast drainagesystemwhile the rest hostsa slowdrainage
fluctuateddiurnallybut were usuallynot closelycorre- system,with transitionalzoneslinking the two. Furtherlated. In a majority of the boreholesthe water level more, the basaldrainagesystemin any particularregion
remainedhigh and nearly constant,commonlyat a level may switchfrom one configurationto the other in recorresponding
to a water pressuregreaterthan local ice sponseto perturbationsin meltwater input.
overburdenpressure,even after the drill reached the
4.1.1. Fast drainagesystem(R/Jthlisberger
chanbed; a drop in the water level, if it occurredat all, was nels). An isolated,water-filledvoid in a glacierwill
delayed for several days to a few weeks. Such experi- tend to be closedby inward ice flow unlessthe water
enceswith boreholewater levelsseemto be ubiquitous. pressurep• equalsthe ice overburdenpressurePi [Nye,
Glaciologistscommonlydescribethe first sort of bore- 1953]. Englacial or subglacialchannelsmay exist with
hole as "connected"to the subglacialdrainage system P,• < Pi if the flowingwater dissipatesenoughenergyas
and, assumingthat the boreholevolume is small com- heat to melt the ice and therebykeep the channelopen
pared with the volume of accessiblesubglacialwater, (Figure 12a). R6thlisberger[1972] presentedthe first
treat'borehole water level as a manometric measure of reasonablycompleteanalysisof the hydraulicsand therwater pressureat the bed. The secondsortof boreholeis modynamicsof steadyflow in a subglacialchannel,and
termed "unconnected" and cannot be used as a manomglaciologistsnow commonlyrefer to such channelsas
eter, asthe holevolumeis probablylargecomparedwith "R6thlisberger" or "R" channels. R6thlisberger asthe volume of accessiblesubglacialwater. Recently, sumedthat subglacialchannelshave a semicircularcross
Waddingtonand Clarke [1995] and Murray and Clarke section and that the flowing water must gain or lose
[1995] have shown that valuable information can be energyso as to remain at the pressure-meltingtempercollectedfrom unconnectedboreholeswhen the top of ature. He derivedthe followingdifferentialequationfor
the boreholecanbe sealed,in their case,by freezing,and steadyflow in a channel:
36, 3 / REVIEWSOF GEOPHYSICS
Fountain and Walder: WATER FLOW THROUGH GLACIERS ß 309
as] - ot(d•i)]P
-•-] -•
= [3
Q-qpe
•
(d(I)/p+l
dPw
(8)
Pi
where (Figure 12b) the coordinates increasesin an
upglacierdirection along the water flow path, z is the
bed elevationrelative to an arbitrary datum, cI) - Pw +
pw#Zis the total hydraulicpotential,Q is the discharge,
Pwis the densityof water, # is the accelerationdue to
gravity,andpe = Pi - Pw is the effectivepressurein the
channel.The term multipliedby o•reflectsthe pressuremelting effect, and [3involveschannelroughnessand ice
rheology.The exponentsp and q are both positiveand
depend weakly on the empiricismchosento describe
turbulent flow in the channel [Lliboutry, 1983]. The
exponentn • 3 follows from empirical ice rheology.
ROthlisberger
[1972]showedthat the form of (8) immediatelyleadsto an importantconclusion,mosteasily
seen for the case in which the local channel
bo
inclination
(0 = sin-• (dz/ds))equals
0, inwhichcase,cI)- Pwand
(8) becomes
d;.
ds: 1--Ot1/(I+p)
Q-q/(l+p•9en/(l+P)
(9)
dpw(•)
The greaterthe discharge,the smallerthe pressuregradient; accordingly,if we envisagetwo nearby channels
andintegrate(9) oversomefinitedistance
x, the channel
carryingthe greaterdischargewill be at a lower pressure
than the other. R6thlisbergerconcludedthat if hydraulic
connectionsbetweenchannelsexist,the largestchannels
shouldcapturethe drainageof the smalleronesand an
arborescentdrainage network should develop. Shreve
[1972] reachedthe sameconclusionby a slightlydifferent line of reasoning.
ROthlisberger's
[1972] analysisappliesstrictlyonly for
steadyflow. This is certainlya poor approximationfor
i
i
d•
i
i
•
•
• dx
•
•X
Figure 12. Schematic of a R6thlisberger channel [after
ROthlisberger,
1972]. (a) The channeltendsto closeby creep
of ice at overburdenpressurePi but tends to be opened by
melting as the flowingwater (pressurePw) dissipatesenergy.
(b) In general, the channelis inclined at some angle to the
horizontal (the x axis). Reprinted from the Journal of Glaciologywith permission of the International Glaciological
Society.
water pressures
(as indicatedby the water levelin boreholesdrilledto the bed) hasbeenproblematic.Predicted
temporal variations of dischargeare commonlylarge, values of Pw are commonlymuch less than measured
and channelsprobablyflow full of water only a small values [Engelhardt,1978; Hooke et al., 1990; Fountain,
fraction of the time. The steadyflow approximationis 1994]. Lliboutry [1983] argued that this primarily reprobablyreasonablefor channelsfed from the accumu- flectedan inadequatedescriptionof the channel-closure
lation area, but even in this case,channelsmay not be physicsand that the correctionentailed consideringthe
full of water. Weertman[1972] and Hooke [1984] both complicatedstressstate created by glacier slidingpast
assessed
theoreticallythe likely extent of open-channel bedrock obstacles,as well as a proper choice of ice
flow in semicircularchannelsand predicted that open- rheologyparameters.Hooke et al. [1990] suggestedthat
channelflow under a constantdischargewill occurif the the discrepancybetween measured and predictedPw
ice thicknessH i is lessthan a criticalvalue Hcrit = const could be resolvedif R channelsare actuallybroad, and
Qa(dcI)/ds)
b,witha • 0.07-0.08andb • 0.46.Hooke they proposedan ad hoc modificationto ROthlisberger's
concludedthat open-channelflow should be common [1972] analysisin line with their idea about channel
beneath steeplyslopingalpine glacierslessthan a few shape.Predictedwater pressuresfor the modifiedchanhundred meters thick. Data to assess this conclusion are
nel shape were in good agreementwith the observed
sparse.Fountain [1993] andKohler[1995] inferred from borehole water pressuresat Storglacifiren.Finite eleanalysisof tracerinjectionsthat while open-channelflow ment modeling of R channel evolution in responseto
probablydid occur,it wasrestrictedto verythin ice near variable water input [Cutler, 1998] supportsHooke et
the glacierterminus(i.e., in the ablationarea) and thus al.'s conjectureabout channelshape.
not nearly as extensiveas Hooke's calculationswould
In consideringthe discrepancy
betweenpredictedand
measuredPw it is worth reflectingon whether borehole
have predicted.
Application of (8) to predict measuredsubglacial water level shouldeven be consideredas a piezometric
channels fed from the ablation area, in which case,
310 ß Fountainand Walder: WATER FLOW THROUGH GLACIERS
36, 3 / REVIEWSOF GEOPHYSICS
Figure 13. Subglacialconduitincisedinto ice near the marginof South CascadeGlacier. The heightof the
conduitis --•1.5 m. Note three importantfeatures:The ice is restingon unconsolidated
sediments,the channel
is not full of water, and the cross-sectional
shapeis flattenedinsteadof semicircular.
ilar resultsbearingon the hydraulicconnectionbetween
subglacialchannelsand the surrounding,presumably
slowbasaldrainagesystem.At both glaciers,water level
measurementsin arraysof boreholesin the ablationarea
indicatedthe existenceof a zone,elongatedalongthe ice
flow direction but only a few tens of meters wide, in
which basalwater pressurefluctuatedgreatly and commonly fell to atmosphericvalues.To either side of this
zone, basalwater pressurewas generallyhigh and fluctuated relativelylittle. A plausibleinterpretationis that
ever intersected an R channel. If a borehole intersects a
an R channel existed and was efficiently connectedto
part of the basalhydraulicsystemthat drainsto a sub- the ablation-zoneinput, whereasthe adjacent (slow)
glacialchannel,then boreholewater levelswill necessar- hydraulicsystemwas poorly connectedto the channel
ily reflectPw greater than that in the channel[cf. En- and wasfed from farther upglacier.We will elaborateon
gelhardt,1978]. Until a borehole can be drilled that this idea in our discussionof the temporal evolutionof
unambiguously
intersects
a subglacial
channelandthatis the basal drainagesystemin section5.
not adverselyaffected by englacial water input, it is
4.1.2. Slow drainagesystem. The slowdrainage
perhapsprematureto discountthe quantitativeaccuracy systemcomprisesseveralmorphologicallydistinctflow
of (8). Severalinvestigators
seemto have drilled bore- pathways.Most of the dischargein the slow system
holes that came tantalizinglyclose to basal channels. movesthroughcavitiesand subglacialsediment.A wideWater level in boreholeU of Engelhardtet al. [1978]fell spread, thin water film also forms part of the slow
to the glacier bed a few days after the borehole was system;this film accommodates
little water flux but may
completed,and a soundingfloat loweredinto the bore- affectthe glacierslidingspeedaswell aswater chemistry
hole did not stop at the bottom of the boreholebut ran [Hallet, 1976, 1979].
out along some sort of basal passageas far as it was
4.1.2.1. Subglacialcavities: A subglacialcavity
allowed to go. Hantz and Lliboutry [1983], Fountain forms where slidingice separatesfrom the glacier bed
[1994], and Hubbard et al. [1995] found that in a few (Figure 14). Large cavitiesbeneaththin ice are someboreholes,there were large diurnal pressurefluctua- times accessiblefrom the glaciermargin [e.g.,Anderson
tions,with minimum valuesof Pw closeto atmospheric et al., 1982]. Cavityformationis favoredby rapid sliding
pressure,and concludedthat theseboreholeswere effi- and high bed roughness[Nye, 1970]. Lliboutry [1965,
cientlyconnectedto R channels.
