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The level of the Grimsvotn subglacial lake, Vatnajokull, Iceland, monitored with SPOT5 images
E. Berthier, H. Bjornsson, F. Palsson, K.L. Feigl, M. Llubes, F. Remy
To cite this version:
E. Berthier, H. Bjornsson, F. Palsson, K.L. Feigl, M. Llubes, et al.. The level of the Grimsvotn subglacial lake, Vatnajokull, Iceland, monitored with SPOT5 images. Earth and Planetary Science Letters, Elsevier, 2006, 243, pp.293-302. �10.1016/j.epsl.2005.12.027�. �hal-00280170�
Vatnajökull, Ieland, monitored with SPOT5
images
E. Berthier
a,∗
H. Björnsson
b
F. Pálsson
b
K. L. Feigl
c
M. Llubes
a
F. Rémy
a
a
LEGOS/CNRS/UPS, 18av. Ed. Belin, 31401, Toulouse Cedex 9, FRANCE
b
Institute of Earth Sienes, Universityof Ieland, Reykjavík,ICELAND
c
DTP/CNRS/UPS,14av. Ed. Belin, 31400, Toulouse, FRANCE
Abstrat
We desribe the vertial displaement eld of an ie shelf oating on a subglaial
lake,Grímsvötn,loatedunderneaththeVatnajökullieap (Ieland).Theupliftis
measuredusingtheorrelationoftwosatelliteoptialSPOT5imagesaquired5days
apart with similar, non-vertial inidene angles. This is the rst time orrelation
ofoptialimageshasbeenusedto measurevertialdisplaements. Ourtehnique is
suitableformapping short-termelevation hangesofglaiers.Ifthesurfaefeatures
arepreserved,vertial displaementsan be measuredevery 25mwithan auray
ofabout 0.5m.
TheupliftmapofGrímsvötnshowsthat10.9(±1)km
2
ofiewasoatingbetween
11and16August2004.Theieshelfroseby1.7(±0.6)mindiatingthatthevolume ofliquid waterinthelake inreasedby0.018 (±0.007) km
3
.Oureldobservations
show thatsurfae melting due to meteorologial proesses ontributed 70 %of the
aumulated water, hene, the rest originated from ie melted by the subglaial
geothermal ativity. The power required to melt 0.005 km
3
(water equivalent) of
basaliein5daysis4000MW.Theappliabilityofthetehniqueanbeextendedto
volanologyandseismology,andevenlandslidesorsubsidene,whenner-resolution
optial images beome available. Applied to two pairs of images, it ould solve for
the3-dimensional displaements ofthe Earth's surfae.
Key words: Geothermal ativity, subglaial hydrology, SPOT5,Ieland, image
orrelation
PACS:
∗
Correspondingauthor
Email address: etienne.berthiernes.fr(E. Berthier).
Explorationof subglaialhydrology on a regionalsale by monitoring glaier
surfae displaements from spae is a hallenging task. The displaementsof
the ie surfae may be due to aumulation and release of water in basal
storage or water merely lubriating the bed and aiding glaier sliding. These
hanges inbasal water ontent are importantto monitorbeause they partly
ontrolglaier andiestreamdynamis(1;2),espeiallyduringsurges(3;4).
Suh vertial displaements have been monitored in situ at single ground-
based points and along proles by geodeti and DGPS surveying and aerial
photography (1; 5; 6; 7). During the last 15 years, satellite and airborne re-
mote sensing tehniques have aptured variations in topography over large
areas. These tehniques inlude repeated prolingby laser orradar altimetry
(8;9;10),butintermsof auray(withinfewentimetres)and spatialover-
age(100 ×100kmforaSARsene)SARinterferometry(InSAR)isthemost eient tehnique for mappingelevationhanges(11; 12). However, with the
exeptionofold,high,polarareasoflowaumulationrate(13),onventional
InSAR annot be applied if images are separated by more than 1 to 3 days
(14). Spekle traking alleviates this shortening in ertain ases (15). In our
ase, on the temperate Vatnajökull ie ap, only C-Band SAR images sepa-
rated by one day orrelate well enough for interferometri omparison (16).
