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The layering of polar firn [Elektronische Ressource] : investigations of the climatic impact on polar firn structure using high resolution density measurements and 3D-X-ray-microfocus-computer-tomography / Maria Hörhold

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The layering of polar firnInvestigations of the climatic impact on polar firn structure usinghigh resolution density measurements and3D-X-ray-microfocus-computer-tomographyMaria HörholdAlfred-Wegener-Institut for Polar and Marine ResearchColumbusstrasse27568 BremerhavenGermanyUniversität BremenFachbereich Geowissenschaften (FB5)Bibliotheksstrasse 128359 BremenGermanyGutachterProf. Dr. H. MillerProf. Dr. K. HuhnPrüferProf. Dr. S. KasemannProf. Dr. F. WilhelmsPromotionskolloquium3. November 2010ErklärungHiermit versichere ich, dass:• ich die beiliegende Arbeit ohne Hilfe Dritter• und ohne Benutzung anderer als der angegebenen Quellen und Hilfsmittel ange-fertigt• und die den benutzten Quellen wörtlich oder inhaltlich entnommenen Stellen alssolche kenntlich gemacht habe.ContentsContents 51 Summary 72 Zusammenfassung 113 List of Publications submitted for the Thesis 174 Introduction and Objectives 194.1 Topic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.3 Main questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.4 State of the art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265 Methods 315.1 Literature survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.2 Firn cores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315.3 High resolution gamma absorption method .

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Thelayeringofpolarfirn

Investigationsoftheclimaticimpactonpolarfirnstructure

resolutionhighandmeasurementsdensity

3D-X-ray-microfocus-computer-tomography

iaMarHörhold

Alfred-Wegener-InstitutforPolarandMarineResearch

asseusstrColumb

nevBremerha27568

manGery

BremenersitätUniv

(FB5)wissenschaftenGeoachbereichF

liotheksstrBib1asse

Bremen28359

ymanGer

using

3.

embervNo

2010

Prolloquiumomotionsk

.Prof

.rD

.F

Wilhelms

erPrüf

Kasemann

S.

.rD

.Prof

.Prof

rD.

K.

Huhn

hterGutac

.Prof

.rD

H.

Miller

Hiermitversichereich,dass:

Erklärung

ichdiebeiliegendeArbeitohneHilfeDritter

undohneBenutzungandereralsderangegebenenQuellenundHilfsmittelange-

tigtref

unddiedenbenutztenQuellenwörtlich

solchekenntlichgemachthabe.

oder

inhaltlich

entnommenen

Stellen

als

Contents

Contents

ySummar1

Zusammenfassung2

3ListofPublicationssubmittedfortheThesis

ObjectivesandoductionIntr44.1Topic...................................
4.2Background................................
4.3Mainquestions..............................
4.4Stateoftheart..............................

Methods55.1Literaturesurvey.............................
5.2Firncores.................................
5.3Highresolutiongammaabsorptionmethod...............
5.3.1Missinglayers...........................
5.4Permeabilitymeasurements.......................
5.5X-ray-microfocus-computer-tomography(CT)..............
5.6MicrostructuralanalysisusingMAVI...................

DiscussionandResults6

5

5

7

11

17

1919212526

3131313233343435

39

6.1Parameteroflayering...........................39
6.2Generationoflayering..........................44
6.3Evolutionoflayeringwithdepth.....................44
6.4Layeringinmicrostructureandairpermeability.............47
6.5Layeringatdifferentsites.........................50

lusionsConc7

57

8ProblemsandOpenTopics59
8.1Methodicallimitations..........................59
8.2"Global"microstructure..........................60
8.3Convectionoftheupperfirn.......................62

9Acknowledgement

yliographBib

APublication1-Thedensificationoflayeredpolarfirn

65

76

73

BPublication2-Fromrandomdepositiontoafirncorerecord-ontheimpact
ofimpuritiesonthedensificationofpolarfirn-afirstapproach113

CPublication3-Grainsizeoflayeredpolarfirn-evolution,variabilityanda
newgraingrowthmodel153

DPublication4-Theimpactofaccumulationrateontheanisotropyandair
permeabilityofpolarfirnatahighaccumulationsite193

EPublication5-LatticeBoltzmannmodelingoftheairpermeabilityofpolar
233firn

ySummar1

Thepolarfirnstructureisinvestigatedintermsoflayeringusinghighresolutionden-
sitymeasurementsof19firncoresandX-ray-microfocus-computer-tomographyimage
analysisof6surfacefirncores.Theimpactoflocalclimateconditionssuchasannual
meantemperatureandaccumulationrateonthegeneration,structureandevolutionof
thelayeringisstudied.Wefindatallsitesahighvariabilityindensityandmicrostruc-
tureduetothelayeredcharacterofthefirn.Thestandarddeviationofthemeasured
physicalpropertiesisusedasaproxytoparameterizethelayeringandtocomparethe
degreeoflayeringatdifferentsites.Mainresultsare:

1.Thedifferentsitescanbedistinguishedbythedegreeoflayering,i.e.variabilityin
densityandmicrostructure.Thevariabilityingrainsizeincreaseswithdecreas-
ingannualmeantemperature,accumulationrateandmaximumtemperaturegra-
dient.Siteswithloweraccumulationrateandannualmeantemperatureshow
highervariabilityandthusahigherdegreeinlayeringintheupperfirncolumn
thansiteswithhigheraccumulationrateandannualmeantemperature.This
means,thatasitefromthehighEastAntarcticPlateaucanbeexpectedtoshow
higherlayeringcomparedtositesfromcoastalregionsofAntarctica.

2.Thelayersseemtobecreatedrandomlyatthesurface.Inthisstudyaseasonal
variabilitywithconstantfrequencyindensitycouldnotbedetectedwithinthe
presenteddata.Possiblereasonscanbeahighvariationinaccumulationrate,
thatcansuperposeaseasonalityindeposition,orlargehorizontaldiscontinuity,
whichmeans,thatapunctualfirncoresitewouldnotcapturealllayers.However,

7

withthedatainvestigatedinthisstudyitcanbehypothesized,thatsurfacefirn
stratigraphydoesnotshowaseasonallayering.

3.Thedensityvariabilityisnotcontinuouslydecreasingwithdepth,butshowsa
ratherrapiddropintheupper10-20meterdepth,whichisfollowedbyasecond
maximumindensityvariability.Thisleadstoincreaseddensityvariabilityatthe
depthintervalofthefirn-ice-transition.

4.Thefrequencyandamplitudeofthedensityvariabilityischangingwithdepth.
Eventhoughthereisnoseasonalsignaturewithinthenear-surfacevariability,in
thedepthintervaloftheseconddensityvariabilitymaximum,thedensityfluctua-
tionsshowaseasonalfrequencyatmediumtohighaccumulationratesites.

5.Thedensityvariabilitydevelopsacorrelationwiththeconcentrationofthecalcium
ionwithdepth.Atthesurfacenocorrelationisevident.Atthedepth-intervalof
theseconddensityvariabilitymaximumthecalciumconcentrationandthedensity
variabilityshowaremarkablyhighcorrelation.Togetherwiththeshiftinfrequency
ofthedensityvariability,thisindicatesanimpactof(seasonalvarying)impurities
onthedensificationofthefirn.

6.Thesummaryoftheresults2-5indicates,thattheseasonalstratigraphyinice
corerecords,whichisassumedtobeformedbyacontinuousdepositionatthe
surfaceandyieldsthebasisofpaleo-climatestudies,isnotnecessarilyformed
atthesurfacebydepositionalmechanisms,butbydensificationandsnowmeta-
morphismdeeperdowninthefirncolumn,influencedbyimpurities.

7.Thelayeringisdisplayedinthemicrostructure,butshowsaverycomplexpattern
astheresultofthecombinedeffectofinitiallayering,sinteringandshort-term
conditions:climatelocalinchangesa)Thelayeringiscreatedrandomlyatthesurface,initiatingacertaincombi-
nationofdensityandmicrostructure.Withineachdepthintervalthelayering

showsalinearcorrelationindensityandgrainsize,sothatthegrainsize
couldbeparameterizedviadensity.Thetrendofthiscorrelationhowever,
differsforthedifferentsitesandchangeswithdepth.
b)Thefirnlayersallundergotherathergradualprocessofsintering-thein-
creaseindensityandgrainsize,whichisdeterminedbytheaccumulation
rateandannualmeantemperatureofasite.Alongtermtrendindensity
andgrainsizeisobserved,describingthedensificationandgraingrowthof
depth.withnfirthec)Short-termchangesinlocalclimateconditions,suchasvariationsinac-
cumulationrateortemperaturegradientatthesurfacesuperposetheini-
tiallayeringandthegradualsintering,bychangesinthemetamorphismof
thesnow.Increasedordecreasedexposuretonearsurfacetemperature
gradientsorwind-ventilationcausesmoreorlesscoarseningormoreor
lesspronouncedanisotropywithinthestructure.Thecoarseningleadstoa
short-termincreaseinporesizeorairpermeabilitywithdepthuntilamaxi-
mumat2-4meterdepths.Thisisobservedespeciallyatthefirncoresfrom
lowaccumulationratesitesinAntarcticaandatthefirncorefromtheGreen-
landsite.Accordingly,themostcoarsenedstructuresintermsofporesize
canbeexpectedatsiteswithlowaccumulationrate.Thesefindingsimply,
thatventilationoftheuppermostfirnlayerscanbeexpectedtobelargestat
lowaccumulationratesites.

8.Thecombinationofinitiallayering,sinteringandcoarseningatthesurfacein-
ducesanoveralldiverseevolutionofmicrostructurevariability.Therelationsbe-
tweendensity,microstructureandairtransportpropertiesareinfluencedbyeach
oftheseconditionsverydifferently.Whereasthefirnlayershowanegative,lin-
eartrendinthedensity-grain-sizerelationship,thesinteringshowsalineartrend
aswell.Butthesinteringshowsatrendwithoppositesign,andthecoarsen-
ingshowsanon-linearpattern,whichischangingwithdepth.Thisleadstoa

complexpatternofdensity-microstructurerelationship.Thereforeasimplepa-
rameterizationofmicrostructuralcharacteristics,suchasspecificsurfacearea
andgrainsize,orairpermeability,withdensityisnotstraightforwardinpolarfirn.

9.Neverthelessthemicrostructurefromtheseverydifferentsitesandverydiverse
metamorphicstatesshowssomesurprisinglywelldefinedrelationships:thespe-
cificsurfaceareaofthefirnsamples,whichcanbedeterminedbyseveralmeth-
ods,canbedescribedbijectivefromthemeasuredchordlength(averageinter-
sectionoftheicephasewithaline).Thisstrengthenstheassumption,thatoptical
propertiesofsnowandfirncanbedescribedbyaneffectiveradiusofspheres,
showingthesamespecificsurfaceareaasthemeasuredsample.Foranyappli-
cationswheretheeffectiveice-air-interfaceofthefirnisimportant,(air-exchange,
chemicalinteractions,interactionswithopticalproperties,microwaves),theeasy-
to-measure-specificsurfaceareaissufficienttoobtaintheeffectiveradiusofthe
firnstructure.Thisradiuscaneasilybeincludedintograingrowthmodelsorgrain
sizemodelingfromremotesensingsurfaceobservationssuchastheModerate
(MODIS).adiometerSpectrorImagingresolution

Furthermore,astructuremodelindexiscalculated,whichdescribestherelation
ofcurvatureandsurfaceofthefirn.Thisindexseemstobeawelldefinedfunc-
tionofporosityforallinvestigatedfirnsamplesofthisstudy.Thisindicates,that
despitethediversepatterninoriginallayeredmicrostructurecreatedatthesur-
face,sinteringandcoarsening,topologicalsimilarstructuresdevelopduringthe
wholefirnmetamorphismprocess.

2Zusammenfassung

DieStrukturdespolarenFirnsalsporösesgeschichtetesMediumwirdmitdenMetho-
denderGammaAbsorptionan19FirnkernenundbildgebendenVerfahrenderRöntgen-
Computer-Tomographyan6Firnkernenuntersucht.DabeiwirdinsbesonderederEin-
flussderlokalenklimatischenRandbedingungen,wieAkkumulationsrateodermittlere
JahrestemperaturaufdieEntstehung,StrukturundEntwicklungvonSchichtungerkun-
det.DieStandardabweichungdergemessenenDichteundKorngrößewirdgenutzt,um
dieSchichtungzuparameterisierenunddieIntensitätderSchichtunganverschiedenen
Lokationenzuvergleichen.HauptergebnissedieserStudiesind:

1.DieverschiedenenLokationenunterscheidensichdeutlichinderSchichtungs-
Ausprägung.DieKorngrößenvariabilitätnimmtmitabnehmenderAkkumulations-
rateundmittlererJahrestemperaturzu.LokationenmitgeringerAkkumulations-
rateundJahresmitteltemperaturzeigeneinestärkereSchichtunginDichteund
KorngrößealsLokationenmithöhererAkkumulationsrateundJahresmitteltem-
peratur.Demnachkannmanerwarten,dassFirnkernevomOst-Antarktischen
PlateaueinestärkereSchichtungaufzeigen,alsFirnkernevondenKüsten-nahen
Gebieten.

2.DieSchichtungscheintohneSystematikausdemZusammenspielvonWind,
Temperatur,SonneneinstrahlungundSchneefallanderOberflächezuentste-
hen.IndenDatenderhiervorliegendenStudiekonntekeinesaisonaleFre-
quenzinderDichtevariabilitätdetektiertwerden.MöglicheUrsachedafürkönnte
einestarkeVariabilitätinderAkkumulationsratesein,diedasFrequenzsignalver-

11

wischt.WeiterhinkönntedieTatsache,dassdieSchichteneinegroßehorizontale
Variabilitätaufweisen,dazuführen,dassnichtallelokaldeponiertenSchichten
miteinemFirnkernerfasstwerden.DiehiervorliegendenDatendeutenaberda-
raufhin,dassimOberflächen-FirneinfachkeineSaisonalitätvorhandenistund
dieSchichtenirregulardeponiertwerden.

3.DieVariabilitätinderDichtenimmtnichteinfachkontinuierlichmitderTiefeab.
AllehieruntersuchtenFirnkernezeigenvielmehreinenschnellenAbfallinder
DichtevariabilitätbiszueinerTiefevon10-20Metern.DarunternimmtdieVari-
abilitätwiederzuundzeigtsomitauchinTiefen-IntervallendesFirn-Eis-Übergangs
Amplituden.erhöhtedeutlich

4.DieAmplitudeundFrequenzderDichtevariabilitätändertsichmitderTiefe.Ob-
wohlanderOberflächekeinsaisonalesSignaldetektiertwurde,zeigenKerne
miteinermittlerenbishohenAkkumulationsrateeindeutlichesSignalinderFre-
quenzderjeweiligenAkkumulationsrateindemTiefen-IntervalldeszweitenMaxi-
mumsderDichtevariabilität.

5.DieDichtevariabilitätentwickelteineKorrelationmitderKonzentrationdesCalcium-
IonsmitderTiefe.AnderOberflächegibteskeinedetektierbareKorrelation.
InderTiefedeszweitenVariabilitäts-MaximumsisteinesignifikanteKorrelation
zwischenderDichteundderCalciumKonzentrationzufinden.Zusammenmit
demHerausbildenderFrequenzderAkkumulationsrateeinerjeweiligenLokation
deutetdasdaraufhin,dassdieVerdichtungvonFirnvonVerunreinigungen,die
anderOberflächesaisonaleingetragenwerden,beeinflusstwird.

6.ZusammenfassendsinddieErgebnisse2-5einHinweisdarauf,dassdieSaison-
alitätinderSchichtunginEis-Bohrkernen,nichtwieangenommendurcheinen
kontinuierlichenAblagerungvonMaterialanderOberflächegeneriertwird.Vielmehr
lassendieErgebnisseerkennen,dassdieSaisonalitätinderSchichtungdurch
dieVerdichtungundMetamorphoseunterEinflussvonVerunreinigungenerstmit

wird.ausgebildeteTiefder

7.DieSchichtungfindetsichauchinderMikrostrukturwieder,zeigtabereinkom-
plexesVerhalten.DerGrundisteineÜberlagerungvonursprünglicher,ander
OberflächegenerierterSchichtung,SinterungundkurzzeitigenÄnderungenin
Randbedingungen:klimatischenlokalendena)DieSchichtungwirdzufälliganderOberflächegeneriert,wodurcheinebes-
timmteKombinationvonDichteundMikrostrukturfestgelegtwird.Innerhalb
einesTiefen-IntervallszeigtdieVariabilitätderSchichtungeinelineareKo-
rrelationzwischenDichteundKorngröße,sodassdieKorngrößeüberdie
Dichteparameterisiertwerdenkann.DerTrenddieserKorrelationunter-
scheidetsichfürdieverschiedenenLokationenundändertsichmitder
.eTiefb)AlleFirnschichtenunterliegendemgraduellenSintern-dasAnsteigender
DichteundderKorngrößemitderTiefe,wasdurchlokaleAkkumulations-
rateundTemperaturvorgegebenwird.Demnachkanneinlangfristiger
TrendinDichteundKorngrößebeobachtetwerden,derdieseVerdichtung
unddasKornwachstummitderTiefebeschreibt.DieserTrend,zeigtein
positivesVorzeichen(zunehmendeDichtekorrespondiertmitzunehmender
Korngröße),wohingegenderTrendinnerhalbeinzelnerTiefen-Intervalleein
negativesVorzeichenhat(hoheDichtekorrespondiertmitkleinerKorngröße
t).ehrumgekundc)KurzfristigeÄnderungenderlokalenklimatischenRandbedingungen,wie
zumBeispielVariationenderAkkumulationsrate,könnendieSchichtung
unddasSinterndurcheineveränderteMetamorphoseüberprägen.Durch
erhöhteodererniedrigteExpositionderSchichteninoberflächennahenTemperatur-
Gradienten(durchÄnderungenderAkkumulationsrate),kanndieStruktur
verstärkteoderabgeschwächteVergröberungerfahrenodereinemehroder
wenigerstarkausgeprägteAnisotropie.DieseVeränderungenbeeinflussen

immermehrereSchichtengleichzeitigundverändernderenStruktur.Die
VergröberungführtzueinemkurzfristigemAnstiegderPorengrößeundPer-
meabilitätmitderTiefezuMaximainbiszu2-4MeternTiefe.Daswurdevor
allemfürdieLokationmitniedrigerAkkumulationsrateinderAntarktisund
andemeinenKernausGrönlandbeobachtet.Diegröbstenundsomitver-
mutlichamhöchstenpermeablenStrukturenindenoberenFirnschichten
sindindenNiedrig-AkkumulationsgebietenderAntarktisundinGrönland
ten.arerwzu

8.DieKombinationvonanfänglicherSchichtung,SinterungundverstärkterMeta-
morphoseanderOberflächeinduzierteinevielfältigeEntwicklungderVariabil-
itätderMikrostruktur.DieSchichtungzeigteinenlinearenTrendinDichteund
Korngröße.AuchdieSinterungzeigteinenlinearenTrend,mitumgekehrten
Vorzeichen.ÄnderungeninderoberflächennahenMetamorphoseundsomitin
demGradderVergröberungsindnichtlinear.DiesedreiProzesseführenzu
einemkomplexenVerhältniszwischenDichteundMikrostruktur.Ausdiesem
GrundkannesimpolarenFirnkeineeinfache,direkteParametrisierungvon
mikro-strukturellenParameternwiespezifischeOberfläche,KorngrößeoderPer-
geben.meabilität

9.DieMikrostrukturderFirnkernezeigttrotzdersehrunterschiedlichenRandbe-
dingungeneinigeüberraschendeindeutigeBeziehungen:DiespezifischeOber-
fläche,welchemitdenunterschiedlichstenMethodenimFirnermitteltwerden
kann,kannein-eindeutiganhanddermitdemRöntgen-Computer-Tomographen
gemessenenChord-Längebeschriebenwerden.DieChord-LängeisteinMaß
fürdiemittlereAusdehnungderEis-oderPorenphaseineinerRichtunginnerhalb
einerProbe.DiesesErgebnisunterstütztdieAnnahme,dassoptischeEigen-
schaftenvonSchneeundFirnmiteinemeffektivenRadiusalsKorngrößen-Parameter
beschriebenwerdenkönnen.DereffektiveRadiusentsprichtdemRadiusvon
gleichgroßenKugelnineinerMatrix,diedieselbespezifischeOberflächehaben

wiedieFirnprobe.FüralleAnwendungen,indenendieeffektiveEis-Luft-Fläche

imFirneineRollespielt(Luftaustausch,chemischeInteraktionvonAtmosphäre

undSchnee,optischeInteraktionen,Mikrowellen),istdierechteinfachzubes-

timmendespezifischeOberflächeausreichend,umeineneffektivenRadiusals

Korngrößen-Parameterzubestimmen.DieserRadiuskannwiederuminKornwachstums-

ModellenoderAnwendungenzurBestimmungderKorngrößeausderFernerkun-

dungverwendetwerden.

WeiterhinkonnteeinGrößen-invarianterStruktur-Parameter(Struktur-Modell-Index

SMI)berechnetwerden,derdieBeziehungzwischenKrümmungundOberfläche

derStrukturbeschreibt.AllehieruntersuchtenFirnprobenzeigeneinefastein-

deutigeBeziehungvonPorositätunddemStrukturModelIndex.Obgleichder

enormenVielfaltderanderOberflächegeneriertenSchichtung,derSinterung

unddemVergröbern,werdendurchdieFirn-Metamorphoseüberalltopologisch

ausgebildet.ukturenSträhnliche

3

ListofPublicationssubmittedfor

Thesisthe

licationPub•1

Thedensificationoflayeredpolarfirn
M.W.Hörhold,S.Kipfstuhl,F.Wilhelms,J.Freitag,A.Frenzel
SubmittedtoJournalofGeophysicalResearch,EarthSurface,accepted.

Pub•2lication

Fromrandomdepositiontoafirncorerecord-ontheimpactofimpurities

onthedensificationofpolarfirn-afirstapproach
M.W.Hörhold,T.Laepple,J.Freitag,S.Kipfstuhl,M.Bigler,H.Fischer
ation.preparIn

•3licationPub

Grainsizeoflayeredpolarfirn-evolution,variabilityandanewgraingrowth

modelM.W.Hörhold,S.Linow,W.Dierking,J.Freitag
ation.preparIn

17

licationPub4

M.W.Hörhold,M.R.Albert,J.Freitag(2009)

Theimpactofaccumulationrateontheanisotropyandairpermeabilityof

polarfirnatahighaccumulationsite

JournalofGlaciology,Vol.55,No.192,pp.625-631.

5licationPub

Z.Courville,M.Hörhold,M.Hopkins,M.Albert

LatticeBoltzmannmodelingoftheairpermeabilityofpolarfirn

SubmittedtoJournalofGeophysicalResearch,EarthSurface,accepted.

utions:ibcontrOwn

–permeabilitymeasurementsoftheHerculesDomesamples;

–micro-CTmeasurementsofallsamples;

–3D-imageanalysiswithMAVIofallsamples;

–modelingpermeabilityusingmicrostructureparameter;

–discussionofthemodelingresults

ObjectivesandoductionIntr4

T4.1opic

Thisstudydealswiththeinternalstructureandlayeringofpolarfirn.Snow,accumulat-
ingontopofthepolaricesheets,graduallycompactsandsintersunderitsownweight
toformfirstfirnandthenice.Thepolarfirncomposestheupper60-120meterofthe
polaricecapsandisporousandpermeabletotheair(Figure4.2).Thefirncolumn
showsanalternationofverydifferentlayerscharacterizedbyalargevarietyofphysical
properties.Thesestratigraphicsequencesarecreatedatthesurfacebydiscontinuous
snowaccumulation,wind,seasonal,diurnalorfasterchangesinweatherconditions.
Thisresultsinlayersofdifferentparticlecompositionwithdifferentgrainsize,shape,
densityorairpermeability,whichcanbevisuallydistinguished(Figure4.1,lefthand
side).Thestratigraphyofthefirniskeptduringthecompactionandsinteringandvis-
ibleevenwithintheicecorerecord(Figure4.1righthandside).Thestratigraphyofa
siteissupposedtoreflectthelocalclimateconditionsofthissiteandithasbeenoften
usedasadatingtoolinfirnandicecoreanalysis.
Infirnstudiestheprocessesofsintering,densification,coarseningandmetamorphism
areoftendiscussedwithdifferentmeaning.Inthefollowingweusesinteringasade-
scriptionofamaterialprocess,wheregrainsizeanddensityincrease(Kang2005)
withdepthofthefirncolumnandtime,asafunctionoftheoverloadpressuredueto
thelayerspermanentlyaccumulatedontop.Densificationisusedasthetermforthe
overallincreaseindensitywithdepthfromsurfacedensitiesofsnowofapproximately

19

eFigur

4.1:

Left:

Snow

pit

at

Summit

sunbyilluminatediswall

Station,

eenland.Gr

The

eethr

meter

deep

snow

lightthroughasecondpitbehind,sothatthesin-

glesnowlayersarevisible,picturebyZ.Courville,June2008.Right:Line-

Scanofanicecoresegmentwithtransmittedlightfrom2700mdepthfrom

theGreenlandicecoreNGRIP,unpublisheddata,picturebyS.Kipfstuhl

300-500kg/m3tothedensityoficeof917kg/m3.Thedensificationratedifferswith
accumulationrateandannualmeantemperatureatthedifferentsites.Snowmetamor-
phismistheumbrellatermforthechangeofthesnowstructureafteritsdeposition
ontheground.Thesnowgrainsimmediatelychangetheirstructureandformbonds.
Adistinctionisdrawnbetweentemperaturegradientmetamorphism,whereenhanced
massflowalongthetemperaturegradientdistinctivelychangesthesnowstructure,and
isothermalmetamorphism,werethechangesinthesnowstructurearedrivenbylocal
watervaporgradientsduetodifferencesincurvature.Coarseningindicatesasinter-
ingprocessundertemperaturegradientswithasimultaneousincreaseingrainsize
andporesize.Thecompletestructureshiftsfromcomplex,small-scalestructuresto
smooth,large-scalestructures.Thisisobservedtohappenintheupperfewmetersof
polarfirn,duetotemperaturegradientsalteringthesnowmetamorphism.

oundkgrBac4.2

Inmanytopicsofpolarresearch,thedensificationofthepolarfirnplaysanimportant
role.Thedensificationiscloselylinkedtothelayeringofthefirn,sincethelayering
inducesavariabilityindensity(Cuffey2008).Researchquestionslinkedtodensityand
layeringaretheconvectionofthesurfacefirnandtheairpermeability,thedensification
ofthefirnatdifferentsitesandtheentrapmentofairbubblesintotheiceaswellas,
regardingremotesensingtechniques,theinteractionofelectromagneticwaveswith
thesnowandfirnpack.
Thepaleo-archiveofpolaricesheetsisuniqueasitdirectlyrecordstheatmospheric
compositionintheairbubblesoftheice(Blunier&Schwander2000).Butthefirnforms
ahighlyporousmedium,whereairconvectionanddiffusionenableadistinctexchange
withtheatmospheredowntodepthsofseveral10sofmeter.Thisleadstoanagedif-
ferencebetweentheairbubblesentrappedandthesurroundingice(deltaage).Inthe
uppermostpartofthefirn,thesocalledconvectionzone(Figure4.2),theairisperma-
nentlyexchangingwiththeatmospherebyconvectionandhasthereforeatmospheric

concentrationsinaerosols(Figure4.2).Belowtheconvectionzone,inthefirncolumn
withstaticair,gasesmainlyexchangebymoleculardiffusionandgravitationalsettling.
Heretheairexperiencesfractionation(Figure4.2).Takingtwogascomponentswitha
constantrelationshipintheatmosphereovertime,anychangeinthisrelationshipdue
tofractionationinthefirncolumncanbeusedtocalculatetheheightofthestatic-air
firncolumn(Blunier&Schwander2000)andthusestimatetheclose-offdepthandthe
ageoftheenclosedair.Theextendofthediffusivezonedeterminesthemainpart
oftheagedifferencebetweeniceandairbubbles.Withfractionationmodelsthisage
differencecanbemodeled,iftheextendofthediffusivezoneandthedepthofclose-off
isknown.Theclose-offdepthisgivenasthesumofheightsoftheconvectionzone
andthestatic-airfirncolumn.Anunknownextendoftheconvectionzoneinducesan
uncertaintyintheclose-offdepthandthereforealsointhecalculationoftheagediffer-
enceofenclosedairandsurroundingice.Thereforemeasureddataofthedepth,until
airventilationofthesnowandfirnispossible,areveryimportantforestimationofthe
deltaagebetweeniceandairbubblesinpolarrecords.
Theconvectionofthesurfacefirnispossibleduetothehighairpermeabilityofthe
snowstructure.Airpermeabilityoffirnhasbeenmeasuredatseveralsites(Albertetal.
2000,2004,Rick&Albert2004,Courvilleetal.2007)andanincreasewithdepth,until
amaximumatdepthsof2-4meterwasfound.Layeringintroducesavariabilityinthe
permeabilityprofile,andsingleimpermeablelayerscandecreasetheairexchangeof
thewholeunderlyingcolumn,duetotheirspecificmicrostructure.Forexample,wind-
orsuncrustscanreducetheairpermeabilityinthefirncolumn,aswellaswindpacked
snowfromstormevents(Albert&Perron2000).Thusthelayeringhasadirectimpact
onthefirnventilationandtheextensionoftheconvectionzoneinthesurfacefirn.
Duringthedensificationprocesstheairoftheporespacedisintegratesintosingleair
bubblesandenclosesintotheice(Figure4.2).Theclose-offdepthisdefinedasthe
depth,whereacriticaldensityisreached(Landaisetal.2006)andtheairgetsen-
closed(Figure4.2),dependingontheannualmeantemperatureofthesite(Martinerie
etal.1992).Firnmodelssystematicallyfailinpredictingtheclose-offinglacialtimes,

4.2:eFigur

Aintervalsdepthentferdifthewithsheeticeanomfrcolumnaofscheme

ofsnow(0.1m),firn,bubblyiceandpureice(lefthandsideandascheme

oftheupperapproximately100meteroftheicesheet,representingthefirn

column.Thedifferentstagesofairtransportprocessesandenclosureare

indicated.

becauseoftheunknownextensionoftheconvectivezoneandthepoorestimationof

thedepth,wherefirsthigh-densitylayersinterruptupwardsexchangewiththeatmo-

sphere-i.e.definetheupperlevelofthesocalledlock-inzone,wheretheairenclosure

isstarted.Earlysealingofgasesbyhorizontalimpermeablelayers(Severinghaus&

Battle2006),i.e.highdensitylayers,canenhancefractionation,whichaltersthefirn

gasmeasurements.Atsiteswithaveryhighvariabilityindensitythehigh-density

layerclose-offratherearly,whileotherlayerskeepconnectedporesdowntogreat

depths.Accordingly,aprofoundunderstandingofthelayeringanditsevolutionwith
depthdowntothefirn-ice-transitioniscrucialwhenunderstandingtheprocessofair
2006).al.et(LandaisenclosureThedensificationoffirnisusuallydescribedasamoreorlesscontinuousincrease
indensityindependenceoftheannualmeantemperatureandaccumulationrateofa
site(Herron&Langway1980,Maeno&Ebinuma1983,Arnaudetal.2000,Goujon
etal.2003).Oftenmeandensityvaluesareobtainedfromthefieldandthephysical
processofdensificationisconnectedtocriticalmeandensityandrelatedmicrostructure
changes.However,thelayeringofthefirninducesatremendousvariabilityintothehigh
resolutiondensityprofiles,andthus,definingacriticaldensityanddepthisactuallynot
straightforward.Singlelayersreachthesecriticaldensitiesatdifferentdepthsandthe
shiftfromonedensificationregimetoanothercouldbethoughtofamoreorlessgradual
transitionorevenalayer-specificprocess.
Thelayeringindensityisnotonlyimportantfortheunderstandingofthedensityevo-
lutionwithdepthbutalsofortheobservationoftheicesheetswithremotesensing
techniques.Theestimationofice-sheetvolumevariationsisoneofthegoalsofsatel-
literadaraltimetry.ThelaunchofthenewsatelliteCryoSat2inApril2010hasgained
muchattention,sinceitsorbitisdesignedsuch,thatitwillscanthepolarregionswitha
hightimeresolution,sothatchangesinicesheetelevationcanbedetectedseasonably
(www.cryosat.de).However,amajorobstacletothecorrectinterpretationofthedata
liesinthecomplexinteractionwiththereflectingsnowpack(Legresy&Remy1998,
Cuffey2008).Thesignalisreflectedatthelayerinterfacesandscatteredattheice
grainsandmatrix.Dependingontheappliedwavelengthsthevolumeofinteractioncan
beseveralcentimetersdowntoseveral10sofmetersdeep.Layeringandgrainsize
aresupposedtoplaythemostimportantrolesinthebackscatterbehaviorofelectro-
magneticwaves(Rottetal.1993,Surdyk&Fily1993,Kärkäsetal.2002).Analysisof
thedataobtainedfromremotesensingoftencontainsthecorrectionofthemeasured
surfaceelevationbyadensitymodeloftheupperfirncolumn.Thelayeringofthefirn
isincludedinthesemodels,sincethesurfacedensityseemstovarythroughtheyear

andseasonalvariationsinthedensityprofileneedtobeconsidered,whencalculating
theelevationchange.
Formanyapplicationstheconsiderationofmeanvalues,suchastheone-metermean
density,mightbesufficient.Nevertheless,theproblemsofairtransportproperties,air
enclosure,densificationandinterpretationofremotesensingdatacannotbesolved
withoutconsideringthestratigraphiclayeringofthefirn.Theongoingimprovementin
measurementtechniquesandresolutionenablesafasterandmoredetailedobserva-
tionofthepolarfirnstructure(Marshalletal.2007,Pielmeier&Schneebeli2003).The
integrationofthevariabilityintomodelsisstillachallenge.Parameterizingthevariabil-
ityinphysicalpropertiesofthefirnwillimprovetheunderstandinganddescriptionofthe
firnstructureandthusincreasethescientificgaininboth-themonitoringoftheactual
changesoftheicesheetsaswellastheinterpretationofresultsfromicecorerecords.

questionsMain4.3

Manydetailedsnowpitstudiesoflayeringareavailablefromlocallyrestrictedareas.
However,duetodifferentmethodsappliedandindividualdescriptionanddefinitionof
layersorgrainsize,acomparativeanalysisisdifficulttoaccess.Asystematicstudyis
missingaswellasacomparableobjectivemeasureoflayering.Someofthemainopen
are:questions

AWhatislayering?Howtoparameterizeit?