1968] was the first to proposethat cavitationplayed a
Studiesby Fountain [1994] and by Hubbard et al. critical role in glaciersliding.In later papers[Lliboutry,
[1995] at two different glaciersyielded intriguinglysim- 1976, 1978, 1979]he arguedthat there were two typesof
measurementof water pressurein an R channel.Borehole water level doesnot reflect basalwater pressureif
water entersthe boreholeeither at the glaciersurfaceor
englacially.Surfacerunoff can be divertedfrom a borehole, but the sameis not true for water entering englacially, and there is a substantialbody of evidencethat
boreholes do commonly intersect englacial channels
during drilling. Moreover, although R channelshave
certainlybeen seen at the marginsof glaciers(Figure
13), thereis no unequivocal
evidencethat a boreholehas
36, 3 /REVIEWS OF GEOPHYSICS
Fountain and Walder: WATER FLOW THROUGH GLACIERSß 311
cavities: "autonomous" cavities containing stagnant
meltwater hydraulically isolated from the subglacial
drainagesystemand "interconnected"cavitieslinked to
R channels.Lliboutry [1976] also proposedthat sliding
speedshould depend on the effective pressurePe in a
network
of R channels
and interconnected
A.
cavities.
Walderand Hallet [1979],Hallet andAnderson[1980],
and Sharpe! al. [1989] mappedsmall-scalegeomorphic
featureson recentlydeglaciatedcarbonatebedrocksurfaces and concludedthat widespreadcavitation must
haveoccurredbeneathsomesmallalpine glaciers.Steep
concavitiesdownglacierof localbedrockknobsor ledges
were often deeplyscallopedand similarin appearanceto
the surfacescreatedby turbulentwater flow over limestone
in caves
and
subaerial
environments.
Cavity
Motion
Because
B
theseconcavities,which covered20-50% of the deglaciated surfaces,could not hold water subaerially,they
couldhaveexperiencedextensivedissolutiononly if water had been confinedover them, as in subglacialcavities. In every one of the mapped examplesthe overall
basal drainagesystemwas nonarborescent.
The hydraulicsof steadyflow througha cavitysystem
wasinvestigatedtheoreticallyby Walder[1986]and more
completelyby Kamb [1987].A subglacialcavityopensas
ice separatesfrom the bed at the upglaciermarginof the
cavity and closesby the creep of ice into the cavity.
Energy dissipatedby flowing water also enlargesthe
cavity,but this effect is minor exceptin the orificesthat
link large cavitiesbecausenearly all of the head loss
occursin the orifices.Analysesby Walder and Kamb
B.
0
10 Meters
scale
approximate
A
A'
/ ///
Ice>//
//
///
.•- Cavity
-•./•
>
:
lead to the result
Q • u•(d•/ds)•/2p•-3
(10)
where ub is the slidingspeedand m = 0.5-1. The key
featureof (10) is that water flux increasesaspefalls,that
is, as Pw rises. Thus there is no tendency for many
smallercavitiesto drain into fewer, larger cavities,contrary to the situation with R channels.Another key
feature of a cavity drainagesystem,shownparticularly
clearlyby Kamb [1987],is that for a givendischargethe
water pressurein the cavitysystemmustbe muchgreater
than in an R channelsystem.
Consideringagain Figure 14, it seemsapparent that
an arborescent
R channel network
should be much more
B
//
:
/
/
//
Ic•.
/
/
)>
//
B'
/
/ • Orifice
/,/ /
Figure14. Idealizedsubglacial
cavitynetworkin (a) plan
viewand (b) crosssection[afterKamb, 1987].Unshadedareas
are regionsof ice-rock contact;shadedareas are regionsof
ice-rockseparation(cavities).Flow directionsin the cavities
are indicatedby arrows.Orificesare the mostconstrictedparts
of the cavitynetworkand accountfor mostof the energylosses.
efficientat evacuating
meltwaterthana nonarborescent
cavitynetwork. The channelnetwork has shorter average flow paths,thus shortertravel times,than the cavity
network.We alsoexpectthe behaviorof tracersinjected
into the subglacialdrainagesystemto be very different
for the two cases:Tracersinjectedinto a cavitynetwork
shouldtend to become highly dispersed,with multiple
concentrationpeaks resultingfrom comparativelylong
travel timesand multiple flow paths,whereasin a channelized systemthe travel times shouldbe shorter, and
dispersionshouldbe muchless.Field data suchas those
from Variegated Glacier,Alaska [Brugman,1986;Humphreyeta!., 1986], supportthis conclusion.
4.1.2.2. Subglacialwater film:
Weertman[1962,
1964, 1966, 1969, 1972] arguedthat meltwaterdrainage
involveda widespread,thin water layer at the glacierbed
(Figure 15). He argued [Weertman,1972] that basal
channelswere inefficient at capturingmeltwater generated at the glacierbed (by geothermalheat and energy
dissipatedby basal sliding) and that basallygenerated
water must flow in a thin layer, typically---1 mm thick.
Weertman's[1972]argumentfor the inabilityof channels
to capturemeltwatergeneratedat the glacierbed relied
on peculiaritiesof the stressdistributionnear a channel
312 ß Fountain and Walder: WATER FLOW THROUGH GLACIERS
36, 3 / REVIEWS OF GEOPHYSICS
connectingcavitiesto one another.Becausetheseobservationswere all made on highly solublecarbonatebedrock, it is uncertain how representativethey are of
glacier beds in general. However, it seemsclear that
beneathat leastsomesmallalpine glaciers,Nye channels
constitutea morphologicallydistinct part of the slow
drainagesystem.Within the contextof present-daytheory, however,their hydraulic behavior, at least on the
mappedglacierbedsmentionedabove,is simplythat of
elongatedorificesin a cavitynetwork.
4.1.2.4. Subglacialsediments: RecentlydeglaciFigure 15. Regelationfilm of water at the ice-rockinterface.
in a material with the rheologicalpropertiesof glacier
ice; he concludedthat except near the margins of a
channelthe pressuregradient at the glacierbed would
drive water awayfrom the channeland that water layer
drainagewas the only plausiblealternative.Weertman's
[1972] argumentwas formulatedwith the implicit assumptionsthat (1) the glacier-bedrockinterfaceis planar and free of rock debris and (2) the bedrock is
impermeable.Actual glacierbedsare roughon a range
of length scales,and it is probable that there would
alwaysbe flow paths through the zone of supposedly
adversepressuregradient. Moreover, if there is a permeable layer of rock debrisat the glacierbed, and this
seemsto be typicallythe case,then meltwatercanflow to
a channelthroughthe permeablerock debris.The water
layer concept has two other problems.Nye [1973]
pointedout a fundamentalinconsistency
in postulatinga
widespreadwater layer that providesboth a. path for
local redistributionof meltwaterinvolvedin the regelation-slidingprocess,which requiresa layer thicknessof
---1 txm, and a path for basally generated, throughflowingmeltwater,with a characteristiclayer thickness
of --•1 mm. Some other pathsmust existto allow for the
net downglacierflow of meltwater.Finally, a water layer
at the glacierbed is not stableagainstperturbationsin
layer thickness.The instability,proposedby Nye [1976]
and analyzed by Walder [1982], arises because the
thicker the layer, the more energyis dissipatedby viscousforcesand thus the greater is the melt rate. Variationsin water layer thicknessare therefore magnified,
and protochannelstend to develop.
4.1.2.3. Nye channels: Nye [1973]suggested
that
ated bedrock surfacesnearly devoid of unconsolidated
sedimentare rare, and it is likely that mostglaciersare
in fact underlainby a spatial!yvariable,perhapsdiscontinuouslayer of rock debris(Figure 17), whichfor simplicity (and without sedimentological
connotations)we
will call glacialtill. The till actsas a confinedaquifer as
long as it is muchmore permeablethan the underlying
bedrock(Figure 18); this seemsto have been first recognizedby Mathewsand Mackay [1960],althoughit was
not widelyappreciatedby glaciologists
until the work of
Boulton and Jones[1979]. Even a pervasivebasal till
layer, however,can evacuateonly a smallfractionof the
total water flux throughthe glacier.Consider,for example, a till layer with a thicknessB - 0.1 m and a
hydraulic
conductivity
K in therangeof 10-8-10-4 m/s,
values that are plausiblein light of the field evidence
discussedbelow. Assumingthat this layer coversthe
entire glacierbed, of width W transverseto the ice flow
direction,the net meltwaterflux throughthe layer is
The gradient(1/pw#)(d•/ds), determinedlargelyby the
ice-surfaceslope[e.g.,Shreve,1972],is typically--•0.1for
alpineglaciers.
TakingW = 1 km, we findQDarcy
•'
10-7-10-3 m3/s,ascompared
withtypicalmelt-season
discharges
of --•1-10m3/sandwinterdischarges
of perhaps0.01-0.1m3/s[cf.Lliboutry,
1983].Analogous
calculationswith similar conclusionshave been presented
for till aquifersbeneath ice sheets[Boultonand Jones,
1979] and ice streams[Alley, 1989]. We concludethat
most of the water draining from a till-floored glacier
either avoidsthe bed altogetherand simplyflowsengla-
R channelsmustbe transientfeatures,beings[tueezed
shut as they are advectedagainstthe upglaciersidesof
bumpson the glacierbed, and that the maintenanceof
continuoussubglacialmeltwater drainagerequires the
presenceof channelsincisedinto the bed (Figure 16).