On the other hand, optial images orrelate over longer intervals, typially
froma few days in the aumulation area to afew years in the ablation zone
of temperate glaiers. Suh optial images have previously been used to de-
sribehorizontalmotion of glaiers (17; 18), horizontal displaements aused
by earthquakes (19; 20), and landslides(21). Here, we present the rst mea-
surementof vertialmotionobtained by orrelating optialimages.Weapply
our method todetermine the extent and magnitudeof the uplift of aoating
ie shelf during the lling of a subglaial lake (Grímsvötn) loated in the in-
terior ofthe Vatnajökull ieap (8200 km
2
)in southeast Ieland. Inthe near
future, Earth's surfae elevation hanges indued by earthquakes, landslides
orvolanoes ould alsobe monitored with asimilar tehnique.
2 Site desription
TheGrímsvötnsubglaiallakeissituatedinanie-lledalderaattheGrímsvötn
volanientre (Figure1,N 64.41
◦
, W17.33
◦
).The intense geothermalativ-
ity ontinuously melts the ie and meltwater aumulates in the subglaial
lake. Its level rises until the lake drains subglaially (at an interval of 1 to
10years) inlarge oods(namedjökulhlaups inIeland) tothe outwash plain
Skeidarársandur (7). A 270-m-thik ie shelf oats onthe lake. To the south
to the north and northeast as the water level rises (7; 22). Moreover, ie is
oasionallymeltedby volanieruptionsinthe Grímsvötnvolano.Its mean
eruption frequeny has been lose to one per deade during the eight past
enturies (23). The most reent eruptions took plae in1934, 1983, 1998 and
November 2004.
Monitoringthe lake level of Grímsvötn is essential for foreastingthe timing
of jökulhlaups. A non dierential(navigational) GPS reeiver, loated atthe
entre of the oating ie shelf, monitors its elevation ontinuously (Figure
2). Preise surveys using geodeti GPS reeivers are also performed about
6 times a year. From June 2003 to late Otober 2004, the oating ie shelf
rose by 60 m. Then, it dropped suddenly due to an abrupt drainage of the
lake,leadingtoa jökulhlaup.Aneruption ofthe Grímsvötn volano starteda
few days later, presumably triggered by the 15-m-drop inthe lake level (24).
The volano geothermaluxllsgraduallythelake,whoseabrupt subsidene
release the overburden pressure and triggers an eruption.
Observationsoftheareaoftheoatingieoverarerequiredforestimatingthe
lake volume and, onsequently, the size of the outburst oods. After the lake
drains in a jökulhlaup, the areal extent of the ie shelf an be delineated by
theoutermostrevasseswhihareformedwhentheieshelfabruptlysubsides
(22).Yet,thisaposteriori approahannotforeasttheamountofwatertobe
released. A previous study has used InSAR from the ERS satellites tandem
mission to map the extent and rate of the uplift during the period 1996-
1999 (7). Sinethe tandemmissionended, wepropose a new methodology to
monitorglaier surfae elevation hanges fromsatelliteoptial images.
3 Methodology
Our method uses the orrelation of two optial SPOT5 images to measure
their osets in the line and olumn diretions and then derive the vertial
omponent of the displaement eld. This tehnique measures the projetion
of a ground displaement
~δ [δλ, δφ, δz℄ in the foal plane of the sensor (with λ thelongitude, φ the latitude,andzthe loalvertial axis).This foalplane
anbedenedbytwounitvetors
−−→
Ulin and−−→
Ucol indiatingthelineandolumn
diretions respetively (Figure3).
Ifθ isthe inideneangle (varying by± 2
◦
throughoutthe images)and αthe
(azimuth)anglebetween the linediretionandthe North (varyingby±0.01
◦
and thus onsidered asonstant), the oordinates of
−−→
Ulin and −−→ Ucol are
−−→
Ulin = [−sinα,−cosα,0] (1)
−−→
Ucol = [cosθ cosα,−cosθ sinα, sinθ] (2)
Theorrelationofthesatelliteimagesmeasuresthedisplaementsδcol andδlin δcol =~δ·−−→
Ucol (3)
δlin=~δ·−−→
Ulin (4)
Ifthehorizontaldisplaementsδλ andδφ anbenegleted,Equation3simply
redues to
δz = δcol
sinθ (5)
Apurely vertialmovementwillthusindue anosetinthe olumndiretion
(Figure3).Furthermore,Equation5showsthatlargeinideneanglesinrease
the sensitivity to vertial motion. For the images used in this study, the 27
◦
inidene angles lead to a sensitivity of the order of 0.45, i.e. 45% of the
vertialmotion should bevisible inthe olumn-oset eld.