BHowislayeringgenerated?

CHowislayeringevolvingwithdepthandtransferredtothefirn-ice-transition?

DHowislayeringdisplayedinthemicrostructureandairpermeability?Istherean
explicitlinkbetweendensityandmicrostructure?

EDoesvariabilitydifferfordifferentsites?Whatistheimpactoflocalclimateonthe

microstructure?Istherearegionalvariability,whichisdetectablewithremote
sensing,i.e.whatcreatestheobservedregionsofsimilarbackscatterbehavior?

Thisstudyaimstostartansweringthesequestionsandtogiveacontributiontothe
overallpictureofpolarfirnstructureanddensification.

4.4Stateoftheart

Inmanysnowpitstudiesthedifferentlayersaredescribedbytheirvisualappearance,
whichismainlydeterminedbygrainsizeanddensity.Sequencesoflayerswithachar-
acteristicalternationofphysicalpropertiesareoftenconsideredasannualdeposition
(Gow1965,PalaisJ.M.1982,Davisetal.1996,Zwally&Jun2002).Highdensitylay-
ersareusuallyassociatedwithwinterdeposition,whereaslowdensitylayersareoften
correlatedtosummerdeposition(Gow1965,Benson1971,Alley1988,Landaisetal.
2006,Severinghaus&Battle2006).Theseasonalvariabilityislinkedtoseasonally
varyingvaluesinionconcentrationorisotopicpropertiesofthefirnlayers(Kreutzetal.
1999).Alternatinghighandlowdensitylayersarecreatedatthesurface,reduceinampli-
tudewithdepth(Jun&Zwally2002,Zwally&Jun2002)andcanstillbedistinguished
atthedepthofthefirnicetransition.Higher-densitywinterlayersbecomeimperme-
ablebeforelower-densitysummerlayers(Martinerieetal.1992,Landaisetal.2006,
Severinghaus&Battle2006).Thelayeringisnotonlydisplayedindensitybutalsoin
microstructureandairpermeability.Quiteoftenlargegrainedfirnlayersareobserved
aslowdensityandhighpermeabilitylayersandviceversa.Sowithalternatingdensity,
theseparametersalsoalternateinthefirncolumn(Nakaya&Kuroiwa1970).Itisa
commonassumption,thattheserelationships,developedattheverysurfaceoftheice
sheet,arekeptandtransferreddowntothefirn-ice-transition.Anychangeinsurface
patternduetoaccumulationratechanges,weatherconditionsortemperaturewillbe
directlytransferredtothefirn-ice-transitionandstoredintheice,presumingtheyare

displayedinthelayeringofthefirn.
Differentlocalclimateconditionswillresultinadifferentfirnstructureandlayering.It
ishypothesizedthatsiteswithhighaccumulationrateshowahighvariabilityindensity,
thusamorepronouncedlayering,sinceeverysinglelayerisburiedratherfastunder
newsnowaccumulation.Moreoverthesesitesaresupposedtoshownoconvection
zonebutaratherextendedzoneatthefirn-ice-transition,weresinglelayersareimper-
meable,whileothersarestillopen(Landaisetal.2006).Siteswithlowaccumulation
shownovariabilityindensity,becauseofvanishedlayering,aconvectivezoneandhet-
erogenousfirn-ice-transition(Kawamuraetal.2006).Thecommonideais,thatatlow
accumulationsites,theoriginallycreatedstratigraphywillvanish.Duetothelongexpo-
suretimeatthesurface,anydifferenceinthelayerswilldisappearandthefirnshowsa
moreorlesshomogenousstructure.Thisinturnwillresultinlessvariabilityindensity
ansition.n-ice-trfirtheatThesedifferentstructuresinlayeringandmicrostructureresultinverydifferentbackscat-
terbehaviorofthefirncolumn(Rottetal.1993,Surdyk&Fily1993).Satelliteremote
sensingcanbeusedtostudythefirnstructureonamuchlargerscalethanground
basedmeasurementswouldallow.Regionsofsimilarbackscatterweresummarizedto
snowclasses,whicharesupposedtoshowasimilarstructure(Rotschkyetal.2006,
Tranetal.2008).Thesesnowclassregions,displayverywelltheknownaccumulation
rateandtemperaturedistributionsaswellaselevationandwindpattern.Accordingly,
thefirnstructureisinfluencedbytheselocalclimateconditionsdifferentlyatthevarious
.sitesThesummarizedstateoftheartconcerningtheabovestatedquestions(paragraph4.3)
is:

ALayeringisdisplayedinthedifferentphysicalpropertiesofthefirn,suchasden-
sityandmicrostructure(Gow1965,Benson1971,Rundle1971,Alley1988),but
publisheddataareeitherrestrictedtoasinglesiteorlackobjectiveandrepro-
ducibleparameterforcomparison.Acomparativedatabaseismissingandthus

aparameterizationofthelayering,withassimilableproxies,isstilllacking.

BThelayeringisthoughttobecreatedatthesurfaceduetoseasonalvaryingsnow
deposition.Atsomesiteswinterdepositionisreportedtoshowhighdensityand
smallgrains,whereassummerdepositionshowslowdensityandlargegrains.At
othersitesthisrelationhasbeenobservedtheotherwayaround.Alltogether
thecommonassumptionprevails,thataseasonalsequenceoflayersiscreated
everyyear,whichcanbeusedtodatethefirncore(Martinerieetal.1992,Jun
&Zwally2002,Li&Zwally2004,Severinghaus&Battle2006).However,reports
ofseasonalityinsnowpitsfromdifferentsitesareinconsistentandsomestud-
iesoncorrelationofvisiblestratigraphy,seasonalvaryingionchemistry,isotope
measurements(Stenbergetal.1999,Karlöfetal.2006)questiontheimageofa
generalizedannuallyresolveddepositionhistorydisplayedinthestratigraphyof
n.firthe

CThisstructureoflayeringiskeptduringdensificationdowntothefirn-ice-transition.
Theamplitudeofdensityvariabilityisassumedtoslowlydecrease,untiltheden-
sityoficeisreached(Jun&Zwally2002,Zwally&Jun2002,Li&Zwally2004,
Landaisetal.2006).Nonetheless,firstmeasurementswithhighresolutionden-
sitydatashowamorecomplicatedpicture,eitherwithincreasingdensityvari-
ability(Gerlandetal.1999,Freitagetal.2004)orwithachangeincorrelationof
densityandbackscatterbehavior(Hawley&Morris2006).Againascarcedata
baseisgiventoverify,whetherthesefindingsaretheresultofsingularchar-
acteristicsofthespecificsitesoriftheyindicateamoreglobalbehavioroffirn
densification.

DLayeringisdisplayedinboth-densityandmicrostructure.Atasinglesitegrain
sizeislinkedtodensity.Andasthedensitychangestroughtheseasons,the
grainsizedoesaswell.Thisrelationiskeptandstoredintotheice.Notmany
comparabledataareavailableuntilnow.Fromfirstmeasurementsofgrainsize

anddensityofnearsurfacesamplesandsamplesnearthefirn-ice-transition,a
changeintherelationshipofgrainsizeanddensityhasbeenreported(Freitag
etal.2004,Fujitaetal.2009).

EHighaccumulationsitesareexpectedtoshowhighdegreesoflayeringwithlarge
variabilityindensityandlowaccumulationsitesareexpectedtoshowlowtozero
degreeinlayeringandonlysmallvariabilityindensityormicrostructure(Kawa-
muraetal.2006,Landaisetal.2006).However,nodataareavailabletoprove
this,neitherthevariabilityofdifferentsitesatthesurfacenoratdepthsofthe
firn-ice-transition,wherethisdifferenceinlayeringissupposedtoinfluencethe
airenclosure,havebeensystematicallyinvestigatedsofar.

Notonlythescarcedatabutalsothecontradictoryobservationsaswellasunexpected
findingsfromsporadichighresolutiondatamotivatethisstudy.Theaimistogenerate
acomparativedataset,wherethelayeringfromsurfacedowntothefirn-ice-transition
atdifferentsitescanbeinvestigated.

Methods5

yvesurLiterature5.1

Publicationsfromthelast50yearswerecollectedinordertosummarizeavailableob-
servationsoffirnstratigraphyontheAntarcticicesheet.Thesiteswerecollectedina
databaseandinformationabouttheoccurrenceoflayering,hiatusordepthhoarwere
noted.Sometimesnolayeringwasdetected,sometimesseasonalsequencesoflayers
wererecorded.Theresultsofthissurveywereplottedonamap,usingArcGis,inorder
toidentifyspecificregions,probablyindependenceonelevation,accumulationrate,
windfieldorannualmeantemperature(Figure6.8).

coresFirn5.2

Thestudiedfirncorescoverabroadrangeinannualmeantemperatureandaccumu-
5.1).(FigureaterlationFirncoresfromtheGreenlandicesheetareallsituatedontheplateau,butdifferdis-
tinctivelyinaccumulationrateandtemperature.TheAntarcticfirncoresoriginatenot
onlyfromdifferentsitesoftheplateaubutalsofromcoastalregions,suchasB25from
BerknerIslandorthePreIPICScoresB38,B39,DML95andDML97fromnearcoastal
DronningMaudLand.Withthiscollectionoffirncoresaverybroadrepresentationof
firnstructureandpropertiesshouldbeaccessible.ThetwoextremesitesaretheB38
firncorewithhighestannualmeantemperatureof-18.1°Candunusuallyhighaccumu-
lationrateof1.25meterw.e.peryear.Thelowerendinaccumulationrateandannual

31

Figure5.1:Theannualmeantemperatureandaccumulationrateofthestudiedfirn
coresites.Crossesmarkpositions,weretemperatureandaccumulationrate
wasdeterminedfrommeasurements.Closeddiamondsmarksites,were
eitherthetemperatureortheaccumulationratewasestimatedfromeither
nearbysites(DP7,B33)orfromMODISdata(HD).Atallfirncoreshigh
resolutiondensitymeasurementswereconducted,redcirclesmarkfirncore
siteswereadditionallyCTmeasurementswereconducted.

meantemperatureisrepresentedbytheDomeCareawith-53°Cand0.025meter
w.e.peryearrespectively.AdetailedlistoffirncoresisshowninTable1ofpublication
1and2fordensitymeasurementsandTable1ofpublication3forCT-measurements,
.elyrespectiv

5.3Highresolutiongammaabsorptionmethod

Highresolutiondensityprofiles,withaverticalresolutionfrom1to5mm,wereana-
lyzed.Mostfirncoreprofilesofdensityrawdatawereavailablefrompreviousmea-
surementcampaigns.Toextendtherangeoflocalclimateconditions,8firncoreswere
measuredwithinthisproject.ThesearetheEDC2coreandtheFireTrack(FT)firn
corefromtheAntarcticDomeCsite,4firncoresfromcoastalDronningMaudLand,

Antarctica(PreIPICS),theB36firncoreastheupwardsextensionofapreviouslymea-
suredfirncoreB37nearKohnenStationinDronningMaudLand,Antarctica,andthe
approximately15meterlongfirncorefromsiteDepot700,providedbytheNorwegian-
AmericanTroll-South-Poletraversein2007-2008.

Figure5.2:Measurementofhighresolutiondensityusinggammaabsorptionmethod.

Densityismeasuredbyanon-destructivegamma-absorptionmethod.Themeasured
intensityoftheattenuatedgamma-beamtroughtheice(Figure5.2)istransferredinto
adensitysignalusingBeer’slawandtheknownmassabsorptioncoefficientofice,the
intensityofthebeaminairandthediameterofthefirncore(Wilhelms1996,2000).The
dataarecorrectedforbreaksandcorecatchermarksbylinearlyremovingtheoutlier
andinterpolatingoverthegap.

5.3.1Missinglayers

Thehighresolutiondensitymeasurementmethodenablesadetailedstudyofthelay-
eredstructureofthefirn.However,inordertoincludealldensities,occurringatasite,
intothestatisticalanalysis,alllayersneedtobecapturedinthemeasuredfirncore.But
oftenfirncoresbreakduringthedrillingprocedureandalsolater,duringthehandling
ofthefirncorepieces.Evenmoreinmanycasestheupper5-6meteroffirncoresites

arenotsampled,duetothefragiletextureofnearsurfacefirn.Itisespeciallythelow
densitylayers,whichconsistofveryloosesnowandshowaweakstrength.Duringthe
processingofthedensityrawdata,depthintervals,whichshowbreaksorsomehow
disturbeddata,areremovedandinterpolated.Therefore,lowdensitylayersmightbe
underrepresentedwithinthedensityanalysis.

measurementsermeabilityP5.4

PermeabilitymeasurementswereconductedusingthedevicedesignedbytheCold
RegionsResearchandEngineeringLaboratory(Albertetal.2000),basedonShimizu
(1970).Aflexiblerubbermembraneisinflatedaroundthecoresampletocreatean
air-tightseal.Pressureandflowratesaremeasuredthroughthesample.Tenmea-
surementsatincrementalflowratesareconductedanditisensured,thatthepressure
versusflowratefollowsDarcy’slawandislinear(Albertetal.2000,Courvilleetal.
2007).Permeabilitywasmeasuredattwofirncores,theHerculesDomefirncoreand
theDepot700firncore,incooperationwithDr.ZoeCourville,fromtheColdRegion
ResearchandEngineeringLaboratory,USA.

5.5X-ray-microfocus-computer-tomography(CT)

Themicrostructureoffirnsampleswasmeasuredat-25°CusingaSkyScan1074X-
ray-microfocus-computer-tomography-ScannerwithapolychromaticX-raybeamwith
40kVand1000μA(Figure5.3).Thecompleteupper1-2mofeachfirncore,ifavail-
able,weresampled.Otherwiseapproximately40cmweresampledeverymeter.From
eachdepthintervalfirncorepiecesarecutinto2.5cmthickslices.Fromeachslicea
cylindricsamplewithadiameterof2cmisdrilledwithaboreholesaw.Thesampleis
placedonamoveableturntablebetweenX-ray-sourceanddetector.Duringthescan-
ningprocedurethetablerotatesatintervalsof0.9°.Asetof400shadowimagesis
capturedwhiletherotationcompletesacircle.Withadigitalconvolutionalgorithmthe

shadowimagesaretransformedintoaseriesofhorizontalcross-sectionimageswhich
representthe3-Dstructureofthefirnsample,basedonthelocallydifferentabsorption
ofX-rays.

Figure5.3:TheComputer-Tomographisoperatedinthecoldroom.Snowsamplesare
placedonatableinsidethetomograph.Ateveryrotationstepashadow
taken.isimage

Theresolutionofthereconstructedimagesis40μmforthefirncoresB26,B36,DP7,
FTandHDand15.7μmforthefirncoreB38.
TheX-ray-microfocus-computer-tomography-measurementsdeliveracoarserresolu-
tionthanthedensitymeasurements.Valuesareaveragedoveravolume(vertical
depth)of1.6cmsidelength.Furthermorediscontinuoussamplesaretaken,which
restricttheamountoflayersconsideredineachdepth-interval.

5.6MicrostructuralanalysisusingMAVI

The3DanalysissoftwareMAVIwasdevelopedbytheFraunhoferInstitutefortheimage
analysisof3Dcomputer-tomographyimages.Thegreyvalueimagestackisloaded
intothesoftware.Forimageanalysisthesamplesarecroppedtoacubeof1.6x1.6

x1.6cmsidelength(400x400x400voxels).Afterapplyinga3x3x3median
filter,theimageisseparatedinvoxelsrepresentingsolidiceorair-filledvoids.For
thissegmentationaglobalthresholdvalueisdeterminedfromthebimodalgrey-value
histograms.AirandicehavealargedifferenceinX-rayabsorptionandthemeangrey
levelsoficeandairdifferbyasmuchas100units.Thereforeaclearseparationofthe
poreandicephaseisgiven,eventhoughtheglobalthresholdoffersarathersimple
methodofsegmentation(Figure5.4).Ontheresultingbinarized3-Dimageanobject
filterisapplied,removingallvoxelsaddinglessthan1%tothevolumefractionofeach
.phase

Figure5.4:Imageprocessingprocedure:thecylindricsampleiscroppedtoacube(a)
andbinarized(b).Thefinalimagerepresentsthecomplete3Dstructureof
thefirnsample(c),3-DimagefromHerculesDomeasanexample,white:
grainsicevoids:space,air

Morethan1400binarizedvolumeimageswereanalyzedintheframeofthisstudyfor
microstructuralproperties.Herethetermmicrostructureisrestrictedtothefollowing
ties:proper

SSAThe(optical)specificsurfaceareaisameasureofthesizeoftheice-air-interface
inrelationtothesamplemass.Itcanalsobeobtainedbyothermethodsand
thereforecomparedtoobservationsinliterature.Withinthisstudyitcouldbe
proved,thatabijectiverelationshipbetweenthesizeoftheicephaseintermsof
chordlengthandthesurfaceareaexists(Publication3).

ReffInordertoassureacomparativemeasureoffirnstructuretheopticalspecific
surfaceareawascalculated,whichrepresentstheice-airinterfaceaccessibleto
gasesperunitmass.FromthattheeffectiveradiusReffcanbedetermined.It
representstheradiusofequalsizedsphereswithasimilarspecificsurfacearea
asthefirnstructure.Withthefirnsamplesfromthisstudyitisshown,thatthe
representationofthefirnstructurebyspheresissufficientenoughtodescribe
theair-ice-interfaceaccessibletogasesorinteractionwithmicrowaves(Publica-
tion3).Thiseffectiveradiusistakenasameasureofgrainsize,whichcanbe
obtainedfromseveralmethodsinthefieldandinthelabandthuscaneasilybe
comparedtoothermeasurementsorusedwithingrainsizemodels(Publication
3).Inthefollowingthetermgrainsizeisalwaysrelatedtotheeffectiveradius.

lporeTheporechordlengthlpore(aswellasgrainchordlength)isameasureofthe
averageintersectionlengthsofalinewiththeair(orice)phase.Itcanbede-
terminedfordifferentdirections.Thechordlengthcouldbeusedasagrainsize
parameter,butinthisstudythegrainchordlengthisexplicitlynotusedasgrain
sizeparameter,buttheabovedescribedeffectiveradius.

anisotropyTheanisotropyiscalculatedbytheratioofthefractionofsurfacenormalvectors
pointingintothehorizontaldirectionandthefractionofsurfacenormalvectors
pointingintotheverticaldirection.Iftheratiohasvalueslowerthanone,more
surfacenormalvectorspointintotheverticalsection,i.e.thestructureishorizon-
tallyelongated.Avalueofoneindicatesisotropicstructuresandvalueslarger
thanoneverticallyelongatedstructures,i.e.verticalanisotropy(Publication4).

SMIAsizeindependentstructuremodelindexSMIhasbeendevelopedinprevious
studiesinordertocomparestructures,thataresufficientlysimilarliketheice
phasefromdifferentdepthsinthefirncolumn.Ithasbeenusedinexperiments
withtemperaturegradientandequi-temperaturemetamorphismsetups(Schnee-
beli&Sokratov2004,Kaempfer&Schneebeli2007).Theindexisdeterminedby

thecurvatureoftheicephaseandthesurfaceareainrelationtothevolumeofthe

firn.Itenablesasizeindependentcomparisonofstructuresandtheircurvatures

(Ohseretal.2009).Positivevaluesindicateconvexsurfacessuchassingleice

grains.Valuesaround4areobtainedbysphericalstructures,valuesof3indicate

cylindricalstructuresandvaluesaroundzerorepresentflatsurfaces(Ohseretal.

2009,Schneebeli&Sokratov2004).Negativevaluesindicateconcavesurfaces,

thenumbersequalintheirmeaningconcerningtheshape(i.e.-4,sphericalen-

closure,-3cylindricalenclosure),butthesignofcurvatureisreversed.

DiscussionandResults6

6.1Parameteroflayering

Thedifferentlayersofthefirncolumninduceavariabilityindensity.Thisisvisualizedby
alighttableimageandthecorrespondinghighresolutiondensityprofile(Figure6.1).
Thelightsourceisbelowthefirncorepiece.Layerswithhighdensityabsorbmore
lightandappeardark,layerswithlowdensityabsorblesslightandappearbright.The
scatteringoflightislargeratlayerswithlargegrainsandsmalleratlayerswithfine-
grainedfirn.Thedifferentappearanceinbrightnesscorrespondstodifferentdensities
andgrainsizes(Figure6.1).
Inordertoparameterizethislayeringinducedvariabilityinthedensityprofile,themean
densityissubtractedfromthemeasureddensity(Figure6.2a).Fromtheresidualsignal
therunningmeanofaslidingwindowof1meterlengthandthestandarddeviationofthe
mean(Figure6.2b)arecalculated.Thisstandarddeviationistakenasthemeasure
ofvariabilityindensityduetothelayeringofthefirn.Inthefollowingthisstandard
deviationisusedtostudyhowthevariability,andthusthelayering,behaveswithdepth
(Publication1and2)andhowitvariesatdifferentsites(Publication1and3).
Thelayeredinducedvariabilityisnotonlydisplayedindensitybutalsointhemicrostruc-
ture.TheCTmeasurementsareconductedwithacoarserresolution,neverthelessthe
variabilityiscapturedwell(Figure6.3aandb,examplefromFTfirncore).Theden-
sityobtainedfromCT-measurementsfollowsthefluctuationindensityobtainedwiththe
gammaabsorptionmethod.Thisvariabilityisdisplayedinthemicrostructure,suchasis

39

Figur6.1:e

ondepthmeter6.6morfecorfirnEDCtheofpieceecorfirnlongmc55A

alighttabletogetherwiththehighresolutiondensityprofile.Darkareas

representfinegrainedfirnwithhighdensityvalues,brightareascoarse

grainedfirnwithlowdensityvalues.Thelayeringinducesavariabilityin

.density

thegrainsize,aswell.Inordertoparameterizethevariabilityinthemicrostructure,the

meanandstandarddeviationofeverydepthintervalwascalculated(Figure6.3c).This

means,thateverysetofsamplesfromaonemeterfirncorepiece(inmostcases16

samples)isconsideredasonedepthinterval.Fromthissetthemeanandthestandard

deviationarecalculated(Figure6.3c).Thisstandarddeviationistakenasaparameter

forthelayeringinducedvariabilityofthemicrostructure(Figure6.3d).Itcanbetaken

tocomparethevariabilityatdifferentsites.

eFigur

6.2:

Detail

omfr

high

esolutionr

terremovingmean(b).The

density

ismean

Fromtheresidualdensitythe

latedwithaslidingwindow.

mean

profile

(a)

and

the

esidualr

density

af-

subtractedfromthemeasuredprofile.

and

the

dstandar

deviation

ear

calcu-

eFigur6.3:

(a,methodabsorptiongammaomfrdensityesolutionrHigh:FTline)eygr

togetherwiththedensityvaluesobtainedbymicro-CT(a,blackcrosse).

TheCT-measurementsdisplaythevariabilityindensityandmicrostruc-

tureduetothelayering.Grainsizeshowslargevariability(b).Themean

andthestandarddeviationsdofeachdepthintervaliscalculated(c)and

canbeusedtocomparevariabilityatdifferentsites(d).

Thevariabilityinmicrostructurewithinthedifferentlayersisvisibleinallparameters

obtainedby3Danalysis.Eachlayershowsadistinctcombinationofmicrostructuralpa-

rameters,andeachdepthintervalischaracterizedbydifferentrangeinthemicrostruc-

tureproperties.Especiallygrainsize(heretheeffectiveradius)orspecificsurfacearea
displaythelayeringintheirvariabilityinthesamemannerasdensity.Sitesshowinga
highdensityvariabilityalsoshowahighvariabilityingrainsizeandviceversa.Parame-
terslikeporechordlengthoranisotropy(Figure6.4)displaynotonlythevariabilitydue
tolayeringbutalsothevariabilityastheresultofcoarseninganddensification.

Figure6.4:Thestandarddeviationsdofdensity,effectiveradius,porechordlength,
specificsurfaceareassa,densityandanisotropyofthedepthintervalsat
theB26siteinGreenlandobtainedbyCT-analysis.

ContributionTopicA:Thedifferentsnowlayerscreatedatasitebysingledeposition
eventscomposeaninhomogeneousfirnstructure.Thepolarfirnconsistsofsinglelay-
ers,eachcharacterizedbyspecificdensityandmicrostructure.Asreportedinliterature
densityandgrainsizearethemostclearandpronouncedparameters,inwhichthe
layersdiffersignificantlyandwhichcanbeusedtoquantifythevariability.Thislayer-
ingcanbeparameterizedbythestandarddeviationofphysicalparametersofthefirn
layers,suchasdensityorgrainsize(Publication1and3).

6.2Generationoflayering

Inordertotestthecommonassumption,thatthelayeringatthesurfacedisplaysthe
alternatingdepositionofannualaccumulation,theapparentfrequenciesinthedensity
variabilitywereinvestigated.Forthatthemeterdepthscalewastransferredtometer
water-equivalentdepth.Thisremovestheeffectofthinningandenablesacomparison
oflayersfromdifferentdepthandsites.Italsomeans,thatifthereisaseasonalfre-
quencyinthedensityvariability,thefrequencyanalysisshouldrevealadistinctpeakin
thefrequencyoftheaccumulationrate,becauseoftherepetitionofsequencesoflayers
everyyear.Forall17firncoreswithhighresolutiondensitymeasurementsreaching
thedepth-intervalofthefirn-ice-transition,thisinvestigationinthefrequencydomain
wasconducted(Publication2).Inmostcaseswedonotfindaclearsignatureinac-
cumulationratefrequencyinthesurfacedensityvariability,butaratherbroadrangein
apparentfrequencies.Itseems,thatwiththehighresolutiondensitydataaseasonal
alternationoflayerscannotbedetected.Thelayersseemtobecreatedrandomlyat
.acesurfthe

ContributionTopicB:Thecommonassumptioninliteratureis,thatthefirnlayersare
theresultofseasonallyvaryingfirndepositionandthatdensityaccordinglyvarieswith
aseasonalfrequency.Inthisstudy,theanalysisofhighresolutiondensityprofilesdid
notrevealaseasonalfrequencyinlayeringinthesurfacefirn.Thelayeringofthefirn
seemstobecreatedrandomlyatthesurface(Publication2).

6.3Evolutionoflayeringwithdepth

Atallinvestigatedsitesthevariabilityindensitydecreaseswithdepthandthenin-
creasesagain(Publication1).Theminimumisobtainedinadepthintervalof10to20
meterwaterequivalent(Figure6.5).Thefollowingincreaseissmallestforthelowac-
cumulationsitessuchasEDC2andB36/B37(Figure6.5).Thepeakishighestforthe

6.5:eFigur

Thestandarddeviationsdofdensitywithmeterwaterequivalentforthe
17firncoresites.FirncoresfromGreenlandareshowninyellow-brown
colors,Antarcticsitesinbluecolors.

coastalsitesB38andB39.Thedepthofthemaximumsecondpeakandthedecrease

towardsthedensityoficediffersforthedifferentsites(Publication1).Takingother

observationsintoaccount,forexamplethefindingofaflipinthedensity-backscatter-

intensityrelationship(Hawley&Morris2006)oraflipindensity-electricalconductivity

relationship(Gerlandetal.1999)atasimilardepthinterval(Fujitaetal.2009),itoc-
curs,thattheoriginallowdensitylayersdensifyfasterthantheoriginalhighdensity
layers.Theformerlowdensitylayersovercomethehighdensitylayers.Thiswould
explaintheminimumindensityvariability(atthecross-over)andthefollowingincrease

invariability.Itfurthermorewouldexplaintheflipintheabovementionedrelationship.

Becauseopticalpropertiesarelinkedtograinsize,anoriginallylargegrainedlayer
withlowdensityhasdevelopedtoalargegrainedlayerwithhighdensitybelowthe

cross-over(Publication1).Howeverfromcomparisonstudiesofhighresolutiondensity
measurementstohighresolutiongrainsizemeasurements(unpublisheddatabySepp

Kipfstuhl)itseems,thatthisshiftisnotacontinuousprocess,butthattherearedepth
intervals,wheretheflipingrain-sizeanddensitycanbeobserved,justnexttodepth-

intervals,wherethisisnotthecase.Theincreaseindensityvariabilityseemstobethe
resultofamorecomplexprocessindensification.
Lookingattheevolutionofthefrequencyofthedensityvariability,achangeinthe
intensitiesofthefrequencydomainwithdepthisdetected.Atthesurfaceabroadsignal
isobservedformostsites,atthedepthofthevariabilityminimumnodistinctsignalin
thefrequencydomaincanbedetected.Belowwefind,thatatmainlymediumtohigh
accumulationratesites,thesecondpeakindensityvariabilityshowsthefrequencyof
theaccumulationrate(Publication2).
Theseasonalityindensityvariability,whichwasnotdetectableatthesurface,develops
withdepth.InthisstudyCalciumconcentration,asoneionspeciesdepositedwithinthe
snowandmeasuredbycontinuousflowanalysis,from5firncoreswasinvestigatedand
linkedtothedensityprofile.AcorrelationanalysisofdensityandCalciumconcentration
wasconducted,whichsupportstheabovestatedobservationofachangingfrequency
inthedensityvariabilitywithdepth.AtthesurfacenocorrelationbetweenCalciumcon-
centrationanddensitycanbedetected,butitincreasestosignificantvaluesandshows
highestcorrelationinthedepthintervaloftheseconddensityvariabilitymaximum.The
hypothesisis,thatseasonallyincorporatedimpuritiesintothesnowlayersatthesur-
face,alterthedensificationofthesinglelayersandthusreshapethelayeringofthefirn
downtodepthsofthefirn-icetransition(Publication2).

ContributionTopicC:Inmostpublicationsandfirnmodelsusingdensityvariabilitya
gradualdecreaseofvariabilitywithdepthisassumed.Thevariabilityindensityfromthe
surface,suchashighdensitywinterlayersandlowdensitysummerlayers,isassumed
tobekeptduringdensificationandstillpronouncedatdepthofthefirn-ice-transition.In
thisstudyitisfound,thatthelayeringinducedvariabilityisnotlinearlydecreasingwith
depth,butrapidlydecreasesandthenincreasesagain(Publication1).Thevariability
furthermorechangesthefrequencyandamplitudewithdepth.Fromarandomlycre-
atedsignalatthesurfaceavariabilitywithaseasonalfrequencydevelopswithdepth

(Publication2).Itseems,thatthelayersarealterednon-linearlybyimpuritiesorany
otherparameter,whichareincorporatedintothesnowatthesurfacewithaseasonal
variability.Accordinglyanycompositionofdensityandmicrostructure,createdatthe
surfaceischangingnon-linearlywithdepth,whichwouldexplainthechangeinthere-
lationshipofdensityandphysicalproperties,asreportedinliterature.

