STATE OF BALANCE OF THE CRYOSPHERE
C. J. van der Veen
ByrdPolarResearch
Center
OhioStateUniversity,
Columbus
Abstract. The current state of balance of the terrestrial ice
sheetsand glaciersis poorlyknown.What little dataare
availablesuggest
that,worldwide,mountainglaciershave
receded since about the mid-nineteenthcentury, with
occasional
interruptions
of theretreat.The interiorpartof
theGreenlandice sheetappearsto be thickeningor in near
equilibrium,but this ice sheetmay be thinningin the
coastal areas. Estimates of the mass balance of the
1. INTRODUCTION
Antarcticice sheetsuggestthat it is positive,althoughthe
errorlimits allow for a slightlynegativebalance.There is
an urgentneedto greatlyimprovethe currentestimatesand
to monitor the ice sheetscontinuouslyfor changesin
volume and extent.A programbasedon satelliteobservation techniques,
in cooperation
with ground-based
surveys
repeatedover long time periods(many yearsor decades),
appearsto be mostopportune
to achievethis.
When consideringonly part of a glacier,the effect of ice
flow, which may either remove or add mass from any
Almost94% of all waterpresenton the Earthandin its location, must also be taken into account. In that case it is
atmosphere
is storedin theworld'soceans;
snowandicein appropriate
to usethe termnet massbalance.The ice sheet
the cryosphere
accountfor only about1.5% of the total. is said to be in steadystatewhen the net massbalanceis
The bulk of the ice can be found in Antarctica; the volume
of the ice sheet there is about 10 times that of the Green-
zeroeverywhere.
Accumulationis primarilydue to precipitationof snow
land ice sheetand about 160 times as large as the com- and, at the lowest elevations,rainfall. Condensationof ice
bined volume of mountainglaciersand small ice caps. from vaporand wind transportof snowrepresent,in most
Althoughthe water volumeof the cryosphere
is much cases,only a minor contribution.An exceptionto this is
smallerthan that of the world's oceans,small changesin centralAntarctica,where condensationis an appreciable
thevolumeof grounded
icecanhavedireconsequences
for fractionof the accumulation[e.g.,Bromwich,1988]. In the
global sea level. This becomesmore obvious when caseof floating ice tonguesand shelves,basal freezing
considering
the volumeof groundedice in termsof sea may be important,but for groundedice the primary
level equivalentas givenin Table 1. It shouldbe stressed location for accumulation is the surface.
that mostof the numbersgivenin thistablecontainlarge
Two importantfactorsthataffecttheamountof snowfall
uncertainties.
at the surface are the temperatureof the air and the
Because considerable amounts of the ice in Greenland
orography.The latter effect resultsin increasedsnowfall
and Antarctica are below the present-daysea level, a near the edgesof ice sheetsand on the upwind side of
completemelting of these ice sheetswould lead to a glacier-coveredmountains,where the steep slopesforce
smallersealevel rise than that corresponding
to the total the moist air to flow upward.Atmospherictemperatures
volume of ice storedthere. Furthermore,melting of the havea largeeffecton accumulation
in thattheyrestrictthe
largefloatingice shelvessurrounding
WestAntarctica
has maximum snowfall. This limitation occurs because the
no direct effect on sea level, and hence these are not atmospherecannot carry unlimited amounts of water
included in Table 1.
vapor;the humidityof theatmosphere
dependsstronglyon
Changesin ice volumeoccurwhenthe massbalanceis the air temperature.This means that, with increasing
nonzero.A positivemassbalancemeansthattheglacieris elevation
(decreasing
temperature),
a criticalheightis
growing (expanding);glacier retreat is causedby a reached,above which snowfall startsto decreaseas a result
negativemassbalance.Thusa crucialissuefor futuresea of the reducedmoisture-carrying
capacityof the atmoslevelchanges
is thecurrentmassbalanceof theterrestrial phere.So it is not surprisingthatin the centralregionsof
ice masses.
East Antarctica(with a mean summertemperatureof
The massbalanceof a glacieror ice capis thedifference -30øC and a mean winter temperature
of -65øC)
betweenthe amountof snowand ice accumulatingon the [Schlesinger,1984], snowfallis extremelylow, lessthan
glacier and ice loss from melting and icebergcalving. 0.05m yr-• [Giovinetto
andBentley,1985].
Reviewsof Geophysics,
29, 3 / August1991
Copyright1991 by theAmericanGeophysical
Union.
pages433-455
8755-1209/91/91 RG-00784 $15.00
Papernurnber91RG00784
ß 433
ß
434 ß Van der Veen: STATEOF BALANCEOF THE CRYOSPHERE
29, 3 /REVIEWS OF GEOPHYSICS
TABLE 1. SomeData on the Cryosphere
West
Antarctica
East
Glaciers and
Antarctica
Greenland
2.1
3.4
9.9
25.9
1.8
3.0
0.6
0.2
m water/yr
Equivalentsealevel,m
0.3
9.4
0.1
71.7
0.3
8.3
1.2
0.5
Actual sea level, m
6.0
60.0
7.5
0.5
Lossof ice primarily
by...
calving
calving
calvingand
melting
melting
Dynamicresponsetime,
year
100-1000
10,000100,000
1000-10,000
1O- 1O0
Area,106km2
Volume,106km3
SmallIce Caps
Averageannual
accumulation
After Oerlemans [ 1989].
Melting is one of the processes
thatremovesice from a
glacier.However, it only representsa true loss if the
scalefor adjustment
dependsstronglyon the sizeof the ice
mass under consideration.The responsetime of the
meltwater exits the ice mass instead of percolating Antarctic ice sheet is of the order of tens of thousands to
downward into the firn where it refreezes.
Anotherimportantmechanismby which ice is lost is
icebergproductionat the ice margin.In Greenlandthis
accountsfor about half of the total ice loss. In Antarctica,
icebergproductionis significantat the seawardedgesof
the floatingice shelves.It shouldbe noted,however,that
this hasno consequences
for sealevel. Oncethe formerly
groundedice flowsacrossthegroundingline andentersthe
floatingice shelves,it hasno furtherimpacton sealevel.It
may thereforebe more relevant to consideronly the
volume of groundedice, in which case the important
parameterdescribingthe lossof ice is therateat whichice
is flowingfromgroundedregionsintofloatingice shelves.
Changes in ice volume are the consequenceof an
imbalance between net accumulation and ablation. The ice
sheetwill adjustits patternof flow to compensate
for this
imbalanceuntil an equilibriumconfigurationis reached.
This configurationis commonlyreferredto as the steady
state,becausethe geometryof the glacier,and the associatedpatternof flow, will remainconstantwith timeas long
as the accumulationand ablationdo not change(and other
boundaryconditions
alsoremainconstant).
In nature, ice massesrarely achieve a steady state
becausethe atmospheric
boundaryconditions,determining
to a large extent the accumulationand ablation,are
continuouslychanging.Becauseice massesreact actively
(i.e., by adjustingthepatternof flow) to changingclimatic
conditions that cause a nonzero mass balance, their
100,000 years,whereasthe responsetime of a typical
mountainglacieris about100 years;the responsetime of
the Greenland ice sheet lies somewhere in between these
extremes(1000-10,000 years). As a result, a climatic
changewill have its first impact on mountainglaciers,
which are generallybelievedto be sensitiveindicatorsof
climate[e.g.,Oerlemans,1986a].Conversely,
thedifferent
components
of the cryospheremay still be adjustingto
changesin climate that occurredat different times in the
past. Whillans [1981] calculatesthat southGreenlandis
presentlyrespondingto climatic changesthat happened
during the last 10,000 years, approximately,whereas
centralEast Antarcticais reactingto changesthat took
placeover thepast200,000 years.
The wide rangeof responsetimes makesit difficult to
distinguish
betweenpossiblecausesof observedchanges.
For example,Reeh and Gundestrup[1985] arguethat the
present-daythickening of the interior regions of the
Greenlandice sheetmay in part be the resultof downward
movementof Holoceneice, slowly thinningthe bottom
layer of relativelysoft Wisconsinice. (This tendsto make
the glacierstiffer so that ice velocitiesbecomesmaller.)
On the other hand, Zwally [1989] proposesthat this
thickeningmay be indicativeof a warmerpolar climate,
associatedwith the global waxmingduring the present
century.Becauserecent trends may be developingon
long-termchanges,additionaldata(suchaspastaccumulationrates)and long-termmonitoringare neededto address
theissueof why changesmay be occurring.
Whateverthecausesmay be, the volumeof ice storedin
the cryosphere
is continuously
changing.Thesechanges
may be dramatic,such as the collapseof the northern
responseis, in many instances,very complicated.Feedback processessuch as the coupling between surface
elevationand snowfall or melting, or the glacio-isostatic
adjustmentof the Earth's crustto a changingice load,can
stronglyamplify the glacier'sresponse[cf. Oerlemansand hemisphere
ice sheetsafterthelastglacialperiod,or they
Van der Veen, 1984].
canbe moresubdued,as seemsto be the caseat present.
The dynamicresponseof glaciersto changesin climate Assessingthe current rate of change is fundamentalto
canbe describedby diffusivekinematicwavetheory[e.g., developingscenariosfor sea level changein the (near)
Hutter, 1983, chap.6]. Accordingto this theory,the time future.Unfortunately,very little is knownaboutthe current
29, 3 / REVIEWS
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Van derVeen:STATEOF BALANCE
OF THECRYOSPHERE
ß 435
stateof balanceof terrestrialice. In fact, only a handfulof
find that the retreat of four European glaciers can be
mountainglaciershave been monitoredfor changesin
volumeoveran extendedperiodof time.For the largeice
capsin Greenland
andAntarctica
thepictureis evenworse.
Spotmeasurements
of snowaccumulation,
melting,and
icebergproduction
are extrapolated
over entiredrainage
explainedby an increasein the averagesummertemperature of about0.5ø- 1.0øC.