Studiesof recentlydeglaciatedbedrocksurfacescited in
section
4.1.2.1
in connection
with
the distribution
of
cavities[Walderand Hallet, 1979;Hallet and Anderson,
1980;Sharpet al., 1989] alsorevealedlarge numbersof Figure 16. Nye channels(channelsincisedinto subglacial
Nye channels,typically---0.1m deep,preferentiallyori- bedrock).A Nye channelmay be accompaniedby a R6thlisented alongthe former ice flow directionand commonly berger channelincisedinto the overlyingice.
36 3 /REVIEWS
OF GEOPHYSICS
Fountain and Walder: WATER FLOW THROUGH
GLACIERS ß 313
Figure 17. Basal ice restingon unconsolidatedsedimentsat South CascadeGlacier. The photographwas
takenin a R6thlisbergerchannelnear the glaciermargin.The tape measureat the right showsthe scalein both
inches(numbersin front) and centimeters(numbersin rear).
ciallyor elsepassesdirectlyfrom englacialconduitsinto
basal conduits.
The characteristicsof subglacialchannelscoexisting
with a till aquifer (Figure 19) were analyzedby Walder
and Fowler [1994]. The geometryof a sediment-floored
channeldevelopsin responseto flow interactionswith
both the ice roof and the sediment
floor. As in the case
of a rock-flooredR channel,the channelis enlargedby
meltingof the ice and shrunkenby inwardcreep of the
ice. In addition,the channelmay be enlargedby fluvial
erosionand dosed by inward creep of the till [Boulton
and Hindmarsh,1987]. Walder and Fowler showedthat
a networkof sediment-flooredchannelsmay existin two
asymptotically
distinctconditions:either an arborescent
network of sediment-flooredR channelsat Pe > • or a
stabledependson the magnitudeof• (determinedprimarilyby the creeppropertiesof the ice and sediment)
and the hydraulicgradient,whichis approximatedby the
ice-surfaceslope.For very low hydraulicgradientstypical of ice streamsand ice sheetsthe drainage network
should comprisenonarborescentcanals.For large hydraulic gradientstypicalof alpine glaciersthe drainage
systemshould comprisearborescentR channelsover
relatively "stiff" till, with propertieslike those of the
Breidamerkurj6kulltill in Iceland [Boultonand Hindmarsh, 1987]; however,as was pointed out by Fountain
and Walder[1993], for alpine glaciersfloored by relatively "soft" till [e.g.,Humphreyet al., 1993] the stable
drainagesystemwouldconsistof nonarborescent
canals.
nonarborescentnetwork of wide, shallow, ice-roofed ca-
nals eroded into the sedimentat Pe < I•, where • is a
"critical" effectivepressure.Which drainagenetwork is
Figure 18. Drainage through subglacialtill. Beneath most
temperatealpineglaciersa thin layerof unconsolidated
till lies
betweenthe baseof the glacier and the underlyingbedrock.
Figure 19. Subglacial"canals"coexistingwith subglacialtill.
Canals tend to be enlarged.as the flowing water removes
sedimentasboth bed load and suspendedload. Enlargementis
counteractedby the tendencyfor canalsto be closedby inward
movementof sedimentby creepor massfailuresfrom the canal
walls. Energy dissipatedby the flowingwater also melts the
overlyingice and counteractsthe tendencyfor ice creep to
close off the canal.
314 ß Fountain and Walder: WATER FLOW THROUGH GLACIERS
/
/
///Sole
_.•r' //
of glacier -x
I
I// %...
('
!//•
• •,.:..' ,,.T
.'"'.
'......
.
/•;..
' \ ,//Waternuea
--•,•,.•
gap
..-- :,.. ' ..'
"-"::-
36, 3 / REVIEWSOF GEOPHYSICS
neither of the other two samples,and (2) the Pe value
duringtesting,considering
the strongdependence
of K
onpe at lowpe [cf.Boultonet al., 1974].The measuredK
valuesprobablyall correspond
to verylowvaluesof Pe'
Estimated hydraulic conductivityvalues of till inferred from in situ measurementsvary substantially.
Severalin situ measurementsyield valuesbroadly consistentwith laboratorydata and valuesfor subaerialtill
aquifers.For SouthCascadeGlacier,Fountain[1994]
estimatedthe hydraulicconductivityrange from • -
rate (as
Figure 20. Hypotheticalmicrocavitynetworkat the ice-till 10-7 to 10-4 m/son thebasisof themigration
interface.Smallcavitiesmayform at the lee of relativelylarge observedin severalboreholes)of diurnalwaterpressure
claststhat protrudeabovethe meansurfaceof the till into the fluctuations.The boreholesintersecteda region where
flowing ice.
dye-tracertestsandwaterlevelmeasurements
suggested
thata basaltill la•erprobably
provided
hydraulic
communicationto a low-pressure
basalchannel.Using the
Basaldrainageover a till bed may alsoinvolvelinked
same
approach,
Hubbard
et
al.
[1995]inferredthe same
cavities, even if all of the bedrock irregularities are
range
of
•
for
till
at
the
base
of
Haut Glacierd'Arolla
smotheredby till. The cavitiesin this casewouldsimply
and also inferred that • decreasedwith distance away
be gapson the downglacier
sideof clastsprotrudingup
into the ice (Figure 20), as was pointedout by Kamb from a subglacialconduit.A muchlargervalue of hydraulicconductivity
for till beneathGornergletscher
has
[1987].
been
inferred
from
borehole-response
tests
by
Iken
et
al.
Clearly, there must be important interactionsbe[1996]:
0.02
m/s,
a
conductivity
valise
typical
of
medium
tween the subglacialtill layer and the basal conduits,
regardless
of the exactgeometryof the latter.Although to coarsegravel[Domenicoand Schwartz,1990,p. 48].
the amountof water actuallyexchangedbetweenthe till Similarlylarge (or even larger)valueswere originally
and the basalconduitsmay be small,the till providesa inferred by Stoneand Clarke [1993] from Trapridge
tests,but more repathwayfor smoothingout water pressuredifferences Glacier, Canada,borehole-response
cent
work
by
Stone
et
al.
[1997]
involving
the detailed
betweendistinctconduits.Dependingon the efficiency
of the subglacial
conduits,
the porepressure
pp within applicationof inversetheoryhasyieldeda revisedestipart of the
the till aquifer may be closeto Pi, with potentially mateof 5 x 10-4 m/s in the connected
system.
Muchsmaller
values
(K • 10-9-10
-8
importantimplications
for the mechanical
propertiesof drainage
the till.
m/s) have been inferred by Waddington
and Clarke
A consistentset of measurementsis beginning to [1995] for till in unconnectedregionsof the bed of
emergefor the hydrological
characteristics
of subglacial TrapridgeGlacier on the basisof long-termborehole
till. For tills that seemto be dilatedowingto activeshear waterlevelvariations.The situationat TrapridgeGlacier
deformationthe porosityis typicallynear 0.4; nonde- is somewhatunusualbecauseof severalfactors:(1) the
glacierisprobablyon thevergeof surging,
(2) the highly
formingtills have a porositymore commonlyof-0.250.3 (Table 2). There is considerably
more variabilityin correlated behavior of water levels in connected borecommonlynear (or greater
the apparenthydraulicconductivity(Table 3), as one holes,with waterpressures
pressure,
suggests
that locally,
might expect from the 6-order-of-magnituderange than)the ice overburden
(10-•2-10-6 m/s) reportedfor subaerial
till aquifers the glacieris nearlyfloatingon a.layerof water,and(3)
[Domenicoand Schwartz,1990,p. 48]. Laboratorymea- the glaciermarginsare frozento their bed,forcingall
surements of tills from beneath Breidamerkurj6kull meltwaterto drain downwardthroughthe subglacialtill
[Boultonet al., 1974], ice 'streamB, Antarctica [En- and underlyingbedrock.
Another estimateof in situ • for basaltill is wildly at
gelhardtet al., 1990], and Storglaci•iren
[Iversonet al.,
1994]yieldvalues
in therangeof 10-9-10-6 m/s.It is
variance
with
all
other
data
discussed above.
difficultto comparethesevalueswithoutknowledgeof
(1) the till grain-sizedistribution,
whichwasgivenfor the
Breidamerkurj6kulltill [Boultonand Dent, 1974]but for
"anomalous"K value followsfrom our interpretationof
a tracer test at the bottom of a borehole in ice stream B
[Engelhardt
etal., 1990].The flowrate of subglacial
water
TABLE 2. P,orosityof SubglacialTill
Location
TrapridgeGlacier,Yukon Territory, Canada
Ice stream B, West Antarctica
Ice stream B, West Antarctica
This
Porosity
0.35-0.40
0.32-0.40
0.40
Reference
Stoneand Clarke[1993]
Blankenshipet al. [1987]
Engelhardtet al. [1990]
36, 3 / REVIEWS OF GEOPHYSICS
Fountain and Walder: WATER FLOW THROUGH GLACIERS ß 315
TABLE 3. Apparent Hydraulic Conductivity of Subglacial Till
Location
Hydraulic Conductivity,m/s
Reference
In Situ Estimates
Breidamerkurj6kull
5 X10 -4
10 -9
10-7_10 -4
10-7_10 -4
10 -6
Storglacifiren
10-7
Ice stream B
10 -9
Various tills
10- •2-10 --6
Trapridge Glacier
Trapridge Glacier
South Cascade Glacier
Haut Glacier d'Arolla
Stoneet al. [1997]
Waddingtonand Clarke [1995]
Fountain [1994]
Hubbardet al. [1995]
Boultonet al. [1974]
LaboratoryMeasurements
Iversonet al. [1994]
Engelhardtet al. [1990]
SubaerialTill Aquifers
Domenicoand Schwartz[1990]
between two boreholes,inferred from tracer injection, enoughthat flow is actuallyturbulent.)The microcavity
was 30 m/h. Assumingthe validity of Darcy's law and concept seemsbetter grounded physicallythan Alley's
estimatingthe hydraulicgradientfrom the surfaceslope [1989] suggestion
that flow takesplace in a nonuniform
of theicestream(3.5x 10-4 to 1.25x 10-3, according"Weertman" water layer. On theoretical grounds it
to Shabtaieet al. [1987]), we estimateK = 6.6-24 m/s, seemsplausiblethat drainage at the bed may also inabout an order of magnitude greater than for coarse volve wide, shallow, nonarborescent canals incised into
gravel [Domenicoand Schwartz,1990].
the till [Walderand Fowler, 1994], particularlyif water
It is not entirely clear how to interpret the variousin reachesthe bed from the glacier surface.Realistically,
situ values of K cited above. The values were all based on
the hydraulicsof these various scenariosare probably
simple models that assumeda homogeneous,isotropic indistinguishable.The precise geometry of the flow
till layer of constantthickness.Furthermore, one must pathsis lessimportant than the conclusionthat a highbe careful in comparingthe derived • valueswith those conductivity,nonarborescentflow path probably does
for subaerialtill aquifers,whichmay havebeen affected exist.