6.4Layeringinmicrostructureandairpermeability

Measuredgrainsizeprofilesshowalargelayer-inducedvariability.Inordertoseethe
correlationtodensity,thetrendofgrainsizeindensitywasinvestigated(Figure6.6).
Withinasingledepthinterval,thestructurallayeringshowsalinearnegativecorrela-
tionwithdensity-thelargerthegrainsthelowerthedensity(greylinesinFigure6.6).
Suchalineartrendinmicrostructureanddensitywasfoundforallsites,eventhough
theslopeofthetrendisincreasingwithincreasingage(atasinglesite)anddecreas-
ingaccumulationrateandtemperature(comparingdifferentsites).Thewarmestsite
B38evenshowsapositivetrendingrainsizeandmicrostructureasdotheverysur-
facesamplesattheB36site.Thisindicates,thattherelationshipbetweendensityand
grainsizeforfreshsnoworfirnfromrelativelywarmsites,isadifferentonethanthe
relationshipofolder,metamorphosedandcolderfirn.Theoveralltrendofdensification
andsinteringshowstheoppositecorrelation(insign)-anincreaseingrainsizewith
increasingdensity(bluelineinFigure6.6).Thisrelationshipissufficienttoparameter-
izethelongtermbehaviorofaveragedensityandgrainsizeatdifferentlocalclimate
conditions,eventhoughtherelationwithinthesingledepth-intervalsisverydifferent.
Finallyathirdprocesscanbeobserved,shapingthemicrostructureofthefirnandsu-
perposingboth-theinitiallayeringandthesinteringprocess.Shorttermchangesin
localweatherconditionsleavetheirimprintonthemicrostructureandsuperposethe
longtermtrendofsintering.Inthenear-surfaceregiondownto4-5meterdepthsnow
metamorphismandverticalmasstransfercanbeenhancedbytemperaturegradientef-
fects.Iftheaccumulationratechangesonashort-termtimescale,certainlayersspend

6.6:eFigur

Thegrainsize(a)andspecificsurfacearea(b)oftheFTfirncorewithden-
sity.Greylinesindicatethesingledepthintervals,withincreasingdepth
andagemovingfromlighttodarkgrey.Orangepointsmarkthemean
valueofeachdepthintervalandthebluelinetheoveralltrendwithin-
.densityeasingcr

longertimewithinthisdepthintervalthanothers,experiencingenhancedtemperature
gradientmetamorphism.Thiscanbedisplayedinincreasedcoarsening,anisotropyor
airpermeability,whichisvisibleinboth,lowandhighdensitylayers(Publication4).
Thecoarseningisdisplayedinatemporaryporesizeincreasewithdepth(Figure6.7
a),whichinturnfavorsincreasedpermeabilityvalues(Figure6.7candd).Largerpore
channelsandacoarsefirnstructurecanprovideanenhancedventilationofthesnow
pack,evenbelowadepthofsomecentimeters.Coarseningseemstooccurdowntoa
depthof2-4meter,untiltheweightoftheoverlyingfirnlayersovercomescoarsening
anddensificationtakesover.Thepeakisdisplayedinamaximuminairpermeability
andinanisotropyin2-4meterdepth.
Tosummarize,therearethreedifferentprocesses,determiningthevariabilityinmi-

6.7:eFigur

ofevolutionThetheatdepthwith(b)opyanisotrand(a)lengthdchorepor

differentsites.ThemeasuredairpermeabilityoftheHerculesDomesite

(c)andtheDepot700site(d,unpublishedDatabyZoeCourville)witha

maximumin2.5and3meterdepth,respectively-notethedifferentscale

duetothelargedifferenceinpermeabilityvalues.

crostructureanditsrelationtodensityvariability:1.Thelayeringisrandomlycre-

atedatthesurface,settingupacertaincorrelationingrainsizeanddensity.2.The

overallgradualsinteringanddensificationincreasesgrainsizeanddensityinequal

rates.3.Shorttermchangesinexposuretimes(i.e.accumulationrate)oflayer

sequencesleadtoacoarseningofthestructure,completelysuperposingtheinitial

density-microstructurecorrelationandthelinearincreasewithdepth.Aparametrization

ofe.g.specificsurfaceareainordertoeasilydetermineeffectiveopticalparameters
fromdensitymeasurementsisnotstraightforward,becauseofthedifferentimpactof
thesethreeprocessesonthedensity-microstructurecorrelationinpolarfirn.

ContributionTopicD:Inpreviouspublicationsasystematicstudyofthelinkbetween
density,densityvariabilityintermsoflayeringandmicrostructurehasrarelybeencon-
ducted.Thecommonideais,thatcorrelationsindensityandmicrostructurearecreated
atthesurfaceandlinearlytransferredtoice.Thiswouldenableaparameterizationof
microstructureproperties,suchasgrainsize,fromdensity,sincealinearcorrelationis
assumed.Withthedataobtainedinthisstudy,itappears,thatmicrostructuredisplays
variabilityinamanyfoldway.First,thelayeringinducesacorrelationwithdensity,sothat
grainsizereflectsthelayeringasitisexpressedindensity-lowdensitycorresponds
tolargegrainsandviceversa,exceptforthesurfacesnowofB36andthefirncoreB
38.Second,theoveralldensificationandgraingrowthresultinagradualincreasein
grainsizewithdensity,whichcanbeparameterizedandmodeledforthedifferentsites
(Publication3).Andthird,shorttermchangesinaccumulationratecanalterthetime,
certainlayersareexposedtostrongtemperaturegradientsatthesurface.Thisleads
toincreasedcoarseningofthestructureandresultsinincreasedairpermeabilityand
anisotropy(Publication4andPublication5).TheeffectislargestattheGreenlandsite
B26andatthecoldandlowaccumulationratesitesinAntarctica.

6.5Layeringatdifferentsites

Theliteraturesurveydidnotyieldasystematicpictureoftheoccurrenceofcertain
stratigraphicfeaturesinrelationtolocalclimateconditions.Theindividualdescription
anddifferentmeasurementmethodsareoftenverydetailedandinformativebutdonot
alwayspermitacomparativeanalysis(Figure6.8).Eventhoughsomefeaturesmightbe
detectablefromthedistributionofcertaincharacteristics(Figure6.8),aninterpretation

isnotpossible:iftheoccurrenceofforexamplesignsforahiatusinaccumulationare
notreportedforasite,itdoesnotmean,thatthereisnohiatusatthissites.Itjust
indicates,thattheauthorsdidnotnotice,sincethefocusofthestudyandtheobservers
wassettoothertopics.
Thehighresolutiondensitymeasurementsallowacomparisonofthelayeringnotonly
atthesurfaceofthedifferentsites,butalsoatthedepth-intervalofthefirn-ice-transition.
Inthisstudythestandarddeviationistakenasameasureforthelayeringofasite
andbythatacomparisonbetweendifferentsitesispossibleinanobjectiveandrepro-
ducibleway.Asproxyofthelocalclimateconditions,theannualmeantemperature,
theaccumulationrate,themaximumtemperaturegradients(endofsummer)within10
cmdepth-intervals,asobtainedfromsurfacetemperatureobservations,andthetime,
alayerspendswithina10cmdepthinterval(determinedfromaccumulationrate)are
en.takThesurfacedensityvariabilityisdecreasingwithincreasingannualmeantemperature
andaccumulationrate(Publication1),whereasthedensityvariabilityatthefirn-icetran-
sitionisincreasingwithincreasingannualmeantemperatureandaccumulationrate.
Thediversebehaviorofthestandarddeviationwithdepthindicatesthedifferentpro-
cessesinfluencingthemicrostructure.Mainlythegrainsizeisdisplayingthevariability
duetothelayeringsimilarthandoesthedensity.Thesurfacetrendingrainsizevari-
abilityissimilartothetrendindensityvariability(Figure6.9).Lowaccumulation(low
temperature)sitesshowahighervariabilityingrainsize,thanhighaccumulation(tem-
perature)sites(Figure6.9).Theincreaseinporessize(Figure6.7a)andporesize
variability(Figure6.10a)withdepthtowardsamaximumbetween2-4meterdepth,in-
dicatingthecoarsening,canbeobservedatalmostallfirncoresites.OnlytheB38core
doesnotshowanymaximuminabsolutevaluesoranincreaseinvariability.Thepore
chordlengthandanisotropyvariability,asanexample,arehighestfortheGreenland
B26siteatthesurface,followedbythecoldAntarcticsites.However,todeterminethe
layeringandtheresultingvariabilitynotallmicrostructureparameterseemtobeuseful.
Grainsizeissuggestedasaparameter,displayingthelayering,asitisgeneratedatthe

eFigur

6.8:

Example

of

the

eliteratur

.survey

Dark

blue

points

esenteprr

inliteratureintermsofstratigraphy,andsites,where

servationwasreported,arehighlightedinlightblue.

entiationferdif

is

possible

omfr

observations.these

sites

belowthe

Not

that

described

ob-stated

no

egionalr

Figure6.9:ThestandarddeviationofReffoftheupperdepth-intervalswithannual
meantemperature(a),accumulationrate(b),temperaturegradientatthe

surfaceinlatesummer(c)anddurationtimewithin10cm(d)

surfaceandwhichiscorrelatedtodensity.Poresize,anisotropyandairpermeability

donotonlyvarybecauseoftheinitiallayeringbutchangetheirvariabilityasaresultof

ing.sinterandcoarsening

Thevariabilityofthedifferentmicrostructurepropertiescanbehavedynamicallywith

depthatasinglesite.Thedegreeinvariabilityatthesurfaceandtheevolutionwith

depthdiffersignificantlyforthedifferentsites.Thisverydifferentimplementationand

evolutionofvariabilityatthedifferentsitescanhelptounderstandtheobserveddiffer-

enceinbackscatterbehaviorofdifferentfirntypes.Notonlythedegreeinlayeringbut

alsothevariabilityingrainsizewithinacertaindepth-intervalwillalterthebackscatter

6.10:eFigur

with(b)opyanisotrand(a)lengthdchoreporofdeviationdstandarThe

depthforthedifferentsites.

ofmicrowaves.Thequantificationofvariabilityobtainedinthisstudycanbeusedto

identifythefirncharacteristicsgeneratingcertainbackscatterbehaviorinfutureinvesti-

.gations

ContributionTopicE:Themostcommonideainliteratureis,thathighaccumulation

ratesitesshowahigherdegreeinlayeringandthusahighervariabilityindensitythan

lowaccumulationratesites.Thedatapresentedhereshow,thatthevariabilityishigher

atlowaccumulationandlowtemperaturesites.Thisiswelldisplayedinthemicrostruc-

turevariability(Publication3)anddensityvariability(Publication1).Hightemperature

accumhighandulation

Grainsizeanddensity

kscatterbac

viorbeha

of

sitesshowlessvariability

iabilityrav

the

firn

ni

inentakbecan

erentdiff

regions

bothinanddensity

futuretheto

of

Antarctica.

better

.ucturemicrostr

understand

the

7lusionsConc

WithhighresolutiondensitydataandmicrostructureinformationfromX-ray-microfocus-
computer-tomographythelayeringcanbedescribedandquantifiedbyusingthestan-
darddeviationasparameter.Itisshown,thatlowaccumulationandannualmeantem-
peraturesitesarecharacterizedbyalargerdegreeoflayeringthanhighaccumulation
andannualmeantemperaturesites.Buttheyalsoshowanincreasedcoarseninginthe
upperfirnmeters,inducinganincreaseinporesizeandpermeabilitydownto2-4meter
depths.Despitetheincreasedlayeringandthusvariabilityindensityandmicrostruc-
ture,theairpermeabilitycanbelargerandtheconvectionzonemoreextended,than
atsiteswithhigheraccumulationrateandlesslayering.Lowaccumulationsitesshow
largestsurfacevariability,whereashighaccumulationsitesshowlargestvariabilityat
thedepthintervaloftheseconddensityvariabilitymaximumandthefirn-ice-transition.
Theresultsofthisstudypointout,thatthestratigraphy,i.e.theamplitudeandthefre-
quencyofthedensityvariability,isnotaconstantpropertyoffirn,whichiscontinuously
buriedinthefirncolumnwithdepthandtime.Theoriginalsurfacedensityanditsvari-
ability,theoriginalsurfacegrainsizeanditsvariabilityandincorporatedimpuritiesas
wellastheinteractionofthefrequenciesofthedensityvariabilityandimpurityconcen-
trationvariabilityconfigurethedynamicevolutionofthelayeringofthefirnwithdepth.
Theexpressionoflayeringinthemicrostructurepropertiesischangingwithdepthand
time.Theinitialmicrostructurevariability,createdatthesurfacebydepositionissuper-
posedbytheinteractionofsinteringordensificationandcoarsening.Thisinterplayis
governedbythelocalclimateconditionsandinducesdifferencesinthecorrelationof
densityandmicrostructure,suchasgrainsizeorspecificsurfacearea.Thefindings

57

ofthisstudyimply,thatthelayeringhasnostaticmemory.Thelayeringisnotkept

constantlywithdepthandsequencesoflayersfromthesurfacedonotcorrespondto

similarsequencesoflayersatthefirn-ice-transition.Theprimarysurfaceinformation

suchasstartingdensity,microstructureandimpuritycontentdeterminethesubsequent

evolutionofthelayeringwithdepth.Butthereisnolineartransformationofsurface

propertiestogreaterdepths.Anylinkofsurfacepropertiesintermsoflayeringtolocal

climateconditionscannotbedirectlyextrapolatedtothepropertiesatthedepthofthe

firn-icetransitionandviceversa.

Thelayeringofpolarfirnshowsarandomgenerationatthesurfaceandaverydynamic

evolutionwithdepth,whichisinfluencednotonlybythemicrostructureandthelocal

climateconditionsbutalsobyimpuritiesincorporatedintothefirnatthesurface.

8ProblemsandOpenTopics

Methodical8.1limitations

Thelimitationsofthemeasurementsofhighresolutiondensityandmicrostructurefrom
X-ray-microfocus-computer-tomographyanalysisareshortlydiscussedhere.
Hoarlayers,asoftenobservedinthefieldtoformbelowthesurfaceorthinicecrustsare
difficultorimpossibletodetectwiththegammaabsorptionmethod.Hoarlayersform
looseandveryfragilefirnlayerslayersandgetdestroyedduringthedrilling,transport
andmeasurementprocedure.Icecrustsareverythin,ofteninarangeofonemmand
arethereforenotdetectablewiththeresolutionandmeasurementsetupusedinthis
study.Thisgivesadefinitelimitationofthemethod.
Theproblemofmissinglowdensitylayersduetothedrillingandmeasurementproce-
durecouldhaveaneffectonthecalculatedvariabilityvalue,i.e.decreasedvariabilities
duetolackingextremevaluesinthelowerrange,oronthefrequencyanalysis,since
missingpeakscouldchangetheobservedfrequency.Itcanbeassumed,thatdueto
theveryhighnumberoffirncoresincludedinthisstudy,andtheverybroadrangein
localclimateconditions,thesefirncoresrepresent,anyirregularitiescanbeneglected.
However,onlymeasurementsofcompletefirncoresectionsinoriginalconditioncan
provethesefindings.Thereforeadrillingdevice,whichisabletocapturefragilelow
densitylayers,especiallyfromlowaccumulationareas,isneeded,inordertogetmore
completefirncorepiecesfordensityanalysis.
TheX-ray-microfocus-computer-tomographymeasurementsallowamorecarefulhan-

59

dlingoffragilefirnsamples,butthelimitationinsampleresolutionanddiscontinuity
leadstoadifferentcalculationofstandarddeviationofthemicrostructure.Inorder
tocomparethevariabilityofdensityandmicrostructure,highresolutioncontinuous
measurementsofmicrostructurepropertiesarenecessary.Thenewlyinstalledice
coreX-ray-microfocus-computer-tomography-scannerattheAlfred-Wegener-Institute
(J.Freitag)enablesacontinuoushighresolutionmeasurementofboth,densityandmi-
crostructureandthereforprovideamuchmoredetailedimageofthelinkandevolution
.tiespropertheseofNexttodensityandgrainsizeimpuritiesseemtoplayanimportantroleinthewhole
processofsinteringanddensificationofpolarfirn.Inordertounderstandtheinter-
actionofimpurities,densityandmicrostructurethedatasetofhighresolutiondensity
andmicrostructureneedstobecompletedwithhighresolutionionmeasurementsfrom
ContinuousFlowAnalysis.Fromtheresultofthisstudy,themergeofthesethreedata
setsseemstobethemostchallengingandmostessentialstepinthenearfuture.

"Global"8.2ostructuremicr

ThemicrostructuredataoftheX-ray-microfocus-computer-tomographymeasurements
allowanintensestudyofpolarfirnmetamorphism,duetothelargerangeinlocalcli-
mateconditionsrepresentedinthisdataset,andthelargeagedistributiontheycover.
Thebasicideaistofindaglobaldescriptionofthemetamorphismprocess,whichen-
ablesadirectcomparisonofthemicrostructureofdifferentsites.Thereforethedegree
orstageofmetamorphism,i.e.ametamorphosefactor,needstobederived,includ-
ingnotonlylocalclimateconditions,butalsothelocaltemperaturegradientsatdifferent
depths,thetimeacertainfirnlayerspendswithinthesedifferenttemperaturegradients,
andage.Firsttestsweredone,butnosufficientdescriptionforthemetamorphosefac-
torwasobtainedyet.Thisneedstobecontinuedinfuturestudies.
However,thedatashowasurprisinglydefinitebehaviorintermsofshape.Inorder
tocomparetheshapeoftheicegrainsorstructureofthedifferentfirnsamples,the

structuremodelindexiscalculated(Figure8.1).Withdecreasingporositytheindex
decreasesfromvaluesaround2tovaluesofapproximately-3.Themoststrikingfeature
is,thatdespitetheirverydifferentgrainsizesandlocalclimateconditions,almostall
samplesofallfirncoresitesfollowadefinedline.OnlyathighporositiestheDP7
samplesscatteraround1.AndatlowporositiesB38samplesscatteratvaluesabove
zero,eventhoughallothersamplesshownegativevaluesatsimilarporosities(Figure
8.1).Itseemsthatthereisaclearlinkbetweenporosity,whichisanindicatorfordensity
andthusdepthandtime,andthestructureoftheicephaseofthefirn.
Forhighporosityfirn,theicephaseshowseithersinglegrainsorbondedgrains,with
sinterednecksandanoverallconvexstructure.Veryfreshsurfacesnowwithdendritic
shapesorcupshapedhoarcrystalswouldshowevenhighervaluessuchasthesnow
fromDP7.Asolderthesnow,theicephasebecomessmoother.Towardsdecreased
porositytheicephasebecomesasolidmatricwithporesincluded.Thusthesurfaceof
theicecanbeexpectedtoturntoconcavevaluesfortheindex,sinceitisthenenclosing
thepores.TheB38firnisburiedsofastduetoitsoutstandinghighaccumulationrate,
thatthestructurehasnotimetoevolvemucheventhoughporosityisdecreasingrapidly.
Accordinglytheshapeofsinglegrainedmatrixiskeptevenatverylowporosities.
Nevertheless,allotherfirncoresitesshowaremarkablyuniquepatterninthisstructure
modelindexandporosity.Despitetheirextremelydifferentlocalclimateconditions,
densityprofilesandmicrostructureevolution,agloballysimilarbehaviorinshapecan
beextractedfromthedata.Thisshapecouldbeanindicatorofthedegreeofsintering
atacertainporosityofpolarfirn.
Thisfindingisafirsthintforasimilartopologicalevolutionofpolarfirnstructureunder
snowmetamorphism,eventhoughthelocalconditionsdiffersignificantly.Futurestud-
iescouldconcentrateonthedeterminingfactors,thatcontrolthestructureevolutionof
thefirn,especiallyunderconsiderationofthemetamorphosefactor.

8.1:eFigur

ucturstrThetheNotesamples.andsitesallofosityporwithindexmodele

highvaluesatlowporositiesoftheB38firncoreandthescatteredvalues

athighporositiesoftheDP7site.

8.3Convectionoftheupperfirn

Theventilationoftheuppersnowandfirnpackisdifficulttoaccess,sinceitincludesa

horizontalcomponent,whichcannotbeaddressedwithfirncorestudies.Horizontally

permeablefirnlayerscanleadtoaintenseventilationofthefirn,evenwhentheyare

buriedunderlesspermeablelayers.Oftenfirnlayersshowaratherdiscontinuousextent

andundulations,whichenabletheconvectionwithinthefirnunderhorizontalpressure

gradients.Thisproblemisevenmoreemphasizedbythereportedobservationofnets

ofcracksintheuppersnowandfirnlayersatextremelylowaccumulationratesites.

Thesecracksformdeepverticalchannelsinthefirnandintroduceamuchmorecom-

plexandlargerscalephenomenonofairventilationthancanbeanalyzedwithsingle

pointfirncoremeasurements.However,consideringlessextremeconditions,linking

measurementsofmicrostructureanddirectmeasurementsofairpermeabilitycande-
liveracoarseunderstandingofthemagnitudeoftheabilitytoventilateairinconnection
tosnowmetamorphismatthedifferentsites.Thedirectmeasurementofairperme-
abilityofpolarsnowandfirnisrathertime-consumingandtimeextensive.Therefore
formerstudiestriedtolinkmicrostructurecharacteristicstoairpermeability,inorderto
parameterizeairflowwitheasy-to-measuremicrostructureproperties.
With3-DX-ray-microfocus-computer-tomographyinformationnotonlyoftheporesize
butalsoofthetortuosityandconnectivityoftheporescanbeobtained.Firsttestsyield,
thatsimpleempiricalrelationshipscanfairlywellpredictlowtomediumpermeabilityval-
uesandthevariabilityofpermeabilityduetothelayeringtoacertaindegree.Buthigh
permeablelayersarealwaysunderestimated,sincesimplemicrostructureproperties
donotdisplaytheexistenceoflargeairpathwayswithinthesample.Withtheavailable
datasetoftwodirectlymeasuredpermeabilityprofilestogetherwith3-Dmicrostruc-
tureanalysis,acomprehensivestudycanbeconductedandevenextendedonmore
firncoresites,whereonlymicrostructuredataareavailable.Thisispartofafuture
projecttogetherwithDr.ZoeCourvillefromColdRegionResearchandEngineering
Laboratory,USA.Poresizedistributionsincomparisontotortuositymeasurementsand
directpermeabilitymeasurementscanimprovetheunderstandingoftheconnectionof
airpermeabilityandmicrostructureandtheoverallpictureoffirnconvection.
Theoverallgoalcouldbetodeviatearoughestimationoftheextentoftheconvection
zonebyknowingthedepth,atwhichmaximainairpermeabilityareobtainedatthedif-
ferentsites.Ifitispossibletomodeltheairpermeabilitywiththeavailablemicrostruc-
turedata,thanthesetoffirncoresinvestigatedinthisstudyallowsacomparisonof
thesnowmetamorphisminconnectiontothecoarsening,thedevelopmentoftheair
permeabilitymaximumwithdepthandthelocalclimateconditions.Thisinturnwould
helptounderstandtheformationandextensionofaconvectionzoneatthedifferent
locationswithdifferentclimateconditions,evenextendedtoglacialtimes.

9Acknowledgement

ThisworkisfundedbytheDeutscheForschungsgemeinschaft(DFG)grantFR2527/1-
1.IverymuchthankmysupervisorsProf.HeinrichMillerandProf.KatrinHuhnfor
theirsupportandcomplaisantguidanceinthelastyears.
IamverygratefultoProf.MaryAlbertandDr.ZoeCourvilleforalong-lastingandfruitful
cooperation,aninvitationtoGreenlandandmanyhelpfulcommentsandexchangeof
ideas.Theprojectwouldhavebeenmuchlesscolorfulwithoutyou.Thankyouso
much.Noexpeditionwithoutlovelyfancypeople-thankstotheNEEM-Traverseteam
2007foragreattimeandmuchpatiencewithusandourrollingcoffeebar.Andthanks
totheunforgettablebest"Snow-freaks"teamever(Zoe!),forthegoodtimeandthe
goodjobatSummitStationandapolarbearnecklace.
AlargethanksisduetoDr.JohannesFreitagandDr.SeppKipfstuhlforthelongsome
supportofandindailylife.Muchoftheprogressofthisthesisisduetoyourunbowed
abilitytochallengewell-believedtheories.
Dr.SergioFariahasnotonlyspendmuchtimeinunderstandingtheproblemsand
helpingwiththisthesis.Healsofoundtherightwordsattherighttime(moreoften,
thanhethinks).Thankyouverymuch,Sergio.
IwarmlythankPeterSperlichforbeingthemostrelaxedofficemateandthebestexpe-
ditionmateonecanimagine-Ihavelearnedalotfromyou.Forherfriendshipandher
muchneededcompanyinourofficeIthankKatrinWolff.Fortheirfriendship,theoffer
togethelpandanswersallthetimeandthebest"monday-motivation-cake"IthankIlka
WeikusatandBirtheTwarloh.Mycomputerandmewouldhaveneverbecomebest
friendswithouttheunwearyhelpofChristineWesche,thanksforthatandeverything

65

elseyouhelpedwith,nomatterwhattimeoftheday.Daysandnightsinthecoldlab

canalsoturnouttofeellikeanexpeditionandIverymuchthankAndreasFrenzelfor

hiscompanionshipandnever-endingsupportatgoodandatbaddays.Icannotname

allmembersoftheAWI-glaciologygroup-Ithankyouallforagoodtimeandthebest

coffeeonearthandIwishyouallthebestforthefuture.

LastbutnotleastIthankProf.Dr.h.c.Sauerbreyand

andsupport,whichenabledmefinishingthethesis.

aurF

.Dr

Bohnet

rof

their

usttr

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JOURNALOFGEOPHYSICALRESEARCH,VOL.???,XXXX,DOI:10.1029/,

1Thedensificationoflayeredpolarfirn

M.W.H¨orhold,1S.Kipfstuhl,1F.Wilhelms,1J.Freitag1A.Frenzel1

M.W.H¨orhold,AlfredWegenerInstituteforPolarandMarineResearch,AmHandelshafen
12BuildingD,Bremerhaven,D27568,Germany.(Maria.Hoerhold@awi.de)
S.Kipfstuhl,AlfredWegenerInstituteforPolarandMarineResearch,AmHandelshafen12
BuildingD,Bremerhaven,D27568,Germany.(Sepp.Kipfstuhl@awi.de)
F.Wilhelms,AlfredWegenerInstituteforPolarandMarineResearch,AmHandelshafen12
BuildingD,Bremerhaven,D27568,Germany.(Frank.Wilhelms@awi.de)
J.Freitag,AlfredWegenerInstituteforPolarandMarineResearch,AmHandelshafen12
BuildingD,Bremerhaven,D27568,Germany.(Johannes.Freitag@awi.de)
A.Frenzel,AlfredWegenerInstituteforPolarandMarineResearch,AmHandelshafen12
BuildingD,Bremerhaven,D27568,Germany.(Andreas.Frenzel@awi.de)

1AlfredWegenerInstituteforPolarand
MarineResearch,Bremerhaven,Germany

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X-2H¨ORHOLDETAL.:DENSITYVARIABILITY
2Abstract.High-resolutiondensityprofilesof16firncoresfromGreen-
3landandAntarcticaareinvestigatedinordertoimproveourunderstanding
4ofthedensificationoflayeredpolarfirn.Averticalresolutionof1to5mm
5enablesustostudythedetaileddensificationprocesses,andtheevolution
6ofthelayeringandtheresultingvariabilityindensitywithincreasingdepth.
7Thedensificationoflayeredfirnisimportantfortheprocessofairenclosure
8iniceandisconnectedwiththeobservedformationofanon-diffusivezone.
9Wefindthat(1)meandensityprofiles,obtainedfromhigh-resolutionmea-
10surements,onlypartlyshowcleartransitionsindensificationrateatdensi-
11tiesof550,730or820-840kg/m3,astheyarecommonlyusedinliterature.
12(2)Thedensityvariability,inducedbythelayering,showsasimilarpattern
13atallsites:highvariabilitiesatthesurface,arapiddroptoarelativemin-
14imuminvariabilityatmeandensityof600-650kg/m3,followedbyasec-
15ondrelativemaximum.(3)Thisleadstoincreasedvariabilityatdensitiesof
16thefirn-icetransitionformostofthesites.(4)Thevariabilityatthesurface
17decreaseswithincreasingmeanannualtemperatureandaccumulationrate,
18whereasthevariabilityatthefirn-icetransitionincreases.Wecanexclude
19achangeinlocalclimateconditionsasanexplanationforthedensityvari-
20abilitysincethefirncoresinthisstudycoverabroadrangeinmeanannual
21temperature,accumulationrateandage.Overall,high-resolutiondensitypro-
22filesdeliveramorecomplexpictureofcompactionofpolarfirnasalayered
23granularmediumthanhasbeenobtainedfrommeandensityprofilesinthe
past.24

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H¨ORHOLDETAL.:DENSITYVARIABILITY

X-3

ductiontroIn1.25Density,asaphysicalpropertyofpolarfirn,isimportantnotonlyasamaterialcharac-
26teristic,butformanytopicsofpolarresearch.Thisincludesthemonitoringandmodeling
27oficesheetmassbalance,bymeansofground-penetratingradarorsatellitelaseraltimetry
28[LiandZwally,2002,2004;Rottetal.,1993;Rotschkyetal.,2006],andtheenclosureof
29airbubblesintheiceduringthetransformationfromsnowtoice[Martinerieetal.,1992;
30Schwanderetal.,1997].
31Differentdensificationprocesses,actingatcertaindepthintervalsofthefirncolumn,
32havebeeninvestigatedanddiscussedbyothers[AndersonandBenson,1962;Alleyetal.,
331982;MaenoandEbinuma,1983;Alley,1987;EbinumaandMaeno,1987;Paterson,1994;
34Arnaudetal.,1998;Salamantinetal.,2009].Mean”critical”densityvaluesof550,730
35and820-840kg/m3areoftendenotedforchangesinthepredominanceofmicro-scale
36processes.Examplesareparticlerearrangement[Gow,1974;HerronandLangway,1980;
37EbinumaandMaeno,1987;Paterson,1994;Salamantinetal.,2009],grainboundary
38sliding,recrystallization,creep[MaenoandEbinuma,1983;EbinumaandMaeno,1987]
39andairbubbleshrinking[Gow,1974;Martinerieetal.,1992].Yettherearehintsthat
40thesecriticaldensitiesvaryconsiderablyfordifferentsnowandfirntypes[Alleyetal.,
411982;Johnson,1998;Freitagetal.,2004].Deformationandgrainboundaryslidingseem
42tooccurconcurrentlyfromtheverybeginningofcompaction[Arnaudetal.,2000],and
43grainboundariesinmicrostructureimagesshowsignaturesofdynamicrecrystallizationin
44shape,orientationandnumberratherthanstructuresresultingfromnormalgraingrowth
45[Kipfstuhletal.,2009].Modelsoffirndensificationusuallyconsiderameandensityprofile

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X-4H¨ORHOLDETAL.:DENSITYVARIABILITY
46[HerronandLangway,1980;Barnolaetal.,1991;Arnaudetal.,1998,2000;Goujonetal.,
472003].Theevolutionofdensitywithdepthisoftenlinkedtomeanannualairtemperature,
48accumulationrateandsurfacedensity[HerronandLangway,1980;MaenoandEbinuma,
491983;Martinerieetal.,1992],overburdenpressure[Kamedaetal.,1994]orsurfacewinds
50[CravenandAllison,1998].
51Polarfirnisahighlylayeredmediumandthusexhibitsheterogenousmaterialproperties
52[Gow,1974;HansenandBrown,1986].Stratigraphyiscreatedbyseasonalchangesof
53thelocalclimaticconditions.Athighaccumulationsitesthestratigraphyismadeby
54layersfromsinglesnowfallordriftevents,whileatlowaccumulationsitesmostlikely
55onlysummerandwinterprecipitationcreatestratigraphy.Layerscanbedistinguished
56notonlybytheirbulkdensitybutalsobygrainsizeandshape,hardness,viscosityand
57coordinationnumber.Accordingly,variabilityinsuchdifferentpropertieswillleadto
58differentresponsetopressureloads[Palaisetal.,1982;HansenandBrown,1986;Johnson,
591998;Alleyetal.,1982].
60Furthermore,theincreaseindensityseemstovarynotonlywithinthefirnlayersbut
61alsowithtime.ZwallyandLi(2002)observeseasonalvariationsinice-sheetelevationand
62linkthesetovariabledensificationratesthroughtheyear.Thevariabilityindensification
63iscausedbyseasonallychangingtemperaturesandaccumulationrates.Theirmodelsshow
64thattheamplitudeofdensityvariabilityincreaseswiththeaccumulationrate,whereas
65thefrequencydecreaseswithincreasingaccumulationrate.Thisvariabilityvanisheswith
66depth[LiandZwally,2004].
67Thelayeringandtherelatedvariabilityindensityisanimportantfactorwhendiscussing
68theagedifferencebetweenairenclosedinbubblesandthesurroundingice.Aslongas

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69theporesareconnectedwiththesurface,anexchangewiththeatmospherebydiffusionis
70possible.Thedepth,andthusage,whenporeclose-offisexpected,isoftenderivedusing
71meandensitycriticalvalues[Martinerieetal.,1992;Schwanderetal.,1997].However,
72consideringlayering,andthusdensityvariability,consequentlyleadstodepthintervals
73wheresomelayershavealreadyreachedtheporeclose-offdensity.Otherlayersstillshow
74connectedpores.Thisdepthintervalisoftenreferredtoanon-diffusivezone,whereaircan
75escapeupwardsbutnodownwardairexchangeispossible.Itiscommontointerpretthe
76high-densitylayers,whichapproachtheporeclose-offdensityfirst,astheinitiallyhigh-
77densitylayersoriginatingatthesurface(oftenreferredtowinterprecipitation)[Martinerie
78etal.,1992;SeveringhausandBattle,2006].
79Recently,thedegreeoflayeringhasbeenconsideredasaparameterinfluencingthe
80extentofthenon-diffusivezone.Landaisetal.(2006)suggestthatstronglayering,asis
81expectedforhighaccumulationsites,resultsintheexistenceofanon-diffusivezone.At
82lowaccumulationsites,thelayeringvanishesatthesurfaceandanon-diffusivezoneisnot
83expected.AlsoKawamuraetal.(2006)suggestthatthethicknessofthenon-diffusive
84zonegenerallydependsontheamplitudeofdensityvariabilityduetothelayeringatthe
85surfaceandthehorizontalextentofsinglelayers,typicallygeneratedbyseasonalvariations
86ofdepositedsnowdensity.
87Densityvariabilitygeneratedbylayeringcanbeinvestigatedbyusinghigh-resolution
88densitymeasurements.Weusethetermhigh-resolutiontorefertoaverticalresolution
89of1to5mmwithdepth,whichismuchhigherthanthetypical1maverages.This
90resolutionissmallcomparedtothethicknessofsinglelayers,whichisusuallyfoundto
91beintherangeofseveralcm.High-resolutiondensitymeasurementsofpolarfirnwere