In the EuropeanAlps the MedievalOptimum(a period
of relativelymild climate)endedaround1300 A.D., and
glaciersstartedadvancing.Major advances,whichbrought
basins,if not the entireice sheet,to determinethe net mass the glaciersin the Alps and in northernScandinaviato
balance.It shouldcomeas no surprisethat the different theirLittle Ice Age maximum,startedin the secondhalf of
estimates
encompass
a wide rangeof valuesso thatonly the sixteenthcentury.In southernScandinaviathe major
advancedid not occur until the latter part of the sevenqualitative
assessments
arewarranted.
Belowis a summaryof availableobservations
andmass teenthcentury.In Iceland,evidenceof expandingglaciers
century.
balance estimates. The division commonly used in is lackinguntil the lastdecadeof the seventeenth
glaciologyis followed.The cryosphere
is partitioned
into Although less well documented,glaciers on the North
threeparts:the mountainglaciersandsmallice caps,the American continent seem to have followed a similar
Greenland ice sheet, and the Antarctic ice sheet. The pattern(cf. Grove[1988] for a detailedoverview).
Glaciers have receded since about the mid-nineteenth
cryosphere
hasothercomponents
as well (permafrost,
sea
natureof
ice, and land snow cover), but their combinedwater centuryworldwide.The scaleandthewidespread
volume is very small comparedto that of land-based thisrecessionare comparableto that of the advanceprior
glaciers,
andthustheirpotentialeffecton sealevel(if any) to the Little Ice Age maximum. The retreat has not been
uninterrupted,
however.Small readvances,or slowingof
is negligible.
The majorimpediment
to a moreaccurate
assessment
of the rate of retreat of the ice fronts, have occurred
the massbalanceof glaciersand ice sheetsis the time- worldwide in the 1880s and 1920s. In a number of cases
consumingtechniquesinvolved in conventionalfield the temporaryadvance can be attributed to increased
programs.The most frequently used techniquesare snowfall and/or lower annual temperatures.It appears,
discussed in section 5 to illuminate the difficulties and however, that these interruptions were only minor
inherent errors involved and also to stress the need for a
disturbances
superimposed
on a continuingtrendof glacier
comprehensive
programaimed at measuringthe mass retreat.More recenttrends(since1960) suggestthata shift
balanceof mountainglaciersas well as the polarice caps. from a regime dominatedby shrinkingand receding
A programthatinvolvessatelliteobservations
seemsto be glaciersto a moremixedregimehastakenplace.Whereas
mostopportune
asprovenby resultsof studies
discussed
in in 1960, about6% of some400 glacierswere advancing;
section 6.
'
this percentageincreasedto about 55% in 1980 [Wood,
1988]. Mass balancedata are availableonly for some50
glaciers,but theseindicatea similar mixed pattern.For
2. MOUNTAIN
GLACIERS
example,observedglaciersin Austriaincreasedin volume
from 1960 to 1980, while glaciersin Switzerland,the
duringthis
Mountainglaciersand small ice capsin generalare SovietUnion, and Canada(mostly)decreased
active and susceptibleto small changesin climate. period [Wood, 1988]. Haeberli et al. [1989] observea
Evidencefor this sensitivityto climateis the widespread similartrendof an increasingnumberof growingglaciers,
advanceof mountainglaciersduringthe Little Ice Age, mostnotablyon themaritimeslopesof mountainranges.
which started in the thirteenth and fourteenth centuries
A number of numerical modeling studieshas been
[Porter, 1986] and culminatedbetweenthe mid-sixteenth
andthemid-nineteenth
century[Grove,1988].The shiftin
equilibriumline altitude between the Little Ice Age
maximaandthepresentoneis estimated
by Porter[1981]
to be about 100 to 200 m for the northernhemisphere
mid-latitudeglaciers.If this shift can be attributedto
changes in the mean atmospherictemperature,and
assumingthe averagelapserate hasremainedcloseto its
undertakento simulatehistoricglacierfront variationsover
the last few
centuries [Oerlemans, 1986b,
1988;
Huybrechtset al., 1989; Stroevenet al., 1989]. When
forcingthe modelwith localclimatedata,simulations
are
not very successful
and, in particular,fail to simulatethe
retreatobserved
duringthe lastcentury.But whena global
forcingderivedfrom an energybalanceclimatemodel is
used, the simulationsyield much better results. This
thatvariationsin theglobalradiationbalancemay
presentvalue (5-6øC/km), the averagetemperaturesuggests
differencebetween the presentand the Little Ice Age be very importantand supportsthe resultsof Oerlemans
maximum
isabout0.5ø- 1.2øC.In fact,thisdifference
may [1986a],who foundthat valley glacierscan be extremely
be closer to the lower limit if snow accumulation was
sensitiveto changesin the radiationbudget.This means
higher during the colder periods when the glaciers that the worldwideretreatof mountainglaciersmay, in
advanced,asappearsto havebeenthecasein theEuropean part, be caused by the increased concentrationsof
gasesin theatmosphere.
Alps [Orombelli and Porter, 1982]. Smith and Budd infrared-absorbing
It shouldbe notedthat variationsin glacierlengthare
[1981] argue that the temperaturechangeaffectingthe
glaciersrefersmostlikely to the summertime only. They not alwaysproportionalto volumechanges.For example,
436 ß Van der Veen: STATE OF BALANCE OF THE CRYOSPHERE
29, 3 / REVIEWSOF GEOPHYSICS
after surging,the snoutof a glaciermay have advanced Here V representsice volume, expressedin meters sea
considerably,even thoughthe ice volumehas decreased. levelequivalent.
The initialstate(1850A.D.) is definedby
For this reason,Meier [1984], in his effort to estimate the
theinitialice volume,VR= 0.45 m sealevelequivalent,
contributionof small mountainglaciersto risingsealevel, andthe initialglobalmeansurface
temperature
T•. T
considers
only 37 northernhemisphere
glaciersfor which representsthe actual temperature,for which Oerlemans
long-term time seriesof ice volume are available.By uses(with t the time in yearsA.D.),
extrapolatingthese data to accountfor all other unT - T• = •l(t - 1850)3,
measuredglaciers,Meier concludesthat, for the period
1884 to 1975 A.D., glacierwastageappearsto accountfor
one third to one half of the observed rise in sea level, basedon the resultsof the Villach II discussion
[Jaeger,
althoughthe errormarginis quitelarge.It may be pointed 1988].
out that thiscontributionapproximately
equalsthefraction
Figure1 showsthecontribution
of mountain
glaciersto sea
of the observedsea level rise that is not explainedby level as calculated
from the simplemodelfor the period
thermalexpansionof theoceans.
1850-2050((x = 0.05 yr-1 K-1, 13= 4.5 K) [following
The averagerate of eustaticsealevelrisebetween1900 Oerlemans,1989]. At the end of this period the rise in
and 1961 attributedby Meier [1984] to melting glaciers temperatureis 2.16 K. Comparingthis curve with that
andsmallice capsis 0.46+ 0.26mmyr-!. Morethana from Meier [1984] showspoor agreementbetweenthe
third of this contribution
derives from the mountains
borderingthe Gulf of Alaska.Otherappreciablecontributionsare from the high mountainsin CentralAsia and the
PatagonianAndes[Meier, 1985].
Oerlemans[1989] tries to quantifythe net contribution
of mountainglaciersto changingsea level by basinga
schematicmodel on the following assumptions:
(1) the
equilibrium ice volume decreasesexponentiallywith
temperature;
(2) the rate of glacierwastageis proportional
to the remainingice volume relative to the equilibrium
volume and to the temperatureperturbation;and (3) the
responsetime of all mountainglacierscanbe characterized
by a singlenumber.Undertheseassumptions
thechangein
ice volumestoredin mountainglaciersand small ice caps
is givenby the followingequation:
d--•=-a(T- TR)[V- VRexp{-(T- TR)/13}].
modeland observations.
By usingc• = 1.0 yr-1 K-1,
agreement
improvesconsiderably,
at leastfor theperiodup
to about1950 A.D. The subsequent
deceleration
in glacier
retreatis notsimulated
by thesimplemodel.Thisis mainly
becausethe curvesshownin Figure 1 stronglyreflectthe
cubicincreasein temperature.
3. THE GREENLAND
ICE SHEET
3.1. The Interior
Few direct observationsof the changesof surface
elevationin Greenlandare available.Bauer et al. [1968]
comparemeasurements
overtheperiod1948-1959 alonga
40-krn stretch of the Exp6dition GlaciologiqueInternationale au Groenland 0EGIG) transect (Figure 2),
coveringthe main part of the ablationzone on the western
•- 1.0 yr-1K -1
_20]
p-4.5 K
0.05 yr-1K-1
c) 15
p=4.5
m lO
z
-
5
z
•
o
1850
2000
YEAR
2050
AD
Figure 1. Estimateof thecontribution
of mountain
glaciersandsmallice capsto risingsealevel
(relativeto the 1900 stand),basedon the simplemodelof Oerlernans
[1989].The heavycurve,
extending
from 1884to 1975,is theestimate
of glaciermeltfromMeier [1984].
K
29,3/ REVIEWS
OFGEOPHYSICS
VanderVeen:
STATE
OFBALANCE
OFTHECRYOSPHERE
ß437
81 ø
75 •
72 ø
69 ø
"'•'"' JAKOBSHAVNS
GLACIER
66 ø
0•'"••
©DYE
63 ø
0
KM
500
60 ø
52 ø
44 ø
36 ø
Figure 2. Locationmapfor Greenland.