In closingour discussion
of the subglacialtill layer we
by consolidation[e.g.,Boultonand Dent, 1974]or diagenetic processes
subsequent
to beingexposedby retreat- should emphasizethat the hydraulicpropertiesof the
ing ice. Even with thesecaveats,however,it seemslikely subglacialtill, and perhaps the till itself, seem to be
that the exceptionallylarge value of • for ice stream B patchy,with a characteristiclength scaleof---10-100 rn
representssomethingother than Darcian flow through beneath alpine glaciers[Engelhardtet al., 1978;Stoneet
the till; for one thing, the Reynoldsnumber is too high al., 1994; Fountain, 1994; Harper and Humphrey,1995]
for Darcy'slaw to be valid [cf. Stoneand Clarke,1993,p. and ---100-104
rn underice sheets[Alley,1993].Until
332]. In line with Kamb's [1991] analysisthe large ap- more is learned, categoricalstatementsabout the propparent • probablyreflectsthe flow througha networkof erties of subglacialtill shouldbe regardedwith skepticonnected
"microcavities"
at the ice-till
interface.
This
situationis analogousto water movementthroughfractured rock, in which case,flow throughfracturesdominatesflow throughthe rock'spore space[Domenicoand
Schwartz,1990].
As a simpleillustrationof the relative conductivities
of a till layer and a microcavitynetwork, considerthe
situation sketchedin Figure 20 with the microcavities
idealizedfor simplicityas gapsof uniform width h covering a fraction f of the bed. The effective hydraulic
cism.
4.2. Synopsis
and Implications
Until about the mid-1980s,subglacialwater flow was
almost invariably interpreted within the context of an
assumedR channeldominateddrainagesystem.The R
channelconcepthad successfully
formed the basisfor a
quantitative theory of outburst floods from glacierdammedlakes [Nye, 1976;Clarke, 1982] and waswidely
conductivity
Kef
f of a slit of widthh is pw#h2/12•w, applied;for example,Bindschadler[1983] discussedthe
where •Xwis the viscosityof water; correctingfor the link between basal hydrologyand ice dynamicsof an
fraction of the bed coveredby microcavitiesgivesKeff = Antarctic ice stream and a surgingglacier within the
fpw#h2/12•w
. Forf = 0.1-0.5wefindKef
f = 0.1-10m/s contextof classicR channeltheory. It was known both
for h = 0.3-15 mm. If we accountfor the tortuosityof theoretically[e.g.,Lliboutry, 1968;Nye, 1970] and from
the actual flow paths along the ice-till interface, the studiesof exhumed glacier beds [Walder and Hallet,
estimatesof h would be perhapsa factor of 2 greater. 1979; Hallet and Anderson, 1980] that cavitation was
For comparison,Kamb [1991] suggested
that the micro- probably common, but the hydrologicsignificanceof
cavitygapshave a characteristic
width of---1 mm. (We cavitieshad barely been explored.An analogousstateagain note that the Reynolds number may be great ment couldbe made aboutthe hydrologicsignificanceof
316 ß Fountainand Walder: WATER FLOW THROUGH GLACIERS
unconsolidated
sedimentat the glacierbed [Engelhardt
et al., 1978].
By about 1990 the way that glaciologistsenvisaged
basalwater flow had greatlychanged,largelyowingto
5.
36, 3 / REVIEWSOF GEOPHYSICS
TEMPORAL
THE DRAINAGE
EVOLUTION
OF
SYSTEM
Meltwater dischargefrom temperatealpine glaciers
varies typicallyby about 2 orders of magnitudefrom
for an explanationof observations
from surgingVarie- winter to summer,so it seemsplausiblethat the subglagatedGlacier[Kambet al., 1985]andrapidlymovingice cial drainage system must also undergo seasonal
streamB in Antarctica[Blankenship
et al., 1987].Theo- changes.Data bearingon this questionare sparse,as
rieswere developedto elucidatethe hydraulicsof water little informationis availableexcept for the ablation
flowthroughlinkedcavities[Walder,1986;Kamb,1987], season. Moreover, there is not much of a theoretical
deformabletill [Alleyet al., 1987],and till-flooredchan- foundation for understandingtime-dependentdischarge.
nels [Walderand Fowler,1994].The interpretiveframeIt is very unlikely that a robustsystemof R channels
work shiftedto one in whichglaciologists
usuallytried to
cansurvivefrom year to year exceptperhapsbeneathice
explainfield data from anyparticularglacierin termsof
only a few tensof metersthick. This is readilyseenby
a basaldrainagesystempresumedto be dominatedby consideringthe fate of a channel of radiusR that beone or anotherof threemorphologically
distinctcompo- comesemptyof water at the end of the melt season.The
nents:R channel,cavity,or till.
channelwill tend to be closedby inwardcreepof ice,
We believethat the most significantgeneralconclu- with the channelradiusas a functionof time givenby
sionto be drawnfrom the last3 decadesof investigations [Weertman,1972]
is that the basaldrainagesystemis highlyheterogeneous
in both spaceand time. It is probablethat the various
R(t) = Ro exp (-t/,)
(12)
componentsof the subglacialdrainagesystemhavenow
all been identified,and their hydraulicshave been rea- whereR 0 is the radiusat the end of the melt season.The
sonablywell described.However,the distribution,spa- characteristictime ß is proportionalto p•-n, where n •
tial extent, and seasonalevolutionof each drainage- 3. For ice thicknesses >-150 m a channel that has sursystemcomponentunder any particularglacier are still vivedthe winterwill havea radiusat the beginningof the
of --<10
-3 R0,probably
nomorethana few
uncertain.The way in which the drainage-system
com- meltseason
ponentsinteractalsoremainspoorlyunderstood.These millimeters for even the main trunk channels. A similar
issuesneedto be addressed
to improveour understand- argumentcan be made for the closureof Nye channels
ing of both glacier dynamicsand hydrology.The link and sediment-flooredcanals.In contrast,a cavitynetbetweenthe subglacialdrainagesystemand groundwa- work oughtto be able to survivefrom 1 year to the next
ter flow alsoremainsunexploredasidefrom grossgen- becausecavitiesare maintainedopenprimarilyby basal
slidingand only secondarilyby melting.As long as slideralizations[cf. Lliboutry,1983].
ing
does not ceasein winter and the accumulationof
To summarize,the drainagesystemunder any given
sediment
is not too great, cavitiesstayopen, although
glaciercomprises
severalor all of the morphologically
some
of
the
linksbetweenthe cavitiesmaybecomequite
distinctcomponentsdescribedin this section.A slow,
constricted.Thuswe suggestthat the subglacialdrainage
nonarborescent
drainagesystem,comprisinga mixture
systembeneaththe entireglacierat the beginningof the
of elementsincludingcavities,permeabletill, and conmelt seasonshouldtypicallybe cavitydominated,with
duitsincisedintothebed(i.e.,Nyechannels
andcanals), the cavitiesprobablypoorly connected.A similar sceprobablycoversmost of the glacierbed and is nearly nario hasbeen discussed
by Raymond[1987]in connecfixedrelativeto the bed.The waterpressurein the slow tion with glacier-surgeinitiation,whichwe will discussin
drainagesystemis commonlycloseto the ice-overbur- section8. In the caseof a sediment-flooredglacierthe
den pressure.A fast drainagesystemconsisting
of arbo- cavitieswill be located at the downglaciersidesof isorescentR channelsmay also exist.The fast drainage lated bedrockprotuberances
or relativelylargeboulders
sysiem,
beingincised
intothe baseof the glacier,
is that protrude abovethe mean local till surface[Kamb,
advectedby glaciermovementand probablyundergoes 1987].
continuousrearrangementas the sliding ice interacts
At the beginningof the melt season,once meltwater
with the roughbed beneath.The water pressurein the penetratesthe winter snowpack,it flows into crevasses
fast drainagesystemis commonlymuchlessthan the ice and preexistingenglacial channelslinked to the creoverburdenpressure;indeed,the fastdrainagechannels vasses.In the eventthat suchlinkswere severedduring
may be only partly full most of the time, in which case winter, water will pond in the crevasseswhile slowly
the flowis unpressurized
exceptat timesof peakdiurnal escapingthrough intergranularpassagesor microfracdischarge.Both the fast and slowcomponents
of the turesin the ice; the escapingwater eventuallyenlarges
basaldrainagesystemprobablyundergomajortemporal theseflow pathsby melting, and the cycleof englacial
changes,particularlyat the beginningand end of the channeldevelopmentstartsanew.The englacialnetwork
melt season, as discussedin section 5.
of channelsbeginsto fill again,and water makesits way
the realization
that R channels could not form the basis
36, 3 / REVIEWS OF GEOPHYSICS
.