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X-6H¨ORHOLDETAL.:DENSITYVARIABILITY
92publishedbyGerlandetal.(1999)fortheB25corefromBerknerIsland,Antarctica,and
93byFreitagetal.(2004)fromsiteB26,Greenland.Bothobservedthatthevariability
94decreasesrapidlyintheupper20-30m.Below,thevariabilityincreasesagain,yieldinga
95secondrelativemaximum.Gerlandetal(1999)alsofoundanegativecorrelationbetween
96densityandelectricalconductivitymeasurements(ECM)intheupperfirncolumn,which
97changedat30mdepthtoapositivecorrelation.HawleyandMorris(2006)published
98highresolutionprofilesofboreholedensityloggingtechniquesandopticalstratigraphyat
99Summit,Greenland.Theyfindapositivecorrelationbetweenopticalbrightnessreflections
100anddensity,whichdecreaseswithdepthandturnstoanegativecorrelationbetween20
depth.m25and101102Gerlandetal.(1999)andFreitagetal.(2004)explainedthesecondrelativemaxi-
103mumindensityvariabilitybythemoreefficientdensificationofcoarsegrained,initially
104low-densityfirn,comparedtofinegrained,initiallyhigh-densityfirn.Thiswouldlead
105toacrossoverinthedensityprofiles.Thedepthatwhichthedensitiesofcoarseand
106finegrainedfirnareapproximatelyequalisassociatedwiththeminimumindensityvari-
107ability.Thisobservationindicatesthatbelowthevariabilityminimum,theinitiallylow
108densityfirnlayersshowhigherdensitiesthantheinitiallyhighdensityfirnlayers,which
109wouldexplaintheswitchintheECM-densitycorrelation.Otherauthorsconsideredthis
110secondmaximumindensityvariabilityasasingularabnormalfinding,possiblyduetoin-
111terannualchangesinweatherconditions[LiandZwally,2002].HawleyandMorris(2006)
112explainthechangefrompositivetonegativecorrelationbetweendensityandbrightness
113bythetransitionfromgrainboundaryslidingtopressuresinteringasthedominantfirn
114densificationmechanism.Recently,discontinuoushigh-resolutionprofilesofdensityand

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115crystalorientationofafirncorefromDomeFujiwerepublished[Fujitaetal.,2009]show-
116ingaswitchfrompositivetonegativecorrelationbetweendensitymaximaandstructural
117anisotropyat30mdepth,supportingtheideasofGerlandetal.(1999)andFreitaget
al.(2004).118119Thesepublicationspresentedtheresultsoffirncoresfromsinglesites.Inthisstudywe
120extendtheworkbyGerlandetal.(1999)andFreitagetal.(2004)with14morefirncores
121fromGreenlandandAntarctica,coveringabroadrangeoflocalclimateconditions.High-
122resolutiondensitymeasurementsareobtainedwiththegamma-attenuationmethod.We
123shortlydiscussthepossibleimpactofmicrostructureandimpuritiesonthedensityand
124densification.Atthispointwecannotprovetheroleofmicrostructure(onagrain-scale)
125inthisstudysincenomicrostructuredataareavailablewiththisresolution.However,the
126availabledataallowaprofoundexaminationofmacro-structuralpropertiesofthefirnand
127thedensification.Ourhigh-resolutiondensitymeasurementsrevealthefollowingresults:
1281.Meandensityprofilesobtainedfromhigh-resolutionmeasurementsdoonlypartly
129displayatransitionindensificationrateat550,730and820-840kg/m3.
1302.Allfirncorespresentedhereshowasecondmaximumofdensityvariability,asfirst
131reportedbyGerlandetal.(1999).Accordinglyaneffectofchangesinlocalclimate
132orweather,assuggestedbyLiandZwally(2002),canbeexcluded.Theminimumin
133variabilityisreachedatmeandensitiesaround600-650kg/m3,whilethemeandensity
134andamplitudeofthesecondmaximuminvariabilityvariesfromsitetosite.
1353.Amoreefficientcompactionofinitiallylessdenselayersleadingtoacrossover,as
136suggestedbyGerlandetal.(1999)andFreitagetal.(2004),canexplaintheobserved
137densityvariabilityandtheswitchincorrelationofdensitytoECMandbrightness.This

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X-8H¨ORHOLDETAL.:DENSITYVARIABILITY
138processofdifferentialcompactionalsomeansthattheinitiallydenselayersfromthe
139surfaceexhibitlowerdensitiesatthefirn-ice-transition.Thehigh-densitylayerswhich
140createasealingeffectatthefirn-icetransitionmightoriginateaslow-densitylayersatthe
surface.1411424.Thevariabilityatthefirn-icetransitionincreaseswithincreasingmeanannualtem-
143peratureandaccumulationrate,whereasthevariabilityatthesurfacedecreases.Low
144accumulationsitesalsoshowrelativelyhighnear-surfacedensityvariability.Thisobser-
145vationgivesreasontoquestionadirectlinkbetweenthedegreeofsurfacelayeringand
146theextentofanon-diffusivezone.

dsMetho2.tInstrumenandMaterial2.1.147Thehigh-resolutiondensityprofilesof16differentsitesfromGreenlandandAntarctica
148areinvestigated.Thefirncoresweredrilledandmeasuredinatimeintervaloveralmost
14920years.Thefirncoresarefromareaswhichcoverabroadrangeinmeanannualsurface
150temperature,accumulationrateandelevationandoriginfromGreenlandandAntarctic
151PlateauregionsbutalsofromAntarcticcoastalregions.ForfurtherdetailsseeTable1
2.ableTand152153Thedensitywasmeasuredusinganon-destructiveloggingsystemincludingaL¨offel
154densimeter[Wilhelms,1996].ThemeasuredintensityIoftheattenuatedgamma-ray
155beamthroughtheicecoreisconvertedintoadensitysignal.UsingBeer’slaw,the
156intensityofthebeaminairI0,themassabsorptioncoefficientμice=0.085645m2kg−1±
1570.1%[Wilhelms,1996,2000]andthediameterdoftheicecore,thedensityρcanbe
:ybcalculated158

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X-9

I1−ρ=d·μ·ln(I0)(1)
159DetailsandbackgroundofthemethodaregiveninWilhelms(1996;2000).Gerlandet
160al.(1999)andFreitagetal.(2004)discusseddensitydataobtainedbythismethodand
161comparedittodensityprofilesobtainedwithcomputer-tomography[Freitagetal.,2004].
162Usuallytwoonemeterlongcorepiecesareputinacradleforameasurementrun.The
163diameterismeasuredevery10cmmanuallywithacalliperandtheninterpolatedoverthe
164lengthofthecorepiece.Scratchesfromcorecatchersandbreaksaredocumented.All
165measurementswereconductedbetweentemperaturesof-10◦Cand-35◦Ceitherinthe
166coldlaboratoryoftheAlfredWegenerInstitute(AWI),Bremerhaven,Germanyorinthe
167field,usingacomparablemeasurementsetup.

2.2.cessingProData168Afterthemeasureddiameterisinterpolatedandusedtocalculatethedensityaccording
169toequation(1),therawdataarecorrectedforcorebreaksandscratches,bymanually
170removingsingleoutliersandlinearlyinterpolatingovertheresultingdatagaps.
171Twodifferentprocessingstrategiesareused.First,thedensityversusdepthprofileis
172investigatedandaveragevaluesarecomparedtofielddataandtotheHerron-Langway
173model[HerronandLangway,1980].Themeasuredrawhighresolutiondensityisshown
174inFigure1A(lightgrey).Arunningmeanusingaslidingwindowofonemeterlength
175iscalculated(Figure1A,darkgreyline).Comparisonwithfielddataofonemeterlong
176icecoresectionsyieldsgoodagreement(Figure1A,brownline).Themeandensitydeter-

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177minedfromhigh-resolutionmeasurements,notedasmeandensityinsections3.1and4.1,
178iscomparedtodensityvaluescalculatedfromtheHerron-Langwaymodel.
179Secondly,thedensityprofileisconvertedtowaterequivalentdepth(mw.e.).Again
180averagevaluesarecalculatedaswellasastandarddeviationasameasureofdensity
181variability.Theconversionleadstounequaldistancesbetweendatapoints(i.e.low
182densitysnowatthesurfacecorrespondstosmallerincrementsinmw.e.depththanhigh-
183densityfirnatgreaterdepths).Thereforeeachdensityprofileisre-sampledtoequidistant
184pointsasnotedinTable2(columnpoint-distance),dependingonthesamplingrateof
185themeasurements(Figure1B,lightgreyline).
186Theconversionfromactualdepthtowaterequivalentdepthenablesacomparisonofthe
187layersfromthenear-surfaceareawithlayersfromgreaterdepths,sincetheeffectofthe
188thinningoflayersduetocompactionistakenintoaccount.Furthermorethewaterequiv-
189alentdepthscaleprovidesameasureoftheoverburdenpressureandenablesacomparison
190ofthecoresatsimilaroverburdenpressures.Inordertoremovefluctuationsornoiseon
191smallerlengthscalesthanthelayering,thedataaresmoothedusingamovingaverage
192window(Figure1B,darkgreylinecoveringtherawdata;windowsizeinTable2(last
193column)).Tostudythedensityvariabilitythedataaredetrended,usinganexponential
194fit(Figure1B,blueline):

ρ=y0+A1·exp(−τ1z)+A2·exp(−τ2z)(2)

195Afterdetrending,thestandarddeviationσρ,withaslidingwindowofsizeN=1000and
196astepsizeof500datapoints(Figure1B,brownline)is:

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Ni(ρi−ρ¯)2
(3)=σρN197whereρiisthedensityatpointiandρ¯themeandensityofwindowN.Inorderto
198comparethedifferentcoresandtheirstandarddeviationwehaveseveralpossibilitiesto
199defineN:weeithercalculatethestandarddeviationoverafixedwaterequivalentdepth
200intervaloroverafixedtimeinterval.Theformerresultsinthecomparisonofdifferent
201time-intervals,thelatterinthecomparisonofdifferentdepth-intervals.Wecalculated
202thestandarddeviationbytakingafixednumberofdatapoints(N=1000),overwhich
203thestandarddeviationiscalculated.ForasufficientlylargeN,thecalculatedstandard
204deviationisindependentofthewindowsize.
205Forthesamewindowsize,ameandensityofthedepth-densityprofileinwaterequivalent
206depthiscalculated(Figure1B,yellowline).Thisvalueisthemeandensityatacertain
207depth(mw.e.)correspondingtothestandarddeviationatthisdepth(mw.e.).Inthe
208followingwerefertothisvalueasmeandensityofthedensity-depthprofileinwater
209equivalentdepthsinsections3.2,4.2,4.3and4.4..
210Martinerieetal.(1992)introducedanempiricallinearrelationshipofmeasuredair
211volumeinicecorestoannualmeansurfacetemperatureandthecriticaldensityρcritat
212whichtheairisolationoccurs.Weusethisrelationtocalculatethemeanclose-offdensity
213ρcritatourfirnsites:

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214withρice=917kg/m3thedensityofpureiceandTtheannualmeansurfacetemperature
215inKelvin.Knowingtheclose-offdensity,themeasuredvariabilityσρatthatdensityis
216thendeterminedfromthemeasurements.
217Totesttheassumptionofarelationshipbetweenthelayeringatthesurfaceandthe
218extentofthenon-diffusivezone,wecomparethedensityvariabilityatthesurfacewith
219thedensityvariabilityatthefirn-icetransition.Thelatterisdefinedbythemeandensity
220obtainedfromequation(4)andtherelatedstandarddeviation.Todeterminesurface
221variabilitywefirstdefineintervalsforwhichthestandarddeviationiscalculated.We
222chosetoshowmorethanoneintervaltoillustratetheextremelydifferentaccumulation
223ratesatthesites.Thereforefromeachsite,one-meterdepthintervalsstartingfromthe
224surface(interval1,figure9)to6mdepth(interval6,figure9)areconvertedtowater
225equivalentdepthandthestandarddeviationiscalculatedfollowingequation(3).This
226time,Nisthenumberofpointswithineachoftheonemeterlongintervals.
227Toestimatetherelativeerrorofthedensitymeasurements,theerrorsineachtermof
228equation(1)havetobeconsidered.Therelativeerrorindensityhasbeenestimatedas
2294.24%atthetop2mand1.47%at100mdepthforthecoresB16,B18,B31,B32,B33
230[Wilhelms,2000].Theresultingabsoluteerrorsare10-15kg/m3intheuppermeters
231and8-12kg/m3ingreaterdepths.ForcoresB17,B19andB21,B38,B39,DML95,
232DML97,B36/B37andEDC2therelativeerrorisreducedto1.65%intheupper2m,
233decreasingto0.66%at100mdepth[Wilhelms,1996,2000].Theerrorreducesbecause
234oftheuseofeitherastrongergamma-raysourceorahigherresolutionmeasurement
235[Wilhelms,1996,2000].Thisleadstoabsolutevaluesaround5-6kg/m3foralldepths.
236Thestandarddeviationiscalculatedover1000datapointsandthusaveragesoverthe

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237randomerrorassociatedwitheachsinglemeasurementpoint.Wethereforeassumethat
238thestandarddeviationobtainedbytheprocessingdescribedabovegivesagoodmeasure
239ofthevariabilityindensityduetothedifferentstratainthefirn.Thestandarddeviation
240asatermofdensityvariabilityhasbeenusedbyGerlandetal.1999,Freitagetal.2004
241andFujitaetal.2009.Formoredetaileddiscussionoferrorestimationofthegamma-
242attenuationmethodsee[Wilhelms,1996,2000]and[Bretonetal.,2009].

Results3.yDensitMean3.1.243Themeandensityprofilesobtainedfromhigh-resolutiondataareshownanddiscussed
244withrespecttochangesindensificationrateatdifferentcriticaldensitiesandwithrespect
245topredictedprofilesusingtheHerron-Langwaymodel.
246First,themeasuredhigh-resolutiondensityprofilesoftheB25core[Gerlandetal.,1999]
247andtheB26core[Freitagetal.,2004]aredisplayed,togetherwiththe1maverages(Fig-
248ure2).Thepreviouslypublisheddatawereincludedinthisstudytoshowthatapplying
249theabovedescribedproceduresyieldssimilarresultsasshowninearlierpublications.All
250meandensityprofilesareshownandthecommonlyassumedmeancriticaldensities,at
251whichachangeindensificationrateisexpected,areindicatedwithdashedlines(Fig-
252ure3).ForsomesitestheHerron-Langwaymodelwasusedtopredictdensityandthe
253resultsarecomparedtothemeandensityprofilesobtainedfromhigh-resolutiondensity
4).(Figuretsmeasuremen254255Assumingachangeindensificationrateatthecriticaldensitiesof550,730or820-840
256kg/m3,theslopeofthedensity-depthprofilesshouldshowadistinctchangeatthese
257densities.ThisisexpressedintheHerron-Langwaymodel,wherethedensityincreases

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258withdifferentratesasafunctionofdepthbelowandaboveadensityof550kg/m3[Herron
259andLangway,1980].Hence,eventhoughwedonotconsidertheincreaseindensityas
260afunctionoftime,wecanstudythedensity-depthprofilesintermsofanabruptchange
261intheslope,whenacriticaldensityisreached(Figures3and4).Weobserveaweak
262transitionintheslopeofthedensity-depthprofilesatdensitiesbetween550and580
263kg/m3forhighaccumulationsitessuchasDML95(Figure3),whereasthecoresB26and
264B29showthistransitionatmuchlowerdensitiesbelow500kg/m3;thesameholdsfor
265B36/B37(Figure4).TheB25coreshowsadistinctchangeintheslopeatapproximately
266550kg/m3buttheEDC2coreshowsnoabruptchangeatall(Figure4).Achangeof
267densificationrateat730kg/m3isnotobservedinanyofourdensity-depthprofiles.Alsoa
268distinctchangeat820-840kg/m3isnotapparent,howeveraslow-downindensity-increase
269ispresentfordensitieshigherthan840kg/m3.
270SomeexamplesofthemeandensityprofileandthepredictedprofilesusingtheHerron-
271LangwaymodelareplottedinFigure4.TheprofilesofB25,B29andB26withmoderate
272temperaturesof-27◦Candapproximately-30◦Candaccumulationratesof0.14-0.18m
273w.e.peryeararepredictedfairlywell(B25,B26,andB29),butfortheEDC2site,the
274Herron-Langwaymodeloverestimatesthemeasureddensity.Thisleadstoa5-6meter
275offsetinthedepthatwhichthedensityof840kg/m3isreached.Thefirnisolderwhen
276reachingthisdensitythanthemodelpredicts.Ontheotherhand,theHerron-Langway
277modelunderestimatesthedensificationatB38.Themodelrunendsatameandensityof
278approximately794kg/m3at83mdepth.Thisdensityisobtainedinthemeanmeasured
279profileatadepthofapproximately59m.Thefirnapproachingacertaindensityismuch
280youngerthanpredictedbythemodel(Figure4).

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3.2.DensityVariability
281Thelayeringofpolarfirninducesavariabilityobservedinhigh-resolutiondensitypro-
282files.Thevariabilitychangeswithincreasingdepthandmeandensity(Figure5).The
283standarddeviation,σρ,asameasureofthislayeringisshownaswaterequivalentdepth
284(Figure6A)andwithmeandensityofthedensity-depthprofileinmw.e.(Figure6B).
285ThebehaviorofσρatdifferentlocalclimateconditionsisdisplayedinFigure7.
286Theevolutionofatypicalhigh-resolutiondensityprofile,hereB26,isshownindetail
287(Figure5).B26representsatypicalfirn-coresitefromtheGreenlandplateau,witha
288moderatemeanannualtemperatureof-30.6◦Candaccumulationrateof0.18mw.e.per
289year.Visually,thedensityvariabilitychangesitsshape,amplitudeandfrequencywith
290increasingdensityanddepth.Largefluctuationsareobservedatlowermeandensities
291(Figure5,5and8mdepthinterval).Athighermeandensitiesaround600kg/m3(20m)
292theamplitudedecreases,butforevenhigherdensitiesaround700kg/m3theamplitudes
293increaseagain(25and40mdepth).Thevariabilityvanishesatdensitiesabove800kg/m3
294(Figure5,75mdepth).
295Thevariability,σρ,withdepthandincreasingmeandensity(ofthedensity-depthprofile
296inwaterequivalentdepth)isdisplayedforallfirncores(Figure6).Theamplitudereaches
297aminimumatadepthofapproximately10mw.e.andthenincreasesagain.Thisyieldsa
298secondrelativemaximumbeforeitfinallyfallstowardszero(Figure6A).Theminimumin
299densityvariabilityoccursatmeandensitiesbetween600-650kg/m3(Figure6B),whereas
300themeandensityofthefollowingsecondmaximuminvariabilityseemstovaryslightly.
301Atmeandensitiesofthefirn-icetransitionsomecoresshowhighamplitudesinσρ(B38,
302B39forexample)whileforothercorestheamplitudeisdecreasing(EDC2andB36/B37).

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303Inordertogetabetteroverviewoftheinfluenceoflocalclimateconditions,thepro-
304fileshavebeensortedintofivegroups,A-E,ofsimilarannualmeantemperatureand
305accumulationrate(Figure7).Inallfivegroupsthestructureofrapiddecreaseofσρto
306aminimumat600-650kg/m3andasecondmaximumbelowisfound.B25isplotted
307intwogroups.ThedensityvariabilitydecreaseofB25intheuppercoreissimilarto
308theAntarcticcores,whilethesecondmaximumismoreconsistentwiththeGreenland
309cores,asaretheclimateconditions.Finallywecalculatedtheaverageforeachgroupto
310determinetypicalbehavior(Figure7f).ForcomparisontheaveragesofeachgroupA-E
311canbeseeninFigure7F.ExceptforgroupC,thedroptotheminimumissimilar,but
312thepatternsclearlydivergeinextentandamplitudeofthesecondmaximum.Whereas
313groupsA,B,C,andDdifferinamplitudeofthesecondmaxima,butnotthatmuchin
314position,groupEshowsthesecondmaximumatdistinctivelylargermeandensities.
315Insummary,allfirncores,coveringabroadrangeofclimateconditions,showasimilar
316rapiddecreasefollowedbyasecondmaximumofdensityvariability.Thecoresshowa
317similarstructureofσρabovetheminimum.Themeandensityoftheminimumvariability
318seemstobealwaysatapproximately600-650kg/m3,whereasthemagnitudeandthe
319positionofthesecondmaximumseemtovaryaccordingtotheenvironmentalclimatic
site.aofconditions320

Discussion4.yDensitMean4.1.321Accordingtotheliterature,depth-densityprofilesshouldshowchangesintheslopeat
322densitiesof550,730and820-840kg/m3.Weexpectedthemeandensity-depthprofiles
323fromhighresolutiondensitymeasurementstoclearlyshowthesetransitions.Thefirst

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324transitionindensificationrateissuggestedatameandensityof550kg/m3[Herronand
325Langway,1980]asaresultofparticlerearrangementgainingmaximumpackingdensity
326[Arnaudetal.,2000].Inourresultsthedensityatwhichthischangeoccursvariesfrom
327densitiesbelow500kg/m3atB36/B37orB29uptodensitiescloseto600kg/m3atB38
328(Figure4).Itseemsthatthecriticaldensity,atwhichthedensificationratechanges,varies
329atthedifferentsites.Differentsnowandfirntypesmayexhibitadifferentdensityatwhich
330thecompactionmechanismchanges.Atasinglesitewithstronglayeringeachlayerwill
331reactdifferentlytotheappliedload[Freitagetal.,2004;Alleyetal.,1982].Transitionsat
332theotherdensitiesof730and820-840kg/m3arenotclearlydetectable.Itisreasonable
333toassumethatdifferentmicrostructuralprocessesanddeformationpatternstakeplaceat
334alldepthsandthedominanceofeachoftheseprocesseswillshiftrathersmoothlyfrom
335onetoanotherwithinthefirncolumn[Kipfstuhletal.,2009].Differentprocessescanalso
336occurconcurrently[Arnaudetal.,1998;Salamantinetal.,2009]andcriticaldensities,
337markingatransitionofthedominanceofmicrostructuralprocesses,canvaryoveralarge
338densityrange[Johnson,1998].
339Thefirncoresrepresentingclimateconditionsconsideredintheset-upoftheHerron-
340Langwaymodelareverywellreproducedbythemodel(Figure4).Foradensity-depth
341relationshipatmediumclimateconditionsthisrathersimple,phenomenologicalmodelis
342stillapplicable,evenifasharptransitionatameandensityof550kg/m3isnotapparent
343inmostoftheprofilespresentedhere.Arnaudetal.(2000)showedthatthemaximum
344packingdensity(theoretically550kg/m3)istemperaturedependent.Itdecreaseswith
345decreasingannualmeantemperatureofasite.Thiswouldexplaintherangeofdensities
346atwhichachangeintheslopeinthedensity-depthprofilecanbeobservedinourdata.

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347Decreasingorincreasingthiscriticaldensitywouldprobablyrevealabetterfitofthe
348Herron-LangwaymodelwiththeEDC2orB38firncoredata.Salamatinetal.(2008;
3492009)findthecriticaldensityatgenerallyhigherdensities,correspondingtothecessation
350ofparticlerearrangementattheclosestpackingdensity.Theyexplainthelowercritical
351densityof550kg/m3tobeonlyanintermediatestageinwhichparticlerearrangement
352andplasticityworktogether,ashasbeenproposedbyEbinumaandMaeno(1987).No
353suchsharptransitionsatdensitiesbetween640and680kg/m3,aswerefoundwiththe
354modelbyEbinumaandMaeno(1987),areidentifiedinourmeasuredprofiles.
355TheHerron-Langwaymodelincludedfirncoresfromabroadrangeoflocalclimate
356conditions,includingSouthPoleandVostokatthelowerendofaccumulationrateand
357surfacetemperaturerange[HerronandLangway,1980].Nevertheless,themodelisnot
358applicabletotheconditionsatDomeCandtothoseatthePreIPICScoresites(i.e.
359B38).OnepossibleexplanationforthedistinctdeviationoftheDomeCfirncoreis
360thedifferentdepositionandlocalclimatepattern.Socalleddiamonddustaccompplishes
361muchoftheaccumulationatVostokorDomeFuji,whereasthemassinputatDome
362Cisdominatedbyprecipitationfromsynoptic-scaleweathersystems.Theproblemof
363extendingempiricalmodelstoabroaderrangeofclimateconditionshasbeendiscussed
364earlier[Arnaudetal.,2000;Martinerieetal.,1992].Ourdataemphasizetheneedfor
365aphysicalmodel[Arnaudetal.,2000;SalamatinandLipenkov,2008;Salamantinetal.,
3662009],butthehigh-resolutionmeasurementsneedtobeconsideredintheoverallconcept
densities.criticalof367

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4.2.DensityVariability
368Wheneveragranularmediumcompacts,themeandensityincreases.Whathappens
369tothedensityvariabilityisnotknown.Toourknowledgenoworkispublishedthat
370investigatesthedensificationofagranularmediumuntilporeclosure.Ifweassume
371homogenouscompactionwithsimilardensificationratesfordifferentlayersinagranular
372stratifiedmedium,wewouldexpectasteadydecreaseinvariability.Thedensitiesof
373low-densityandhigh-densitylayersoriginatingatthesurfaceincreasesteadily.Thus,
374theirdensityvaluesconvergewithacorrespondingreductioninvariabilityandobtaina
375commonvalueatthedensityofice(Figure8A,dashedline).
376Weappliedtwodensificationmodelstolookatthemodelbehaviorintermsofdensity
377variability.TheHerron-Langwaymodel[HerronandLangway,1980]isparameterized
378withmeanannualtemperatureandaccumulationrate.Wecanusedifferentsurface
379densitiestosimulatevariability.Bystartingwithtwolayersofdifferentdensityatthe
380surface,weobtainthreestagesintheevolutionofσρ(Figure8A,diamonds).Inthefirst
381stage,thelinearincreaseindensityofthetwolayersissimilar,givingnochangeinσρ,in
382thesecondstage,thelayerwiththeinitiallyhigherdensityhasalreadypassedthedensity
383of550kg/m3andcontinuestodensifyatanexponentialrate,whiletheotherlayerstill
384experienceslineargrowth.Thisleadstoarapiddropinσρinthesecondstage.Atthe
385thirdstage,thesecondlayerhasenteredtheexponentialgrowthregime,andσρdecreases
depth.withlinearlyalmost386387ThemodelintroducedbyBarnolaandPimienta[Barnolaetal.,1991]includesanem-
388piricalfunctionthatconsidersstructuralvariationsduringdensification[Arnaudetal.,
3892000].Itstartsatadensityof550kg/m3.Weusedmeasuredvaluesforσρatmean

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390densityof550kg/m3tostartthemodel.Themodelproducesanexponentialdropofσρ
391(Figure8A,circles).Neitherofthetwoemployedmodelscanreproduceorexplainthe
392measuredevolutionofdensityvariability(Figure8A,crosses).
393Thedrivingforceforthedensificationintheupperpartofthefirncolumnisthe
394overburdenpressureduetoongoingaccumulationofnewsnowontopofeachlayer.The
395overloadpressureisdeterminedbythedensityandthicknessofthelayersontop.Thus
396thewaterequivalentdepthgivesameasureoftheoverburdenpressureandenablesa
397comparisonofthedrivingforceatthedifferentsites.Untiltheminimumvariability
398atapproximately600-650kg/m3orapproximately10mw.e.depthisreached,the
399variabilityprofilesforallsitesaresimilar(Figure6A),butbelow,thisdepth,density
400variabilitydiverges.
401Ifweassumethattheoverburdenpressuredeterminesthedensificationratedowntothe
402variabilityminimum,theexplanationfortheobserveddensificationbehavioristhemanner
403inwhichfineandcoarsefirnstructuresrespondtoload[Alleyetal.,1982].Whereascoarse
404crystalsarejoinedbyrelativelywideneckstofewneighbors,crystalsinfinefirntendto
405bemoresphericalandarejoinedbynarrowneckstomanyneighbors.Thustheformer
406structureisfarfromclosestpackingandwillundergosignificantparticlerearrangement
407underanappliedload,whereasthelatterismorestable[Alleyetal.,1982].Gow(1974)
408observedfirnlayerswithlowdensity,correspondingtocoarse-grainedlayers,toshowless
409strengthtooverloadpressurethanhigh-densityfirn,correspondingtofinegrains.The
410surfacelayerswithdifferentdensitiescompactatdifferentrates,thelow-densitylayers
411fasterthanthehigh-densitylayers,leadingtoafastdecreaseofσρuntilaminimumin
412densityvariabilityisreached.Atthisminimuminvariabilitythelayershavethesame

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413density.Continuousdensificationwithdifferentratesleadstoequaldensitiesofthelayers
414atacertaindepth(crossover),afterwhichtheinitiallylow-densitylayersbecomedenser
415atafasterrateandexhibithigherdensitiesthantheoriginalhigh-densitylayers.
416Byapplyingasimpleexponentialfittotheminimumandmaximumdensitiesofthe
417high-resolutionprofilewithacrossoveratameandensityofapproximately600-650kg/m3,
418wecanhighlightthedifferentcompactionratesandtheresultingvariability(Figure8B).
419Wedonotconsidertowhatextentthelowandhigh-densitylayerscontributetothemean
420density.Abetterapproachcouldbeobtainedbyusingequation(2),wherethedepth-
421densityrelationisrepresentedbytwocoefficientsandamplitudes,whichwouldhavethe
422physicalmeaningofthedifferentdensificationrates.
423Currently,fewdetailedmicrostructuraldataareavailable.Freitagetal.(2004)showed
424thatthenegativegrain-size-densitycorrelationobservedinthenear-surfacefirnswitches
425toapositivecorrelationbelowtheminimumattheB26core.Belowthecrossover,high-
426densitylayerscontainlargegrains[Freitagetal.,2004],whereasinthenear-surfacelayers,
427low-densitylayersareusuallycharacterizedbylargegrainsizes.Thisimpliesthathigh-
428densitylayersatthefirn-icetransitiondonotnecessarilyresultfromhigh-densitylayers
429atthesurfaceandviceversa.Fujitaetal.(2009)alsofindaswitchindensityand
430structuralanisotropyobtainedfrommicrostructureanalysis.Theswitchinthecorrelation
431ofdensityandbackscatteredlight,asobservedbyHawleyandMorris(2006)atdepthsof
432approximately20meterscouldalsobeexplainedbysuchacrossoverofcoarse-grainedand
433fine-grainedfirnlayersintheirdensities.Ofcoursefirnconsistsofmorethanthesetwo
434examplelayersandnotallwillshowsucharelationshipingrainsizeanddensity-increase.