28 ø
438 ß Van derVeen:STATEOF BALANCE
OF THECRYOSPHERE
29, 3 / REVIEWS
OF GEOPHYSICS
2
z
Z-1
0
"'-2
0
200
400
600
DISTANCE
FROMWESTCOAST (KM}
Figure3. Observed
surfaceelevation
changeof theGreenland
ice sheetbetween1959and1968
alongtheEGIG line [fromSeckel,1977].(Reproduced
by courtesy
of the Commission
for
ScientificResearchin Greenland.)
marginof the ice sheet.They find a loweringof the ice
Reehand Gundestrup
[1985] estimatethe massbalance
surface
of about0.33rnyr-1.Because
thesurvey
markers of the ice sheetin the Dye 3 area from observedice
usedfor markingthe surveysitesmove alonga rough thickness,accumulation
rates, surfacevelocities,and
surface,extrapolationof the altitudesmeasuredin 1959 to surface
strainrates.By considering
thedivergence
of the
thoseof thecorresponding
positions
in previous
yearsis an ice flux they calculate that the surface elevation is
importantsourceof uncertainty.
increasing
at a rateof 0.03_+0.06m yr-•. Thisis considerThe measurements
of Seckel[1977] for the period ablylessthanthe1 rnyr-• increase
calculated
byMellor
1959-1968 coverthe entireEGIG profile acrossthe ice [1968], who uses the same techniqueas Reeh and
sheet.In theablationzonethesurfaceappears
to be falling Gundestrup
[1985].However,thislargevalueis basedon
at a rateof about0.25m yr-•. In theaccumulation
zonethe the application
of unrealistically
largevaluesof surface
ice sheetis thickeningat an averagerateof about0.085 m velocityandtransverse
strainrate.
yr-•, exceptfor theeast-facing
slope,wheretheobserva- Kosteckaand Whillans[1988] usea numericalflow line
tions indicate a decrease of the surface elevation of a few
modelto compute
themassbalancealongtheOhioState
centimeters
per year(Figure3).
University(OSU) and EGIG transects.Measuredsurface
More recently,Zwally et al. [1989] analyzedsatellite velocitiesare comparedwith velocitiescalculatedfrom
radar-altimeter data and concluded that the surface up-glacialaccumulation
rates,ice thicknesses,
and flow
elevation
southof 72øNis increasing.
Comparing
meas- line spreading.
Their resultsindicatea positivemass
urements
from the Geosat(1985) andSeasat(1978)radar balancecorresponding
to a thickening
of 0.06 + 0.08 m
altimeters,
theobserved
spatiallyaveraged
rateof thicken- yr-• along
theOSUtransect
andnear-equilibrium
condiingisabout0.233_+0.030m yr-•. These
results
suggest
a tions(0.0_+0.07rnyr-•) alongtheEGIGline.
muchhigherrateof thickeningthando themeasurements Bindschadler
[1984]usesa similarcomparison
between
made along the EGIG line. Furthermore,whereasboth
the balanceflux at the terminusand the actualice flux to
Baueret al. [1968]andSeckel[1977]find a loweringof estimate
themass
balance
of thedrainage
basinfeeding
the
the ice surfacein the ablationzone,Zwallyet al. [1989] Jakobshavns
Glacier.His resultssuggest
thatthisbasinis
infer a thickeningin the marginalzonesabovethe 700-m in equilibriumor slightly thickening.Kosteckaand
elevation contour as well (their measurements
do not
includethe coastalpart of the ice sheetwhere the ice
surfaceis lessthan700 m, presumably
because
therethe
slope-induced
errorbecomes
toolarge).It is notclearhow
thesedifferences
canbe explained.
Whillans
[1988]arguethatthismaybe explained
by the
accumulation
rate valuesusedby Bindschadler
[1984].
Thesewere determined
by interpretation
of layering
observed
in shallowpitsandtendto be largerthanthe
30-yearaverages
obtainedfromice cores.
29, 3 / REVIEWSOF GEOPHYSICS
Van der Veen: STATEOF BALANCEOF THE CRYOSPHEREß 439
3.2. Outlet Glaciers
Many authorshaveattemptedto estimateeachof the terms
on theright-handside,but largeuncertainties
still exist[cf.
Reeh, 1985]. Table 2 gives some of the massbalance
An extensive overview of glacier fluctuations in
Greenlandis presented
by Weidick[1968]. Most (geological) informationis availablefor westGreenland.Many of
the glaciersdrainingthe inland ice have been retreating
sincethe middleof the nineteenthcentury.As is the case
for most Europeanmountain'glaciers,this retreat was
interruptedby periodsof readvance,or halt of the recession,around1890 and 1920. More recentdatasuggestthat
estimates available in the literature. These estimates
suggestthat the Greenlandice sheetis not greatlyout of
balance,althoughan accurateassessment
of the present
transfer of mass between the ice sheet and the oceans is not
possible.
for the northernmost lobes of the inland ice a new read4. THE ANTARCTIC
ICE SHEET
vancemay havestartedaround1960.Duringthereadvance
around1890, many glacierlobesreachedtheir maximum
extentof theLittle Ice Age. The readvanceof 1920 was,in
general,of a lesserextent.
Localglaciersin westGreenland(i.e., thosenot draining
the inland ice) reached their Little Ice Age maximum
before the nineteenthcentury and possiblyas early as
1750. Most of the local glaciersremainedclose to this
maximumpositionup to the mid-nineteenth
centurywhen
retreatset in. Between1860 and 1880 therewas a general
readvanceof the ice fronts, albeit of less magnitudethan
earlier advances.Recessionof the glaciersfollowed,with
the highestrate of retreat occurringbetween 1920 and
Uncertainties arise because accumulation rate measure-
stabilize the ice front.
rather qualitativesummaryof the presentsta•e of
4.1. Large-Scale
Studies
Estimates
of the massbalanceof entiredrainagebasins
(shown in Figure 4) are in most casesbased on a few
scattered
observations
and involvelargemarginsof error.
mentsare usuallyavailablealong a traverseextending
inlandfrom thecoast.Furthermore,
properdelineationof a
particulardrainagebasin hingeson the availabilityof
accuratesurfacetopographymaps. In fact, some of the
studiesmentioned
belowdo not considerdrainagebasins,
but geometrically
regularareas.This obviouslyintroduces
1940. Since 1940 the rate of recession has decreased for
anothersourceof error,namelythe estimateof the amount
mostof the local glaciers.Again, the generalretreatwas of ice enteringtheregionunderconsideration
throughthe
interruptedby shortand minor readvances,
between1915 inlandboundaries.
For this reason,the followingdiscusandthe 1920s,whichwere in manycasesonly sufficientto sionof resultsfrom large-scalemassbalancestudiesis a
From eastGreenland, little information is available. The
knowledge.
maximum extent of the glaciers there occurredin the
middleof the eighteenthandnineteenthcenturies,although
a laterreadvancearound1890 seemsto havebroughtmany
ice frontscloseto their Little Ice Age maximumreached
during previous advances. Several investigatorshave
reported that many glaciers in east Greenland have
retreatedstronglyduringthiscentury[cf. Weidick,1968].
observations of the ice front near the Dumont d'Urville
3.3. Mass Balance of the Entire Ice Sheet
base, which show a retreat. The differencemay be
explainedbecausecertainablationprocesses
could have
Lorius [1962] gives a synthesisof glaciological
investigations
conducted
in Terre Ad61ie,mainlyduring
theInternationalGeophysicalYear. The massbalancefor a
sectorwhoseouteredgeis the coastbetween135øEand
142øEappears
to bepositive,
corresponding
to a thickening of about0.1 m yr-•. This is in contrast
with visual
The changein ice volumeV is the differencebetween been underestimated and because the calculations are
based on only a few scatteredsurface measurements.
by meltingM andicebergcalvingC:
Anotherpossibilitysuggested
by Lorius [1962] is that the
coastal
retreat
may
be
the
response
to climatechangesin
dV
the
past.
d• =A -M -C.
the annual snow accumulation A and the annual loss of ice
TABLE
2. Estimates of the Mass Balance of the Greenland Ice Sheet
Accumulation
Loewe[1936]
Bauer[1955]
Bader [1961]
Benson[1962]
Bauer [1966]
Weidick[1985]
+425
+446
+630
+500
+500 + 250
+500 + 100
Ablation
--295
-315
-120 to -270
--272
-330 + 165
-295 + 100
Expressed
inkm3water
equivalent
peryear.
Total
Calving
--150
-215
-215
-215
--280 + 140
-205 + 60
-20
-84
+145 to + 295
+13
-110
+ 555
0 + 260
440 ß Van der Veen: STATEOF BALANCEOF THE CRYOSPHERE
29, 3 / REVIEWSOF GEOPHYSICS
0ø
Weddell
\
.•,"
•
\
Mizuhe
•lafeau
Kemp Land
MacRobertso•
•
Land
I
ry
/
EAST
/
/
90øW
i
,
:• l:'¾
/
ß
WEST•.,•L.. -- -- --.
ANT ! ARCTICA
•
I
A NTARCTI CA
I B•yrd
Stn
/
\
/
\
90øE
"• -- •/
I
q
Ikes
_\
oss
Shelf
Sea
ß
0
KM
1000
Stn
d'Urville
./
180 ø
Figure4. Location
mapforAntarctica.
Dashed
linesindicate
theboundaries
ofthemajordrainage
basins.
Cameron [1964] discussesthe mass balance of the ice
sheet in the Budd Coast area near Wilkes
station and
concludes
that the ice sheetis thinningthere.However,he
considers
a rectangular
area,ratherthana naturaldrainage
basin,sotheremaybe an importanterrorin theestimateof
ice massflowinginto the region.Cameron[1964] argues
that the massbalancein thisareais mainlydependent
on
local snow accumulationand entirely neglects the
contributionof inlandice flow into this area.His arguments,however,are not very convincing,and his conclusion about the state of balance of the ice sheet in this
massis aboutthreetimesas largeas the lossof ice at the
front,suggesting
an average
thickening
of 4 cm yr-•. An
updated
assessment
by Allison[1979]basicallygivesthe
same results.
Local studies in the coastal area of MacRobertson and
KempLandsalsosuggest
a positivebalance.Mellor [1959]
considers
thecoastal
region
between
45øEand80øEandfinds
a surplus
of accumulation
overlosses,
although
hefeelsthat
the availabledataare insufficientto claim that the ice sheetis
growing.MorganandJacka[1981]usemeasurements
made
alonga traverse
routein MacRobertson
andKempLandsto
regionmaybe challenged.
calculate
theicefluxacross
thetraverse
route(approximately
ThedrainagebasinfeedingtheAmeryIce Shelfthrough parallel
tothecoast,
following
the2000-melevation
contour).
the LambertGlacierhasbeenstudiedextensively
by the Comparison
with the calculated
massinput from snow
Australians. Budd et al. [1967] conclude that the mass
accumulationin the basininlandof the traverseshowsthat the
balanceof thisdrainagesystemis positive.Supplyof ice
netmassinputisalmosttwiceaslargeasthemassoutflow.