Fountain and Walder: WATER FLOW THROUGH GLACIERS ß 31 7
to the glacierbed.Initially,the basaldrainagesystemis
:
/
:
x
:
unable to cope with the increasedmeltwater flux. The
initialresponse
will essentially
be like that proposedby
Iken et al. [1983],who measuredverticaluplift of the
surfaceof Unteraargletscher,
Switzerland,at the beginning of the melt season'Water pressurewill increase,
and cavitieswill enlarge.During thisperiodof time the
glacierwill storelargevolumesof water, consistent
with
the observations
of Tangborn
etal. [1975]andWillisetal.
[1991/1992].
The rate of waterinputto the glaciervaries Figure 21. Hypothetical broad, shallowconduit incisedinto
slowlyin time aslongasthe availablestoragein the firn the basalice, a variantof the standardconceptof a semicircularR6thlisberger
channel.Basalchannels
maybe broadand
andthe seasonal
snowpack
are greatenough.Therefore,
shallowbecause
icecreepsinwardlymorequicklyat the topof
in the ablationzone the water flux into the glacier the channel(whichis not full at timesof lowflow)thanat the
interior must begin to exhibit large diurnal variations sidesof the channel(wherethe creeprate is reducedby the
oncetheseasonal
snowhasmelted[Nienow,1994].Once effectof dragat the ice-rockinterface).
this happens,englacialchannelsfed from the ablation
zoneenlargeand cut downrapidly,and the partsof the
basalhydraulicsystemfed by these channelsbecome sentiallyice-roofedbraidedstreamsand interpretedthe
subjected
to largedailyvariationsin waterpressure.
The progressive
decreasein dispersivity
as reflectinga detransientincreasein water pressures,as well as in the creasein the degreeof braiding.Fountain[1993] inmelting causedby the increasein flow, enlargesthe jected dye mostlyinto crevassesat South CascadeGlaorificesin the basalcavitysystem.If the englacialwater cier and comparedthe measuredtravel time of tracers
flux,andthusthepressure
perturbation,
isgreatenough, with that derived from calculations based on a model of
cavityorificeswill enlargeunstablyand spawnan R turbulent flow in conduits. He also concluded that the
channelsystem[Kamb,1987].However,if the fluxreach- subglacial
conduits
wereshallowandbroadandthatthey
ing the bed throughan englacialconduitis sufficiently were pressurizedearly in the melt seasonbut evolved
small,the localcavitysystemwill remainstable.Thuswe towardopen-channel
flow asthe seasonprogressed.
envisagethat both the fast and slowcomponents
of the
basaldrainagesystemreceivewater directlyfrom the
glaciersurfaceand that R channelsrepresentthe con- 6. WATER STORAGE
tinuationat the glacierbed of the largestenglacialconduits.TheseR channels
probablyendurethroughoutthe
Glaciersstoreand releaselargevolumesof water on
melt season[Sharpet al., 1993a]as long as the water dailyto seasonal
timescales
[Tangborn
et al., 1975],maksupplyfrom the glaciersurfaceis sufficientto melt the ing short-term runoff prediction difficult. Outburst
ice wallsand thuscounteractcreepclosure.
floods,resultingfrom englacialand subglacialwater
Becausethe hypotheticalprocessof R channeldevel- storageand release,are probablycommonto mostglaopmentdescribedaboveis drivenby water input from ciers;sniallfloods,with a peak discharge
not much
the surface, it seemsreasonablethat this sort of devel- larger than the typicalmaximumdaily flow, probably
opmentin the basaldrainagesystemshouldprogress occurfrequentlybut are rarely detected[cf. Warburton
upglacieras the.melt seasonprogresses.
Evidencefor and Fenn, 1994],whereaslarge, destructivefloodsare
sucha spatialprogression
hasbeenpresented
byNienow rare. Water storagealsoaffectsglaciermovement.Surg[1994], who inferred from dye-tracerstudiesat Haut ing glaciersstore large volumesof water, and major
Glacier d'Arolla that the boundarybetween a slow, surgeslowdownsas well as surgeterminationsare cornonarborescent,
wintertimedrainagesystemand a fast related with the releaseof storedwater [Kambet al.,
R channelsystemmovedupglacierthroughtime as the 1985;Humphreyand Raymond,1994].The rapid flow of
snowline on the glaciersurfaceretreated.
ColumbiaGlacier,Alaska,seemsto be controlledbythe
Data bearing on the seasonalevolutionof the basal volumeof storedwater [Meieret al., 1994;Kamb et al.,
drainagesystemare sparse.Seaberget al. [1988] and 1994]. More generally,the ability of glaciersto store
Hock andHooke [1993]injecteddyeinto moulinsin the watermodulatesrapid changesin the basalwater preslowerpart of the ablationarea of Storglaci•iren.
They sureandmayhelpto increaseandsustainglaciermotion
calculatedsubglacial
flow speedsmostlyin the rangeof by distributinghighwater pressureover large bed re0.1-0.2 m/sand alsofoundthat the dispersivity
progres- gions[Humphrey,1987;Alley, 1996].
sivelydecreased.They inferredthat the basaldrainage
Small, temperate alpine glaciersseem to attain a
systemincludedshallowbut verywide conduits(Figure maximumseasonalwater storageof ---200mm of water
21), not at all like the classic
conception
of an R channel averagedover the area of the glacierbed, with daily
but similar to the predictedgeometryof canalson a fluctuations
of as muchas 20-30 mm [Tangborn
et al.,
sedimentbed (Figure19). Seaberg
et al. [1988]andHock 1975;Williset al., 1991/1992].It is temptingto assume
and Hooke [1993] suggested
that the conduitswere es- that subglacial
cavitiesprovidethe capacityfor mostof
..
318 ß Fountain and Walder: WATER FLOW THROUGH GLACIERS
the storage,but this is questionable.The volume of the
former linked cavity systembeneath CastleguardGlacier,Alberta, wasinferred to be equivalentto an average
water layer thicknessof only ---27mm [HalletandAnderson, 1980], and this figure is within a factor of 2 for
exhumedcavitysystemsat Blackfoot Glacier, Montana,
United States[Walderand Hallet, 1979] and Glacier de
Tsanfleuron,Switzerland [Sharpet al., 1989]. The discrepancybetweenthe estimatedstoredvolume and the
likely storagecapacityof subglacialcavitiesis also evident when we considerthe situationat Variegated Glacier,where the volumeof water storedduringthe glacier
surgeof 1982-1983wasequivalentto a layer of water --•1
rn thick [HumphreyandRaymond,1994].This seemslike
an implausiblylarge amountof water to storein subglacial cavities,even if a majority of the glacierwas separated from the bed, unlessthe glacierbed was extraordinarily rough.
Subglacialtill may play an important, althoughnot
predominant,role in seasonalwater storage.An unconsolidated till layer covering the entire glacier bed, a
questionablescenario,and having a thicknessof, say,
0.25 rn and a porosityof 0.30 would provide a storage
volume equivalent to a 75-mm-thick layer of water.
Accommodatingas much as 200 mm of storedwater in
a basal till layer would require that the till be substantially thickerthan that suggested
by the limited borehole
data from alpine glaciers[e.g., Engelhardtet al., 1978;
Stone et al., 1997]. Furthermore, diurnal variations in
water storageprobablycannotbe explainedwith reference to basal till. The fractional changein storagein a
saturated till layer is given approximatelyby SsAh,
where Ss is the specificstorage,a measureof the water
volumestoredor releasedasthe till layeris strained,and
,
36, 3 / REVIEWSOF GEOPHYSICS
cases.Water storagein surgingglaciersalso involves
water-filledsurfacepotholes[Sturm,1987]and crevasses
[Kamb et al., 1985]. Near-surfacestorageof this sort
implies that water is in fact backed up in englacial
passages.
7.
OUTBURST
FLOODS
A glacial outburst flood, sometimescalled by the
Icelandicterm "j6kulhlaup,"may be broadly definedas
the sudden,rapid releaseof water either storedwithin a
glacier or dammed by a glacier. Although outburst
floodsare perhapsbestknownfor the hazardstheypose
in alpine regions,they are not limited to suchglaciers
but are also associatedwith large tidewater glaciersin
Alaska [Mayo, 1989] and Icelandicice caps[BjOmsson,
1992]. The Pleistocene Missoula floods, the largest
knownterrestrialfloods,were causedby periodicdrainage of an enormouslake dammedby the Cordilleranice
sheet in western North America. Floodwaters swept
across
an areaof ---3x 104 knl2 in present-day
Wash-
ingtonState,creatingthe uniquelandscapeknownasthe
ChanneledScabland[Waitt, 1985].
Most observedoutburst floods involve drainage of
glacier-dammed
lakes.The water either drainsthrougha
subglacialtunnel and appearsat the glacierterminus,or
drainsthrough a breachbetweenthe glacier and valley
wall. For drainagethroughsubglacialtunnels,drainage
occurs,to a first approximation,when the lake level rises
sufficientlyto nearly float the ice dam [Bj6msson,1974].