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435Nevertheless,itcanbehypothesizedthatthetwoexamples(lowestandhighestdensity)
436determinetheboundaryvaluesinwhichthedensityvariabilityiscreated.
437Belowtheminimum,theprofilesofσρdivergeconsiderably.Itisapparentthatthe
438overloadpressureisnolongerthedeterminingfactorbelowthisdepth.Theamplitudes
439invariabilityclearlyincreaseagain,butnotasafunctionofoverloadpressure.Other
440factors,independentfromtheload,seemtomodulatethedensityvariabilityatthispoint.
441Thefirncorescoverdifferenttimeintervals-fromlessthan60years(B38)tomorethan
4422900years(EDC2).Accordingly,thebehaviorofthedensityvariabilityisnotalocal
443climatesignal,becausewestudydifferenttimeseriesintervals,butastructuralproperty
444oflayeredfirncompaction.
445Acrossoverindensityofinitiallycoarse-grained,low-densitylayersandfine-grained,
446high-densitylayers,asdiscussedabove,couldbeonepossibleexplanation.High-resolution
447grainsizedataareneededtoexaminetheimpactofgrainsizeonthedensificationofthe
448differentlayers.Anotherpossibilitycouldbetheinclusionofimpuritiesorchemistry
449intothefirn.Theinteractionofimpuritieswiththefirnisrarelyinvestigated.From
450icecoredatathecoherenceofhighdustconcentrationswithverysmallgrainsintheice
451matrixisknown,whichindicatesanimpactofimpuritiesonphysicalpropertiesoftheice
452[Svenssonetal.,2005].Alsomicrostructuralparametersapparentinsinglelayers,such
453asgrainshapeortexturalanisotropymightcometoplayarole,afteracertaindensityor
454grain-geometryisobtained.Salamatinetal.(2009)showedtheimportanceofgrainsize
455andcoordinationnumberinthedensificationprocessandthusinthedeterminationofthe
456close-offdensityanddepth.Bothimpuritiesandmicrostructurecanalterthedensification

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457rateofthefirn.Theanalysisofthisimpactisbeyondthescopeofthispaper,butatopic
h.researcfutureof458

4.3.Variabilityatthefirnicetransition
459Inordertotesttheassumptionofadirectlinkofsurfacelayeringtothevariabilityatthe
460firn-icetransition,relatedtoanextensionofanon-diffusivezone[Landaisetal.,2006],we
461comparethedensityvariabilityatthefirn-icetransitionwiththedensityvariabilityatthe
462surfaceandlinkittothemeanannualtemperatureandaccumulationrate.Wecalculate
463themeandensitiesforairenclosure,usingequation(4)anddeterminethecorresponding
464valueinσρ(Table3).Wefindanincreaseinvariabilityatthefirn-icetransitionwith
465increasingmeanannualtemperature(correlationcoefficientofthefitr=0.822)and
466increasingaccumulationrate(Figure9A,r=0.634and9B,r=0.73,orangeline).This
467observationsupportstheassumptionofadependencyofdensityvariabilityatthefirn-
468icetransitiononmeanannualtemperatureandonaccumulationrate,assuggestedby
469Landaisetal.(2006)andKawamuraetal.(2006).
470Forthesurfacevariabilitywefindaclearnegativetrendwithtemperature(r=-0.35
471intheuppermostlayersandr=-0.92at6mdepth)andaccumulationrate(r=-0.617/
472-0.44intheuppermostlayersand-0.73/-0.86at6mdepth).Thehigherthetemperature
473oraccumulationrateatasite,thelowerthedensityvariability,whichistheoppositeofthe
474trendofthevariabilityatthefirn-icetransition.Wefirstcalculatethetrendforthewhole
475rangeofaccumulationrates(Figure9A1).Inordertomakesurethattheextremelyhigh
476accumulationratesofthePreIPICScoresdonotinfluencethetrend,wethenexcludethe
477PreIPICSdataandre-calculatethetrendovertheresidualrangeofaccumulationrates
478(Figure9A2).Theresultisthesameinbothcases-thedensityvariabilityatthesurface

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479decreaseswithmeanannualtemperatureandaccumulationrate.Thisdecreaseindicates
480adecreaseinthenumberoflayersapparentatacertaindepthintervalwithincreasing
481meanannualtemperatureandaccumulationrate.Accordinglylow-accumulationsites
482seemtohavemorepronouncedlayeringthanhigh-accumulationsites.Thisfindingisin
483contradictiontothecommonassumptionthatlow-accumulationsitesshowonlyweakora
484lackoflayeringcomparedtohigh-accumulationsites[Landaisetal.,2006]becauseofthe
485longexposuretotemperaturegradientsandinsulation.Becauseoftheoppositetrends
486ofdensityvariabilityatthesurfaceandatthefirn-icetransitionwithincreasingmean
487annualtemperatureandaccumulationrate(Figure9)wecannotconfirmadirectlinkof
488layeringatthesurfacetotheextentofanon-diffusivezonenearthefirn-icetransition.It
489seemsthatthesurfacestratigraphyofpolarfirndoesnotdirectlyimplythevariabilityat
490thefirn-icetransitionorthethicknessofanon-diffusivezone.
491Equation(4)estimatesthemeandensityofclose-off[Martinerieetal.,1992].Itis
492assumedthathigh-densitylayersapproachingclose-offdensityatshallowerdepthsseal
493offlow-densitylayersfromthefreeatmosphereandthusincreasetheairvolumeenclosed
494inlow-densityfirn.Thedepthatwhichthisdensityisapproachediscrucialforthe
495estimationoftheagedifferenceoficeandair.However,theproblemofdensityvariability
496makesthedefinitionofthisclose-offdepthveryvariedanditisusedverydifferentlyin
497theliterature[Arnaudetal.,1998,2000;Landaisetal.,2006;Kawamuraetal.,2006;
498Loulergueetal.,2007].InTable3welistthemeandensityandmeandepthatwhichthe
499airisolationisobtainedfromequation(4),togetherwithsomedatafromliterature.Even
500thoughnophysicalmeaningcanbeextractedfromthesevalues,wealsoshowthedepth
501valuesatwhichthesedensitiesoccurforthefirstandthelasttimeinthehigh-resolution

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502densityprofile.Examinationofthesedepthshighlightsthevariabilityandrandomness
503oftheoccurrenceofcriticaldensitiesanddepthintervalswithrespecttomeanannual
504temperature,accumulationrate,locationormeasureddensityvariability.
505Thequestioniswhetherthedegreeofverticaldensityvariabilityisthekeyparameter
506fortheairclose-offdepth.Thehorizontalextentofhigh-densitylayersatthefirn-ice
507transition(initiallylow-densitylayersatthesurface)andthusthehorizontalvariability
508ortheroughnessoflayers[Martinerieetal.,1992],mightplayanimportantrolein
509definingthedepthatwhichfirnairisfinallysealedofffromtheporespaceabove[Freitag
510etal.,2001].Inthatcasetheparameterstoexaminemorecarefullyaretheconditions
511atwhichlayersareformedandhowlayersareextendedhorizontallyinplane.This
512includesnotonlytheprecipitationitself,butthewindandredistributionbywind,which
513shapethesurface,createsurfaceroughnessandgeneratesinglesnowlayerswithacertain
514thicknessandhorizontalcontinuity.Itmightbenecessarytoconsiderthewindduration,
515speedandredistributionofsnowparticles.Itmightalsobeimportanttolinkthesurface
516variabilitywiththeamplitudeoftemperaturevariationatasite:abroadertemperature
517rangeoccurringovertheyeargeneratesalargerdifferenceinthedensitybetweensingle
518layers.Withincreasingaccumulationratethisimpactwillcease,thusthedegreeof
519variabilitywilldecrease,asissuggestedbyLiandZwally(2004).

Conclusion4.4.520Weinvestigatedmeandensityprofilesanddensityvariabilityobtainedfromhighreso-
521lutionfirncoremeasurements.Ourresultsemphasizetheneedforaphysicalmodelfor
522predictingmeandensityprofiles,inordertobeabletoapplyittoabroadrangeofclimate
523conditions.Furthermorethestudyofhigh-resolutiondensitygivesdetailedinsightinto

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524thephysicalprocessofcompactionofstratifiedfirn.Inthedensityprofilesinvestigated
525wefindfewornodistincttransitionsinthedensity-increasewithdepthatmeandensities
526of550,730and820-840kg/m3,asfoundelsewhereintheliterature.
527Densityvariabilityasameasureofthelayeringofpolarfirnshowsadistinctpattern
528atallsites,excludinglocalclimateconditionsasanexplanation,andquestioningthe
529commonideaofhomogenouspolarfirndensification.Themoreefficientandfastden-
530sificationofinitiallylow-densitylayers,overcomingthedensityofinitiallyhigh-density
531layers(crossover),explainstheobservationsofthevariabilitypatternandaswitchin
532correlationofdensityandelectricalconductivity[Gerlandetal.,1999]anddensityand
533intensityofback-scatteredlight[HawleyandMorris,2006].Italsoimplies,thatthehigh-
534densitylayersatthefirn-icetransitiondonotoriginatefromhigh-densitylayersatthe
535surface.Inordertounderstandtheevolutionofthedensityvariabilityandtoverifythe
536crossoverindensityprofileofdifferentlayersortheimpactofimpuritiesandmicrostruc-
537ture,thedensificationprocessneedstobeinvestigatedonamicro-scale.Thereforeafirn
538corestudyincludinghighresolutionprofilesofchemistry,microstructureanddensityis
539stronglyneeded.Traditionalmethodstoobtainsuchprofilesareverytimeconsuming.
540Butnewmethodsareprogressing,enablingafastandaccurateanalysisofmicrostructure
541[Kipfstuhletal.,2009].Thesetechniqueswillprovidemoredetailedinformationinthe
542future.Inordertolinkfirnlayersintheirextent,thicknessandinitialdensitytotheair
543enclosureprocess,thelateralextensionandcontinuityoftheseslayersneedstobecon-
544sideredaswell.Thereforeknowledgeaboutwindintensity,durationofwinddeposition
545eventsandthesubsequentcreationofwind-packedlayersononehand,theextentand
546distributionoflowdensitylayersatthesurface,ontheotherhand,iscrucial.

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547Acknowledgments.WethankthefieldteamoftheNorth-Greenlandtraverse1993
548-1995;DanielSteinhageandtheteamofthePreIPICStraverse2006/2007andHans
549OerterandtheteamoftheDML-pre-sitesurvey1997/1998.Weareverygratefulto
550Dr.ZoeCourvilleforcarefulreadingofthemanuscript.Wealsothankthetwoanony-
551mousreviewersfortheirhelpfulcomments.ThisworkispartlyfundedbytheDeutsche
552Forschungsgemeinschaft(DFG)grantFR2527/1-1.

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X-33

Table1.The16firncoresiteswithposition,meanannualtemperature,T,andaccumulation
rate,b.Referencesforthedataare:(1)Schwager[2000],(2)Wilhelms[1996,2000],(3)Freitag
etal.[2004],(4)Gerlandetal.[1999],(5)Sommeretal.[2000],(6)Oerteretal.[2000],(7)
EPICA[2006],(8)Schwander,Oerter,pers.comm,(9)EPICA[2004].
Campaign/NamelatlonhTb.YearReference
ofs.l.a.region◦◦m◦Cmw.e.drilling
GreenlandNGTB1675.9402-37.62993040-270.1421993-1995(1),(2)
NGTB1775.2504-37.624828201993-1995(1),(2)
NGTNGTB2B11880.00076.6170-41.1374-36.403321852508-30-300.1080.1041993-19951993-1995(1),(1),(2)(2)
NGTB2677.2533-49.21672598-30.60.181993-1995(1),(3)
NGTB2976.0039-43.49202874-31.60.1531993-1995(1),(2)
tarcticaAnBerknerIs.B25-79.6142-45.7243886-270.141995(4)
DMLB31-75.5815-3.43032669-420.0631997(5),(6)
DMLDMLB3B323-75.0023-75.16700.00706.498528823160-420.0610.04419981997(5),(5),(6)(6)
DMLB36/37-75.00250.06842891-44.60.0672005/2006(7)
PreIPICSPreIPICSB3B398-71.4083-71.1621-9.9167-6.6989654690-17.9-18.10.771.252006/20072006/2007(8)(8)
PreIPICSDML95-71.5680-6.6670540-19.20.552006/2007(8)
DomePreIPICSCDMLEDC297-75.1000-72.0640123.35000-9.55833233760-53-20.40.0250.4919992006/2007(9)(8)

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Table2.Themeasurementsetupsandthedataprocessingparametersforthe16firncores.
Moredetailsaregivenin[Wilhelms,1996,2000].
Campaign/NameYearofActivitysourceSamplingPointAveraging
regionmeasurement(1990)ratedistancewindow
GBqmmmmw.e.points
GreenlandNGTB161995/199625.96335
NGTB171995/199611110.916
NGTB181995/1996111335
NGTB211995/1996111335
NGTB261995/199625.9610.916
NGTB291995/199625.9610.916
tarcticaAnBerknerIs.B25199525.96335
DMLB311997/199825.9654.43
DMLB32199/199825.9654.43
DMLB33199825.9654.43
DMLB36/372007/200611110.911
PreIPICSB38200711110.916
PreIPICSB39200711110.916
PreIPICSDML95200711110.916
PreIPICSDML97200711110.916
DomeCEDC2200811110.911

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5X-3

Table3.Theairisolationdensityρcrit,calculatedusingequation(4)[Martinerieetal.,1992],
thecorrespondingdensityvariabilityσρ,close-offdepth(meandepth)andthedepthatwhich
theairisolationdensityisreachedthefirst(topdepth)andthelasttime(bottomdepth)within
thehighresolutiondensityprofile.Inthelastcolumnmeasured/modeledmeanclose-offdepths
areaddedfromthefollowingreferences:(1)[Schwanderetal.,1997]forNGRIPandGISP2
asclosestpointstoB16,(2)[Kaspersetal.,2004],(3)[Landaisetal.,2006]afterModelsby
Arnaudetal.(2000)andPimientaetal.(1991);withNGRIPastheclosestpointtoB29.
regionCampaign/Nameρcritσρ(ρcrit)mean(ρcrit)depthtop(ρcritdepth)b(ottomρcrit)depthdepthLiterature
kg/m3kg/m3mmmm
GreenlandNGTB16819.27312.262763566971/72(1)
7B1NGTNGTB18820.80612.8078595466
NGTB21820.80612.9072625172
NGTNGTB2B296821.319820.84810.513.22568695359777866/67(3)
tarcticaAnBerknerDMLIs.B3B215826.997819.15610.271314.571982567550866760/59(3)
DMLB32826.99711.2794867793
3B3DMLDMLB36/37827.4958.115488779874(2)
PreIPICSB38815.00316.586685683
PreIPICSPreIPICSB3DML959815.514814.9117.10813.4153584877
10.0261816.072DML97PreIPICSDomeCEDC2832.0194.5932999310498.6(2)/100(3)

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H¨ORHOLDETAL.:DENSITYVARIABILITY

B25

raw density, gamma absorption averaged density, gamma absorption one meter bag density, eld

B25900800)3700600Density (kg/m500 raw density, gamma absorption averaged density, gamma absorption one meter bag density, eld400300A20406080100120
Depth (m)35900308003)700 raw density 5 point running average25σρ
exponential t for detrending 1000 data point average20600 1000 data point standard deviation (kg/mDensity (kg/m153)500104005300B20Depth (m w.e.)406080
Figure1.Themeasuredhigh-resolution(greyline)densityrawdatawithdepth(A)together
withtheonemeteraverage(runningmean)fromhigh-resolutiondensitymeasurements(dark
line)andtheonemeterbagvaluesmeasuredinthefield(brownline)forcomparison.The
high-resolutiondensityrawdatawithdepthinmeterwaterequivalent(B)afterre-samplingto
equidistantpoints(lightgreyline),togetherwiththesmootheddataafterapplyingarunning
meanaveragewindowofsizeasdenotedinTable2(darkgreyline).Theexponentialfitfor
detrendingisdisplayed(blueline)aswellasthemeanvaluesofaslidingwindowof1000data
points(yellow),correspondingtothestandarddeviationoftheslidingwindowof1000datapoints
wn).(brodetrendingafter

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B 25900800)3700600Density (kg/m500400300

H¨ORHOLDETAL.:DENSITYVARIABILITY

B 26900800)3700600Density (kg/m500 measured400 mean300

A050100150B050100150
Depth (m)Depth (m)

7X-3

Figure2.High-resolutiondensityprofiles(greyline)ofB25(afterGerlandetal.1999)
andB26(afterFreitagetal.2004),togetherwiththe1meteraverage(blackline).Thelarge
variabilityinthedensitybecomesvisible,evenatgreaterdepths.

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8X-3920880840800760720)3680640Density (kg/m600560520480440400360

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H¨ORHOLDETAL.:DENSITYVARIABILITY

50

EDC B 31 B 32 B 36/37 B 33 B 16 B 17 B 21 B 18 B 29 B 26 B 25 B 39 B 38 DML97 DML95

100150Depth (m)

Figure3.Meandensityprofiles(1mrunningmeanaverage).Lowaccumulationsitesare
plottedinblue,mediumaccumulationsitesingreenandhighaccumulationsitesinbrown.
Commonlyconsidered”criticaldensity”valuesof550kg/m3,730kg/m3and820-840kg/m3
areindicatedbydashedlines.Formostofthecoresatransitionat550kg/m3isnotobviously
detectable.Atransitionatdensityaround730kg/m3isnotvisibleinanyprofile.Formost
ofthecoresachangeindensificationrateoccursatdensitiesabove840kg/m3,butadistinct
t.apparennotistransition

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900EDC2)8003700Density (kg/m600500400

H¨ORHOLDETAL.:DENSITYVARIABILITY

A050Depth (m)100150
900B 25)8003700Density (kg/m600500 measured, mean Herron-Langway400

900B 36/37)8003700Density (kg/m600500400

B050Depth (m)100150
900B 29)8003700Density (kg/m600500400

9X-3

C050100150D050100150
Depth (m)Depth (m)900900B 38B 263)8003)800
700700Density (kg/m600Density (kg/m600500500400400050100150F050100150
EDepth (m)Depth (m)Figure4.Selectedmeandensityprofilesincomparisontomodeleddensityprofilesusingthe
Herron-Langwaymodel(blackline).TheHerron-Langwaymodelreproducestheprofilesofthe
B25,B26andB29cores-withmoderatemeanannualtemperaturesandaccumulationrates(C
-E)well.ButthemodelfailsfortheEDC2corewithlowaccumulationrateandtemperature
andtheB38corewithhighaccumulationrateandtemperature(AandF).
DRAFTOctober7,2010,8:07pmDRAFT

112

0X-4

H¨ORHOLDETAL.:DENSITYVARIABILITY

11.0z =~5m~8m~12m~20m~25m~40m~53m~75m~117m
43.57.53.50.859.027.518.51.082.533.011.51.244.08.04.01.459.528.019.0Depth interval (-0.9 - z - +0.9 m w.e.)83.033.51.612.044.58.54.51.860.028.519.52.083.534.012.52.245.09.05.02.460.53004005006003700800900
)Density (kg/mFigure5.Detailsofthehigh-resolutiondensityofB26core.Thiscorerepresentsatypicalfirn
corefromtheGreenlandplateau,withmoderatemeanannualtemperatureandaccumulation
rate.Fromlefttorightthemeandensityanddepthincrease.Eachprofilecovers1.8mdepth
w.e.,whichequalsapproximately10yearsatthissite.Intheupperpart(5and8mdepth)
thedensityvariationsarecharacterizedbylargeamplitudesandrandomfrequencies.Towards
greaterdepths(20mdepth)theamplitudesdecrease.Belowtheamplitudesincreaseagainand
moreregularfrequenciesseemtoappear(25-53mdepth).Below53mdepththevariability
decreasesuntilitvanishesatdepthsof75m.

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H¨ORHOLDETAL.:DENSITYVARIABILITY

B17 B16 B 20 B18 B26 B21 B29 B31 B25 B33 B32 EDC B36/37 B39 B38 DML97 DML95

2030405060708090100
Depth (m w.e.)

1X-4

504540 B17 B16 B 20 B18 35 B26 B213)30 B29 B25 B31
B33 B32 (kg/m25 B38 B36/37 B39 EDC
σρ DML97 DML95 20151050A0102030405060708090100
Depth (m w.e.)50454035)330 (kg/m25σρ 20151050DRBAFT350400450500550October6007,2010,65038:07pm700750800850900DRAFT
)Density (kg/mFigure6.Measureddensityvariabilityσρofallcoresasafunctionofdepthinmw.e.(A)and
meandensity(B).Allprofilesshowarapiddropinσρwithaminimumatapproximately10m
3()/(A)114

X-42H¨ORHOLDETAL.:DENSITYVARIABILITY
B31 40T -53 °CA 0.025 m w.e. EDC40T -42 - -44.6 °CA 0.044 - 0.067 m w.e B32
B33 3)303)30 B25 B36 /37
(kg/m 20(kg/m 20
σρ 10 σρ 10
00A4005006007003800900B4005006007003800900
)Density (kg/m)Density (kg/m40T -30 °CA 0.104 - 0.108 m w.e. B21 B18 40T -27 - -31.6 °CA 0.14 - 0.18 m w.e. B16 B25
B17 3)303)30 B26
B29 (kg/m 20(kg/m 20
σρ 10 σρ 10
00C4005006007003800900D4005006007003800900
)Density (kg/m)Density (kg/m40T -18.1 - -20.4 °CA 0.6 - 1.3 m w.e B39 B3840 A B
DML95 C3)30 DML97 3)30 D
E(kg/m 20(kg/m 20
σρ 10 σρ 10
00E4005006007003800900F4005006007003800900
)Density (kg/m)Density (kg/mFigure7.Measuredσρofthefirncoresgroupedbytemperatureandaccumulationrate
intervals.ThelowesttemperatureandaccumulationrateinA(EDC2),secondlowestinB
(DML).ThelowaccumulationsitesfromGreenlandareshowninC,notethattheminimumis
notwelldeveloped,themoderateGreenlandcoresareshowninD.TheB25coreisplottedwithB
andD,sincethedropseemstobetterfitwiththeDMLcores,whereasthesecondmaximumfairly
wellfitstotheGreenlandcores.FinallyEshowsthePreIPICScoreswithhighesttemperatures
andaccumulationrates.InFtheaveragedprofilesofeachofthegroupsareplotted.Themean
densityoftheminimumisrestrictedto660-650kg/m3(greyshadedarea).

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H¨ORHOLDETAL.:DENSITYVARIABILITYX-43
30 σρ if Herron-Langway with σρ / ρice - ρ = 1σρ initial as measured
25 σρ measured Barnola-Pimienta with σρ initial as measured
)320(kg/m 15σρ 1050A400450500550600Density (kg/m6503)700750800850900
90070850608007506503)70050 σρ
40 600Density (kg/m(kg/m500550 σρ σρ measured 2 layer approximation30)3
45020400350103000250B01020304050607080
Depth (m w.e.)Figure8.Measured(crosses)andmodeledσρofB26.Assumingalineardropofσρwith
increasingρ(dashedline),modeledσρusingtheHerron-Langwaymodelwithtwodifferentstart-
ingdensities(diamonds)andσρwhenapplyingthePimientamodel,startingatadensityof550
kg/m3(circles).ThreedifferentstagesofthelatteroccurduetothesetupoftheHerron-Langway
model(seetext).InBthehigh-resolutiondensityprofileofB26isshownwiththeresultingσρ
(grey).Inaddition,twoexponentialfitsareindicated-onestartingatlowerdensities(orange
line)andtheotherstartingathigherdensities(blueline).Duetodifferentratesindensification,
themodeleddensityprofilescrosseachotheranddeviatefromeachotheroncemorebelowthe
crossoverdepth.Towardsthedensityoficebothfitsconverge.Theresultingσρisplottedwith
dots.wnbroDRAFTOctober7,2010,8:07pmDRAFT
116

4X-4

H¨ORHOLDETAL.:DENSITYVARIABILITY

5050 2m 1m 4m 3m r = -0.35)40r = -0.61 5m close-off 6m)40
333030(kg/m 20(kg/m 20r = -0.92
σρ σρ 1010r = 0.634r = 0.822r = -0.7300A 10.20.40.60.81.01.2B-50-40-30-20
Accumulation Rate (m w.e.)Temperature (°C)50r = -0.4440)330(kg/m σρ 20r = -0.86 10r = 0.7380A 20.040.08Accumulation Rate ( m w.e.)0.120.16
Figure9.Relationshipbetweenσρatthesurfaceandatclose-offdensities.Densityvariability
σρatporeclose-offdensities(brownline),calculatedafterequation(4)andσρatthesurface
(dashedlines)fordepthintervalsfrom0(brightgrey)to6m(darkgrey)depthareshownagainst
increasingaccumulationrate(A1andA2)andtemperatureB.InA1thewholeaccumulationrate
rangeofallfirncoresisplotted.InA2theextremelyhighaccumulationratesofthePreIPICS
coresareexcludedandthenewfitsarecalculated.Forincreasingaccumulationrateandmean
annualtemperatureσρatthesurfaceisdecreasing,whereasσρattheporeclose-offisincreasing.

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B

n2-FlicatioPub

randommor

depositiontoafirncorerecord-

theimpactofimpuritiesonthe

densificationofpolarfirn-afirst

hoacappr

no

Inpreparation.Hörhold,M.W.,Laepple,T.,Freitag,J.,KipfstuhlS.,Bigler,M.andFis-

,cher.H

118

NameJ.forpreparedManuscriptwithversion3.2oftheLATEXclasscopernicus.cls.
2010December16Date:

Ontheimpactofimpuritiesonfirndensity
M.W.H¨orhold,T.Laepple,J.Freitag,S.Kipfstuhl,M.Bigler,andH.Fischer
AlfredWegenerInstituteforPolarandMarineResearch,Bremerhaven,Germany
ClimateandEnvironmentalPhysics,PhysicsInstitute,UniversityofBernandOeschgerCentrefor
ClimateChangeResearch,UniversityofBern,Switzerland
Correspondenceto:M.W.H¨orhold(Maria.Hoerhold@awi.de)

oductionIntr1

Icecoresprovidehighlyresolvedrecordsofatmosphericparametersforthelast1,000,000years
(EPICA,2004).Aerosolsanddustparticlesaredepositedandincorporatedintotheiceandallow
togetherwithisotopesclimateandtemperaturereconstructionofthepast.Togetherwiththeenclo-
5sureofairintobubbleswithintheiceduringthedensification,whichprovideadirectmeasurement
offormeratmosphericcomposition,theseproxiesmakeicecoresauniqueclimatearchive.
Atadequateaccumulationratesthechemicalcomponents,ionconcentrationsordustimpurities
aredetectedwithinfirnandicecoreswithseasonalvariability(Fischeretal.,1998;G¨oktasetal.,
2002;Kreutzetal.,1999;Sommeretal.,2000).Theseseasonalvariationsareoftenusedtodatethe
10cores(Rasmussenetal.,2006).
Animprovedunderstandingofthefundamentalfactorsthatcontrolthechemistryofasnoworice
sample,thetransferfromasurfacesignaltoanicecorerecordandthedensificationprocesswith
therelatedairenclosurewillallowanevenmoredetailedandaccurateinterpretationofrecords,
reconstructingpastclimateconditions.Thedensificationandtheevolutionofdensityvariabilityof
15polarfirnisacrucialprocesswhichisstillnotfullyunderstood.Justrecentlytheimportanceof
theexactknowledgeoffirndensificationforanalyzingelevationmapsovertimeformassbalance
estimates(LiandZwally,2002)viaremotesensinghasbeenemphasized(Cuffey,2008;Helsen
etal.,2008).Toimprovetheanalysisofboth,dataobtainedbyremotesensingmethodsaswell
astherecordsmeasuredinicecores,itisnecessarytodeterminetheprocessesandinteractionsof
20chemistry,impuritiesandphysicalpropertiesofthefirn.
Inmanyapplicationsthedensityprofileisdescribedbycontinuouslyincreasing1meterbulk

1

119

densitiesorapproximatedbyempiricaldensity-depthrelationships(Alleyetal.,1982;Arnaudetal.,
1998,2000;ArthernandWingham,1998;Freitagetal.,2004;HerronandLangway,1980;Liand
Zwally,2004;Wilhelms,2000;ZwallyandLi,2002;Salamantinetal.,2009).Butthefirncolumn
25iscomposedofalternatinglayersdistinguishableinmicrostructureanddensity.Snowpitstudies
deliverdetailedobservationsofthedifferentsnowlayers,presumablycreatedbyseasonalvariations
inlocalclimateconditions(Alley,1988;Benson,1971;Cameron,1971;Gow,1965;Koerner,1971;
Kreutzetal.,1999;Palaisetal.,1982;Rundle,1971;Shiraiwaetal.,1996).Thedensityprofilein
snowpitsissupposedtobethemostreliableindicatorofseasonalvariationsinthefirn(Taylor,1971;
30Horietal.,1999).Accordingly,theseseasonalcyclesofsnowandfirnlayerdensityareconsidered
inmanyapplicationssuchasthemodelingoffirndensificationforthevalidationofairbornemass
balancestudies(LiandZwally,2002;ZwallyandLi,2002;Helsenetal.,2008).Inthesemodelsit
iscommontoassumeanasymptoticallydecreaseofdensityvariabilitywithdepth(2002).
However,detailedknowledgeaboutthetransferofsurfacedensityvariabilitydownthefirncolumn
35islacking.Itisacommonideathattheseasonalvariabilityinpolarfirndensitycreatedatthesurface
ispreservedinthefirnandicecolumn(Kawamuraetal.,2006;Landaisetal.,2006;LiandZwally,
2002;Martinerieetal.,1992;SeveringhausandBattle,2006;ZwallyandLi,2002).Theimplicit
assumptionisthatthedensityvariationatthesurfacesurvivesthedensificationprocessoverthe
entirefirncolumnandcausesmeasureddensityvariabilityalsoattheclose-offdepth.Inreturnthese
40densityfluctuationscouldimpactthebubbleenclosureprocessduringclose-off(Martinerieetal.,
1992;Kawamuraetal.,2006;Landaisetal.,2006;SeveringhausandBattle,2006).
Thesnowdepositionisdeterminedbycombinedeffectsoftheannualcycleinatmosphericpro-
cesses,irregularsurfacedepositionanderosionandre-distributiondisruptingtheinterpretationof
annuallayeringanddiageneticprocessesoccurringafterburial(Palaisetal.,1982;Jones,1983;
45Fisheretal.,1985).Thereforetheinterpretationofstratigraphicobservationsisnotstraightforward.
Becauseofstronglyvaryingorevenmissingaccumulation,erosionandre-deposition,layersare
created,whichcanobliterateorcombineseveralyearsofaccumulation(Rundle,1971;Petitetal.,
1982).Theseasonalvariationintheatmosphereisnotnecessarilydisplayedinthesnow(Wolffetal.,
1998;Udistietal.,2004)andaclearcorrelationbetweendensityvariabilityandisotopesignature
50couldnotbefoundyet(Stenbergetal.,1999).
Thelinkbetweenanysignalincorporatedintothesnowandtheactualsignalthatremainsinice
coresisunclear(Fisheretal.,1985;Karl¨ofetal.,2006;Birnbaumetal.,2010).Theassumptionofa
persistentdensityseasonalitythroughoutthefirncolumndoesnotnecessarilyhold.Withthisstudy
weaimtoimprovetheunderstandingofdensificationandtheroleofimpuritiesinthedensification
55process.WeanalyzetheevolutionofdensityvariabilitywithdepthoffirncoresfromGreenlandand
Antarctica,obtainedfromofhigh-resolutiondensitymeasurements.Wefindnoseasonalvariability
indensityatthesurfacebutadistinctseasonalityingreaterdepthsinhighaccumulationratesites.

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120

Wehypothesize,thatimpuritiesinthesnowandfirnofpolaricesheetsalterthedensificationand
60thusthevariabilityoffirndensity,introducingaseasonalsignaturewithdepth.Unfortunatelymulti-
specificionrecordsdonotexistformostofthefirncoresinhighresolution.Accordinglywecon-
centratehereonseasonalresolutionCarecordsmeasuredbycontinuousflowanalysis(R¨othlisberger
etal.,2000;Kaufmannetal.,2008),whichareavailableforanextendedsetoffirncores.Forthese
coreswestudytheco-evolutionofdensityandCaconcentration.

65Method2

Highresolutiondensitymeasurementsareconductedat17firncoresfromGreenlandandAntarctica
(Wilhelms,1996,2000;Freitagetal.,2004;H¨orholdetal.,accepted).Theverticalresolutionvaries
between1-5mm.Thefirncorescoverabroadrangeinannualmeantemperatureandaccumulation
rate.Positionofthecorescanbefoundintableone.Thedensityismeasuredusinganon-destructive
70loggingsystemincludingaL¨offeldensimeter.DetailsaregiveninWilhelms(1996;2000).
Wefurthermoreusehighresolutionionmeasurementsfromcontinuousflowanalysis(CFA)
(R¨othlisbergeretal.,2000;Sommeretal.,2000;Kaufmannetal.,2008).Themeasurementsofthe
firncoresB31,B32,andB33fromDronningMaudLand,AntarcticawerecarriedoutatNeumeyer
Station(Sommeretal.,2000;G¨oktasetal.,2002).Furthermoretwounpublisheddatasetsfromfirn
75coresfromGreenlandareanalyzed.TheCFAmeasurementswereconductedatthecoldlaboratory
attheAlfred-Wegener-Institute,Bremerhaven,GermanyandattheUniversityofBern,Switzerland.
ForanalysiswerestrictourselftotheCaionwhichisusuallydepositedwithaseasonalamplitude
2004).al.,et(RuthCorebreaksandcorecutsaremanuallyremovedfromthedensitydatasets.Asmallnumberof
80outliers(<1%)areremovedfromtheCadatasetsbyvisuallyinvestigatingthehistogram.Cacon-
centrationsareanalyzedonalogarithmicscale,astheconcentrationvaluesfollowalog-normal
distribution.Thedensityandchemistrydataaretransferredtothewaterequivalent(w.e.)depth
scaleandaveragedto5mmw.e.meanvalues.Lowfrequencyvariationsinthedensityrecordsare
removedusingafiniteresponsehighpassfilter(cutofffrequencyforB38andB390.2mw.e.,0.5m
85w.e.forallothercores).ThedepthdependenceofthedensityvariabilityandthatoftheCa-density
relationshipareanalyzedona5mw.e.slidingwindow.Forthisanalysis,thestatisticsstandard
deviationasameasureofvariabilityandPearsoncorrelationasameasurefortheCa-densityrela-
tionshipareused.AsthedensityandCaanalysiswereperformedondifferentmeasurementdevices,
aslightdepthuncertaintybetweenbothmeasurementscannotbeexcluded.Thisisaccountedforby
90calculatingthemaximumcrosscorrelationina50mmw.e.windowinsteadofasinglecorrelation
estimate.Thestatisticalsignificanceoftherunningcorrelation,includingthedepthuncertainty,is
determinedbyaMonteCarloexperiment.Therefore,thechemistrydatawasreplacedbysurrogate
datawiththesameautocovariancestructure,andthecorrelationanalysisisrepeated10000times.

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Toanalyzethedepthdependentbehaviorofdensityandchemistryinthefrequencydomain,wees-
95timatethewaveletsamplespectrumusingtheMorleywavelet(sowaspackage(MaraunandKurths,
2004;Maraunetal.,2007)).Waveletanalysisisacommontoolforanalyzinglocalizedvariationsof
powerwithinadataseries(TorrenceandCompo,1998),evenifthedominantmodesofvariability
arenon-stationary.Itisthereforeperfectlysuitedforourapplicationinwhichweseektoidentify
annualcyclesandtheirdependenceonfirndepth.Pointwisesignificantareasagainstawhitenoise
100backgroundspectrumareestimatedusingMonteCarloexperiments(Maraunetal.,2007).However,
onemustnotethatpointwisesignificancetestingwillresultinalargeofspurioussignificantpatches,
asawavelettransformcontainsmultipletesting,andadjacentareasinthewaveletsamplespectrum
arenotindependent(Maraunetal.,2007),(alsoseeSupplementFigure1).Theresultsarenotsen-
sitiveonthechoiceoftheinterpolationresolution(1-10mm),thelowpassfilteringmethod(Finite
105responsefilter,orsplinefit)andthecutofffrequency.Toinvestigatepotentialartifactscausedbythe
calculationprocess(transfertowaterequivalentscale,interpolation,filteringandstatisticalanaly-
sisonamovingwindow),weadditionallyperformthecompletecalculationprocessonasurrogate
dataset.ThisconsistsoftheB19icecoredatawithdensityvaluesreplacedbyarandomtimeseries
withthesameautocovariancestructureastheB19density.Theresults(SupplementFigure1)show
110thatourstatisticalproceduredoesnotproduceanyartifacts.