29, 3 / REVIEWS
OF GEOPHYSICS
Van derVeen:STATEOF BALANCE
OF THECRYOSPHERE
ß 441
the resultsof Whillans
Naruse [1979] interpretsthe resultsof two surveys to a steadystate.This conf'u-ms
(1969 and 1973/1974)alonga 250-km-longtriangulation [1976]basedon analysisof radioechodeterminedlayering
chain in the inland region of the Mizuho Plateau in the ice sheet.Thesedata suggestthat the ice sheetnear
(approximately
followingthe 72øSparallel).Results Byrd Station is close to steady state. However, small
indicatea largethinningof the ice sheetat a rateof about deviationsfrom equilibrium as calculatedby Whillans
0.7 m yr-•. Thisneednotberepresentative
for theentire [1973, 1977]wouldnotbe detectableby thistechnique.
The Siple Coast is characterizedby a number of
plateau,however.Shimizuet al. [1978]estimatea rather
seeFigure
largepositivebudgetfor theentiredrainage
basinfeeding fast-flowingice streams(labeledalphabetically,
the ShiraseGlacier.It is thusvery well possiblethat the 5) draining into the Ross Ice Shelf, and separatedby
observed
thinningin the interioris local,or of veryrecent virtuallystagnantinterstreamridges.So far, ice streamsB
occurrence.
and C have been studiedextensively.Of these two, ice
A review of available measurements in the Antarctic
stream C is anomalous in that it has all characteristics of an
Peninsulaand the WeddellSearegionis givenby Doake
[1985].He concludes
thatthereis no definitiveevidenceof
significant
changes
in massbalancethere.Whateverfew
dataare availablesuggest
a net massloss,but no quantita-
activeice stream,exceptthatvelocitiesare very low (about
tive estimates are warranted.
[Shabtaieet al., 1988]. Ice streamA is dischargingmore
ice thanis beingaccumulated
in the catchmentareaandis
currently thinning at a rate of 0.08 with a standard
The two drainagebasinsdischarging
into the RossIce
Shelfappearto havea positivemassbalance[Giovinetto
et
al., 1966; Giovinettoand Zumberge,1967]. An updated
estimateby Bentley[1985]indicates
thatinflowfromEast
Antarcticainto the easternpart of the Ross Ice Shelf
1 rnyr-•) [McDonald
andWhillans,1988].Thissuggests
that this ice streamhas recentlystoppedand is currently
thickening
at its accumulation
rate(0.12+ 0.02 rn yr-•)
deviation
of 0.03rnyr-• [Shabtaie
et al., 1988].Similarly,
the mass balance of ice stream B shows a deficit cor-
responding
to a thinningrate of 0.06 + 0.04 rn yr-•
[Whillansand Bindschadler,1988]. It may be notedthat
westernpartof theice shelfis in, or closeto, a steadystate. this rate is significantlysmaller than earlier estimates,
on theboundaries
of
The drainagesystemof the West Antarcticice sheet mainlyas a resultof betterconstraints
flowingintotheRossIce Shelfappears
to be gainingmass the catchmentarea. Accordingto Shabtaieet al., [1988],
thepatternof thickness
changealongice streamB is rather
at present.
complex(Figure6). Thereappearsto be a slightthinning
4.2. Local Studies
in the catchmentarea, a large thinning of the two
B1 (1.26+ 0.37rnyr-•) andB2 (0.57+ 0.23rn
Apartfrom the studyof Naruse[1979] on the central tributaries
in themainbodyof theicestream.
It
Mizuho Plateau,very few local studieshavebeenunder- yr-•) anda thickening
taken. The region upstreamof Byrd Station (West is not clearwhatcausesthiscomplexbehavior,althoughit
a transientresponse
to eithera changein internal
Antarctica)has been studiedby Whillans[1973, 1976, suggests
1977]. On a moreregionalscalethe Siple Coastareahas dynamics,or an adjustmentto a change in external
been investigatedin detail by variousgroupsof U.S. forcings.At the mouthof ice streamB the Crary Ice Rise
scientists.
complexis thickeningat an averagerate of 0.14 + 0.09 rn
et al., 1987],whichmaybecaused
by the
Upstream
of theByrdStationborehole,
a straingridwas yr-• [MacAyeal
imbalance
of
ice
streams
A
and
B.
Bindschadler
et al.
deployedin 1963-1964andresurveyed
in 1964-1965and
[1989a]
calculate
the
regional
pattern
of
thickness
change
againin 1967-1968.The gridextendsover 163 km from
the ice divideto the boreholesite.Along the grid,relative in the vicinity of Crary Ice Rise and find significantrates
ice movementcan be calculatedfrom the repeatsurveys, of thickeningupstreamof the ice rise and important
while net surface mass balances were obtained from
thinning downstream,assumingzero basal melting or
changesin pole heightsover periodsof up to 8 years. freezing.The net massbalanceof the entirearea is near
Whillans [1973] uses these data to calculate the mean zero, but the regional differencescannot representa
volumeflux alongthe grid and comparesthesewith the redistributionof mass already within the region concurrentrate of surfaceaccumulationupstreamof points sidered,becausethe regionof massgain is upstreamof the
alongthegrid.He concludes
thatneartheice dividetheice regionof massloss.Rather,theseresultssuggestthat the
sheet seemsto be in equilibrium.Farther downstream, iceriseis migratingin thedirectionof thegroundingline.
however,the volumeflux is largerthan that requiredfor
equilibriumby as much as 15% near Byrd Slation. 4.3. Mass Balance of the Entire Ice Sheet
Estimatingthe stateof balanceof the entire Antarctic
Althoughsomedifferences
maybe causedby thetraverse
not followingthe ice flow exactly,or by complexflow at ice sheetis hamperedby a lack of accumulationrate data
depth,it seemsmostlikely that the calculated
difference overlargepartsof the interior.Becausesurfaceablationis
between actual and balance flux is due to ice sheet
negligible,ice lossis achievedthroughcalvingat the ice
thinning.A similar,butmorecareful,analysisis presented fronts and throughbasal melting under the peripheral
by Whillans[1977]. Again,calculations
indicatethat the floatingice shelves.Althoughbasalmeltingis believedto
regionis thinning
slowly(0.03rnyr-•),butit is stillclose occurin extensiveareasunderthe groundedportionof the
exceeds the outflow at the ice front. In contrast, the
442 ß Van der Veen: STATEOF BALANCEOF THE CRYOSPHERE
•'•
'•
29, 3 / REVIEWSOF GEOPHYSICS
G3G5
C
!
t
•
ROSS
D•••_•m•
'•,•. E
G7
0
ICE SHELF
KM 200
Figure
5.MapoftheSiple
Coast,
West
Antarctica.
Heavy
lines
correspond
tothegates
across
ice
stream
B through
whichicefluxesarecalculated
by Shabtaie
et al. [1988];thedashed
line
indicates
thegrounding
line(afterShabtaie
etal.[1988,Figure
3];reporduced
bycourtesy
of the
International
Glaciological
Societyandtheauthors.)
JCATCHMENT
AREA
STREAM
,
'['ROSSICESHELF
B
LLI
z
•>
o
z
(j- o.5
u.
--1oo
o
o
ß
260
DISTANCE
400
FROM
860
600
SUMMIT
1000
IKMI
Figure
6.Mean
rateofthickness
change
({-/)versus
distance
along
icestream
B.Themeasured
values
off-/foreach
flowband
blockareplotted
atthecenter
oftheblocks
between
thesuccessive
gates
shown
inFigure
5.Theheight
oftheboxes
represents
theerror
estimate
off-/for
each
block.
(FromShabtaie
etal. [ 1988];reproduced
by courtesy
of theInternational
Glaciological
Societyand
the authors.)
29, 3 ! REVIEWS
OF GEOPHYSICS
Van derVeen:STATEOF BALANCE
OF THE CRYOSPHERE
ß 443
ice sheet,thisprobablyhasa minoreffecton thenet mass minimum at the bottom and a maximum somewhere in the
middleof an annuallayer.Becausethisprofileis preserved
Table3 givesa summaryof massbalanceestimates, for many years, it can be used to detect boundaries
of these
compiled
by Meier [1983].Theseestimates
suggest
that betweenannuallayers.By combiningthicknesses
the mass balance of the entire ice sheet is positive, layerswith profilesof density,annualvaluesof accumulaalthoughthe error limits allow for a slightlynegative tion rates can be calculated.
Averageaccumulationrates since the mid-1950sand
balance. This concurs with the conclusion of Budd and
Smith[1985], who computedbalancevelocitiesover the mid-1960scanbe derivedfrom grossbetaactivityprofiles
cores.Dependingon the local accumulaentire ice sheet and comparedthese with measured of hand-augered
velocities.
Thiscomparison
suggests
thatthetotalsurface tion rates,thesecoreshaveto be about8 to 30 m long, in
accumulation
is nearlybalancedby the outflowof ice at orderto reachthe 1954depth.Samples(10-15 cm long)
themargins,
witha discrepancy
mostlikelyin therangeof from the coresare melted,and the radioactiveisotopesare
on ion exchangefilters. The radioactivityof
0 to 20%. Thecorresponding
loweringof globalsealevel concentrated
budget.
thesefilters is measuredto identify the 1954-1955 and
1964-1965 horizons, which are characterizedby an
increasedlevel of radioactivity(resultingfrom nuclear
5. CONVENTIONAL
GLACIER MEASUREMENT
testsconductedin the atmosphere).Figure 7 showsan
example of a radioactivityprofile measuredin a core
TECHNIQUES
retrievedfrom West Antarctica.The depthsof the high5.1. Accumulation
level samplesare calculatedfrom the drilling records,
Short-termaccumulationrates(yearly averagesor mean allowing for core loss (only in very rare casesis core
values
overa few years)
canbeobtained
frompoleheight recovery 100%) as describedby Whillans and Bolzan
measurements.