As water beginsto leak under the dam, frictionalenergy
dissipationcausesflow to localizein a channel.Initially,
Ah isthevariation
in hydraulic
head.WithSs-"10-4/m the channelenlargesrapidlyby melting,but as the lake
for sandyor gravellytill [cf. Stoneet al., 1997;Domenico level drops,water pressurein the channelfalls, the rate
and the channelcloses,
and Schwartz,1990] and Ah ---100 rn (at most) the of'inwardice creepincreases,
fractional change in storage is ---0.01 or ---1 mm. By thereby terminating the flood. The flood hydrograph
processof elimination we concludethat a substantial commonlyhasa long,gentleascendinglimb and a steep,
fractionof the water storage,both short-and long-term, abrupt falling limb, with the flood lastinga few daysto
is probably englacial [cf. Jacobeland Raymond, 1984; weeks (Figure 22a). Details of the physicshave been
Humphreyand Raymond,1994].
elucidatedby Nye [1976], Glazyrinand Sokolov[1976],
Borehole-video studies [Pohjola, 1994; Harper and Springand Hutter [1981], and Clarke [1982]. Clarke's
Humphrey,1995] suggestthat englacialvoids and con- analysishas the greatestutilitarian value. He showed
duits in small temperate glaciersconstitutea macropo- that the exit hydrographis determinedprimarilyby (1)
rosity of ---0.4-1.3%, although some of this probably the temperature0i•Ai•, volume V, and hypsometryof
comprisesisolated, water-filled voids. Fountain [1992] the lake, (2) the ice overburdenpressurePi where the
estimateda macroporosityof 1% to maintain reasonable tunnel meetsthe lake, and (3) the tunnel roughness
fi
calculated subglacialwater pressures.Englacial water and mean hydraulicgradientG. These factorsare incorstorageis an attractivehypothesisbecausea macropo- porated into two dimensionlessparameters,a "tunnel
rosityof only 0.1% in hydrauliccommunicationwith the closureparameter"otand a "lake temperatureparamebed would be equivalentto a 100-mm-thickwater layer ter" [3. Exit hydrographscan be calculatedif plausible
for a glacierwith an averagethickness
of 0nly 100m. boundson ot and [3 can be estimated.For many alpine
Filling and draining of englacial passageshave been glaciers,ot is relativelysmall, and plausibleboundscan
detectedby radar [Jacobeland Raymond,1984],and the be placedon peak dischargeQMAX evenwithout calcufilling of moulinshasbeen measured[Iken, 1972].Thus lating the complete exit hydrograph.The lower bound
it seemsboth qualitativelyand quantitativelylikely that corresponds
to the casein which0I•AKE= 0øC;the upper
englacialstoragemay exceedsubglacialstoragein many bound correspondsto the casein which tunnel enlarge-
36, 3 / REVIEWSOF GEOPHYSICS
Fountainand Walder: WATER FLOW THROUGH GLACIERSß 319
unless calved ice actually blocks the breach. Breach
closureresultingfrom ice movementis negligible.The
Bo
flood hydrographcommonlyexhibitsa steeprisinglimb
(Figure 22b), similar to floodscausedby the failure of
constructeddams [MacDonaldand Langridge-Monopolis, 1984]. The hydrographdependsprimarily on lake
hypsometry and two dimensionlessparameters, a
Minutes
to hours
"breachroughness
parameter"•/and a lake temperature
Hours to days
parameter
8.
Both
•/ and • depend on the initial lake
Time
volume and depth. Again, approximateboundscan be
Figure 22. Outburst-flood hydrographs for two distinct placed on {2mAXfor casesin which the effect of the
types of water release: (a) flood causedby lake water tun- lake's thermal energyon breach erosionis either neglineling under a glacier and (b) flood causedby release of gible or dominant.
subglaciallystoredwater or by subaerialbreachingof an ice
Simpleempiricisms
havealsobeenusefulfor estimatdam [after Haebedi, 1983]. Reprinted from Annals of Gla- ing {2mAX from lake drainage. Clague and Mathews
ciologywith permission of the International Glaciological [1973] were the first to present a regressionrelation
Society.
betweenQ MAX and V:
ment is dominated by the lake's thermal energy and
frictional dissipationis negligible.
Where a valleyis blockedby a glacieradvancingfrom
a tributaryvalley (Figure 23), the glacier-dammedlake
commonlydrainsthrougha breachbetweenthe ice dam
and an adjacentrockwall [Walderand Costa,1996].The
way in which drainage begins is enigmatic. In some
cases,drainage may begin through a subglacialtunnel
near the valleywall becausethe ice is normallythinnest
at that point. Tunnels formed in this way seem to be
prone to roof collapse,and marginalbreachesdevelop
[e.g.,Liss,1970].Alternatively,becausethe ice-wallcontactis typicallyirregular,seepagethroughthe gapserodes
the ice through frictional.heating, thereby initiating a
breach(M. F. Meier, personalcommunication,
1994).A
theoretical description of breach-drainageoutburst
floodshasbeen givenby Walderand Costa[1996].Their
analysisparallels Clarke's [1982] analysisof tunneldrainageoutburstsin many importantrespects,particularly in the assumptionthat breach enlargementproceedsby melting of the ice. Calving also widens the
breach [Liss, 1970] but is not hydraulicallyimportant
QMAX- bga
(13)
where Q•A_Xis givenin cubicmetersper secondand V
is given in millions of cubic meters and with values of
b = 75 and a = 0.67. Walderand Costa[1996]updated
the Clague-Mathewsrelation by developing separate
regressions
for tunnel drainage(b: 46 and a = 0.66)
and breachdrainage(b = 1100 and a = 0.44). For a
givenvalue of V, Q•A_X for a breach-drainageflood is
commonly much greater than for a tunnel-drainage
flood. The valuesof the constantsfor a breachdrainage
are quite similar to the regressiondevelopedby Costa
[1988] for floodsfrom constructedearthen dams (b =
1200 and a = 0.48). The similarity of constantsis
probablynot fortuitousbut rather reflectiveof the fact
that both were developed for floods that drained
throughrapidly formed subaerialbreaches.The differencesin material propertiesof the damsand in erosion
mechanismsare evidentlylessimportant than the flow
hydraulics,which are the same in both cases.
Another classof outburstfloodsinvolvesthe abrupt
release of water from subglacialor englacial storage
[Haeberli,1983;Driedgerand Fountain, 1989]. Outburst
Figure 23. Contrastingmodes of glacier-dammed
lake formation.
A lake im-
pounded by the advance of a glacier
acrossthe mouth of a tributary valley
(left side of figure) drains through a
subglacialchannel,but a lake formedby
the advanceof a glacierfrom a tributary
valley typically drains through a subaerial breach, usually at the terminus.
Basedon Figure 3 of Walderand Costa
[1996]; copyrightJohn Wiley and Sons
Ltd.; reproducedwith permission.
320 ß Fountainand Walder: WATER FLOW THROUGH GLACIERS
floodsof this type, which are by their nature unanticipated and poorly described,seem to be triggeredby
rapid input of rain or meltwaterto the glacier.Walder
and Driedger[1995] suggestedthat the releasemechanismprobablyinvolvesunstableenlargementof the orificesin a basal cavitynetwork that transformsinto one
that drainswater rapidly.This mechanism,initially proposed in connection with glacier-surgetermination
[Kamb,1987],is alsoconsideredimportantto the annual
reestablishmentof an R channel network [cf. Nienew,
1994;M. J. Sharp,personalcommunication,
1996].Borehole measurements
showingan abruptreorganization
of
the basal drainagesystem,consistentwith the scenario
discussed
here, havebeencollectedat TrapridgeGlacier
[Stoneand Clarke, 1996]. Alternatively,water could be
storedenglacially
in passages
temporarilyisolatedfrom the
subglacial
drainagesystem,
thenreleasedwhenrapidinput
of water to the glacierforcesreconnectionwith the bed.
Floodsfrom internallystoredwater are largelyunpredictable. Walder and Driedger [1995] used statistical
methodsto showthat for SouthTahomaGlacier(Mount
Rainier, WashingtonState), which released 14 or 15
floodsduring a 6-yearperiod, the probabilityof a flood
increasedasthe input rate of water to the glacier(asrain
or meltwater) increased.These resultsagree with the
observationsof Warburtonand Fenn [1994]. Unfortunately,a relationshipof this sort developedfor a particular glacier is unlikely to be applicableelsewhere.A
physicallyplausible,albeit crude, estimateof Q•dAXis
nonethelesspossible.Glaciologicalexperience[e.g.,
Haeberli,1983; Walderand Driedger,1995] suggests
that
the water volume releasedfrom storageduring an outburst flood is likely to be of a magnitudecorresponding
to a water layer ---10-100 mm thick over the entire
glacierbed and that the releasetypicallyoccursduringa
period -r equal to ---15-60 min, althoughsometimesas
longasa day[Warburton
andFenn,1994].Estimatingthe
releasedwater volumeas the productof the glacier-bed
areaA and equivalentwater layer thicknessd and assuminga triangularexit hydrograph,we estimate
36, 3 / REVIEWSOF GEOPHYSICS
glaciersurfaceto the bed, a propositionthat we examine
in section9, the water pressurein bed areas supplied
from the ablationzoneshouldrespondrapidly(probably
within a few minutesto a few hours)to variationsin the
water input at the surface.In contrast,water pressurein
bed areassuppliedfrom the accumulationzone should
respondslowly(probably on a timescaleof days to a
week or more) to varyingwater input at the surface,
owing to delayed transport through snow and firn. A
changein supplyregion from accumulationto ablation
zone should
therefore
be reflected
at the base of the
glacier by a relatively sharp gradient in variationsof
subglacialwater pressure.This may have important implicationsfor glacierdynamicsbecausethe rate of glacier slidingis, in part, related to the effectivepressure
(ice pressureminuswater pressure)at the baseof the
glacier[Iken and Bindschadler,
1986;Janssen,1995].We
expect the sliding speed in the ablation zone to be
greater than that in the accumulationzone duringpeak
diurnal melt periodsbut lesswhen the melt rate is at a
minimum. The ablation zone would then "pull" the
accumulationduringmidday,and the accumulationzone
would "push"the ablationzone during the night. Similarly, the ablation zone would move fastestduring the
first few daysof a rainy period before the water percolated through the accumulationzone and slowestjust
after the rain stopped.This scenariowouldbe 'somewhat
modifiedif mostof the surfacewater input were routed
directlyto subglacialchannels.Not only do the channels
only pressurizea smallpart of the bed, but duringtheir
largest developmentin midsummerthe conduitsmay
onlybe pressurizedduringa shorttime eachday.Under
these conditionsthe accumulationzone may more or
lessconstantlypush the ablation zone. Becausespatial
variationsin glacier movementare smoothedby longitudinal stress-gradient
couplingover a distancerelated
to the glacierthickness[Kamb and Echelmeyer,1986],
differencesin flow speedbetweenthe accumulationand
ablationzonescausedbyvariationsin water input should
tend to increasewith the length of the glacier.