Results3ariabilityVDensity3.1Toinvestigatethedensificationprocessweanalyzetheevolutionofthedensityvariationswithdepth.
ThevariabilityisfirstanalyzedonthefirncoreB29fromCentralGreenland,thatexhibitsa0.15m
115w.e./aaccumulationrate(Figure1).
Thestrengthofthedensityvariability,calculatedasstandarddeviationina5mw.e.sliding
window,isdecreasingwithdepthtoroughly40%ofitsinitialstandarddeviation(Figure1,top
panel).Thisvariabilityminimumisfoundatameandensityof600-650kg/m3correspondingto12
mw.e.depth.Belowthisdepththevariabilityincreasesagain,obtainingasecondpeakaround30m
120w.e.depth.Atdepthsanddensitiesofthefirn-icetransition(820-840kg/m3)thevariabilityisstill
high,untilitvanishesatthemeandensityofice.
Thisrapiddropofvariabilityfromthetopofthecoredowntoavariabilityminimumandthe
followingincreasetosecondmaximumpresumablyresultsfromthefastdensificationofinitiallylow
densitylayers(Gerlandetal.,1999;Freitagetal.,2004;Fujitaetal.,2009;H¨orholdetal.,accepted).
125Thisbehaviorwasfoundforallfirncoresinvestigatedinthisstudy(H¨orholdetal.,accepted).
Toanalyzetheevolutionofthedensityinthefrequencydomainandtoinvestigateiftheannual
cyclecanbedetected,awaveletanalysisisappliedtotheB29core(Figure1,lowerpanel).Atthe
surface,thesignalcoversabroadrangeinthefrequencydomain.Withincreasingdepththevari-

4

122

130

135

Fig.1.Depthdependenceofthedensityvariability(upperpanel)andwaveletspectrumofthedensity(lower
panel)oftheB29firncorefromGreenland.Theminimumandsecondarymaximumofthedensityvariability
aremarkedwithverticallines.Inthewaveletspectrum,thescalecorrespondingtotheaccumulationrate
(horizontalline)andpointwisesignificantareas(blackcontours)aremarked.Atthesurface,thedensityexhibits
strongvariabilityspreadoveralargerangeoffrequencies.Belowadensityminimumataround12mw.e.a
secondaryvariabilitymaximumisdetectedataround30mw.e.depth.Atthisdepth,themaindensityvariations
areconcentratedatthefrequencyoftheaccumulationrate.

abilitydecreasesatallfrequencies.Theareaofminimumvariabilityandthereforelowamplitudes
inthefrequencyspectrum,representsthedepthinterval,wherethedifferenceindensitybetween
thedifferentlayersisminimal.Below,atapproximately15mw.e.depth,adistinctsignalatthe
frequencyoftheaccumulationrateofthefirncoreisfound.Thissignalshowsthemaximumampli-
tudeataround30mw.e.depthwhichissimultaneouswiththeoverallsecondmaximumindensity
variability(Figure1,toppanel).
Thismaximuminseasonaldensityvariationsat30mw.e.depthisparticularyremarkable,asno
seasonaldensitysignalwasdetectedatthesurface.Thus,thedevelopmentoftheseasonalityinthe
firndensitytakesplacebelowthecolumnthatisinfluencedbytheseasonalcycleoftemperatureand
ariables.vclimaterelatedThebehaviorofthefirndensityvariabilityisnotlimitedtothefirncoreB29butisfoundinmost

5

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140145150155160165170175

ofthecoresinvestigatedinthisstudy.Thereforethesamewaveletanalysisisappliedtoall17firn
cores(Figure3,4andSupplementFigure2).Inthefollowingwaveletspectra,thedepths,atwhich
theminimumandthesecondmaximumindensityvariabilityoccur,areindicatedwithavertical
dashedline,thevariabilityitselfisnotshown.
Inalmostallcores,thedensityvariabilityatthesurfaceisdistributedoverabroadrangeoffre-
quencies.OnlyatfirncoreB26adistinctpeakinintensityattheaccumulationrateisobservedatthe
surface.TheB20,B25andB29firncoresshowabroadfrequencysignalatthesurface,including
thefrequencyoftheaccumulationrate.
Inallcores,thesurfacesignalisfollowedbyazonewithaminimumindensityvariability.In
manycasesthiszoneisfollowedbyaninterval,whereadistinctsignalinthefrequencyofthe
accumulationrateappears(B16,B17,B26,B29,B38andB39towardstheendoftherecord,Figure
3,4andSupplementFigure2).Othercoresshowpatchesandislandswithpointwisesignificantly
increasedintensitiesaroundthefrequencyoftheaccumulationrate(B18,B20,B21,B25,B32and
B36).TheEDC2,B31andB33firncoresdonotshowasignificantintensityatanyfrequency,apart
fromthesurfacesignal(SupplementFigure2).Themaximuminintensityoccursatthedepthofthe
secondmaximumdensityvariability.
Itappearsthattheoccurrenceofsignificantintensityofthefrequencyoftheaccumulationrateat
thedepthofthesecondmaximumindensityvariabilityislinkedwiththeamountofaccumulation.
Firncoreswitharelativelyhighaccumulationrate,suchastheB38andB39firncoresfromAntarc-
ticaandtheB16,B17,B26,B29firncoresfromGreenland(allwithaccumulationrateslargerthan
0.142mw.e./a)showasignificantintensityofthefrequencyoftheaccumulationrateatthesecond
maximumindensityvariability.FirncoreswithrelativelylowaccumulationratessuchastheEDC,
B31-B33andB36coresfromAntarctica(allwithaccumulationratessmallerthan0.067mw.e./a)
donotshowanyincreasedintensityatthedepthofsecondmaximumvariabilityindensity.The
Greenlandcoreswithrelativelymoderateaccumulationratesaround0.1mw.e./aaswellastheB25
corefromAntarcticawitharelativelyhighaccumulationratesof0.14mw.e./ashownoclearpeak
inintensityofthefrequencyofaccumulationratebutpatcheswithincreasedintensitiesatseveral
frequenciesatthedepthofthesecondmaximumindensityvariability.
Ourfinding,thatinmanycoresseasonalvariationsindensitydevelopwithdepth,questionthe
theoriginoftheannualcycleindensity.Sinceitcanbeexcluded,thatanewpropertyisintroduced
intothefirnatthedepthwheretheseasonalityisdeveloping,wemustconsideraparameter,whichis
depositedatthesurface,preservedinthefirncolumnandalteringthedensificationofthefirn.Impu-
ritiescouldbeacandidateastheyareoftendepositedwiththesnowandexhibitaseasonalvarying
concentration.Totestthishypothesisweanalyzethehigh-resolutionCaconcentrationprofilesof5
firncores.OurchoiceofCaissimplyduetothefactthatCaistheimpurityparameterforwhichthe
largestamountofmeasurementswereavailable.

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3.2Linkbetweendensity-andCaconcentrationvariability

TovisualizetheCaconcentrationanddensityprofilesindetail,shortintervalsfromthreestagesof
thecoreB29areshown(Figure2).ThecorrelationcoefficientbetweendensityandCaconcentration
isdisplayedforcomparison.Thefirstintervalfromthesurfaceischaracterizedbyhighvariabilityin
180densityandnorelationshipbetweendensityandchemistryvariabilityisobserved(Figure2,upper
panel).ThedensityshowschaoticfluctuationsandnocorrelationtotheCaconcentrationrecordcan
bedetected(panelA).Thesecondintervalfromtheapproximately12mw.e.depthischaracterized
byminimumdensityvariability(Figure2,upperpanel)andasignificantcorrelationwithCacon-
centrationvariabilityisvisible(Figure2,panelB).Atthethirdintervalfromapproximately30m
185w.e.depth,both,thevariabilityaswellastheCaconcentration-densityrelationshipreachamaxi-
mum(Figure2,upperpanelandpanelC).AttheB29firncorethecorrelationbetweendensityand
Caconcentrationincreaseswithdepthandreachesamaximumatthesecondmaximumofdensity
.ariabilityvWefurtheranalyzetheCaconcentration-densityrelationshipforthefirncoresB20,B31,B32and
190B33and(Figure3and4).Allfivefirncoresshowanincreaseindensity-Caconcentrationcorrelation
withdepth,andasignificantcorrelationatthedepthofthesecondmaximumindensityvariability
(Figure3and4,upperpanel).
FortheGreenlandcores,withrelativelyhigh(B29with0.15mw.e./a)andmediumaccumulation
rate(B20with0.1mw.e./a)thecorrelationbetweendensityandCaconcentrationisdistinct(Figure
1953,upperpanel).InfirncoreB29theaccumulationratefrequencyisclearlydetectedinthechem-
istryprofileforalldepths(Figure3,lowermostpanel).Inthedensityprofiletheaccumulationrate
frequencydevelopswithdepthandappearsatthevariabilitymaximum(Figure3,midpanel).B20
doesnotshowtheaccumulationratefrequencyinthechemistryordensityvariabilityprofile(Figure
3,lowermostpanel),butneverthelessasignificantCaconcentration-densitycorrelationisdeveloped
200panel).upper3,(FigureFortheAntarcticfirncoresB31-B33withaccumulationratesof0.044-0.063mw.e./athe
Caconcentration-densityrelationshipisnotashighbutstillsignificant(Figure4,upperpanel).A
significantsignatureofaccumulationratefrequencycannotbedetectedinthedensityvariability
wavelet(Figure4,midpanels).TheCaconcentrationvariabilitywaveletdoesshowsignificant
205intensityclosetothefrequencyoftheaccumulationrate,butnotclear(Figure4,lowermostpanels).

Discussion4

Thewaveletanalysiscanhelptostudytheevolutionofthedensityvariabilitywithdepthandto
detectanannualcycleinthevariations.Thepresentedresultsquestionstheseasonalityofsnow
layersatthesurfaceastheyareoftenreportedfromsnowpitstudies.Mostofthefirncoresdonot
210showadistinctsignalofaccumulationratefrequencyinthedensityvariabilityatthesurface.This

7

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.2.Fig

core.firnB29theofrelationshipDensity-Ca

betweendensityandCaconcentration(redline)are

correlationtheandline)(blackariabilityvdensityThe

shownintheupperpanel.Horizontallinesmarkthe

95%(dashed)and99%(dotted)confidenceintervalsofthecorrelation.ThelowerpanelsA-Cshowdetailed

profilesofthedensityandCaevolutioninthedepthintervalsmarkedintheupperpanel(verticalgreylines).

Thecorrelationvaluesoftheshowndepthintervalsaregiveninthepanels.Atthesurface(A),highdensity

variabilityandnocorrelationaredetected.Attheminimumofdensityvariability(B)apositivecorrelation

betweendensityandCaconcentrationisfoundthatincreasesatthesecondarymaximumofdensityvariability

(C).

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126

Fig.3.Density-Carelationship(upperpanel)andwaveletsspectraofdensity(middlepanel)andCaconcen-

tration(lowerpanel)oftheB20andB29firncores.Theminimumandsecondarymaximumofthedensity

variabilityaremarkedwithverticallines.Inthewaveletspectra,thescalecorrespondingtotheaccumulation

rate(horizontalline)andpointwisesignificantareas(blackcontours)aremarked.Inbothcores,thedensity

variabilityevolvesfromrandomvariationsatthetop,toavarianceminimumataround12mw.e.andtoa

secondarymaximumindensityvariationsconcentratedaroundtheaccumulationrateingreaterdepths.The

spectrumoftheCalciumconcentrationislessdepthdependentandshowsvariabilityattheaccumulationrate

inalldepths.ThecorrelationbetweendensityandCachangesfromnocorrelationatthesurfacetostrong

correlationvaluesbetween10-50mw.e.depth.

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215

220

225

Fig.4.AsFig.3butforAntarcticcoresB31,B32andB33.Inallcores,asignificantcorrelationbetween
densityandCalciumisdetectedindepthsdeeperthanthedensityvariabilityminimum,althoughthedensity-Ca
relationshipsareweakerthanintheGreenlandcores(Fig3).ThedensityandCavariabilityarenotconfinedto
thefrequencyoftheaccumulationrate.Thismightbecausedbyastronginterannualvariabilityinaccumulation.

indicates,thatinthenearsurfacesnownoseasonalvariabilityinthedensityisapparent.Thisisin
linewiththeobservationbyStenbergetal(1999),whodidnotfindarelationbetweenseasonally
varyingisotopemeasurementsanddensityprofilesinsnowpitanalysis.AlsoatDomeFujithe
densityvariabilitydidnotreflectseasonalvariations(Horietal.,1999).Thismightbetheresult
ofdiscontinuousprecipitationthroughtheyearaswellasredistributionanderosionofdeposited
surfacesnowbywind.Theinteractionbetweenwindandunboundedparticlesatthesnowsurface
controlstheinitialdensityofthesnow.Themeteorologicaldatashownoclearseasonalsignalin
windspeedatalmostalllocations(Birnbaumetal.,2010).Furthermoretheroughsurfaceintroduces
ahighspatialvariabilityofpatcheswithdifferentdensity.Thereforeitcanbeassumedthatatmost
sitestheinitialdensityhasnoannualcycle.Thepostdepositionalsnowmetamorphismisdrivenby
temperatureandtemperaturegradientswithaninherentclearannualcycle.However,thisseasonality
seemstobenotimposedonthedensityvariationsbecauseoftheirstrongdependenceoninitial
.densityThewaveletanalysisalsodeliverssurprisingresultsabouttheevolutionofthevariabilitywith
depth.Forallfirncoreswefindrapiddropindensityvariabilityuntilaminimum,displayedbythe
blankzonewithinthepowerspectraatapproximate10-12mdepthw.e.(Figure1andSupplement

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Figure2).Below,theamplitudeinvariabilityincreasesagain,butwithdifferentfrequencies.We
observe,thatatsomefirncores,theincreaseddensityvariabilityingreaterdepths,showsthefre-
quencyoftheaccumulationrate,andthusaseasonalvariability.ThisisincontrasttoLiandZwally
230(2002,2004),whostatethattheseasonalvariabilityindensity,createdatthesurfaceiskeptallthe
waydown,whiletheamplitudeisreducedwithdepth.Ourresultsimply,thattheseasonalityis
developingwithdepthatthesesites,eventhoughnoseasonalfrequencyisapparentatthesurface.
Thiscouldbeahint,thatthedensityrecordspartlyloosetheirmemoryofdensityfluctuationsfrom
thesurface.Withourresultstheassumptionofaseasonalvaryingdensitywhichispreservedinthe
235firnandicecolumn,cannotbeconfirmed.
Wealsoobserve,thatmainlysiteswithmoderatetohighaccumulationratesshowthisdevelop-
mentofaseasonalfrequencywithdepth(SupplementFigure2).Thisindicates,thattheappearance
oftheaccumulationratefrequencyingreaterdepthsisrelatedtothemagnitudeandvariabilityofthe
accumulationrate.Atsiteswithhighandstableaccumulationrates,theseasonalvariabilitydevelops
240withdepth,whereassiteswithloworvaryingaccumulationratesdonotshowthispattern.

4.1Whyisaseasonalfrequencycreatedwithdepth?

Thepresenteddatadonotallowasufficientanalysisofthereasonfortheobserveddevelopment
ofseasonalitywithdepth.Wecanonlycomparethehigh-resolutiondensitydataintermsoflocal
climateconditions,theappearanceandintensityoftheseasonalitywithdepthandafewCaconcen-
245trationprofiles.Neverthelesswestarthereapreliminarydiscussiononpossiblemechanism,since
thequestionisimportantfortheanalysisandinterpretationofdensity-relatedpropertiessuchasthe
aircontentinbubblyice.
TheCaconcentrationexhibitsastrongincreasingcorrelationwithdensitywithincreasingdepth.
Thiscorrelationdoesnotnecessarilyreflectthecausalreasonoftheincreaseofseasonalityinden-
250sitywithdepth.Anyparameterpresentwithseasonalvariabilityinthefirncouldcausetheobserved
changeinthedensityvariabilityfrequency.Possiblecandidates,whichcouldalterthefirndensifica-
tion,areimpuritiesorthemicrostructureofthesnowlayersitself,i.e.grainsize.Inthefollowing
wediscussthelikelihoodofgrainsize,andimpuritiesalteringfirndensity.WeconsidertheCa
concentrationasaproxy,representinganunknownparameter,whichisdepositedwithasimilar
255frequencyastheCaconcentration.
Microstructuralpropertiessuchasthegrainsizeandcoordinationnumberareconsideredaspa-
rametersinfluencingthedensification(Alleyetal.,1982;Alley,1987;SalamatinandLipenkov,
2008;Salamantinetal.,2009).Coarsefirnischaracterizedbylowdensityandfewlargeconnections
toneighborsanddensifiesfasterthanfinefirn,characterizedbyhighdensityandhighconnectivity
260(Alleyetal.,1982).Ifgrainsizeshowsseasonalvariationsitcouldbeapossiblereasonforthe
observeddevelopmentofseasonalityindensitywithdepth.Thereareobservationsfromsnowpits,
linkingmicrostructurepropertiestodistinctseasons.Forexample,depthhoarlayersformedinfall

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265270275280285290295

orspringcouldcarryanotherchemicalcompositionandconcentrationthenfinegrainedsnowfrom
eitherwinterdeposition(Jones,1983)orsummerdeposition(Koerner,1971;Gow,1965;Birnbaum
etal.,2010).However,microstructureseemstobecloselylinkedtodensity.Thestartingdensityand
arelatedcoordinationnumberofthegrainsleadstoadifferentextentoftheintervalatwhichgrain
boundaryslidingactsasmeandensificationregime(Alley,1987;Salamantinetal.,2009).Further
moreastronglinearrelationshipbetweendensityandcoordinationnumberinpolarfirnhasbeen
foundbyFreitagetal.(2008),indicatingthatsinglelayersarecharacterizedbyspecificgrainsize,
coordinationnumberanddensity.Thesefindingsquestiontheindependenceofgrainsizeanddensity
asphysicalpropertiesoftheupperpolarfirnlayers.Additionallyrecentfindingsonirregulargrain
boundariesandchanginggrainsizedistributionswithdepthinpolarfirnindicatedynamicrecrystal-
lizationtohappenatalldepthintervalsinthefirncolumn(Kipfstuhletal.,2009).Thisimpliesthat
thefirnmicrostructureisnotstationarybutchangescontinuallywithdepthandthusdoesprobably
notcarryaseasonalsignalingreaterdepths.Ifgrainsizeanddensityarerelatedtoeachotherin
thesurfacefirn,andifthegrainsundergodynamicrecrystallization,grainsizemustbequestioned
astheparameterintroducingseasonalityinthedensityvariabilityatgreaterdepth.
Polarfirnimpuritiesontheotherhandconsistsofsolublecontentsandmicro-particlesandboth
canbethoughttoalterthedensityofthefirn.Theimpactofmicro-particles,i.edustconcentration,
onthephysicalfirnpropertieshasbeenobservedearlier(Svenssonetal.,2005).Theimpactof
solublechemistryonthesnowandfirnpropertieshasbeeninvestigatedonlyforsurfacesnow.
Fordeeperfirnandicetheimpactofimpuritiesonthegraingrowth(grainboundarymigration)has
beenshownintheory(Alleyetal.,1986a,b).Impuritiesandinclusionssuchasmicroparticlesorair
bubblescanhinderthemigrationofgrainboundariesandthereforereducetherateofgraingrowth.
Thisalteredgraingrowthmighthaveanimpactonthedensityofsinglefirnlayers.Fromdeepice
coreobservationsofgrainsizeanddustconcentrationsitseems,thatdepthintervalswithhighdust
concentration,correlatedwithhighCaconcentrations,showsmallergrainsizesandahigherdegree
ofdeformationthandepthintervalswithlowerdustconcentration(Svenssonetal.,2005).Onthe
otherhandthetheoryandicecoreobservationsholdformatricesoficecrystals,withcontactareas
allaroundeachgrain.Soitisquestionableiftheseprocessesarerelevantforthehighlyporoussnow
andfirnatthesurface,wheremuchmoremobilityanddegreesoffreedomofthesnowgrainsand
possible.isclustericeFromSnow-AirInteractionstudiesitisknown,thatduetoitshighporositymuchofthesnowpack
volumeconsistsofairthatcanbereadilyexchanged.Numerousphysicalandchemicalprocesses
canaffecttracegasesinthesnowpack(DomineandShepson,2002).Thereisalackofknowledge
ofthephysicalandchemicalnatureofnaturalicesurfaces.Adisorderedlayer,oftencalledthe
quasi-liquidlayer,existsonicesurfacesanditsthicknessincreaseswithtemperatureandionsolute
2002).Shepson,and(DomineconcentrationInprincipletherearetwowayshowanincreasedsoluteconcentrationmayinfluencetheinterme-

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300305310315320325330

diatedensificationbelow12mw.e.depthandthebubbleclose-off.Dopingtheindividual(mono-
crystalline)snowgrainswithionicimpuritiesgenerallyincreasestheductilityofice,i.e.itscreep
(Kang,2005).Thus,layerswithhigherimpuritycontentcaninprincipledensifyfaster.
Alternatively,ahigherimpuritycontentatthegrainboundariesandtriplejunctionsshouldin-
creasethethicknessofthequasi-liquidlayercoatingindividualgrains.Themigrationofthisquasi-
liquidbycapillaryforceshasbeenhypothesizedtocontributetothesinteringprocessduringfirn
densification(Dash,1989;Dashetal.,2006).Againahighimpuritycontentatthegrainboundaries
wouldleadtoanaccelerationofthedensificationprocess.Adetailedtheoreticalassessmentofthese
phenomenaisbeyondthescopeofthispaper,however,recentstudiesofthelocationofimpurities
inpoly-crystallineicepointtolargerimpurityconcentrationsatthegrainboundariesandsmaller
onesinthebulkofthesnowgrains.Obviouslythisisdependentontheionicspeciesconsideredbut
overallcouldsupportthequasi-liquidlayereffecttobeapossibleexplanationfortheobservedfaster
densificationofhighimpuritylayersinpolarfirn.
Both,increasedmicro-particleorsolublecomponentconcentrationcouldchangetheproperties
ofthefirnintermsofdensity.Itseemspossible,thatfirnlayerscarryingmoreimpuritiesdensify
faster,thanfirnwithlayerswithlessimpurities.Suchatrendcanbedetectedinthepresenteddata:
LayerswithahighCaconcentrationarecorrelatedwithhighdensityvaluesandviceversa(Figure
2,lowermostpanel).Butthemechanismfortheimpactofimpuritiesonthedensityofthefirncanot
bedetectedwithinthisstudy.
Onthebaseofthepresentedresultswehypothesizethatseasonallydepositedchemicalimpurities
leadtotheobservedsignaloftheaccumulationratefrequencyintheCaconcentrationwavelet(for
exampleB29).ThisCaconcentrationvariabilitywithitsspecificfrequencywillbesuperposed
onthedensityvariability,leadingtotheobservedintensitypeakinaccumulationratefrequencyat
greaterdepths.Allofthefivefirncores,whereCaconcentrationmeasurementsareavailableshowa
significantincreasingCaconcentration-densitycorrelationwithincreasingdepth.
ButsincethethreeAntarcticcoresdonotshowadistinctpeakinthefrequencyoftheaccumula-
tionrateintheirdensityvariabilitywavelet,weassume,thatthetemporalvariabilityofaccumulation
ratedetermines,whetheraseasonalsignalinchemicalimpurityconcentrationisinfluencingtheden-
sityprofile.Siteswithhighaccumulationratesandwithrelativelysmallinter-annualvariabilityin
accumulationrateshowaseasonaldepositionofchemicalcomponents,whichwillbesuperposed
onthedensityvariability.Ifaccumulationrateissmallorshowsalargevariability,evenaseasonal
chemistrydepositionwouldnotleadtoaaccumulationratefrequencyinthedepthdomain.Nev-
erthelessacoherentdensityandchemistryvariabilityrelationshipisfoundbelowtheminimumin
densityvariability,indicatingtheimpactofimpuritiesonthedensityofpolarfirn.

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355

5ConclusionandSummary

Weobserve1.thataseasonalsignalindensitydevelopswithdepth,2.thecorrelationbetween
densityandCaconcentrationdevelopswithdepthandconclude3.thatimpuritiesorayetunknown
parameterincorporatedintothesnowwiththesamefrequencyastheCaconcentration,altersthe
firndensification.Thesnowdensityvariabilityatthesurfaceisratherrandomandonlyforsome
sitesinhabitsaseasonalsignal.Thedensityvariabilityatthefirn-ice-transitionshowsaseasonal
signalatsomesites,butthisseasonalityhasdevelopedwithdepthanddoesnotoriginatefromthe
surface.Eitherimpuritiesoranyparameterwithlikewisefrequencyindepositiondoesalterthefirn
densification.Atdensitiesanddepthsofthefirn-icetransitionwefindincreasedvariabilityindensity.This
densityvarieswithaseasonalfrequency(SupplementFigure2,B16,B17,B26,Figure1,B29).So
onecouldindeedidentifylayers,whichshowasummerorwintersignal,asiscommonlyassumed
(Landaisetal.,2006;SeveringhausandBattle,2006;Kawamuraetal.,2006).However,thevari-
abilityandthusthedistributioninhighandlowdensitylayersisnotaresultofdensitydistribution
atthesurface.Thedensityvariabilityatthefirn-ice-transitionseemstobetheresultofunknown
processalteringthedensityduringburialandaccordinglyalinktooriginalsurfacecharacteristicsin
termsofdensityisnotpossible.Theassumptionofadirectlinktosurfaceconditions,governingthe
layeringanddensityvariabilityatthefirn-icetransitionisnotconfirmed.
OurfindingshavealsoimportantramificationsonthecauseofprecessionalO2/N2variations
foundinrecordsderivedfromairbubblesinpolarice(Bender,2002;Kawamuraetal.,2007).Those
variationsarecausedbyasizedependentfractionationduringthebubbleclose-off(Severinghaus
andBattle,2006).Sincethedensitysignalloosesitsinitialstratigraphicinformationcompletelyin
thetop10-15mofthefirncolumn,adirectlineofinfluenceofthelocalradiationbalanceonthe
surfacesnowdensitycannotbetheultimatereasonfortheobservedO2/N2fractionationatclose-off
depth.

ement.knowledgAc

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surfacesnowalongthetraverseroutefromcoasttoDomeFujiStation,QueenMaudLand,Antarctica,Proc.
NIPRSymp.PolarMeteorol.Glaciol.,10,1–12,1996.
Sommer,S.,Wagenbach,D.,Mulvaney,R.,andFischer,H.:Glacio-chemicalstudyspanningthepast2kyron
threeicecoresfromDronningMaudLand,Antarctica2.Seasonallyresolvedchemicalrecords,Journalof
GeophysicalResearch,105,29423–29434,2000.
Stenberg,M.,Hansson,M.,Holmlund,P.,andKarlf,L.:Variabilityinsnowlayeringandsnowchemistryinthe
vicinityoftwodrillsitesinwesternDronningMaudLand,AntarcticafromDronningMaudLand,Antarctica
2.Seasonallyresolvedchemicalrecords,AnnalsofGlaciology,29,1999.
Svensson,A.,Nielsen,S.W.,Kipfstuhl,S.,Johnson,S.J.,P.,S.J.,Bigler,M.,Ruth,U.,andRthlisberger,R.:
VisualstratigraphyoftheNorthernGreenlandIceCoreProject(NorthGRIP)icecoreduringthelastglacial
period,JournalofGeophysicalResearch,110,2005.
Taylor,L.D.:GlaciologicalStudiesontheSouthPoleTraverse,1962-1963,AntarcticResearchSeries,Antarc-
ticSnowandIceStudies2,16,209–224,1971.
Torrence,C.andCompo,G.:Apracticalguidetowaveletanalysis,BulletinoftheAmericanMeteorolical
1998.61–78,79(1),,SocietyUdisti,R.,Becagli,S.,Benassie,S.,Castellano,E.,Fattori,I.,Innocenti,M.,Migliori,A.,andTraversi,R.:
Atmosphere-snowinteractionbyacomparisonbetweenaerosolanduppermsotsnow-layerscompositionat
DomeC,EastAntarctica,AnnalsofGlaciology,39,2004.
Wilhelms,F.:MeasuringtheConductivityandDensityofIceCores,BerichtezurPolarforschung,AlfredWe-
generInsititutf¨urPolar-undMeeresforschung,191,1996.
Wilhelms,F.:MeasuringtheDieelectricPropertiesofIceCores,BerichtezurPolarforschung,AlfredWegener
Insititutf¨urPolar-undMeeresforschung,367,2000.
Wolff,E.,Hall,J.S.,Mulvaney,R.,Pasteur,E.C.,Wagenbach,D.,andLegrand,M.:Relationshipbetween
chemsitryofair,freshsnowandfirncoresforaerosolspeciesincoastalAntarctica,JournalofGeophysical
Research,103,11,057–11,070,1998.
Zwally,H.J.andLi,J.:Seasonalandinterannualvariationsoffirndensificationandice-sheetsurfaceelevation
attheGreenlandsummit,JournalofGlaciology,48,199–207,2002.

18

136

510

Table1.Thefirncoresiteswithannualmeantemperature,accumulationrateandreferences:

LonLatNamedegdeg

Greenland-37.629975.94026B1NGT-37.624875.25047B1NGT-36.403376.61708B1NGT-36.3078.490B2NGT-41.137480.0001B2NGT-49.216777.25336B2NGT-43.492076.00399B2NGTAntarcticaBerknerIsB25-79.6142-45.7243
-3.4303-75.58151B3DML0.0070-75.00232B3DML6.4985-75.16703B3DML0.0684-75.002536/37BDML-6.6989-71.16218B3PreIPICS-9.9167-71.56809B3PreIPICS-6.6670-71.5680DML95PreIPICS-9.5583-72.0640DML97PreIPICS123.3500-75.1000EDC2CDome

FigureSupplement1Appendix5

AnnualationvElemeanemperatureTma.s.l.degC

30402820250821476218525982874

88626692882316028916906545407603233

19

137

-27-30-30-31.6-31.6

-27-42-42-44.6-18.1-17.9-19.2-20.4-53

AccumulationRate.e.wm

0.1420.1040.1080.180.153

0.140.0630.0610.0440.0671.250.770.550.490.025

References

(2)(1),(2)(1),(2)(1),(2)(1),(2)(1),(3)(1),(2)(1),

(4)(5)(5)(5)(6)(7)(7)(7)(7)(8)

Fig.5.Depthdependenceofthedensityvariability,density-Carelationship(upperpanel)andwaveletspectrum

ofthedensity(lowerpanel)ofanartificialrandomdensitydataset.Theresultsshowconstantdensityvariability

andverysmallcorrelationvaluesasexpectedforarandomdataseries.Thesmallnumberofspurioussignificant

correlationvalues,aswellassomespurioussignificantpatchesinthewaveletspectra

significancetestsarelocal/pointwise,andmultipletestingsareperformed

6FigureSupplement2Appendix

20

138

are

xpected,e

as

both

.6.Fig

spectraeletvawDensityAntarctica.andGreenlandfromcoresfirn12remainingthefor

minimumThe

andsecondarymaximumofthedensityvariabilityaremarkedwithverticallinesandthescaleoftheaccumu-

lationrateashorizontalline.Pointwisesignificantareasaremarkedwithblackcontours.Allcoresshowa

densityvariabilityatthesurface,whichisspreadoveralargerangeoffrequencies.Ingreaterdepths,most

coresexhibitdensityvariabilityaroundthefrequencyoftheaccumulationrate.

21

139

anewgraingrowthmodel

polarfirn-evolution,variability

and

eredyal

fo

esiz

Grain

-

3

nlicatioPub

C

.J

reitag,F

and

.W

king,Dier

,.S

,wLino

,.WM.Hörhold,

In

ation.prepar

140

JournalofGlaciology,Vol.00,No.000,0000

1Grainsizeoflayeredpolarfirn-evolution,variabilityandanew

2graingrowthmodelobtainedbymicro-Computer-Tomography

3

45

6789101112131415

MariaW.H¨orhold,1StefanieLinow,1WolfgangDierking,1JohannesFreitag,1

1Alfred-Wegener-InstituteforPolarandMarineResearch,Bremerhaven,Germany
maria.hoerhold@awi.deE-mail:

ABSTRACT.FirnmicrostructurefromsixdifferentsitesinGreenlandandAntarcticawasinvestigatedby
meansofX-ray-micro-Computer-Tomography.Theeffectiveradiuswascalculatedfromspecificsurface
area(SSA)andusedasameasureofgrainsizethatavoidstheambiguitiesofalternativemethodsofgrain
sizequantification.Theevolutionofgrainsizewithdepth,densityandtimewasinvestigatedatthedifferent
locations,coveringabroadrangeinlocalclimateconditions.Thegrainsizeshowslargevariationswithin
singledepthintervalsateachsite.Bothdensityvariabilityandgrainsizevariabilityarestrongindicators
oflayeringofthefirn.Thevariabilityingrainsizeseemstoamplifiywithdecreasingannualmeantemper-
atureandaccumulationrate.Asimplemodelofgraingrowthisdevelopedwhichenablesapredictionof
therapidgraingrowthattheuppermostmeterdrivenbytemperaturegradients.Thismodelcanbeused
tosimulategrainsizeprofilesasaninputformicro-wavebackscattermodelsinamorerealisticfashion.