This requiresplacingsurveystakes(for [1988]. Taking into accountthe variationin densitywith
ratessince1954-1955 or
example,
bamboopolesor steelconduits)
verticallyin the depth,the averageaccumulation
isabout0 to 1.2mmyr-•.
firn and meaõuringthe exposedlengthsof the poles 1964-1965 can be calculated [cf. Whillans and Bindschadrepeatedly.
Fromtheselengths,surfacemassbalances
can ler, 1988].
Long-termaccumulation
ratescanbe derivedfrom deep
becalculated,
!akingintoaccount
thedepth
variation
of
ice cores.Annuallayershave to be identifiedand transfire densityandsettlingof thefim andpoles.
Yearlyvaluesof accumulation
canalsobe derivedfrom ferred into accumulationrate records.Again, corrections
snowpit studies.
Thisrequiresdigginga pit andlocating have to be made for density variationsas well as for
the previoussummer'ssurface.In many instances
this variationsin accumulationratesupstreamof the borehole
surfaceis markedby a layerof dirt or by a sudden
change site. Some modelingof the local ice flow is requiredto
in density.For example,on theHintereisfemer
in Austria, calculatethe total verticalstrainsincethe time of deposiHoinkes[1957]findsthatthetypicaldistribution
of density tion. Figure 8 showsa recordthus obtainedand allows
with depth,as foundin the winter snowcover,showsa determination of secular trends, as well as short-term
TABLE 3. Estimates of the Mass Balance of the Antarctic Ice Sheet
Ablationon
Accumulation Ice Sheet
Melting Under
Ice Shelves
Calving
Total
-950
+1100to
Kosack
[1956]
Loewe[1956]
+1650
+1200
-2050*
0
0•0
-550
-140 to
Wexler[1958]
Mellor[1959]
Lister[1959]
Wexler[1961]
+1340
+1747
+1906
+880
0•-74
-135
0•'
-1300
-48
-675
-220
-40
-570
-270
-660
05
+1055
+826
05
Kotlyakov
[1962]
+2650
0
-120
-1210
+1320õ
Rubin[1962]
+1439to
0 to-74
-163 to-323 -1276
05
-10
-200
+240
-300
+1200
+1673
Loewe[1967]
+1900
-1450
Excluding
theAntarctic
Peninsula,
in general,
expressed
in kmz water
equivalent
peryear
(compiled
by Meier [1983]).
*May includeevaporation
in accumulation
area.
•Assumed.
•:Zeronetbalanceassumed.
{}Assumed
50% imbalance.
444 ß VanderVeen:STATEOF BALANCE
OF THECRYOSPHERE
o
lOO
ice level around the stake and thus reduceserrors caused
by the small ablationhollows,.the readingsare not
necessarily
a truerepresentation
of theloweringof theice
surface.
Thisisbecause
therateof lowering
of thepeaks
in
/
2.1
mI
i
the microrelief
(on whichthe straight
rulerrests)may
differ from that of the total surface. Miiller and Keeler
[1969] estimatethat the error thus introducedis about_+0.5
i
4.2
29, 3 / REVIEWS
OF GEOPHYSICS
cm.It maybe notedthatsimilarconsiderations
playa role
when measuringaccumulationfrom pole heights.
However,accumulation
measurements
areusuallymadeat
i
1
i
1-yearintervals,whereasablationmeasurements
are often
carried
outthrough
onemeltseason,
withonlya fewdays
between successive measurements. Thus the error is
7.6
1964-65
relativelylargerfor theablationmeasurements.
2000
10
DYE 3
MILCENT
CRETE
954-55
Figure 7. Grossbetaprofile for a West Antarcticstation.Vertical
axis is linear in the samplenumber, with selecteddepths
indicated. Horizontal
bars indicate measured counts for those
samplesmeasured.
1500-
fluctuations[cf. Reeh et al., 1978]. One shouldbe careful
in interpreting
suchrecords,however.As shownby Reeh
et al. [1985], the low-frequency
variationof the Dye 3
record reflects upstream short-distancevariations in
accumulation
rate,ratherthantemporalfluctuations.
5.2. Ablation
Measurements
of ablationare in generalmorecompliCatedthan thoseof accumulation,not in the least because
the ablationzoneof a glacieris, in manyinstances,
less
easily accessiblethan the accumulationarea. There does
not appear to be a practicalmethodof determining
long-term ablation rates. Only seasonalor short-term
averagescan be measuredusing ablation slakes.As for
accumulation
rates,the exposedlengthsof the stakesare
measuredrepeatedly but with a correction made for
vertical
movement
of thestakeduetoiceflow[Nye,1968;
Vallon, 1968]. A majorproblemis to eliminatethe effect
of settlement
in the upperfire layers.Combinedwith the
generally complex microrelief of the ice surface, this
makestheusualtechnique
of measuring
surfacelowering
onSlakes
difficultto interpret,
andcalculated
ablation
rates
500I•
-lO
!
II
lO%
are often inaccurate.
The straight-edgemethodis often usedto eliminatethe
influence of melt hollows around the stakeon the measure-
Figure 8. Accumulationrate records from three Greenland
stations,derivedfrom deepice cores.Annualdataserieshave
ments.Thedistance
fromthetopof thestaketo a straight beensmoothed
by digitallow-pass
filterswithcutoffperiods
of
ruler (0.5-1 m, say)placedflat on the surfaceis measured 120years(heavycurves)and30 years(thincurves).
(FromReeh
[Miiller andKeeler, 1969;Braithwaiteand Oleson,1984]. et al. [1978]' reproducedby courtesyof the Intemational
Societyandtheauthors.)
Althoughthismethodallowsdetermination
of anaverage Glaciological
29, 3 / REVIEWS
OF GEOPHYSICS
Van derVeen' STATEOF BALANCE
OF THECRYOSPHERE
ß 445
To obtainmore accuratevaluesof surfaceloweringfor
DENSITY
an area of 1-m radius aroundthe stake,Maller and Keeler
400
(KG/M3I
500
600
[1969]designed
a starablatometer.
Thisis a six-armmetal
starthatis mounted
onthesurvey
stake.
Eacharmhassix
sleevedholes,thus36 pointscanbe measured
by lowering
a measuringrod througheach hole. This way, some
informationon the local variability in weatheringof the
crustis obtained.This methodthereforeprovidesa more
accurateassessmentof ablation than the straight-edge
method.However,changesin the weatheringcrustfrom
onereadingto thenextmaybe a sourceof uncertainty.
Insteadof estimatingablationfrom surfacelowering
only, which may be morerepresentative
of variationsin
surfacedensityratherthan true ablation,the lattercan be
determinedby measuringchangesin mass.LaChapelle
[1959] discusses
a practicalmethodfor this.Referringto
,.
.--- .-.h 0
.
h1
Figure9, at someinitialtimeto thethickness
of a surface
layerequalsho andhasa knownverticaldistribution
of
bulk density,p(h, to).Aftera timeintervalt• - to has
elapsedthe surfacehas lowered and the thicknesshas
decreased
by an amount•Sh.Becausethe densitycloseto
thesurfaceis, in general,notconstant
with time,thelossof
massin thesurfacelayeris givenby
ho
15-
href
hi
FigUre9. Measurement
of directmasslosson Blue Glacier,
AM=;p(h,to)dh-;p(h,tl)dh,
1958.(FromLaChapelle[1959];reproduced
by courtesy
of the
o
o
International
GlaciologicalSocietyandtheauthors.)
which equals the shadedarea betweenthe two density
curvesin Figure9. Obviously,thismethodis rathertedious of flow. For ice stream B the maximum and minimum size
as it requires sufficient measurements
of density to of the catchmentarea differ by 12% from the average
value,147,000
km2[Whillans
andBindscharier,
1988].
determinethe density-depth
curve.
Finally, ablationcan be estimatedfrom measurements Accumulation
ratesweredetermined
fromthegrossbeta
of surfacerunoff, providedthe firn is impermeable,and activity profilesof shallowcores,as discussedin section
evaporation
is negligible.Becauseof the time lag between 5.1. Also availablefor this regionare earlier valuesfrom
the melt and the surfacedischarge,this methodis not very Bull [1971]. The variabilityapparentin the accumulation
reliableto determinedaily melt rates.
ratesshownin Figure 10 is mainly due to local surface
From comparisonof the differenttechniques
discussed slopeeffects;sastrugiandinterannual
variabilitycontribute
above, Maller and Keeler [1969] concludethat the direct
to a lesserextentto the variability.The areallyweighted
measurement
of massloss(surfaceloweringplus melt in
the uppercrust)appearsto give the bestestimatesof true
meanaccumulation
rateis0.143_+0.014m yr-1.
ablation.
Basalmeltingresultsin lossof ice that is not accounted
for by the dischargemeasureddownstream.
However,this
appearsto be negligibleand is estimatedat 0 _+0.005 m
5.3. MassBalanceof a DrainageBasin
yr-• byWhillans
andBindschadler
[!988].
To assessthe massbalanceof a drainagebasin of a
The outflow is calculatedthrougha gate acrossthe
glacier,the net inputhasto be comparedto the net output. narrowestpart of the ice stream. About 787 surface
As an example, considerthe study of Whillans and velocitieson the transectare derivedfrom repeataerial
Bindscharier [1988] for ice stream B, West Antarctica.
photogrammetry,
with groundcontrolprovidedby Transit
Becauseice flow is almost perpendicularto surface satellite
trackingstations
(cf. WhiliansandBindscharier
elevationcontours,the boundariesof the drainagebasin [1988] for a discussionof the procedureinvolved). In
can be determinedby drawingflow linesperpendicular
to short, positions of surface features (crevasses,drift
elevation contours.This requires an accurate map of mounds,etc.) thatappearon bothsetsof photographs
are
surfacetopography,which for ice stream B has been measured,and velocitiesare calculatedfrom the difference
constructedby Shabtaieet al. [1987], basedon airborne in positionand the elapsedtime interval. Whillansand
radar.Someambiguityin the boundariesof the catchment Bindschadler [1988] estimate the error limits for these
areais unavoidable(seeFigure 10). This couldbe lessened velocities
to be_+12 m yr-•. Thesurface
velocity
profile
if surfacevelocitiesare available,indicatingthe direction alongthe transectis shownin Figure 11. Becausealmost
446 ß Van der Veen: STATEOF BALANCEOF THE CRYOSPHERE
29, 3 / REVIEWSOF GEOPHYSICS
I
!
i
I
1000
900
800
700
I
600 •-,,
500
400
/
- -lOO
/
19ß
/
/
/
/
22ß //
/
/
--200
/
13
15
12
--300
22•
\
\
2,
14
19
18
ooo
--400
20 I
ß
18
\
19
'-t
13ß
\•7\
13ß
•5
11
,ß
15ß
--500
14ß
New Byrd
Station
o
18ß
o
Old Byrd
Station
- -600
13ß
!