2Ad
QMAX• --
(14)
As an example,considera smallalpine glacierwith A =
1 km2.Thebaseflowfromsucha glacier
isprobably
---1
m3/s[e.g.,Fountain,
1993].From(14) we estimate
an
upperboundfor QMAXof ---100m3/s.Floodpeaksof
this magnitude can be extremely destructivein small
alpine drainage basins,particularlyif the water floods
transformto debrisflows [Driedgerand Fountain, 1989;
Walderand Driedger,1995].
8.
AND
LINKS
BETWEEN
GLACIER
HYDROLOGY
DYNAMICS
8.1. Effectof Glacier-Surface
Morphology
Variations in water input to a glacier should affect
basal water pressure.If water movesrapidly from the
8.2. SubglacialHydrology
A large body of data has accumulatedsuggestinga
link betweenvariationsin the basaldrainagesystemand
perturbationsin glaciermovement,but the physicalnature of the couplingremains elusive.The best known
evidence suggestingthe hydrology-dynamicslink involvesseasonalvariationsin glacier-surface
velocity,first
observedby Forbes[1846] at Mer de Glace, France.
Generally, the surfacevelocitypeaks in late springto
early summerin the ablation area; in the accumulation
areathe seasonalvariationmaybe of the oppositephase.
The usual interpretation [e.g., Hedge, 1974] is that
changesin surfacevelocityare too large to be explained
by massbalanceinducedchangesin appliedstressand
that changesin surfacevelocitythereforereflectchanges
in slidingvelocity.Suchan interpretationrequirescaution. Baliseand Raymond[1985] showedtheoretically
36, 3 / REVIEWS OF GEOPHYSICS
Fountain and Walder: WATER FLOW THROUGH
that the transfer of basal-velocityvariationsto the glacier surfaceis sensitivelydependenton the length scale
of suchvariations.They concludedthat broad-scalevariations in basal slidingshouldbe reflected by similarly
broad-scalevariations in surface speed but that very
localizedbasal-velocityvariationscannotbe unambiguouslyresolvedby glacier-surfaceobservations.
A key point of contentionhas been whether sliding
speedis controlledprimarily by the volume of stored
water or by basalwater pressure.Hedge [1974] showed
that the surfacespeedof NisquallyGlacier, Washington
State, peaked before the meltwater dischargefrom the
glacier and also that the speed actually increased
throughoutthe winter, even while meltwater discharge
was falling. He interpreted this to mean that sliding
speedwas controlledby the amount of water stored at
the glacier bed, with the maximumstorageoccurring
early in the melt seasonbefore an efficient basal drainage systemhad developed(in line with our discussion
in
section5). In contrast,Iken et al. [1983] found that the
maximumslidingspeedcoincidedwith times when the
glaciersurfacewas risingmost rapidly, the surfacerise
being thought to indicate water going into storage,
rather than with the time of maximum surfaceelevation;
they interpreted this to mean that sliding speedwas a
function of subglacialwater pressurerather than storage.Iken andBindschadler[1986]subsequently
showeda
correlation between velocity fluctuationsand borehole
waterpressures
at Findelengletscher,
and similarmeasurementshavebeenmadeat Storglaci•iren
[Janssen,
1995].
Probably,the mostdetailedobservationsdealingwith
the link betweenbasal hydrologyand glacier dynamics
are those from Columbia Glacier, a rapidly moving
tidewaterglacier [Meieret al., 1994;Kamb et al., 1994].
Surface-velocity
fluctuationsat two sites7 km apartwere
stronglycorrelatedwith each other and fairly well correlatedwith the boreholewater level at the upglacierof
the two sites but not with the borehole
water level at the
GLACIERS ß 321
localreorganizationof the basaldrainagesystem.Thus
one expectsUb to correlate with storagebut not necessarilywith localPw.
8.3. Glacier Surging
Surgingglaciersexhibit [Raymond,1987,p. 9121] "a
multi-year, quasi-periodicoscillationbetween extended
periodsof normal motion and brief periodsof comparativelyfast motion." A thoroughreview of glaciersurgingisbeyondthe scopeof thispaper(we refer the reader
to the review by Raymond[1987]), but we do want to
highlightrecentdevelopmentsrelated to the studyof the
1982-1983 surge of Variegated Glacier [Kamb et al.,
1985;Humphreyet al., 1986;Kamb, 1987;Humphreyand
Raymond, 1994] that point to regulation of the surge
processby basalwater flow.
Kamb [1987] noted the followingobservationsfrom
Variegated Glacier as the basisfor his surgemodel:
1. Borehole measurements demonstrate directly
that rapid glaciermotionduringthe surgeis due to basal
sliding.
2. Basalwater pressureduring the surgewas close
to the overburden pressure and notably higher than
during the nonsurgingstate. Peaks in water pressure
corresponded
with peaksin slidingmotion in both surging and nonsurgingstates.
3. Major decreases
in surgemotion,aswell as surge
termination,were accompaniedby large flood peaksin
outlet streamsand a lowering of the glacier surface,
indicatingthat the high slidingspeedandwater pressure
during the surgeare coupledwith water storagewithin
and at the bed of the glacier.
4. Dye-tracingexperiments[Brugman,1986]showed
that the mean flow of water in the basaldrainagesystem
was ---25-30 times faster after surge termination than
duringthe surge.Moreover, dye appearedat a number
of locationsacrossthe width of the glacier during the
surge,but in only a singlestream after surgetermina-
lower site.Using estimatesfor rechargeto and discharge tion.
from the basaldrainagesystem,Kamb et al. [1994] con5. Water dischargedfrom the glacier during the
cludedthat variationsin icevelocitywere bestcorrelated surge was extremely turbid; suspended-sediment
conwith variations in the amount of water stored at the
centrationwas much higher, and the averagegrain size
glacierbed.
of suspendedsedimentwasfiner duringthe surgethan in
We appearto be facedwith a conundrum.Models of the nonsurgingphase [Humphreyand Raymond,1994].
the basal-cavitationprocess[Llibeutry,1968;Iken, 1981;
A physicalmodel of surgingthat accountsfor these
Fowler, 1986, 1987;Kamb, 1987] predict an increasein observationswas developedby Kamb [1987], who probasal storagewith an increasein basalwater pressure, posedthat the basaldrainagesystemduringsurgecomyet glaciermovementseemssometimesto correlatewith prised a linked-cavitynetwork, whereas the drainage
storage,sometimeswith water pressure,but not with systemduring the nonsurgingphase consistedof arboboth. Kamb et al. [1994] suggesteda resolutionof this rescentR channels.The cavitysystemis associatedwith
conundrum,as follows: Glacier sliding speed Ub and high water pressureand multiple, tortuous flow paths
basal storageare controlled by (Pw), the basal water leading to prolonged, highly dispersed dye returns.
pressureaveragedover the distancel, the length scale Surge slowdownsand surge termination result from
over which the basalshearstressis effectivelyaveraged large transient increasesin basal water pressurethat
by glacier dynamics[Kamb and Echelmeyer,1986]. The destabilizepart of the cavity system,thereby releasing
basalwater pressurePw measuredat a point, however,is water from storage.Sedimentconcentrationin the meltthe sum of the spatial mean value (Pw) and a local water dischargedfrom the glacier increasedduring the
fluctuatingvalue p•, where p• is controlledby rapid, surgebecausea linked-cavitydrainagesystembroughta
322 ß Fountainand Walder: WATER FLOW THROUGH GLACIERS
36, 3 / REVIEWSOF GEOPHYSICS
largefractionof the glacierbed into contactwith flowing Basalwater flow in an overdeepeningis essentiallyrewater, but the mean suspended-sediment
size dropped strictedto the water alreadyin the basaldrainagesystem
during the surgebecausethe sluggishlyflowingwater in upglacierof the overdeepening;
basalconduitsmay tend
the cavity systemcould not suspendas much coarse to freeze shut where they encounterthe adverseslope
sedimentas could rapidly flowing,channelizedwater, comingout of the overdeepening.
Basalconduitsshould
be most frequently located along the margins of the
[Humphreyand Raymond,1994].
The conditionsthat causesurgeinitiation can alsobe overdeepening.