In the ase of the Grímsvötn ie shelf the horizontal glaier ow is slow and
mainly oriented southward suh that δλ an be negleted, but not δφ. With
these assumptions, ombining Equation 3 and 4, we dedue the vertial dis-
plaement:
δz = δcol−δlin×cosθ× sinα
cosα
sinθ (6)
The auray of the ground displaements obtained by orrelating two opti-
al images is ontrolled mainly by the distortions between the images (25).
The distortions are proportional to the ratio of the baseline (B, the distane
between the two satellitepositions) tothe altitude (H)of the satellite.When
orrelating two images, the B/H ratio measures the apparent horizontaldis-
plaement that will be indued by an error in the digital elevation model
(DEM) of the area (19).In anoptimalsatellite onguration, the two images
areaquiredfromexatlythesameviewpoint,the valueofB/H issmall(typi-
allyless that0.01)andtheosets inolumnonlyreetthe surfaeelevation
hanges.Favorablesituationourswhenthetimeseparationbetweentheim-
age datesisamultipleofthe orbitalyle duration,i.e. 26daysinthe aseof
the SPOT5 satellite. In suh a satellite onguration (alled an exat repeat
pair), aurate measurements of surfae displaements an be obtained even
with avery oarse DEM, asdemonstrated previously (25).
We have mapped the uplift of the Grímsvötn ie shelf by orrelating two
SPOT5 images aquired on 11 and 16 August 2004 (Table 1) with a ground
resolutionof2.5m.TheirfootprintsaredrawninFigure1.Theyhavethelow-
estpossiblegain(1forSPOT5)whihisruialtoavoidradiometrisaturation
ofthesensoronthereetivesurfaeoftheglaier.Forourstudy,weouldnot
obtain satellite image pairs separated by exatly one 26-day SPOT5 orbital
yle due toloud overage and satellitesheduling. Furthermore,in26days,
hanges onthe glaiersurfae ould degrade the image orrelation,espeially
in the upper aumulation area. Consequently, we apply our methodology to
images aquired 5 days apart from slightly dierent viewpoints, with a B/H
ratio of 0.064. In this ase, an error of 10 m in the DEM would reate an
apparent horizontal displaement (in the image olumn diretion) of 0.64 m,
equivalent to a vertial displaement of 1.42 m.An aurate DEM of the ie
ap is thusrequired.
We have alulated a DEM from a seond pair of SPOT5 images aquired
on 7 and 9 Otober 2004 (Table 1). These images have a similar footprint
as the 16 August image (Figure 1). Only a 5 m resolution is available due
tosensor problems. The two days time separation ensures a good orrelation
between the images even in the snow-overed region. The glaier ow in the
slowmovingareasurroundingtheGrímsvötnalderaduringtwodays issmall
enoughtoavoidasystematibiasintheDEM.Errorsorgapsouldalsoresult
fromthe hange in the length of the shadows due tothe dierent aquisition
times of the two images (at 13:25 on 7 Otober and 12:23 on 9 Otober),
in partiular lose to the steep aldera walls to the south and the west of
the ie shelf. The B/H is lose to 1 and optimal for elevation mapping of
the smooth topography of the ie ap. The auray of our DEM is assessed
by omparing its elevation with a kinemati GPS survey ina vehile driving
on the glaier in late September 2004. The auray of the kinemati GPS
measurement is of the order of ± 0.15 m. For the 13800 omparison points, the SPOT5 DEM is 0.75 mlower than the GPS data, with a RMS satterof
7.8 m.On the Grímsvötn ieshelfitself, our DEM has been orreted forthe
vertialdisplaementourringbetween mid-August(dateof theimages used
tomap the uplift)and earlyOtober. The permanentGPS stationonthe ie
shelf indiates an uplift of 4.5m during this period. An error of 10% in this
orretion, whih relies on extrapolating the GPS measurement to the entire
ie shelf, would alter the vertial displaement measurement by less than a
deimeter.