Figure10. Map of theice stream
B drainage
basin,withaccumulation
ratesin centimeters
per
year.Underlined
valuesarederivedfrommeasurements
of grossbetaactivity,whileothervalues
are fromBull [1971].Dashedlinesindicatepossible
boundaries
of the catchment
area.(From
Whillansand Bindschadler
[1988];reproduced
by courtesy
of the International
Glaciological
Societyandthe authors.)
all ice motionis dueto basalslidingon ice streamB, these output
is-8.6 _+6.2km3 yr-•, which
corresponds
toan
velocities are representativeof the depth-averaged averagethinningrate of 0.06 _+0.04 m yr-•. The most
velocities.
importantuncertainties
in this estimateare associated
with
Ice thickness across the ice stream is also shown in
the sparse accumulationrate data above the 1000-m
Figure 11. These were determinedfrom a radio echo elevation
contour
andwiththeaccuracy
of determining
the
soundingflight and are believedto be accurateto _+18m boundaries of the catchment area.
[ShabtaieandBentley,1987].
With thesedata the net massbalanceof the drainage 5.4. Mass Balance of Mountain Glaciers
basincannow be addressed.
Multiplyingthemeansurface
The most frequentlyused methodfor determining
accumulation
for each200-m elevationintervalby thearea changes
in the massbalanceof a glacieris mapping
of thatinterval
givesthenetinputof ice(21.4_+5.2kma historic
frontvariations.
Mostof theinformation
pertaining
yr-•).Theerror,whichalsoincludes
theuncertainty
dueto to glacier
behavior
duringtheLittle IceAgeis based
on
basal melting, originatesfrom uncertaintiesin the accumulationrate and in the areal extentof the basin.By
integratingthe velocityprofile on the transectover the ice
thickness
thedischarge
throughthegateis foundto be 30.0
suchrecords.
However,changes
in lengtharenotnecessarily proportional
to changes
in ice volume.For example,
Nigardsbreen
in Norwayhasa wideaccumulation
areaand
a long narrow tongue,and is very sensitiveto small
+ 1.0kma yr-•. Thedifference
ß
between
theinputand perturbations.
A bettermeasureof volumechangesis
29, 3 / REVIEWSOF GEOPHYSICS
Van der Veen' STATEOF BALANCE OF THE CRYOSPHEREß 447
obtained by taking into account geometric effects.
Oerlemans[1988] proposesto scalethe length variations
by a characteristic
length,definedas the ratio of glacier
area to mean width of the tongue. This improves the
may be expectedto yield resultsthat vary too muchfrom
year to year. During dry summersthe glacier's mass
balance tends to be underestimated, while after a wet
summerthecalculated
massbalancemaybe toolarge.
The glaciologicalmethodrestrictsmeasurements
to net
longer time scales,but as pointedout by Meier [1984], accumulation
on the glacierR and net ablationB. Both can
measurements
of advanceor retreatcan be misleadingin be determinedby the techniquesdiscussedabove. For
sign. It is possiblefor a glacier to increasein volume, example,HoinkesandRudolph[1962] andHoinkes[1970]
while its frontis retreatingat the sametime.
applythe glaciologicalmethodto studythe massbalance
A more quantitativeestimateof the massbalanceof a of the Hintereisferner
in the AustrianAlps. Accumulation
glacier can be obtainedby consideringthe terms in the rateswere determinedfrom pit studies,while ablationwas
massbalanceequation,
measured
usingablationslakes.The volumeof thisglacier
has been steadily decreasing,at least until about the
correlation
between
front variations
and ice volume
8M=N-A-V
on
mid-1960s.
=R -B,
A completelydifferenttechnique
for measuring
changes
in ice volume is the geodetic method. Accurate
where8M represents
the changein ice volume,N the total topographicmaps compiledat different times have to be
precipitation,A the discharge,V total evaporation,R the availablefor this [e.g., Finsterwalder, 1962]. To obtain
net accumulation,and B the net ablation.
reliable estimatesof change,the contourlines must be
In the hydrologicalmethod the water balance of a determinedwith an accuracyof at leasta few decimeters.
precipitationbasinthat includesthe glacieris considered. Such precisioncan be achieved either by classical
This meansthatmeteorologicaldatafor the areasurround- surveyingmethodsor by stereo-photogrammetry
with
ing the glacierare requiredto estimatethe total precipita- controls
provided
by reference
elevations
on the neighbortion N. The dischargeA can be measuredby stream ing solidrock.The majoradvantageof thismethodis that
gauges,downstreamof the glacierfront.A difficulty with glacierchangesover a few years can be measuredwith
thismethodis thatthechangein icevolume,8M, is usually relativelylittle field effort.Inaccuracies
in measuring
the
the smalldifferencebetweenthe two largenumbers,N and surfaceelevationon especially
the snow-covered
partsof
A, and the smaller,and muchlesserknown,evaporationV. theglaciercanleadto uncertainties
thatare toolargefor
Hoinkes [1970] pointsout that the hydrologicalmethod applicationto year-to-yearchanges.
5.5. Numerical Methods
By combiningfield measurements
with a theoreticalor
800
numerical model the mass balance can be estimated. The
most straightforwardmethod is to calculate balance
600
velocities
required
for steadystateconditions
andcompare
ma-1
400
VELOCITY
COMPONENT \
perpendicular
these with measured surface velocities. This can be done
for an entireice sheet[e.g.,Budd and Smith,1985], for a
drainagebasin [e.g., Bindschadler,1984], or along a
to
transect[e.g., Kosteckaand Whillans, 1988]. The balance
velocity is calculated from surface elevations and ice
200
-800(m)
O-
thicknesses
andfromaccumulation
data.A difficultywith
this method is that the calculated balance velocities
- 900
-1000
-1100
correspondto the depth-averaged
ice flux. Thus, to allow
for comparisonwith observed surface velocities, an
assumptionaboutthe verticalvariationin the horizontalice
velocityhasto bemade.If basalslidingis relativelylarge,
this variation is negligible and calculated balance
velocitiescanbe directlycompared
with surfacevelocities.
However,for an ice sheetfrozento thebedthevelocityat
the ice surfacemay be significantlylarger than the
depth-averagedvelocity. Combined with uncertainties
associated
with the constitutive
relationfor polarice [cf.
Figure 11. (Top) Velocity from repeatphotogrammetry;
the
Van
der
Veen
and
Whillans,
1990],
thistechnique
necesdashed
partis interpolated
because
of lackof traceable
surface
sarily
introduces
large
error
limits.
features.(Bottom) Thicknessprofile derived from radio echo
On a smaller scale the mass balance can be estimated
sounding.
(FromWhillansandBindschadler
[1988];reproduced
[Mellor, 1968;Reeh
by courtesyof the International
Glaciological
Societyand the from flux divergenceconsiderations
authors).
and Gundestrup,1985]. Integratingthe equationof
448 ß Van der Veen: STATE OF BALANCE OF THE CRYOSPHERE
29, • / REVIEWSOF GEOPHYSICS
continuityover the ice depthyieldsan expression
relating typicallyseveralmeters.By applyinga retrackingprocethe rate of thicknesschangeto surfaceaccumulation,
ice durethat fits a multiparameterfunctionto eachwaveform,
velocity,andprincipalstrainratesin theflow directionand Martin et al. [1983] were able to eliminate most of this
cross-slope
direction.Becausemeasurements
only provide error. A second source of uncertainties is associated with
surfacevaluesof velocityand strainrates,someassump- the large-scaleslope of the ice surface.The measured
tionsabouttheir variationwith depthhaveto be made.For rangesarefrom the satelliteto thepartof thesurfacethatis
this,Reehand Gundestrup[1985] introducea shapefactor closestto the satellite.On a slopingsurfacethis point is
of the horizontalvelocityprofile, which is assumednot to not the sameas the subsatellitepoint (nadir).Rather,the
vary horizontally. The depth variation in horizontal reflectingpointis displaced
upslopefromthepointdirectly
a slope-induced
error
velocityandtheshapefactorcanbe derivedfrommeasure- beneaththesatellitewhichintroduces
ments of boreholetilting. The main advantageof this betweenthe true range to the nadir and the measured
method is that many sites can be investigatedwith range.For the Seasataltimeterthiserroris almost80 m for
et al., 1983].In thecoastal
areasof
relatively simple field programs.A problem associated an0.8ø slope[Brenner
with the techniqueis that calculatedthickeningratesmay ice sheets,large slopesoften occur, and the altimeterbe heavily influencedby local flow effects.This can be derivedelevationsare least accurate.The slope-induced
alleviatedby using regional values or by investigating errorcouldbe minimizedby reducingthe beamwidth of
(3-dBhalfanglebeamwidthof 0.8ø for the
many neighboringsites and validatingthe resultson a thealtimeter
statistical basis.
Seasataltimeter)[Bindschadler
et al., 1989b].By narrowWhillans[1977] appliesthe depth-integrated
continuity ing the beam,mostof thebeamenergyis focusedcloseto
equation to the flow along the Byrd Station Strain the subsatellite
point, therebyavoidingthe possibilityof
Network, upstreamof Byrd Station,West Antarctica.By returnsfrompointsthatarecloserto the satellite,butaway
integratingthisequationalongthe flow line startingat the from the nadir. Narrower beams require a different
ice divide,a comparison
betweenthe trueice velocityand altimeter design, for example, syntheticradar or laser
the balanceflux can be made.Separatingthe contributions altimeters.
to the total velocityfrom basalslidingand from internal
Bindschadler
et al. [1989b] give a comparison
between
satellite altimeter elevations of the Greenland ice sheet and
shearis an importantsourceof uncertainty.