The morphologyof the subglacialdrainagesystemis
explained, at least qualitatively,in the context of the
channel-cavitydichotomy.Raymond [1987] and Kamb controlledby a number of factors,includingthe distri[1987]suggested
that duringwinter, R channelscollapse bution of englacialconduitsreachingthe bed, ice thickand a high-pwlinked-cavitynetwork develops.Usually, ness,glacierslidingspeed,bed lithology,and bed roughas the melt seasonbegins,the flux of meltwater to the ness. Any one of these factors may be of relatively
bed causeswater pressuretransientsthat destabilize greater or lesser importance at any particular glacier.
parts of the linked-cavitynetwork, and an R channel Generally speaking,the morphologyof the basaldrainnetwork reforms.(We have suggestedin section5 that age systemis heterogeneous.Slow drainage systems,
this scenariois probablycommonto all temperate gla- involving linked cavities,permeable till, and channel
ciers,notjust thosethat surge.)The stabilityof the cavity segmentsincisedinto the bed and trendingalongthe ice
network to pressureperturbationsis controlled by a flow direction,covermost of the bed. The slowdrainage
parameter•= [Kamb,1987]that dependson roughness systemis in poor hydraulic communicationwith a fast
characteristics
of the glacierbed, ice rheology,and gla- systemof R channelsincisedinto the basal ice. The R
cier geometry;in a surgingglacier,as the glaciergeom- channel systemlargely collapsesduring winter and is
etry (primarily the thickness)changeswith time during reformed in the springas a flush of water reachesthe
the nonsurgingphase,a point is reachedat which •= bed and destabilizesparts of the linked-cavitynetwork.
attains a small enoughvalue to stabilizethe wintertime In relatively thick ice, say, 200 m or more, there is
cavitynetwork againstearly melt-seasonwater pressure probably ample opportunity for englacial drainage to
perturbations. When this occurs, the high-pressure become concentratedinto a relatively small number of
linked-cavitysystempersistsand enlarges,and surging trunk conduits,eachcarryinga largewater flux,whereas
begins. Complicationsin this scenariohave been dis- in thin ice, say, 50 m or less, the englacial flow is
relativelymore diffuse,with a large numberof englacial
cussedby Humphreyand Raymond[1994].
conduits,each carryinga small flux of water, reaching
the bed.
9.
UNIFIED
THROUGH
MODEL
OF WATER
A TEMPERATE
FLOW
GLACIER
10.
Water entersthe body of a glacierprimarily through
crevassesand moulins. The englacial drainage system
comprisesa complexcombinationof gentlyinclinedpassagesspawnedbywater flow alongcrevasse
bottomsand
steeplyinclinedpassagesformed by water enlargingintergranularveins.In general,water flowsenglaciallyfor
long distances,perhapsequalto severaltimesthe glacier
thickness,before reaching the bed, although the common presenceof moulinsin the ablationzone indicates
that water can sometimesdescendverticallythrough a
significantfraction of the ice thickness.
The englacialconduitsystemsuppliedfrom the accumulation zone is of relatively limited extent compared
with the systemsuppliedfrom the ablationzonebecause
of the role of the firn in dampingdiurnal variationsin
water input. Much of the water that entersthe glacierin
the accumulationzone probablyreachesthe bed in the
ablation zone. Thus the subglacialarea of influence of
eachzone is shifteddownglacier,and the firn influences
a subglacialarea greaterthan the area it actuallycovers.
The supplyof surfacewater to the bed is inhibitedin
overdeepenedparts of the glacier becausethe gently
inclined parts of the englacialconduit systembecome
pinnedby the downglaciermarginof the overdeepening.
DIRECTIONS
FOR FUTURE
RESEARCH
Glaciologistsneed to adopt a holisticperspectivein
studyingglacier hydrology.Indeed, although we have
written separately about near-surface,englacial, and
subglacialwater flow, the three phenomenaare obviouslycoupled.Influencesin the glacierdrainagesystem
nearly alwaysmove from the glaciersurfacedownward.
Forcingsimposedon the englacialand subglacialpassagesare distinctlydifferent, dependingon whetherwater is suppliedfrom the accumulationzone or the ablation zone.
Coupling between the near-surface and englacial
drainage systemsneeds to be investigatedmuch more
thoroughly.There are almostno data availableshowing
how water
flux to crevasses and moulins
is distributed
over the glaciersurfaceand how this distributionevolves
temporally. These flux data constitute a fundamental
boundaryconditionfor the englacialpart of the drainage
system.
The water flux deliveredto the bed at the points of
couplingbetweenthe englacialand subglacialdrainage
systemsconstitutesthe "upstream"boundarycondition
on the subglacialdrainagesystem.This flux distribution
obviouslycannotbe directlymeasured,but it may still be
36, 3 / REVIEWSOF GEOPHYSICS
Fountain and Walder: WATER FLOW THROUGH GLACIERS ß 323
investigatedonce we recognizethat surfacewater supplied to the englacialdrainagesystemalmostcertainly
becomesconcentratedinto a relatively limited number
of trunk conduitsby the time it reachesthe glacierbed
[Shreve,1972]. It may be possible to use tracers to
delineate the "drainage basins"of the englacial trunk
conduits(i.e., the onesthat reach the bed) and thereby
to estimatethe distributionof rechargeto the subglacial
drainage system,much as tracers have been used to
delineate the gross drainage-basinstructure of entire
glaciers [e.g., Stenborg,1973; Fountain, 1992, 1993;
Fountainand Vaughn,1995].
Someof the theoreticalfoundationsof glacierhydrology theory need to be revisited.Clarke [1994] has recently begun doing this for the case of R6thlisberger
channelsby criticallyexaminingone of the key simplifying assumptions(the neglectof heat advectionby the
water) in R6thlisberger's
[1972] analysis.(At the time of
writing, Clarke's recent work has appeared only as an
abstract,andwe cannotassess
it critically.)There is also
a distinctneed to understandhow the drainage system
shouldrespondto time-varyingwater input. This topic
has been touchedupon by Spring[1980],who explored
the pressure-discharge
relation for sinusoidallyvarying
flow in R channels,and byKamb [1987]in his analysisof
the stabilityof cavitiesto pressuretransients.
The time seemsto be ripe for constructingtheoretical
modelsthat fully coupleglacierslidingand basalhydrology,accountingproperlyfor both the long-rangespatial
averagingimposed by ice dynamicsand the complex,
time- and space-dependentvariationswithin the basal
drainagesystem.Someimportantstudiesthat we believe
canjointly serveas a springboardare thoseof Humphrey
[1987],Murray and Clarke [1995], and Clarke [1996].
Humphrey[1987] presentedthe only analysisto date
of the dynamiccouplingbetweena glacierand its basal
drainage system,albeit within the context of a highly
idealizedview of glacier-bedgeometry.He arguedthat a
completedescriptionof the couplingbetweensubglacial
water flow and glacierdynamicsrequiresone to specify
the following:(1) a force balance at the bed, (2) the
couplingbetweenthe basalshearstressand the stresses
in the body of the glacier, with careful attention to
longitudinalstressgradients,(3) a relationbetweencavity size,slidingspeed,and basalwater pressure,and (4)
a descriptionof the hydraulicsof water flow in the linked
cavities.The mathematicalmodel is complicated,and its
consequences
havenot yet been fully elucidated,but the
resultsare tantalizing.Most importantly,from the perspective of glaciologicallymeaningful measurements,
Humphrey showed that the model predicts no simple
relation between the variation in slidingspeed and the
variation in water pressureas a function of distance
alongthe glacier,althoughvariationsin slidingspeedare
predicted to correlate with basal water storage.These
model predictionsare in line with field data and interpretation from Columbia Glacier [Meier et al., 1994;
Kamb et al., 1994].
Murray and Clarke [1995] developeda "black-box"
model of the subglacialdrainagesystemto explain peculiarities
of the borehole
water
level
data from
Tra-
pridge Glacier, but the conceptsthey developed are
more widely applicable.Murray and Clarke showedthat
observed,time-dependentcouplingbetween connected
and unconnectedboreholescould be modeled by thinking of water pressure in a connectedborehole as a
forcing function to which water pressurein an unconnected borehole must respond.Although their mathematical formulation was somewhatad hoc, they argued
plausiblythat their model coefficientscould be interpreted in terms of physicalprocessesat the glacierbed,
namely, dilation/compactionof porous subglacialsediment, diffusion of water pressuredisturbancesthrough
the sediment, and uplift of the glacier from its bed.
Subsequently,Clarke [1996] has shownthat conceiving
of the subglacialdrainagesystemas consistingof linked
"lumped elements," analogousto an electrical circuit,
provides a powerful basis for explainingmany of the
complicateddata collectedduring---25yearsof borehole
studies.This approachseemsto have great potential for
elucidating the details of basal hydrology at relatively
smallspatialscalesand shorttime periods.In this sense
it complementsHumphrey's[1987] approach,which is
directed at explaininglarge-scale,long time period behavior.
A key issuethat needsmuch more thorough investigation is how the various componentsof the glacial
drainagesysteminteract in spaceand time. The system
components(snow,firn, and surfacestreams;crevasses,
moulins,and other englacialpassages;and basal channels, cavities,and till) are in a state of flux throughout
the year and are unevenlydistributed.
GLOSSARY
Ablation: All formsof masslossincludingsublimation, evaporation,melting, and calving.For alpine glaciers, the term "ablation" is often used, incorrectly,to
mean melt because that is the dominant
means of mass
loss.
Ablationzone: The part of the glacierwhereyearly
masslossexceedsthat gainedby snowaccumulationand
the surfaceexposedin the late summeris ice.
Accumulationzone: The part of the glacierwhere
yearly massgain generallyexceedsthat lost by ablation
and the surface consists of either
snow or firn.
Albedo: The ratio of reflectedenergyflux to incident energyflux from solar radiation.
Arborescent: Tree like, used to describe a network
of channels that converge as the branches of a tree
convergeto a trunk.
Confinedaquifer: A water-bearingformationconfined on the top and bottom by nearly impermeable
formations.
324 ß Fountain and Walder: WATER FLOW THROUGH GLACIERS
Crevasse: A gaping crack in a glacier formed by
tensile stressesresultingfrom glaciermovement.
Fnglacial: Within the bodyof a glacier.
Equilibriumline: Line dividingthe ablationand
36, 3 / REVIEWSOF GEOPHYSICS
who provided thoughtful reviewsat a later stage.L. Faust
assisted with the illustrations.
The Editor thanks Neil Humphrey and Garry Clarke for
technical
reviews.
accumulationzones,where net annual masschangeis
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