Figure 4 depits the surfae elevation hanges measured by omparing the
2004DEM withanolderDEM,produedby airborneInSARimagesaquired
in August 1998 (26). The auray of the 1998 DEM is 2 to 3 m over the
term elevation hange of the Grímsvötn ie shelf. The ie shelf was 55 m
higherin 2004 thanin 1998, albeitseveral drainageeventsduring the 6years
(see the upper panel in Figure 2). Our map shows glaier thikening of 30
to 40 m in the northern Grímsvötn and Gjálp areas due to inow of ie to
the depression reated by the Gjálp eruption in 1996 (27). Farther from the
depression,thinningof theglaierisdeteted.Thisinowhas been monitored
and modelled with InSAR(12; 28).
Usingthe2004DEM,weo-registerandorrelatethesatelliteimagesaquired
inAugust(25).Fromhomologouspointsextrated automatiallyonthestable
(oglaier)area, the16August imageisresampled inthe geometryofthe 11
August image. The area overed by both SPOT5 images (Figure 1) ontains
very few stationnary points. The homologous points are extrated far away
from our area of interest, whih slightly degrades the o-registration of the
two images.
The orrelation of the 11August image with the resampled 16 August image
is performed every 10 pixels using windows of 21 by 21 pixels. Conversion
of osets in image geometry to ground displaements takes into aount the
varying pixel size aross the image. Noisein the displaementmaps is due to
noise in the DEM and hanges at the glaier surfae. Around the Grímsvötn
ie shelf, the mean osets in the image line diretion are small (0.1 pixel)
and slightly positive (not shown). They indiate a mean southward veloity
of 14 m/a, slightly smaller than the 20 m/a measured at the ground-based
GPS station. Osets in the olumn diretionhave to be orreted for a long
wavelength bias. We attribute this bias to the diulty of o-registering the
two satellite images from homologous points loated on the edges of the im-
ages,farawayfromourarea ofinterest.Thisbiasouldalsoresultfromerrors
in the DEM. Beause we are only interested in the relative displaement of
the oating ie shelf ompared to its surroundings, we aount for this bias
by removing from the olumn oset eld a rst-order polynomial whih ap-
proximatesthe olumnosets outsidethe ieshelf(20).The displaementsin
the olumn and lines diretions are then onverted intovertial displaement
using Equation 6. The result maps the uplift of the ieshelf between 11and
16August (Figure 5).
This map indiates a lear uplift zone with positive vertial displaements
of 1.5 to 2 meters. The uplift seems to be stronger in the margin (about 2
meters) than on the enter (around 1.5 meters) of the ie shelf. We annot
onludewhetherthis isarealfeature,beauseanerrorof3to4metersinthe
DEMissuienttoexplainthisdierene. Thismapisusedtodelimitatethe
extent of the uplift zone. The boundaries are displayed on both the SPOT5
image (left panel) and the vertial displaement eld (right panel) in Figure
5. We dedue that the area aetedby the upliftovers 10.9 km
2
(±1) km
2
.
The unertainty (±1 km
2
)isestimated by delimitatingtwie the upliftzone:
an inner and outer limits are drawn and ompared. These two values dier
mainly in the southeast part of the ie shelf where gaps in the DEM (due
to the shadows of the 300 m high aldera walls) were lled by interpolation.
Over this step-like topography, our interpolation leads to an overestimation
ofthe altitudeofthe ieshelf,whih, onsideringthe geometryofthe SPOT5
images, results in an overestimation of the uplift (in red in the left panel of
Figure5).
Overthis10.9 km
2
area,themean upliftis1.7mwithastandard deviationof
±0.6m.Thisstandarddeviationinludesbothmeasurementunertaintyand upliftvariabilityoverthe ieshelf.The meanupliftorrespondstoadisplae-
ment in the olumn diretion of 0.3 pixels. This signal is only slightly larger
than the (onservative) aurayof ± 0.2pixels found in a previous applia- tionofourtehnique(25).Asalreadynoted,themainsoureofunertaintyin
ourmapistheerrorsintheDEM.Errorsouldalsooriginatefromsubtrating
the rst-order polynomial, negleting horizontal ie ow in longitude (δλ) or
fromthe biasesintroduedby the image orrelationitself.