1

16ODUCTIONINTR17In-situdataofmicrostructureoftheupperfirncolumnaredifficultandtimeconsumingtoobtain.Fielddatalackspatialrepresentativity
18andupscalingfielddatacaninprinciplebeaccomplishedusingremotesensingmethods(Domineandothers,2008).Changesinmass
19balanceofthepolaricesheetscanbeinferredfromremotesensingsignatures(Flachandothers,2005;Lacroixandothers,2008).
20Formanycryosphericmicrowaveremotesensingapplications,itisnecessarytoconsidermicrowave-firninteractionsintheupper
21layersofthesnowpack,withwavelength-dependentpenetrationdepthsrangingfromcentimeterstoapproximately100m(Legresy
22andRemy,1998).Inmanystudiesthesignal-snowmicrostructureinteractionhasbeeninvestigated(Flachandothers,2005;Rotschky
23andothers,2006;SrivastavandSingh,1991;Tranandothers,2008).Regionswithacertainpatternofbackscattersignatureswere

141

2

H¨orholdandothers:Firnmicrostructure

24identifiedandassignedtohavespecificfirnproperties(Rotschkyandothers,2006;Tranandothers,2008).However,distinctfielddata
25toparameterizethesesnowclassesarestilllacking.
26GrainsizedataareavailableforsinglepointsofmeasurementinAntarcticaandGreenland(Alleyandothers,1982;Courvilleand
27others,2007;Freitagandothers,2004;Gayandothers,2002;Gow,1969;Gowandothers,2004;Shiraiwaandothers,1996).The
28problemofcomparingthepublisheddataliesinthetheapplicationofverydifferentmeasurementmethodsandthedifferentdefinitions
29ofgrainsize.Furthermoreobservationsdifferintheirtimeoftheyearandinresolution.Seldomasinglestudyconsidersverydifferent
30sites,sothatarelativecomparisonofgrainsizeandgrainsizeevolutionwithdepthobtainedbysimilarmethodsareavailable.Examples
31areNishimuraandMaeno(1985),Shiraiwa(1996),Gayetal.(2002)orTaylor(1971).Maincharacteristicdifferenceingrainsizeand
32grainsizevariabilityintermsoflayeringwerefoundbetweenfirncolumnsfromnearcoastalareas,katabaticwindregionsandthe
33highAntarcticPlateau(Shiraiwaandothers,1996;Gayandothers,2002).
34Thereisalackofacomparablegrainsizedefinition.Recently,theeffectiveradiusdeterminedfromthespecificsurfacearea(SSA)as
35agrainsizemeasurewasintroducedasasuitableparameterconsideringtheinteractionoftheair-ice-interfaceinchemicalorphysical
36processes(Domineandothers,2008).Severalalpinesnowmeasurementsandexperimentswereconductedusingtheeffectiveradius,
37theSSAandotherphysicalpropertiesascomparableparametersfordifferentsnowtypesandtheirchangewithtime(Flinandothers,
382004;SchneebeliandSokratov,2004;KaempferandSchneebeli,2007).Mostcomprehensiveoverviewofavailablesnowproperties
39isgivenbyDomineetal.(2008)foralpinesnowandbyGayetal.(2002)forAntarcticsnow.Acomparableandsystematicstudyof
40polarsnowandfirn,investigatingthegrainsizeintermsoflayeringandevolutionwithdepthandtimeunderdifferentlocalclimate
41conditionsismissing.Forremotesensingapplicationstheknowledgeonfirngrainsizeissubstantial.Thesignalreturnatthesensor
42issensitivetograinsize[e.g.Lacroixandothers(2008);ShiandDozier(2000)]orstronggradientsinmicrostructurepropertiesat
43theinterfaceofdifferentlayerswithinthefirn(Flachandothers,2005;Lacroixandothers,2008;Rottandothers,1993;Shiraiwa
44andothers,1996).Accordingly,thestronglynon-linearparticlegrowthintheupperfirnlayersinfluencedbytheseasonalanddiurnal
45thermalgradientneedstobeconsideredtoapproximatearealisticgrainsizeprofile.
46Variousmethodsformodelinggraingrowthprocesseshavebeendescribedintheliterature.Jordan(1991),Colbeck(1983),Baunach
47andothers(2001)modeltemperaturegradient(TG)growthasaprocessdrivenbythesaturationvaporpressuregradient.Inthiscase,
48grainsgrowonlywhenthereisatemperaturegradientpresentwithinthesnowpack.FlannerandZender(2006),amongothers,
49havecreatedcomplex3Dmodelsoffirnmetamorphismthatconsiderphysicalprocessesofgraingrowthingreatdetail,butrequire
50substantialamountsofcomputationtime.Foranumberofapplications,itisdesirabletouseasimple,fast,empirical1Dapproachto
51modelfirnproperties.MaenoandEbinuma(1983)foundthatsnowgraingrowthcanbedescribedasapressuresinteringprocess,and
52therearemanyexamplesinliteraturewheretheArrheniusequationisusedtomodelequi-temperature(ET)graingrowthasafunction
53ofdepthe.g.byAlleyandothers(1982),Gowandothers(2004),Flachandothers(2005).

142

H¨orholdandothers:Firnmicrostructure

3

54Duetoalackofinter-comparablegrainsizedata,ithasbeendifficulttoassestheaccuracyofgrainsizeprofilessimulatedusing
55abovemethods.Withinthisstudyweaimtofillthegapofmissingcomparablegrainsizedataandpresentasetofgrainsizemea-
56surementsfromclimatologicallyheterogeneoussitesthatcanbeusedtoverifyandimprovegrainsizemodelingforremotesensing
57application.Weusetheeffectiveradiusobtainedfromspecificsurfaceareatoinvestigatethegrainsizeevolutionwithdensity,depth
58andtimeat6differentpolarsitesinGreenlandandAntarctica.Wefindvariabilityduetothelayeringnotonlyindensitybutalsoin
59grainsize.Wefindthatgrainsizeanddensityarelinkedwitcheachotherinspecifieddepthintervals.Largegrainsizecorrespondsto
60lowdensityandviceversa,whereastheoveralltrendwithincreasingdepthandtimeshowsanincreaseofgrainsizewithincreasing
61density.Wefinddistinctdifferencesinabsolutegrainsizeandgraingrowthatthedifferentsites.Butalsotherelationbetweendensity
62andgrainsizevariesfromsitetosite.Wefinallyintroduceanewsimplegraingrowthmodel,whichisabletocapturetherapidgrain
63growthintheuppermostdepthintervalsforawiderangeofpolarclimateconditions.

64METHODS65FirnCoreLocations
66Sixsurfacefirncores,onefromGreenlandandfivefromAntarcticaareanalyzed.Theycoverabroadrangeinannualmeantempera-
ture,accumulationrate,elevationanddistancetothecoast(Figure1,Table1).

B38B36Depot700B26

Hercules DomeDome C

(a)Corelocation–Antarctica(b)Corelocation–Green-
land

Fig.1:ThelocationofthefirncoresinAntarctica(a)andGreenland(b).

6768TheB26firncorerepresentsmediumaccumulationrateandannualmeantemperatureoftheGreenlandPlateau.Thefirncore
69fromDomeCrepresentslowesttemperaturesandaccumulationrateinAntarcticabutonlymaterialstartingfrom6.6meterdepth
70isavailable.TheDP7firncoresiteshowsalmostsimilarannualmeantemperature(estimatedfromModerate-resolutionImaging
71Spectroradiometer(MODIS)surfacetemperaturedata)andaslightlyhigheraccumulationrate(estimatedfromfrominterpolationof

143

4

Table1:Firncorelocationsandenvironmentalconditions

Campaign/NameLatitudeLongitudeTemperatureAccumulationElevation
LocationdegdegdegC[mw.e.·a−1]ma.s.l.
GreenlandNGTB2677.2533-49.2167-31.60.182598
AntarcticaDMLB35/36-75.00250.0684-44.60.0672415.5
PreIPICSB38-71.1621-6.6989-18.11.250690
Norw.-amer.TraverseDP7-75.6534319.24484-51.0∗0.045∗3530
DomeCFT-75.10123.35-53.00.0253233
IPICSHD-86.00-105.00-37.0∗∗0.1802610

H¨orholdandothers:Firnmicrostructure

72accumulationratesofnearbysites(Isakssonandothers,1999).FromKohnenstation(EDMLdrillingsite)2firncoresB35andB36
73areavailable.Furthermore12singlesurfacemeasurementshavebeenconductedinaustralsummer2005/2006atEDML.Whilethe
74HerculesDomefirncore(HD)representsmediumtolowtemperaturesandmediumaccumulationrates,theB38firncorefromthe
75coastalareashowsremarkablehighaccumulationrateandtemperature.InaformerstudyAntarcticsurfacesnowhasbeenclassified
76into10classes,accordingtobackscatterbehaviorofmicrowavesattwodifferentfrequencies(Rotschkyandothers,2006).Thefirn
77coresitesofthisstudycover4ofthesesnowclasses:B38fallsintoclass8,B36(B35)andDP7intoclass4,FTattheDomeC
78siteintoclass3andHerculesDomeintoclass10(Table2).Theclassificationhasbeenroughlydescribedbyknownfeaturesofwind
79pattern,temperatureandaccumulationrate.Butsofar,nogroundtruthdatawereconsidered,indescribingandparameterizingthese
80classes.wsno81Density82Densitiesaremeasuredwithaverticalresolutionof1mmusinganon-destructiveloggingsystemincludingaL¨offeldensimeter.Asa
83radiationsource137Cswasused.Usingthemeasuredgamma-raysignalintensityIinrelationtothesignal’sintensityinairI0,themass
84absorptioncoefficientμice=0.085645m2kg−1±0.01(Wilhelms,1996,2000)andthediameterdofthemedium,thedensityρcanbe
85calculated.DetailsaregiveninWilhelms(1996;2000).Allmeasurementswereconductedattemperaturesof-20degCinthecold
86laboratoryoftheAlfredWegenerInstitute(AWI),Bremerhaven,Germany.Highresolutiondensitymeasurementswereconductedat
87allbuttheHerculesDomefirncore.

144

H¨orholdandothers:Firnmicrostructure

Table2:Firncoreproperties

Namedepthintervaltimeintervalnumberofsamples
maGreenlandB260.012-7.30.025-16.18154
AntarcticaB35/360.29-10.941.79-71.26114/121/12
B380.0325-10.960.157-4.4180
3690.37-112.270.05-11.978DP7374110.825-367.9126.6125-20.36FT228/0.076-15.1HD

5

88ComputerTomographyandImageAnalysis
89MicrostructureimagingwasconductedbyMicro-Computer-Tomography.Cylindricsnowsamplesof2.5cmlengthand2cmin
90diameter(1cmforB38)wereplacedonatableinfrontofaX-raysource.Thetablewasrotatedwithstepsof0.9degandeachtime
91ashadowimageistaken.Withabackprojectionproceduretheseshadowimageswereconvertedtoastackofhorizontalgreyvalue
92images.Theresolutionoftheimagingwas40μmforthefirncoresB26,B36,DP7,FTandHD.ForthefirncoreB38aresolution
93of15.73μmwasused.MicrostructuredataofsnowandfirnobtainedfromComputer-Tomographyareshowntofairlywellreproduce
94thesnowparametersuchasdensity(Freitagandothers,2004)andareusedformanyapplications(KaempferandSchneebeli,2007;
95SchneebeliandSokratov,2004).
96CTmeasurementswereconductedatallfirncores.ForthecoresB36,B38,andDP7theuppermost1-2(DP74)meterweresampled
97continuously.Below,40cm(approximately16samples)weresampledeverymeter.B26issampledeverymeterfromtheverysurface.
98TheHerculesDomedatasetcontainsdiscontinuessampleswithnon-equalstepsthroughoutthefirncore.Thelowermostmeterof
99B38andB26wassampledcontinuouslyagain.Inthefollowingthedatafromsingledepthintervalswillbecomparedasameasureof
100ongoingmetamorphism.Theabsolutenumberofsamplesineachintervaldifferinarangebetween16andmorethan20.Linearor
101exponentialfitswereappliedateachdepthintervaltoparameterizethevariabilityduetothelayering.
102ForimageanalysisthesoftwareMAVI,developedbytheFraunhoferInstituteforMathematics(ArmbrechtandSych,2004)was
103used.Theimagestackisloadedintothesoftwareandtreatedasa3-Dobject.Aftersmoothingbyapplyingamedian3x3x3filter

145

6

H¨orholdandothers:Firnmicrostructure

104theimagesweresegmented.Forestimationofthethresholdvalue,twogaussiandistributionfunctionswerefittedtothegreyvalue
105distribution(onefortheporesandonefortheicephase)ofthreeimagesofeachstack.Thearithmeticmeanofthethemaximimvalue
106ofeachofthegaussiandistributionswastakenasthethresholdgreyvalueforsegmentation.Aftersegmentation,anobjectfilterwas
107applied,toremoveallobjectsaddinglessthen1%totheporeoricephase.Fromthe3-Dbinarizedimages,allrelevantmicrostructure
108informationofthesamplevolumecanbeobtained.
109Fromthemeasuredregionacubeof400x400x400voxels(16x16x16mmforB26,B36,DP7,HDandFT,6.3x6.3x6.3mm
110forB38)wasextracted.Thissizeissufficientlylargeenoughtoberepresentativeinvolumeforthefirnpropertiesconsidered(Coleou
111andothers,2001;KaempferandSchneebeli,2007).Porosityiscalculatedfromthesizeoftheporefractioncomparedtothewhole
112volumeofthesample.Densitycanbecomputedfromtheicefractiontimesthedensityofice(ρice=0.917g/cm3).Thechordlength
113lin3ormoredirectionsasameasureofthegrainliandporelpsizecanbeobtained.ThespecificsurfaceareaSSArepresentsthe
114ice-airinterfaceperunitmass:

SSA=Sρd(1)
115withSSA=thespecificsurfaceareaincm2/gandSdthesurfacedensity-theratiooftotalsurfaceandthetotalvolumeofthesample
116andρthedensityofthesample(Domineandothers,2008).FromthattheeffectiveradiusReff-theradiusofequivalent-sizedspheres
117withthesameSSAcanbeobtainedby:

3Reff=SSA×ρice(2)
118Theassumptionis,thattheicephaseofthesnowandfirncanberepresentedbyicespheresoftheradiusReff.Ifweplotthe
119measuredSSAversusthemeasuredchordlength,wederiveasurprisinglyclearrelationship(Figure2),supportingtheassumption,
120thatthesnowgrainscanberepresentedbyequalsizedsphereswithasimilarSSA.
121AdditionallywecomputedtheSSAfromasphereby:
3SSAsphere∼4×r×ρ(3)
3122withrtheradiusofthesphere=34×lsphere.ThecomputedSSAsphereisfairlywellreproducingthemeasuredvalues(Figure2,red
123line).124TheSSAandthechordlengthlaretwoindependentlyobtainedparameters.PlottingSSAsphereoverlsphereofverydifferentfirntypes
125showsabijectiverelationship(Figure2).Thusfromgeometryitisreasonabletorepresentthefirnmicrostructurebytheeffective
126RadiusReff.InthefollowingtheeffectiveradiusReffisusedasgrainsizeparameter.
127AllmicrostructureparametersobtainedbyMAVIrepresentvaluesofthesamplesvolumestructureofeachfirnsample.Formore
128detailsonmicrostructureanalysiswithMAVI,see(OhserandM¨ucklich,2000;ArmbrechtandSych,2004)

146

H¨orholdandothers:Firnmicrostructure

B 26 B 35/36 surface B 35 B 36 B 38 HD FT DP7 SSAsphere

7

9 B 2687 B 35/36 surface6 B 355 B 364 B 38)3 HD2 FT2 DP7log SSA (cm SSAsphere1009876540.020.040.060.080.100.12
grain chord length z (cm)Fig.2:ThespecificsurfaceareaSSAobtainedfrommeasuredsurfaceanddensitywiththemeasuredchordlengthofthedifferent
sites.InredtheSSA,calculatedfromthemeasuredchordlength,assumingequalsizedspheres,isshown.Theresultsshow,thatusing
specificsurfaceareaundertheassumptionofequalsizedspheresgivesasurprisinglygoodapproximationofthesnowstructure.

129TSRESUL130Density131Thedensityprofiles(smoothedbyarunningmeanof20mm)ofthefirncoresshowlargefluctuationsduetothelayeringofthefirn
132(Figure3)anddifferinthedensificationrate.B38showsthehighestdensity,followedbyHD(densityfromCT-measurements).B26
startswithlowerdensity,butovercomesB36andDP7.FireTrackshowsthelowestdensity.

0.600.55)0.5030.45Density (g/cm0.400.350.30

0

5101520Depth (m)

Fig.3:DensityProfilesofthefirncores

147

B 26 B 36 B 38 FT HD DP7

8

H¨orholdandothers:Firnmicrostructure

133SizeGrainandSSA134Forallsiteswefindarapidincreaseingrainsizeintheupperfewmeter(Figure3A).TheB38siteshowssmallestgrainsizeswhereas
135theDP7siteandtheB26siteshowlargestgrainsizes.IngreaterdepthstheEDCsitehaslargestgrainsizes(Figure3A).TheSSA
136decreasesrapidlyintheuppermostmeters.B38showshighestvaluesatthesurface,DP7andB26lowest(Figure3B).Ingreaterdepths
137theEDCsiteshowssmallestvalues.

0.900.800.70 B 26 B 35 (mm)0.60 B 36e B 380.50R DP7 FT0.40 HD0.30 0.20A0.02.55.07.510.012.515.017.520.0
Depth (m)200180160140/g)2120SSA (cm100806040B05101520
Depth ( m)Fig.4:Theevolutionofgrainchordlengthwithporosity(a),porechordlengthandgrainchordlength(b),thespecificsurfacearea
withporosity(c)andtheanisotropywithgrainsize(d).Thecolorsrepresenttheevolutionwithdepthandtime-lightgreyfromthe
nearsurfacesamplestoblackwiththeoldestanddeepestsamples

138Both,SSAandgrainsizeshowlargefluctuations.Inordertocomparethedensityvariabilitywiththegrainsizevariabilitybothwere
139investigatedindetail(Figure4).Densityandgrainsizesforeverysingledepthintervalarecompared.Alinearfitisappliedforeach

148

H¨orholdandothers:Firnmicrostructure

9

140depthinterval.Theevolutionwithdepthisindicatedbyastepwiseshiftincolorfromlightgrey(near-surfacesamples,youngest)to
141black(deepestandoldestsamples).

142B26143ThisfirncorerepresentsmediumaccumulationrateandtemperaturesoftheGreenlandicesheet.Ontheinter-layerlevelthegrainsize
144showsanegativetrendwithdensity.Lowdensitysampleshavelargegrainsizeandviveversa(Figure4A).Withincreasingdepthand
145agetheslopeincreases.Theslopesrangefromapproximately-0.39mm/(g/cm3)to0.81mm/(g/cm3).Theoveralltrendofgrain
146sizeanddensityispositive-withincreasingdensitythegrainsizeincreases.

147B35/36148ThisfirncoresiterepresentsmediumaccumulationratesoftheAntarcticPlateaufromDronningMaudLand,Antarctica.Thegrain
149sizesofB35andB36alsoshowanegativetrendwithdensitywithinsingledepthintervals(Figure4B).Onlythesurfacesampleand
150theuppermostdepthintervalofB35showapositivetrend(Figure4B).Attheverysurfacehighdensityisassociatedwithlargegrain
151sizeandviceversa.Atallotherdepthintervalsrepresentingdeeperandolderfirn,largedensityvaluescorrelatewithsmallgrainsizes.
152Againtheslopeincreasesfromshallowtosteepvalueswithincreasingdepthandtime.TheB36firncoreshowstrendsfrom-0.8to
153-2.4mm/(g/cm3),thesurfaceintervalshowsamuchhigherslope,whereasthebagsfromcoreB35showvaluesslightlylessthanB
15436,rangingfromapproximately-0.33to-1.44mm/(g/cm3).Theoveralltrendisagainpositive,withincreasingdensitythegrainsize
155increases.

156B38157TheB38firncorecomesfromthecoastalregionofDronningMaudLand,Antarctica.Itisnotonlycharacterizedbyveryhigh
158annualmeantemperaturebutalsobyatremendousaccumulationrateof0.12mw.e.peryear.Thegrainsizeshowsapositivetrend
159withdensityforthesingledepthintervals(Figure4C).Largegrainsizecorrespondstohighdensityandviceversa.Theslopeisnot
160changingmuchwithincreasingdepth.Theslopesarepositive,rangingfrom0.35mm/(g/cm3)atthesurfaceto0.54mm/(g/cm3)at
161thelowermostdepthinterval.Theoveralltrendissimilar-withincreasingdensitythegrainsizeincreases.

162(DP7)Depot700163TheDP7firncorecomesfromthehighAntarcticPlateauwithlowaccumulationrates.ThegrainsizeatDP7siteshowsagaina
164negativetrendwithdensityandtheinter-layerlevel(Figure4D).Theslopeisvaryingintheupperdepthintervals,butisincreasing
165withdepthandtime.Thesloperangesapproximatelyfrom-1.37to-2.6mm/(g/cm3),eventhoughthesurfacebagshowsapositive
166trendof0.913mm/(g/cm3)andsomemediumdepthintervalsvaluesofapproximately-0.6mm/(g/cm3).Overalltrendshows
167increasinggrainsizewithincreasingdensity.SSAshowsapositivetrendwithdensityforthesingledepthintervals,andanoverall
168negativetrend(Figure4D).

149

10

B 260.80.7 (mm)e0.6R0.50.40.300.350.400.453A)Density (g/cmB 380.450.400.35 (mm)eR0.300.250.20C0.350.400.450.5030.550.60
)Density (g/cmFT0.90.8 (mm)eR0.7

H¨orholdandothers:Firnmicrostructure

B 35/ 360.70.6 (mm)0.5eR0.4 B 35 B 360.3B0.300.350.4030.450.50
)Density (g/cm DP70.70.6 (mm)e0.5R0.40.3D0.250.300.3530.400.450.50
)Density (g/cmHD0.70.6 (cm)0.5eR0.4

0.60.3E0.400.420.440.46Density (g/cm0.483)0.500.520.54F0.400.45Density (g/cm3)0.500.55
Fig.5:Detailedgrainsizevsdensityprofilesofthesingledepthintervals.Notethedifferentscales.Foreachdepthintervalalinear
relationshipbetweendensityandgrainsizeisapparent.

150

11

H¨orholdandothers:Firnmicrostructure11
169FireTrack(DomeC)
170TheFireTrackfirncorefromtheDomeCvicinityrepresentsthecoldestsitewithlowermostaccumulationrateofthisstudy.The
171samplingandmicrostructureanalysisstartsatdepthsbelow6meterandanageofmorethan100years.Ontheinter-layerlevelthe
172grainsizeshowsawellpronouncednegativetrendwithdensity(Figure4E).Theslopeisincreasingwithdepthandtime.Itranges
173from-1.696mm/(g/cm3)atuppermostintervalto-4.2662mm/(g/cm3)atthelowermostdepthinterval.Theoveralltrendshows
174againincreasinggrainsizewithincreasingdensity.

175(HD)DomeculesHer176FortheHerculesDome(HD)sitenodetailedsamplingforsingledepthintervalswasconducted.Thereforeitcanonlybeusedtostudy
177theoveralltrendofgrainsizewithincreasingdensity(figure4F).
178Whereastheoveralltrendshowsthewellknownincreaseofgrainsizewithincreasingdensity,theinter-layervariabilityoftenshows
179anoppositetrend.ThefirncoresB26,FT,DP7andB35/B36showthisbehaviorverywell.Onlythenear-surfacedepthintervals(light
180greylines)attheB35/36site,aswellasattheB26siteandalldepthintervalsoftheB38siteshowapositivetrend-increasinggrain
181sizewithincreasingdensity.
182Theslopeofthelinearfitchangesfromsitetosite.Itseemsthatfirncoreswithlowaccumulationratesandannualmeantemperatures
183showthestrongestnegativetrend(FTandDP77).Withincreasingtemperatureandaccumulationratetheslopeisdecreasing(B35/36
184andB26)andturnstopositivevaluesatthewarmestsitewithextremelyhighaccumulationrate(B38).Theslopeisalsoincreasing(in
185negativedirection)withincreasingdepthandage.Surfacedepthintervalsshowweakslopes,whereastheintervalsdeeperdownshow
186gradients.steepmore187Asimplemodelofgraingrowth
188TheArrheniusequationassumeslinearparticlegrowthunderisothermalconditions:

189with

r2(t)=Kt+r02

(4)

K=K0exp(−E/RT)(5)
190Theradiusr(t)ofaparticleisdeterminedfromaninitialradiusr0andgrowthrateK,whichisafunctionofrateconstantK0,
191activationenergyE,gasconstantRandabsolutetemperatureT.ValuesforEvarybetween47.0×103J/mol[Gow(1969)]and
19242.4×103J/mol[Paterson(1999)],whileK0isontheorderof6.75×107mm2/a[Flachandothers(2005)].

151

12

H¨orholdandothers:Firnmicrostructure

193Growthratescalculatedfromtheaboverangeofparametersvaryconsiderably.BuddandJacka(1989)assumedEandK0tobe
194temperature–dependent,andJackaandLi(1994)supplyparameterstofitactivationenergyEandgrowthrateKtotemperature.The
195initialvaluer0isusuallyfixedatanarbitraryvalue,duetoalackofreferencevaluesobtainedfromthefield.

196atesrowthGr197FromthemeasuredgrainsizeprofilesweaimtofindaparametrizationofgraingrowthasafunctionofannualmeantemperatureT¯,
198temperaturegradient∇TandaccumulationrateA.
199Effectiveradiusmeasurementsareavailableforeachfirncoreinstepsof2.5cm,withapproximately16singlemeasurements
200repeatingin1–meterintervalstocapturegrainsizevariability.Todetermineameangrainsizeprofile,effectiveradiiareaveraged
201overthemeasurementintervals.Firnaget(z)correspondingtothemeanradiusatdepthzcanbeestimatedfromthevelocityv(z)=
202A·ρice·ρ(z)−1atwhichasnowlayerisburiedbelowthesurface.
zdzt(z)=0v(z)(6)
203TemperaturepropagationintothesnowpackT(z)ismodeledasanexponentiallydecayingoscillationasdescribedbyPaterson(1999),
204dependingonT¯,amplitudeoftheseasonaltemperaturesignalatthesurfaceΔT,thermaldiffusivityofsnowk,andfrequencyωand
205phaseϕoftheseasonalsignal.Thephasevalueisfixedatthepointofpositivetemperatureamplitude.

T(z)=T¯+ΔTexp−zω/2k·sinωϕ−zω/2k(7)
206AnnualmeantemperatureT¯andamplitudeΔTcanbeobtainedfromtheMODISLandSurfaceTemperatureproduct.Thethermal
207diffusivityiseasilycalculatedfromthemeasuredfirncoredensitiesusingtheempiricalapproachdevelopedbySturmandothers
208(1997).

010-110-210K=dr/dtfrom Paterson-310HercDomeDepot700B38-410B36B35B26-5105.04.54.03.51000/T [K]

Fig.6:Growthratesderivedfromprofiledata,andPaterson(1999)

152

H¨orholdandothers:Firnmicrostructure

13

209Inputdataforthedeterminationofthegrowthratefromradiusmeasurementsaremeangrainsizeprofileswithcorrespondingvalues
210fortemperature,temperaturegradient∇T(derivedfromthetemperatureprofileinequation(8)),densityandfirnage.Thegrowthrate
211K=dr/dtisdeterminednumericallyforeverydepthinterval.Wecomparegrowthratesdeterminedfromourdatasetwithvalues
212publishedbyPaterson(1999)andfindourvaluesingoodaccordance(fig.6),albeitsystematicallylarger.Apossibleexplanationfor
213thiseffectliesintheuseofdifferentmethodstodeterminegrainsize.Thetemperature-dependentactivationenergyEandrateconstant
214K0aredifficulttofittoparametersobtainedfrommeasurements,sincetheyareverysensitivetonoiseinthedata.Forthisreason,we
215chosetodirectlyfitthegrowthrateK,anddeterminecoefficientsforequation(9):
216calculated.K(T)=a0exp(a1[1000/(T¯+∇T)]+a2)(8)
217Weproposeusingthefollowingparametersettoestimatethetemperature–dependentgrowthrate:
0.165=a0a1=−5.218(9)
3.712−=a2

(8)

(9)

218sizeaingrSurface219Thegrainsizeofthenear-surfacelayerr0dependsontemperatureandaccumulationrate:hightemperaturescorrespondtomorewater
220vaportransportandthustofastergraingrowth[Domineandothers(2008)].Higheraccumulationreducesthetimethesnowgrainsare
221subjecttoastrongtemperaturegradientandslowsdownthegraingrowthprocess.
222Toquantifythetemperatureandaccumulationdependencyofthesurfacegrainsize,initialradiir0andtheirstandarddeviationσr0
223wereestimatedfromthemeasuredgrainsizesoftheupper30cmintervalofeachmeasuredindividualprofile.Thiswasdoneforall
224availablegrainsizeprofilesexcepttheFireTrackprofilesinceitstartsatadepthof6m.
0.45B260.400.35HercDome [mm]B35B3600.30fitted r0.25DP7B38R = 0.9890.200.150.150.200.25measured r0.300 [mm]0.350.400.45

Fig.7:Correlationbetweensimulatedandmeasuredsurfacegrainsizes

153

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H¨orholdandothers:Firnmicrostructure

Table3:Initialradii,radiusstandarddeviation,temperatures,accumulationrates

Namer0σr0¯TA
[oC][mw.e.·a−1]
B260.40±0.033-31.600.180
B350.30±0.035-44.600.067
B360.28±0.028-44.600.067
B380.20±0.010-18.101.250
Depot7000.25±0.043-51.000.045
HerculesDome0.35±0.029-37.000.180

225Amultiplelinearregressionappliedtothedatafromtable3yieldsthefollowingrelationshipbetweeninitialgrainradiusr0,mean
226annualtemperatureT¯[oC]andaccumulationrateA[mw.e.·a−1].

227with

r0(T¯,A)=a0+a1T¯+a2A

(10)

a0=0.781±0.019
a1=0.085±0.002(11)
a2=−0.279±0.055
228Inordertotesttheaccuracyofourfit,wecomparedinitialradiideterminedfromequation10withmeasuredvalues.Itcanbeseen
229thatourmultipleregressionapproachreproducesthemeasuredvalueswithsufficientaccuracy.
230esultsrModel231Fig.8showsmodelresultsincomparisonwithgrainsizemodelsfrombyPatersonPaterson(1999)andZwallyandLi(2002).Wechose
232initialradiir0fromequation(11)forbettercomparisonandvariedonlythewayofcalculatingk.Itcanbeseenthattherapidgrain
233growthintheupperlayersinfluencedbyastrongtemperaturegradientarerepresentedmorerealisticallybythenewapproach.Our
234approachoverestimatesgraingrowthforB38,asitewithanextremelyhighaccumulationrateof1.25mwaterequivalentperyearand
235acomparablyhighmeanannualtemperatureof-18oC.FortheDepot700core,theextremegrowthcausedbyaverylowaccumulation
236of≈0.045mwaterequivalentperyearand,inconsequence,thelongexposuretimeofsnowlayerstoalargetemperaturegradient,is
237underestimatedinourmodel.Forintermediatepolarclimateconditions,thesimulatedgrainsizeprofilescloselyfitthemeasurements.

154

238

239

240

241

242

H¨orholdandothers:Firnmicrostructure

DISCUSSION

Fig.8:Modeledgrainsizeprofilesforsixpolarfirncores

15

Thesequenceofunitlayersinthefirnisveryimportantforthepointofviewofremotesensing,becausetheboundaryofunitlayers

reactsasaninterfacebetweendifferentdielectricmaterials.Themainmicrostructuralchangeataninterfaceoccursinthedensityand

grainsizeofthefirnlayer.Oftenthedensityvariabilityistakenasaproxyforstratigraphyandthetotalamountoflayersislinked

tobackscattersignature(Flachandothers,2005;Rottandothers,1993).Withourhighresolutiondensitydatawecannotdefinea

155

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H¨orholdandothers:Firnmicrostructure

243cleardifferenceinvariabilityindensityorintheamountoflayersbetweenthedifferentsites.Shiraiwaetal(1996)alsocomparedthe
244numberofunitlayersin38snowpitsof1-2meterdepthfromthecoastuptotheplateau.Theirnumberoflayerspermeterwashalf
245ashighasthenumberfoundinourstudy-rangingbetween10and20,butacleardifferenceinthetotalamountoflayersbetween
246sitesatdifferentlocalclimateconditionswasalsonotfound(Shiraiwaandothers,1996).Aslighttrendforahigheramountoflayers
247athigheraltitudecouldbeidentified.Thedensityvariabilityintermsoflayeringcannotbedirectlytakenasameasurefornumberof
248layersandwiththatasareasonfordifferentbackscatterbehavior.
249Grainsizeseemstobestronglyconnectedtodensity.Thesitesdifferconsiderablyinabsolutevalues,asdoesthedensity.Shiraiwa
250etal.(1996)findnon-linearaltitudinalchangesingrainsizeandstrongvariationsinregionsofkatabaticwind.Thealterationofgrain
251sizeandtypesandthethicknessofsinglelayersvarycharacteristicallyforthedifferentsites.Thiscouldbeahintforthedifferent
252interactionofsnowandmicrowavesignatures.OntheotherhandGayandothers(2002)findlargevariationsingrainsizealong
253theirtraversefromTerraNovaBaytoDomeC.Thegrainsizeisstronglylinkedtowindpatternsoferosion,crustformationorcalm
254conditions.Theexposureofsnowtotemperaturegradientsonlargetimescalesenablestheformationoflargegrainsandwindcrusts,
255whichinturnexplainaparticularbehaviorinmicrowavesignature(Gayandothers,2002)forexampleattheDomeCvicinity.We
256findclearlydifferentgrainsizesatthedifferentsites.B38withshowsthewarmesttemperature,howeverduetotheextremelyhigh
257accumulationratethegrainsizeisthesmallestofallsites.ThenextwarmsiteistheB26firncoreandindeedweherefindthelargest
258grainsizesofallfirncoresites.OntheotherhandthetwocoldestsitesFTandDP7showsimilarlargegrainsizesingreaterdepth.
259Thisisduetotheverylowaccumulationrateandthelongtime,asnowlayerisexposedtotemperaturegradientsatthesurface.The
260graingrowthisnotonlytemperaturedependent.Thegrainsizeatacertaindepthistheresultofthecompetinginfluenceofannual
261meantemperatureandaccumulationrate.
262Thegraingrowthatasinglesiteisinfluencedbylocalclimatefactorssuchastemperatureandaccumulationrateandprobablyalso
263bytheinitialgrainsizeandgrainsizevariabilitywithinthedifferentlayers.Theoveralltrendforallsitesis,thatgrainsizeincreases
264andSSAdecreaseswithincreasingdensity.NishimuraandMaeno(1985)discussedtheroundingandgrowthoficeparticlesasthe
265mainreasonforthedrasticdecreaseinspecificsurfaceareaintheupperpart(NishimuraandMaeno,1985).Theslowerlinerdecrease
266ingreaterdepthwasattributedtothedevelopmentofbondingandparticles.
267Thetrendwithinsingledepthintervalsisoppositetotheoveralltrend.Ingeneralgrainsizeisdecreasingwithincreasingdensity.
268AlsoTaylor(1971)observedtheinversevariationofdensitywithgrainsize.Forgrainsizetheslopeofthelinearfitsisincreasing
269withdepthandage.Asdeeperinthefirncolumnandasolderthefirn,assteepertheslopeinthetrendofgrainsizeanddensity.The
270exceptionisfoundatB38.Herethetrendwithinsingledepthintervalsfollowstheoveralltrend.Ifwecomparethetrendofgrainsize
271anddensityatthedifferentsites,weagainfind,thatasolderthesnowasmorepronouncedisthenegativetrend.FTasthecoldest
272sitewithlowestaccumulationrateshowsthehighestslope,DP7,withsimilarclimateconditionsandwithsurfacesamplesalsoshows

156

H¨orholdandothers:Firnmicrostructure

17

273ahighslopeingreaterdepths.Theslopeislessstrongatthesurface,sinceitisdevelopingwithdepthandtime.B35/36isthenext
274warmersitewiththenexthigheraccumulationrate.Herewefindalessstrongslopeandthesurfacesamplesshowaweakoreven
275positiveslope.ThesameholdsforB26.FinallyatB38withthewarmesttemperatureandthehighestaccumulationrateshowspositive
276valuesoftheslope.Herethesnowismovingdownthefirncolumnsofast,duetotheextremelyhighaccumulationrate,thatthegrains
277sizehasnotimetoadapttodensityinthewaythanattheothersites.
278Soobviouslythesurface”fresh”snowinhabitsapositivetrend-largegrainsizecorrespondstohighdensities.Assoonasthesnow
279isexposedtometamorphisminthenearsurfacearea-thistrendturnstonegative.Furthermoreitseems,thatatthesurfaceabroad
280rangeindensitycanbecoveredbysmallrangeingrainsize.Ingreaterdepthandwithincreasedagetherangeindensitydecreases,
281whereastherangeingrainsizestaysthesameorevenincreases.
282GrainGrowthModel
283modeltheofDiscussion

284competingimpactoftemperatureandaccumulationrate-thereforeoverestimatingB38samplesandunderestimatingDP7andFT
285samples

286Nophysicalapproach,butsincesuchabroadrangeoflocalclimateconditionsisusedforparameterizingthevalues,goodapprox-
287conditions.polarforimation

288Problemsofthemodelapproach:errorsources

289Advantageofthemodelapproach:easytoapply;useforback-scattermodelsinRemotesensing.