Many othertechniquesexist,suchas modelingthe ice other elevation measurements. These include elevations
flow along a flow line, or part thereof, and explicifiy derivedfromTransit(Doppler)satellitereceiversandfrom
calculating the time evolution [e.g., Huybrechts and the opticallevelingalongthe EGIG line. Figure 12 shows
Oerlemans, 1989]. The level of confidence that can be
the altimeter-derived elevation contours, as well as the
placed on such studiesis largely determinedby the
simplifyingassumptions
involved,andby thesensitivityof
the resultsto poorly known parameters,most notablythe
elevationsare lower than those measuredotherwise,as
rate factor in the constitutive relation.
6. SATELLITE APPLICATIONS
BALANCE
IN GLACIER MASS
STUDIES
6.1. AltimetryOver Ice Sheets
Satellite radar altimetry was used by Zwally et al.
[1983] to map the surface topographyof parts of the
Greenland
ice sheet(southof 72øN)andtheAntarctic
ice
sheet(northof 72øS).They usedmorethan 600,000
elevation measurements over both ice sheets from the radar
altimeter on-board Seasat (in operation from June to
October1978). Becausethisaltimeterwasdesignedfor use
over oceans,which are virtually horizontalwith smallscaleroughness,applicationsto ice sheetsrequirespecial
treatmentof the data (in addition to the correctionsfor
atmospheric
effectsandadjustments
for radialorbiterrors).
First, because of small-scale undulations, the altimeter
sites for comparison.For all comparisonsthe Seasat
shownin Figure13. Alongthe EGIG traversea systematic
trendexists,with thelargestabsolutedifferences
occurring
closerto the ice sheetmargin.This may be causedby a
combination
of largerslope-induced
errorsand a rougher
ice surfaceneartheexterior.It is notclear,however,why
the Seasatelevationsare consistentlylower. It couldbe
that thesedifferences
are due to differentgravitymodels
usedto generatethe orbit ephemerides
for the Seasatand
the Transitsatellites.However,this doesnot explainthe
differences
betweenthe Seasatelevationsand thosealong
the EGIG line, derivedfrom opticalsurveying.Another
possibilityis that the radar pulse penetratesinto the ice
sheet surface, which alters the shape of the return
waveform.Ridleyand Partington[1988] suggestthat this
errorcanresultin an underestimate
of theelevationby as
muchas 3.3 m, dependingon the retrackingmethodused
in thedatareduction.Penetration
is mostlikely to occurin
the regions of highest elevation, which is where
Bindschadleret al. [1989b] found the largestdifferences.
Finally, the possibilitythat the differencesrepresentreal
elevationchangescannotbe ruledout. However,thereare
insufficient
datato eliminateor confirmthispossibility.
experiencedconsiderabledifficulty in predictingsuccessive rangesto the ice surface.Where the surfacedisturOn a smallerscale,Seasat
observations
overa 100-km
2
bancesare too large, no return waveform was recorded,
whereasover the remainingareasthe slowresponse
of the area in southernGreenlandare comparedto a derailed,
tracker causedan error in each range measurementof ground-based
surveyby Gundestrup
et al. [1986]. Their
29, 3 / REVIEWS
OFGEOPHYSICS
VanderVeen'STATE
OF BALANCE
OFTHECRYOSPHERE
ß449
72
70
D
66
¸z
64
LOCATION
OF
GROUND-BASED
ELEVATION
MEASUREMENTS
62
0
100
200
3oo
4oo
DISTANCE (KM)
60
33O
325
3O5
310
315
EAST LONGITUDE
32O
(DEGREES)
Figure12.Elevation
contours
fortheGreenland
icesheet
(south
of 72øN)determined
from
satelliteanfimetryand locationof the sitesof groundobservations
usedfor comparison
[from
Bindschadleret al., 1989b].
450 ß Van der Veen: STATEOF BALANCEOF THE CRYOSPHERE
29, 3 / REVIEWSOF GEOPHYSICS
OSU
EGIG
1980-81
1968
lO
Figure 13. Mean elevationdifferencesfor the comparison
between
altimeter-derived elevations and
those from conventional tech-
I,kl
MOCK
1972-75
DANES
EGIGCRETE
1984-85
1968
o
niques.The years indicatewhen
the ground-basedmeasurements
wereperformed.The lengthof the
vertical bars corresponds
to one
standard deviation [from Bindschadleret al., 1989b].
Z
ul
-lO
-15
conclusionis that the altimeter range measurementsare
where(Ha - H•)i is the elevation
difference
at the ith
crossoverand N the numberof crossovers.
If the repeat
measurements
have randomlydistributedtime intervals,
the dH/dt method is more appropriate.Assumingthat
elevation changes are a linear function of time, and
assumingthatthedataarerandomlydistributedaroundthis
trend,the slopeof a linear fit to the crossoverdifferences
versus their time intervals gives the rate of elevation
change.The advantageof this techniqueis that all repeat
measurements
can be used (insteadof only thosemade
over the specifiedtime intervaldt) and that the effectof
possibleseasonalchangesin eitherthe surfaceelevation,or
radarbackscattering
properties,is reduced(becausethere
6.2. Changes
in Ice Thickness
Repeat measurements
of surfaceelevationoffer a may be summer-winterand winter-summermeasurebias can be detectedby
methodto determinechangesin ice volume, as demon- ments).Also, any measurement
stratedby Zwally et al. [1989]. Theseauthorsuseddata consideringthe interceptof the linear fit at zero time
accurate
to thelevelof thegeoceiver-determined
surface(2
m). However,the altimetertendsto lock onto hills and
peaksin thesurfacetopography
nearthesubsatellite
track;
the lower parts betweenthe hills cannotbe resolved,
becausethe altimeterjumpsfromonetopographic
highto
the next. Thus the rangemeasurements
overestimate
the
true surfaceelevation.Becausea similaraltimetermay be
expected
to makecomparable
errorswhenremeasuring
the
surface elevation, changes in ice thicknessmay be
detectablewith higheraccuracy.
collected
overtheGreenland
icesheet(southof 72øN)by
radar altimeterson board the GEOS 3 (in operationfrom
difference.
The elevation differences obtained from either method
April 1975to June1978),Seasat(Julyto September
1978), containa randomerror.Zwally et al. [1989] determinethe
andGeosat(launchedin March 1985;datafromthefirst 18 magnitudeof this error from repeat altimeter measuremonths were used). Changesin surfaceelevation were ments over short time intervals (less than 15 days).
Dependingon the data set, the standarderror for single
determined
wheresuccessive
subsatellite
pathsintersect.
canbe a few meters.However,eventhough
Zwally et al. [1989] appliedtwo methodsto calculate measurements
elevationchanges.Where a largenumberof measurements thismeansthatthe errorin elevationdifferenceis usually
are availablefor two distinctperiodsby a relativelylarge larger than the actual changein elevation,significant
time interval (dt = 7 years,for the Geosat-Seasat
com- valuescan be obtainedif a sufficientlylarge numberof
is available.Lingle et al. [1990] use
parison),changesin elevationcanbe computedfrom the repeatobservations
averagecrossoverheightdifferencedividedby the time semivariogrammethods to estimate the noise in the
interval. That is,
altimeter measurements
as a function of position (the
dH
1
dt=• ,•-(H2
- H1
)i/N,
semivariogram
is analogousto the autocorrelation
function
usedin analysisof time series).Mean elevationchanges
29, 3 / REVIEWSOF GEOPHYSICS
Van der Veen:STATEOF BALANCEOF THE CRYOSPHERE
ß 451
are computedby averagingthe elevation differences to a changein brighinesstemperatureof about0.6 to 3 K.
obtainedat pointswhereorbitsascending
in latitudeare Comisoet al. [1982] expandedtheradiativetransfermodel
later crossedby orbits descendingin latitude (or vice used in these calculationsand produced comparisons
versa).Eachcrossover
differenceis weightedin proportion betweenseasonalvariationsin brighinesstemperatureand
to theinversesquareof thenoiselevelin thevicinityof the predictedvariationscalculatedfrom the measuredsnow
andgrainsizeprofiles.
crossover
point.The advantage
of thismethodis thatthe temperature
Thesestudiesusedobservations
madeover the polarice
influenceof areaswith exceptionallyhigh noiselevelsis
minimized.Also, the noiseestimatedoesnot dependon a sheetsby the electricallyscanningmicrowaveradiometer
priori knowledgeof error sourcessuch as instrument (ESMR) on board the Nimbus 5 spacecraft,launchedin
calibration or radial orbit errors. This means that this
1973. This radiometeroperatedat a singlefrequency(18
methodmay be suitablefor detectingchangesin mean GHz) and a single polarization.This means that the
propertiesthat contributeto changes
surfaceelevationnear the marginsof ice sheets,where differentgeophysical
altimeternoiselevels are high and variable,due to steep in brightnesstemperatureare not readily separatedwithout
additionalinformation(suchas thephysicaltemperature
of
surfaceslopesandroughsurfacetopography.
For massbalancestudies,changesin ice thickness
areof the snow pack). With the dual-frequencydata obtained
more interest than those in surface elevation. This means from the scanningmultichannelmicrowave radiometer
that the derivedelevationchangeshaveto be correctedfor (SMMR) a distinctionbetween changesin the physical
verticalmotiondue to postglacialisostaticadjustmentand temperatureof the snow and changesin the electrical
the densificationof firn. Zwally [1989] arguesthat for propertiesof the snowbecomespotentiallyfeasible.In an
southernGreenlandboth effectsare likely to be small so exploratorystudy,Jezek et al. [1990] found that differthatthe inferredchangein volumecanbe directlyequated encesin the amplitudeand swingof bothchannels(18 and
37 GHz) are generallyexplainablein termsof electromagto the measured
elevationchangetimesthe ice sheetarea.
netic principles. The amplitude swing of the 27-GHz
channel is larger than that of the 18-GHz channel,
6.3. SurfaceMelting
The intensityof microwaveradiationthermallyemitted reflectingthe increasedthermalmassassociatedwith the
18-GHz waves. Differences in bulk
by an objectis usuallyexpressed
in termsof thebrighiness deeper-penetrating
emissivities
due
to
the
differentpenetrationdepthsresultin
temperature
T•,theemissivity
of theobject
timesitsactual
measured
temperature.