A permanentsurvey stationloatedonthe ie shelf(namedMAST) provides
twoground-basedelevationmeasurements.AstandardGPSreeivermeasures
theelevationevery10minutes.Sinedierentialproessingisnotpossible,the
error of an individual measurement is ± 5 to20 m. Comparison with DGPS measurementsindiatesanunertaintyof±2mforthedailyaverage.Another estimateisprovided bystandardbarometrialtimetrybetween onestationon
the ie shelf (MAST) and another on the mountain Grímsfjall, 3 km south-
east of MAST (Figure5). Barometripressure and temperatureare reorded
every hour atboth stations.The sites are aeted by high winds,and inverse
temperature gradients. The unertainty in this estimation of the elevation
dierene between the two stations is therefore high, ± 2 to 5 m depending onatmospheri onditions.
In Table 2, we ompare the dierent uplift rates and determine if their dif-
ferene isstatisally signiant.Dierent time intervalsare investigated. The
dierene between GPS and barometri altimetry measurements show that
estimating a mean upliftrate for a short-time interval from our ground data
is not robust. The two ground-based uplift rates agree only when the time
interval is as muh as 35 days. In this ase, at the 95% ondene interval,
thegroundupliftrates0.18±0.03and 0.19±0.02m/dayarenot signiantly smallerthan the 0.23±0.1m/day obtainedfrom satellitedata. Thus, assum- ingaonstantupliftrateoverone month, agoodagreementisfound between
satelliteand ground measurements.
The satellite-derived upliftrate (0.23±0.1m/day)is also ingoodagreement with the maximum rates measured with InSAR during the period 1996-1999
SPOT5 imagesagree well with the one determined previously (12; 22).
5 Disussion
Ourresultsallowadisussionofthewaterandenergybalaneofthesubglaial
lake. During our 5-day observation interval in August 2004, the mean lake
level rose by 1.7m over a10.9 km
2
area indiatingthat 0.018 (± 0.007) km
3
of water was added tothe subglaiallake.Water originated fromsurfae and
basal melting. The ontribution of surfae melting is dedued from ground
observations.
Field mass balane measurements are performed yearly in the Grimsvötn
glaierdrainagebasinatseveral sites usinglassimethodsof snow oringfor
winter balaneand stakesreadingfor summerbalane(morethan 30stakes).
Digitalmaps are onstruted of the winter, summer and net balane and the
totalsurfaemeltingintheGrimsvötnwaterathmentwasfoundbyintegrat-
ingoverthesummerbalanemap(29).Continousultra-sonimeasurementsof
loalsurfae elevationindiates thatablationisonstantthroughoutthesum-
mer season and, averaged over the 200 km
2
of the Grimsvötn water drainage
basin, amount to 1.3m (water equivalent)/day. Thus, overa 5-day interval,
surfae meltingontributed about 0.013 km
3
of water tothe lake.
The remaining 0.005 km
3
is due to melting of basal ie by geothermal heat
in the 50 to 60 km
2
surrounding the lake (22; 30). The power required to
melt this muh ie in 5 days is 4000 MW, yielding an average geothermal
ux of the order of 70 W m
−2
. These estimates of the total power and the
geothermal ux are a fator of 1.5 to 2 higher than values over the period
1960-1991 (22). Althoughour short-term estimates are unertain, they might
suggest that basal meltwater from the Gjálp eruption site of 1996 drains to
thelake,leadingtoanoverestimateoftheiemeltedintotheGrímsvötn area.
Assuming a vertial wall bordering the lake we an assess an upper limitof
the total water volume (Vlake)ontained in Grímsvötn
Vlake= (Ziceshelf − Zgrounded)× SSP OT5 (7)
whereZiceshelf stands forthe elevation ofthe ieshelf, Zgrounded the elevation of the ie shelf when it is grounded (dashed horizontal line in Figure 2) and
SSP OT5 the surfae area of the lake estimated by SPOT5 orrelation. Vlake
amounted to 0.74 km
3
inmid-August2004.
From a methodologial point of view, this study permits disussion of dif-