The application
of microwaveradiometryasa shiftsin meanvaluesof brightnesstemperatures
remotesensingtool is basedon thefactthatthe emissivity by like polarizationchannels(that is, brightnesstemperaof an object dependsmainly on its compositionand tures for both horizontally polarized channelsor both
physicalstructure.Thus measurements
of the brighiness vertically polarized channels). Differences between
temperature
provideinformationon the emissivitywhen brighinesstemperaturesof horizontally and vertically
the physicaltemperature
canbe independently
estimated. polarized channelsare associatedwith differencesin
If the emissivitiesof the radiating surface are known, Fresnelreflectioncoefficientsfor eachpolarization.
measurements
of T• canbe usedto inferthephysical Suchdifferencesbetweenthefrequencyandpolarization
of eachchannelsuggestthatvaluableinformation
properties
of theradiatingmedia.The brightness
tempera- response
ture of snowincreasesmarkedlywith wereess[Stilesand on the surfaceclimateof ice sheets(for example,the onset
Ulaby,1980],andtherisein T• at theonsetof surface and extent of surface melting) may be derivable from
meltingis easilydetected.For instance,in the percolation comparisonof the two channels.K. C. Jezek (personal
zone in Greenlandthe increasein brightnesstemperature communication, 1990) believes that variations in the
during the period of summer melting is about 80 K polarizationrate,whichis definedas
compared
to thewintervalue[Zwally,1984,Figure6].
Zwally [1977] developeda theory for calculatingthe
Tbv emitted radiation of an ice sheet as a function of measured
p •
Tbv + TbH
temperature
and profilesof grain size. Measuredemissivities are determinedby taking the ratio of observed
brightnesstemperatureto the mean annual temperature whereT•vandT•uarethebrightness
temperatures
for the
derived for the surface station. Comparisonbetween verticaland horizontalchannelsof particularfrequencies
emissivities thus determined and emissivities calculated
from the theorywere very satisfactory.
Becausethe snow
crystalsizedependson the snowaccumulation
rateandthe
meanannualsurfacetemperature,the effect of changesin
either one of thesequantifieson the bulk emissivityand
brightnesstemperaturecan be estimated.Zwally [1977]
can be used to detect melt features. If this idea can be
substantiated,
it will representa significantimprovement
of our ability to observemelt patternson the polar ice
sheets.Not only will it be possibleto monitorsurfacemelt
over large areasof the ice sheets(which is not very
feasiblewith conventional
field programs),but thismethod
calculates
thata 1ø changein snowtemperature
hasthe will also allow for early detectionof changesin these
equivalenteffectof a 10% changein accumulation
rate;the patterns,whichmay be indicativeof changesin the polar
emissivitychangesby about0.003 to 0.014, corresponding climates.
452 ß VanderVeen:STATE
OF BALANCE
OFTHECRYOSPHERE
6.4. OtherApplications
29, 3 / REVIEWS
OF GEOPHYSICS
[Mellor,1958;Morgan,1973;KrimmelandMeier, 1975;
In addition to the areas discussedabove, satellite Brecher,1986; Whillansand Bindschadler,
1988]. For
imageryandremotesensing
offermanyotheropportunitiesexample,Lucchitaand Ferguson[1986] use successive
for studyingand monitoringthe cryosphere.
Perhapsthe Landsat
images
of ByrdGlacierdraining
theEastAntarctic
most developedapplicationis the mappingof sea-ice ice sheetthroughthe Transantarctic
Mountainsinto the
extent and variationsin it [Swirl and Cavalieri, 1985; RossIce Shelf.Many surfacefeatureson this glacier
Parkinsonet al., 1987; Zwally and Walsh, 1987]. Also, remain
preserved
andvisible
overperiods
of manyyearsso
imageryhasbeenappliedto infer changes
in the seaward thattracking
these
features
allowsmeasurement
of glacier
boundariesof Antarcticice shelves[Swithinbank,1970; velocity.The averagedisplacement
over an intervalof
Partington
et al., 1987;Zwallyetal., 1987].Although
both nearly10years(January
1974toNovember
1983)is 7.5to
theseapplications
do not pertaindirectlyto the studyof 8 km,giving
a velocity
of 750to800myr-•. Thisvelocity
massbalanceof terrestrialice, theyare importantin that is comparable
to thoseestablished
by ground-based
and
changesin the groundedice massesare likely to be aerialsurvey
of thisglacier.
Thusrepeat
satellite
imagery
preceded
by changes
in theextentof seaiceandmigration provides
a rapidandcost-effective
method
of obtaining
of iceshelfmargins.
average
surface
velocities.
Whether
or nottheaccuracy
of
Vast areasof the Antarcticice sheetare still poorly thesevelocitiesis sufficientfor detailedstudiesof ice sheet
mapped.Satelliteimageryprovidesthe only practical dynamics
remainsto beproven.
meansfor viewingtheentireice sheet,because,
in many
cases,the horizontalscaleof topographic
featuresis too
large for standardground-based
surveyingtechniques.7. CONCLUDING
REMARKS
Bindschadler
and Vornberger[1990]useadvanced
very
highresolution
radiometer
(AVHRR) imageryto describe Despitemorethan30 yearsof multinational
effortsthe
andinterpret
surface
features
in theSipleCoastRegionof massbalanceof thetwo polarice sheets,aswell asthatof
West Antarctica.Allhoughtheseimageshave a lower smaller
icecapsandmountain
glaciers,
is poorlyknown.
resolutionthan, for exampleLandsat,thereare major For areasof the polar ice sheetsthat have been studied
advantages
to usingAVHRR. The swathof theimaging extensively,error estimatesare high with the limits
systemis typicallymuchwider than that of the high- encompassing
boththickening
andthinning.
Improving
our
resolution
systemsothatdatacollection
canbeextended
to knowledge
andrefiningcurrentestimates
is imperative
the geographic
pole (Landsatcoverageendsat 82.6øS, before
anycredible
assessment
of theeffects
of a global
whileSPOTdoesnotreachbeyondabout86øS).Further- warmingon the cryosphere,and the associated
consemore, the coverageis more frequentso that chancesof quencesfor sea level, can be made. This means that a
collectingcloud-freedata•aregreatlyimproved.Also,the coherent
programaimedat accurately
determining
the
wide swatheliminatesthe needfor compositing
many massbalance
of thosecomponents
of thecryosphere
that
scenes
together.
The imagediscussed
by Bindschadler
and couldadversely
affectglobalsealevelis needed.
Vornberger[1990] showsmany surfacefeaturesthat can
Conventional
ground-based
surveys
aretimeconsuming
be interpretedin termsof glacierdynamics.For mass andcostlyso thattheareaof coverage
hasto be limited.
balancestudies,
monitoring
thepositionof thegrounding The main advantage
of suchprogramsis that the techline is of primaryinterest.
Bindschadler
and Vornberger niquesinvolvedare well tried,anderrorscanbe assessed
[1990]arguethatthegrounding
lineshould
beidentifiable directlyand,if necessary,
reduced
by additional
fieldwork.
The application
of satellitemeasurement
techniques
is
smoothice shelf, as can be seenas the mouthof ice stream relativelynew in glaciology.
Pioneeringstudieshave
D. The pixel size (1.1 km after being geometricallyshown
thatsatellite
imagery
hasmanypotential
applicacorrected
andresampled)
determines
theaccuracy
of the tions,
suchasdirectmeasurements
of thickness
changes,
or
by the transitionfrom an undulatedice streamto the
groundingline position.However,becauseof the shallow- movement
of theice sheetedges.However,thereare still
nessandrelativelyfiat profileof thesubglacial
bed,small largeuncertainties
prohibiting
highaccuracy.
Therefore
a
changes
in thickness
of theicestreams
mayresultin large combination
of different
techniques
covering
thefullrange
movements
of thegrounding
line,whichshould
bereadily of data is requiredto validate the observationsfrom
detectable
on theseimages.
satellites.Ground-based
surveysof velocitiesand acFor glacierdynamics
studies,
surface
velocities
and cumulation
ratesin key areas,repeated
overlongtime
strainratesare very important.The ice motiondetermines periods(yearsto decades),are still neededto controlthe
therateof discharge
fromtheinteriorpartsof icesheets
to interpretation
of satellitedata. Of course,the great
the ocean.Strainratesprovideinsightinto processesadvantage
of satelliteremotesensing
techniques
is the
associated
withdeformation
andslidingof theicemasses potentiallargearealcoverage
andthe almostcontinuous
andhelpin understanding
the funnelingof ice flow into timecoverageit couldhave.
outletglaciersand ice streams.
From repeatimagery, Because
the WestAntarctic
ice sheetis generally
velocitiesand their gradients(strainrates)can be deter- acknowledged
asposing
a majorthreat,a largenumber
of
minedin a similarfashionas repeataerialphotographyglaciological
studies
haveconcentrated
onthisregion.
The
29, 3 / REVIEWSOF GEOPHYSICS
Van der Veen: STATEOF BALANCEOF THE CRYOSPHERE
ß 4.53
threat arisesfrom the fringing ice shelveshypothesis, REFERENCES
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Sci. andEng., Hanover,N.H., 1961.
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is a
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mayhelpin early
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Ice Sheets,
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I thank Bob Bindschadler, Ken
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Thisworkwassupported
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U.S. National ScienceFoundationgrant DPP-8716447-A02and
the National Aeronautics and Space Administrationgrant
NAGW-2129. Byrd PolarResearchCentercontribution
734.
Ann Henderson-Sellers
was the Editor responsiblefor this
paper. She thanksBill Budd and Kendal McGuffie for their
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