290ComparisonofmodeledgrainradiuswithFlannerandZenner(FlannerandZender,2006)fortemperaturegradientgrowth(their
291”long-term”growthis30days.ButoneexperimentalsetupiscomparabletoDomeC(temperature-50,temperaturegradient20.

292Baunach(Baunachandothers,2001)hascomparabletemperaturegradients(30degreepermeter)

293discussioninitialgainsizeandimpactofgraingrowth(FlannerandZender,2006)

294CONCLUSION295WepresentasimplemodelofsnowgraingrowththatincorporateseffectsofthestrongTGgrowthintheupperlayersofthesnowpack
296aswellasETgrowthatdepthsnolongerinfluencedbytheseasonaltemperaturegradient.OurapproachusestheArrheniusequation
297tomodelparticlegrowthandderivesanempiricalfitofthetemperature–dependentgrowthratefromfirncoredata.Additionally,a
298solutiontotheproblemoffindingarealisticinitialradiusforeqation4ispresented.

157

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299Sincethefirncoresusedtoderiveourmodelparametersetdonotexceedadepthof≈20m,wecannotpredicttheaccuracy
300ofourmodelresultsforgreaterdepthsandrecommendthismodelforremotesensingapplicationsthattoconsiderfirn–microwave
301interactionsintheupperlayersofthesnowpackonly.
302UsingdatafromsixfirncoresfromGreenlandandAntarcticawhichrepresentaveryheterogeneoussetofenvironmentalconditions
303toderiveempiricalparametersforourgraingrowthmodel,wecansafelyassumeourmodeltobeapplicabletotheentirepolarregions.
304Inordertofurthertestthevalidityofourrelationforestimatingsurfacegrainsizes,moredatawillbeneeded.

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160

D

nlicatioPub

4

-

The

impact

of

accumulationrateontheanisotropy

permeabilityairand

highaulationaccum

Hörhold,M.W.,Albert,M.R.,Freitag,J.(2009)

nalJour

of

,Glaciology

ol.55,V

.No

192,

.625-631.pp

161

polarof

site

firn

at

JournalofGlaciology,Vol.55,No.192,2009

625

Theimpactofaccumulationrateonanisotropyandair
permeabilityofpolarfirnatahigh-accumulationsite
MariaW.HO¨RHOLD,1MaryR.ALBERT,2JohannesFREITAG1
1AlfredWegenerInstituteforPolarandMarineResearch,AmHandelshafen12,D-27570Bremerhaven,Germany
wi.deMaria.Hoerhold@aE-mail:2USArmyColdRegionsResearchandEngineeringLaboratory,72LymeRoad,Hanover,NewHampshire03755-1290,USA
ABSTRACT.Thefirstthree-dimensionalpropertiesofpolarfirnobtainedbyX-raymicrotomographyare
usedtostudythemicrostructureofsnowona15mdeepfirncorefromWestAntarctica.Thesnowis
foundtoundergocoarseningdowntoapproximately2.5mdepthbeforegraingrowthanddensification
becometheprevalentmechanismsofmicrostructurechange.Incontrasttopreviousassumptions,
distinctanisotropyoftheiceandporegeometryisobservedthroughouttheprofile,withamaximumat
2.5mdepth.Theairpermeabilityandthedegreeofanisotropyvarywithdepthandcanbelinkedto
short-termchangesinaccumulationrateviatheresidencetimeforwhichacertainsnowlayerstaysin
theuppermost2.5m.Patternsofthedegreeofanisotropyandairpermeabilityofburiedpolarfirnare
relativeindicatorsofpastaccumulationrates.

INTRODUCTIONconditionswouldinfluenceboththemicrostructureand
thepermeability.Atleastatcold,low-accumulationsites,a
Onpolaricesheetsthesurfacesnowandfirnformsalayeredsignatureofchangingaccumulationrateismaintainedinthe
andporousmediumthatremainspermeabletogasesovermicrostructureandairpermeabilityofthefirncolumn.
depthsofmanytensofmeters.LocalsurfaceconditionsEarlierstudiesaddressingpolarsnowmicrostructureused
affectthegenerationandtransformationofthesnowandfirnthinorthicksectionsfromfirnsamplestoobtaininformation
column;thetemperaturebyaffectingtherateofdensifica-aboutthemicrostructure(Gow,1969;Alleyandothers,
tion,andtheaccumulationratebyformingthelayeringand1982;RickandAlbert,2004).Thistechniqueenabledonlya
determiningthetimethesnowisexposedtoinsolationandtwo-dimensionalanalysis,andthequantitativemicroscopy
temperaturegradientsatthesurface.Singlesnowlayersareislimited(Davisandothers,1996).Recently,X-raymicro-
createdbydepositionaleventsandconsistofverydifferenttomographyhasbeenusedtostudyalpineorartificial,
snowtypes,leavingahighlystratifiedfirnpack(Gow,1965;sampledorsievedsnow,observedfordifferenttimeintervals
Alleyandothers,1982;Palaisandothers,1982;Alley,inthelaboratory(Flinandothers,2004;Schneebeliand
1988).SincethepropertiesofthedifferentsnowlayersareSokratov,2004;Kaempferandothers,2005;Kaempferand
verydistinctingrainandporesize,formingdiverseSchneebeli,2007).Inexperimentalset-upsforisothermal
stratigraphichorizons(Palaisandothers,1982),theytrans-metamorphism(Flinandothers,2004;Kaempferand
formdifferentlyinappliedtemperaturegradientsandloadSchneebeli,2007),temperaturegradientmetamorphism
(Alleyandothers,1982).(SchneebeliandSokratov,2004)andmicromechanical
Themicrostructureofsurfacesnowandthestratigraphicstudies(Pieritzandothers,2004),ithasbeenshownthat
andgrain-scalecharacteristicsvaryspatiallywithvaryingsnowcanbecorrectlydescribedusingmicrotomography
accumulationratesontheEastAntarcticicesheet(Wata-andimage-analysistools(Cole´ouandothers,2001).
nabe,1978;Shiraiwaandothers,1996),asdoestheairInthisstudy,forthefirsttime,microtomographyisusedto
permeability(Courvilleandothers,2007).However,itisnotprofilepolarfirnwithvaryinglayersandproperties.A15m
clearhowshort-termchangesintemperatureoraccumu-longfirncoredrilledduringtheUSITASE(International
lationratearereflectedinthefirnpropertiesovertime,asTrans-AntarcticScientificExpedition)campaign2002at
subsequentburialmoveslayersdownthroughthefirnHerculesDomeisusedtoinvestigatethesnowandfirn
column.Forarelativelyhigh-accumulationsiteinWestmicrostructureandairpermeability.HerculesDomeis
Antarctica,RickandAlbert(2004)discusstheimpactofsituatedat868S,1058W,withrelativelyhighaccumulation
temperatureandaccumulationrate,onseasonalandratesof0.16–0.20mw.e.a–1overthelast300yearsandlow
decadalscales,onthepermeabilityandmicrostructureoftemperaturesof–35to–408C(Jacobelandothers,2005).
firn.Albertandothers(2004)reportthatlowaccumulationPermeabilitymeasurementsandmicrotomographyareused
rates,inareasliketheEastAntarcticplateau,causeextremetodescribetheevolutionofthemicrostructurewithtimeand
firnmetamorphism,duetothelengthoftimethesnowisdepth.Weobserveastratigraphicallyinducedhighvari-
exposedtoinsolationandwindatthesurface.Smallabilityinmicrostructureandairpermeabilityandadistinct
differencesinaccumulationratecreateverylargediffer-anisotropyofthefirnthroughouttheprofile.Inaddition,
encesinmicrostructure,permeabilityandthermalconduct-influencesthatinducevariationsofthefirncharacteristics
ivityinthetopmetersoffirn,whichleaveanenduringoveralonger-termtrend(andhence,acrossmultiplelayers)
recordasthefirnbecomesburied(RickandAlbert,2004;impacttheanisotropyandair-permeabilityprofile.These
Courvilleandothers,2007).Theoccurrenceofhighlylonger-termvariationsaresuperposedonthelayeringandthe
permeableandporouslayersatgreaterdepthsinthechangesthatoccurwithdepthduesimplytolayerde-
megadunesareadocumentsthatachangeinclimateposition,densificationandotherprocesses.Byconsidering

162

626

theFig.1.poreAphasereconstructedfrom2.5firnmcubedepth.withWhitesideisthelengthpore16mmphase;showingvoids
grains.icetherepresentthetimethesnowisexposedtonear-surfaceconditions,we
canaccumulationlinktheserate.variationsOurresultstoshort-termconfirmthatchanchagesngesinthein
accumulationrateleaveasignatureinthefirnpermeability
andmicrostructureasthefirnbecomesburied.
METHODSThefirn-corepermeabilitywasmeasuredfollowingthe
Albertprocedures(2004)anddescribedCourvillebyAlbert(2007).andTheothers(2000),measurementsRickwereand
appliedat220homogeneousfirn-coresections,asidentified
noonapermeabilitylight-table,ofdata3–10werecmavlength.ailableDueintoseverpooralcoreintervalsqualityof,
thecoarse-,uppermostfine-and2mandmedium-grat8.5–9.5ainedmlayers,depth.distinguishedHomogeneousby
visualinspectionofthegrainsizerelativetothesurrounding
layers,weresampledineverydepthintervalofthefirncore
forfurtheranalysis.Microstructuralpropertiesofthefirn
grainandporespacewereobtainedat–258CbyX-ray
scannermicrotomogra(1074phySkyusingScan)ainsidemicro-CTacold(computedroom.Atomogrcaphharge-y)
greycoupledlevelsdevicewasused(CCD)asancamerX-raayof768detector.512Cylindricalpixelsandsnow256
andfirnsamplesof2cmdiameterandheightweredrilled
onoutaoftheturntablemainincorefrontwithofatheholesourcesaw,.Tandhewassamplerotatedwasinplaced0.98
intervalsduringscanning.Asetof210shadowimageswas
capturedwhiletherotationcompletedasemicircle.
Aconvolutionalgorithmwithabackprojectionforfan
beamstransformedtheshadowimagesintoaseriesof
three-dimensionaltherepresentingcross-sectionshorizontal(3-D)structureofthesnow.Theresolutionaswellasthe
distancebetweenadjacentreconstructedimageswas40mm,
sotheobjectwasdisplayedbya3-Dgridofgreyimage
values(voxels)withaspacingof40mminthex,yandz
directions.Fordigitalimageanalysisacubicregionof
16mmsidelength(leaving400400400voxels)was
chosshowneninoutofFigurethec1.Tylindricalheimagesample.sizeAissamplelarge3-Denoughimageisto
sufficientlyrepresentthefirnproperties(Ho¨rhold,2006;
2008).others,andreitagFTheimage-processingandanalysisprocedureswere
conductedwithMAVI(ModularAlgorithmforVolume

163

Ho¨rholdandothers:Anisotropyandairpermeabilityofpolarfirn

byImages),theFaraunhofersoftwareforInstituteanalyzing(Armbrecht3-Dandmaterial,Sych,dev2005).eloped
Afterapplicationoffilterandsegmentationprocedures,an
addingadditionallessthanobject1%filtertothewastotalusedporetooriceremovveolume.allobjects
Allparameterswereobtainedandanalyzedreferringto
bythethevolumeratioofofthevoidfirncube.representingTheporosityvoxelsoftoathesampletotalisgivvoxelen
thenumbergrain-oftheandfirncube.pore-chordAmeasurelength,fordefinedgrainandasporethesizemeanis
grainintersectionindifferentofalinedirectionswiththe(OhserobjectandMubeing¨cklictheh,void2000).orThthee
curvmeasurementatureisofbasedtheonsurfacetheareaapplicationandtheofintegraltheofso-calledmean
Crofton’ArmbrechtsandintersectionSych,2005).formulaeThe(OhsersurfaceandMudensity¨cklich,represents2000;
thevolumeratioofofthetheicephase.ice–airsurfaceSmall-grainedandthesnowfromcorrespondingthenear
surfaceroundedwillsnowhaveadeeperlargerdownsurfacethefirndensitycolumn.thanThesintered,integralwell-of
meanmaximumcurvaturecurvisatureatdefinedeachasthesurfacemeanofelement,theintegrminimumatedoandver
the2000).wItholethereforesurfaceisofathemeasurevolumeofthe(OhsercurvatureandofMu¨theckliciceh,
phase’sstructureanddisplaysthesizeandroundnessofthe
weiceobtainmatrix.aDimeanvidedvbyaluetheforthenumberofsample,voxelssoofnegativeachevsample,alues
meanrepresentofaconvmeanexofformsconcavewithinforms,theandfirnpositivcube.evaluesDendritica
crystalswillshownegativevaluesandlarge,smooth
TsurfaceshestrengthresultinofcurvMAVIatureisvthataluesitenablesaroundthezero.3-Dstudyof
surfacestructurechaelementracteofristicsarelatedmicrostructuratothelsurfacecomponentdensity.canEachbe
direction.representedThbeyasurface-normalsurface-normalvdistributionectorwithdisplaitsysspecificthe
directionaldistributionofallsurface-normalvectors.Apart
fromverticagrlatempervitationalaturesettlinggradientsalongresulttheinzverticalaxisinwaterthe-vsnowapor,
oftrathensporttexturewithinistothebesnowexpectedpack.inThustheaverticalpreferentialdirection,directionand
thisisotropicpaperbehaweviourstudyinthethefractionhorizontalofdirection.surface-normalThereforevectorsin
orientatedintwohorizontalandtheverticaldirectionswith
antheraapextioofangletheoffr308actions(ArmbrechtoftheandhorizontalSych,2005).directionsWetake(the
meanofthetwohorizontalfractions)andthevertical
suchdirectionasa(s-nspherefrawillction).beTh1,ewratiohereasfortheanratioistotropicofatexturetexture
textureelongatedelongatedwithininthetheverticalhorizontalplaneplanewillwillbe<1be>1,(Ohserandanda
2000).h,cklic¨MudesignatedDependingononthethelight-table),lengthoftwothetocorefivepiecessubsamples(3–10cm,wereas
analyzedmicrostructurebyofmicro-CTthatandspecificaverlayeraged,.Inorderrepresentingtostudthey
largerwindow-scalelengthfeatures,coveringarunningseverallameanyerswasandappliedweightingwiththea
pointsbythenumberofmeasuredsubsamples.
wereDensityusedtoconvmeasurementsertthistowithinathewateruppermostequivalent2.5mdepthoffirnof
0.9m.Measuredaccumulationrates(personalcommunica-
tiontimefromtakenD.foraDixon,snowla2006)yertowerebethenburiedusedtoatodepthcalculateof2.5m.the

Ho¨rholdandothers:Anisotropyandairpermeabilityofpolarfirn

627

(b)Fig.the2.(a)Tmeasuredheairaccumulationpermeabilityrate.asTheobtainedblackbycurveischemicaltherunninganalysismeantogetheraverwithageovtheerthecalculateddifferentlaresidenceyers,timestartinginthefrom2.5uppermostm.2.5mand

RESULTSdensityimplycoarseningofthetextureuntil2–3mdepth,
accompaniednotonlybymaximumpermeabilityandpore
Atestimates,HerculesbasedDomeoncforthehemicalmostanalysisrecent60andyeardensityaccumulationmeasure-sizebutalsobymaximumanisotropy.Herewereferto
0.12ments,mwa.e.a–1meanisobservaccumulationed(Fig.r2a).ateThofecalculatedapproximatelyresi-sizecoarseningandtheofporefirnassize.aBelogeneralwthat,increaseindensificationboththebecomesgrain
dencetimewithintheuppermost2.5mshowsapeaknearsignificant,andcontinuedgradualmetamorphismde-
68.5mmdepth,depth,aandlocalthenminimumgenerallybelow,adecreases,secondwithpeakalocalnearcreasescreasingtheporegrsizeainandsize.Atporositythiswsitehilethefirncontinuouslyishighlyin-
maximumnear12mdepth(Fig.2a).stratified,witheachlayershowingverydifferentproperties
TheresultsforpermeabilityareshowninFigure2b,andofintermsanisotropofy.Themicrostructure,illustratedvpermeabilityariationinandthedevlongerelopment-term
microstructuralcharacteristicsareshowninFigure3.We
laobservyeringeaofthelargefirn.vForariabilitytheofchordallparlengthametersingrainduesizetoandthetrends,profiles,isnotparticularlyrelatedintothethelaypermeabilityeringbutandtolongeranisotrop-termy
theporeverticalspace(Fthanig.3afortheandb)twowefindhorizontalclearlydirections.largervThalueserafortioprocesses.
ofof1theindicatesnormalvecisotroptoryfra.Vctionsaluesislessplottedthanin1,Figuasrefound3f.Arahere,tioANISOTROPY
showzontalthatplanemorethaninthesurface-normalverticalvectorsplane.Thpointefirninthetexturehori-isAtreachedHerculesatDomeapproximatelythe2.5maximummdepthdegree(Fig.of3d).Howanisotropevery,iisn
contrasttopreviousstudies(Alley,1987),wefindthat
verticaInorderllytoanisotropic.displaythelong-termtrend,therunningmeananisotropydoesexistbelowthat,thoughittendstodecrease
ispermeabilitycalculatedweforallfindparanametersincrease(Figsuntil2b2.5andm3).depth.ForThtheenotwithdecreasedepth.inMoreovermonotonic,thesedatafashion,showbutthatratherthatanisotropthereydoesare
permeabilitybelowisdecreasing,butshowstwolocaldepthsdepthsatatwwhichhichitisanisotropnot.yisstronglypronouncedandother
maximanear6and12mdepth(Fig.2b).Boththegrainsize
theandporetheporesizesizedecreasesincreaseslorawlypidly(Fig.until3a2–3andmb).depth.WhereasBelowthe,modelsYosidaofandorientedotherscrystal(1955)growth.andInColbecnaturalk(1983)snowintroducedsubjected
porosityalmostlinearlydecreaseswithdepth(Fig.3c),tochangesinweather,temperaturegradientsaremostly
curvsurfaceatureradensitypidlyanddecreasethemeanandofincreasetheintegrarespectilovelyfmeanuntilthenorientedinduceinthegrvertiadientscalindirection.water-Tvheaportemperatransport.turegradientsCrystals
2mdepth,continuingtheirtrend,butatmoregradualrates,growbycondensationofwatervaporontheirbottom
belowthis(Fig.3dande).Fortheanisotropywefindanportions,becausethebottomofagrowingparticleiscold
regionincreaseoflountilw2–3anisotropmydepth,betweenand7thenanda8mdecrease,depthbutfollowithwedarelativ(Colbecek,to1983).theaAlleyverageandsnowotherstempera(1982)turefoundatthatitscrystalsheight
byaregionofincreasedanisotropynear10mdepth(Fig.3f).incoarsefirnexhibitastrongverticalshapeorientationnear
integraThelofincreasemeanincurvtheaturechordandlengthstheanddecreasethemeanofofsurfacethethewater-vsurface,aporwandhichheatcantrabensport.attributedtothestrongvertical

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Ho¨rholdandothers:Anisotropyandairpermeabilityofpolarfirn

Fig.horizontal;3.(a,b)blackTheformeanvertical).grain(a)(c–f)andTheporeporosity(b)ch(c),ordsurfacelengthsindensityx,y(d),andmeanzcurvdirections.ature(e)Darkandcurvesratioofrepresentthenormaltherunningvectormeanfractions(greys-n(f),for

Ontheotherhand,SchneebeliandSokratov(2004)foundnorthelinearcompactionwithdepth.Changesinthemeta-
intemperaturegradientexperimentswithdifferentsnowmorphicregimemustbethebasiccause.Amajorparameter
layersthatanisotropyoccurredindense,fine-grainedlayers,determiningthemetamorphismistheimpactoftheaccumu-
whereaslow-densitylayersexposedtosimilargradientsdidlationrate,which,however,isdifficulttoparameterizesince
notshowananisotropytextureafterthesametimeinterval.itsuperimposestheeffectsofthelayeringanddensification.
Ourdatasupporttheseobservations:wefindhighlyporousThemaximumincoarsening,permeabilityandanisotropy
layerstobelessanisotropicthanlessporouslayersintheisobtainedby2.5mdepth,whilebelowthat,densification
samedepthinterval.Thesmall-scalevariabilityinthecombinedwithslowgraingrowthappearstobecomeim-
anisotropyprofileisprobablycontrolledbythedifferentportant.Itappearsthat,atthissite,aslongasacertainlayer
formationofanisotropyinthedifferentlayers.staysintheuppermost2.5m,itisexposedtosignificanttem-
peraturegradients,periodicallyhigherannualtemperatures
andmetamorphicallyinducedcoarsening.Wehypothesize
ACCUMULATIONRATEANDRESIDENCETIMEthatthedegreeofcoarsening,permeabilityandanisotropyof
Fromthemicrostructureandpermeabilitydatawecaneachlayerdeeperdownthefirncolumnisdesignatedbythe
concludethatdespitetheverydifferentpropertiesofthedegreeoftheseparametersat2.5mdepth.Inturnthedegree
differentlayersintermsofpermeabilityandanisotropy,theat2.5mdepthresultsfromthehistorybetween0and2.5m
larger-scalefeaturesshapetheevolutionwithdepth.Thesedepth,i.e.thetimespentinthenear-surfacearea.This
featuresarevisibleinboththelow-andhigh-permeabilityresidencetimedependsonlyontheaccumulationrate.
layersandinthelow-andhighanisotropylayersrespectively.Wetestthepossibilitythatthetimethatsnowspendsin
Theobservedvariabilitydoesnotoriginatefromthelayeringthenearsurfaceinfluencesitspermeabilityandanisotropyat

165

Ho¨rholdandothers:Anisotropyandairpermeabilityofpolarfirn

Fig.4.Theresidencetimewithmeananisotropy(a)andairpermeability(b).

629

depth,byusingthedensitytocalculateresidencetimeinthedepths.Additionallytheanisotropyandtheairpermeability
nearsurface(Fig.2a).Sincetheaccumulationrateandthusofthefirnclearlybehavedifferentlywithregardtothe
thesamplesresidencethanthetimeweremicrostructurecalculatedandonpermeabilitydifferent,scaleshereandweresidencecontributetotimethe(Fig.evo4alutionandofb).firnAccordinglyproperties,otherwithdepth;processesthe
canonlycomparetheevolutionwithdepthofthesetwomecdifferathanismsdepthsforthebelowgenesisseverofalanisotropmetersyinandfirn.permeabilityCourville
differentparametersets(Fig.4aandb).
theAnaverageexaminationanisotropofytheinFiguresidencere4atimeshowinsthatitcomparisonisthezonewith(2007)accumulationobservedapatternmuchonlargermicrostructureimpactofandsmallcpermeabilityhangesin
timesbetweenare7andbriefly8mwhereinterruptedthebyasurroundingphaseoflongdecreasedresidenceinregionsaccumulation.ofveryThislowmightbeaccumulationonethanexplanationinregionsfortheofhighless
coreresidencewasneartime.-surfaceWhensnothew,itfirndidat7–8indeedmspenddepthinlessthistimefirninthepronounceddeeperfirnlainfluenceyers,ofwhecrehangestheincorrelatedaccumulationaccumulationratein
thesurfacenearregionsurface.ofThhighereshortertempertimeaturethatitgradientsspentinmeansthethatnearit-ratehand,wasRickhigherandthanAlbertinthe(2004)showuppermostthatthemeter.groOwthnofthenecotherks
iswasthatlesstheexposedfirntostructurerapidatmetamorphic7–8mshowsprocesses.lowTheverticalresultbetweenpermeabilitythegraireductionnsisatthedepthsdominantbetweenmechanismapproximatelyfor
anisotropy(Fig.4a).AsshowninFigure4a,theresidence2and10m,andthatawarmingoftemperaturesovertime
andtimethusintheresultsnearina-surfacelessareaanisotropicdecreasescharacterbelow.T10hemfeaturesdepthtopwould~10alsomofimpactfirnissubjectmetamorphismtoaatnumberthisofdepth.Teffectshus,thatthe
ofveryshortresidencetimearound11mandat13–14marewouldincludingbetrendsreflectedininsurfacethetemperatpermeabilityureandofburiedaccumulationlayers,
notreflectedinanisotropy.
togetherInFigurewith4bthetheresidencemeasuredtime.Tairhepeakpermeabilityinispermeabilityshown,atrates.measureTheoverthecalculateduppermostresidence2.5m.timeWeisdoannotintegrknowatedthe
2.5mdepthisduetothemaximumofcoarsening.Similarresidencetimeofindividuallayers(e.gwhetheracertain
increasespreviouslyinatdifferentpermeabilitydownhigh-accumulationto2–4mhavpolarebeensitesreported(Albertlayeruppermosthasspentcentimetersacertainandframightctionofthereforethetimebeinexposedtheveryto
andothers,2000;AlbertandSchulz,2002;RickandAlbert,largetemperaturegradients,orwhetheritmonotonically
11–122004).mThcaneagainsecondbelinkedmaximumtothearoundresidence6mtime.depthIncreasedandatmainlybecamegenerburiedatedbelowwithin2.5themupperdepth).fewAnisotropycentimetersisprobablybelow
andresidencebythattimetheairstrengthenspermeabilitytheoftheconnectifirn.vityTheoftheporeresidence-timespacePtheermeabilitysurface,,onwheretheothertemperatuhand,regrcouldadientsbetheareresultlargest.of
minimaat7and11mcoincidewithdistinctpermeabilitylonger-termprocessessuchastheinteractionofairventi-
notminima.apparent,Nevsucherthelessasthetheredecreaseareinareaswherepermeabilityaabovcorrelatione6m,islationconnectivanditywhencoarsening,whicdensificationhincreasedoesthenotporeosizeverruleorporethe
eventhoughtheresidencetimeisincreasing.effect.Thisseemstobethecaseintheupper2.5mat
analyzedNotallchamicrostructurngesinalresidenceparameters,timeareespeciallydisplaatyedingreaterthethisdifferentsite.Tdepthhusintervmorealsneeddifferentiatedtobeinresidencevestigated.timesfor

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630

CONCLUSIONThehighlylayeredpolarfirnreflectstheoccurrenceof
metamorphismofdifferentsnowtypesatlargetimescales
andHerculesunderDome,constantlythechamaximumnginginenvironourmentalpermeabilityconditions.measure-At
sitesments(Albertfromthisandsiteothers,is2000;consistentAlbertwithandmeasurementsShultz,2002;atotherRick
andAlbert,2004)showingapermeabilitymaximumnear
~2.5mdepth.Ourfirstresultsfrom3-Dmicrotomography
scangeneralimagingfirnofcoarseningpolarfirnshow(increasethatinthisbothisgrainaccompaniedsizeandby
interstitialprocessesporeincludingspace)graininthisgrowth,region.neckingBelowandthat,compactionother
influencethemetamorphismofthemicrostructure.The
textureofthefirnshowsdistinctanisotropythroughoutthe
profile,whichisaresultofverticaltemperaturegradients
inandaccumulationsubsequentratewater-vaffectaporthegradients.residencetimeShort-termofcertainchangesfirn
ralapidyersinthemetamorphismuppermosttakesmeterplaceofandthethefirnlargestcolumn,temperwaturehere
gradientsaccumulationoccurra.teWinethefoundafirn-anisotropclearyandsignatureairofc-permeabilityhanging
profilesinthefirnbelowapproximately5mdepth.Ourdata
confirmthateventhoughtheeffectsofchangesaremost
throughpronouncedtimeasinthethefirnnearbecomessurface,buried,theyevenremainatthisevidenthigh-
site.accumulationWLEDGEMENTSCKNOAWandeD.thankDixontheUSfromITASEUnivfieldersityteamof2002Maineforfordrillingprovtheidingcore,the
accumulationratedataofthesite.Thisworkwasfundedin
partbyGermanScienceFoundation(DFG)grantFR2527/1-1
(DandAAD)supportedandbyfundedtheinGermanpartbyAcademicUSExcNationalhangeDiSciencevision
F0229527oundationtoM.grantsAlbert.WNSF-OPPealsothank0538492thetwandoanonyNSF-OPPmous
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nlicatioPub

5

-

Lattice

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permeabilityairtheofmodeling

firnpolar

Courville,Z.,Hörhold,M.W.,Hopkins,M.,Albert,M.

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ann modeling of the air permeability of polar firn ltzmLattice-Bo

odeling of firn eability mAir perm

Zoe Courville

Cold Regions Research and Engineering Laboratory

Hanover, NH USA

Maria Hörhold

iences cgener Institute for Polar and Marine SeAlfred W

any erhaven, GermBrem

Mark Hopkins

Cold Regions Research and Engineering Laboratory

Hanover, NH USA

Mary Albert

Thayer School of Engineering

outh College Dartm

Hanover, NH USA

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Abstract

bined w and firn comaging of sno) im-Densional (3 three-dimRecent advances in

proved the etries have greatly implex geomodeling of flow through comerical mwith num

rk, we combinedore. In this wcrostructuimeability values based on ermability to predict p

cro-comi mcrostructure obtained fromi3-D reconstructions of polar firn mputed

ann model of air flow. oltzmicro-CT) reconstructions and a 3-D lattice-Bmography (tom

easurements of permodeled results to mpared the mWe comeability for polar firn with a

ent wide range of grain and pore scale characteristics. The results show good agreem

the lattice-alues fromeability vodeled perments and meability measurembetween perm

Boltzmann model is types. The lattice-Boltzmle pmann model over a wide range of sa

eability valueasured permedicting mrbetter at ppirical equations for es than traditional em

polar firn.

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1. Introduction

ansport of gases between the atmosphere Snow and firn properties influence the tr

and underlying snowpack and are thus imical transport portant for understanding chem

and interpreting ice cores [Albert et al., 2004]. Vapor transport, in particular, can be

ventilation in firn due to wind menenhanced by “wind-pumping,” pressure drivving o

over surface roughness [Colbeck, 1989]. This effect is especially amplified in areas of

high permeability, large grained (and large-pore-size) snow [Albert, 2002 and Albert et

al., 2004]. Permeability is a material property that affects the ability of a fluid to move

through a porous material. Until recently, it has been impossible to calculate the detailed

flow field through a three dimensional (3-D) heterogeneous porous medium. Past efforts

erical solutions based on either to calculate transport through snow have used num

continuum theory or a simplified representation of the microstructure. Simplified snow

mblage of spherical grains or er an assemcrostructures have been represented by eithi

ing to ped accordtions have been develo and transport equabundles of capillaries,

pirical formemedia such as soils and ilar porous mulas based on research in sim

sandstones [Carman, 1956; Walsh and Brace, 1984; Costa, 2006]. The advantage of this

e-ulas (e.g. porosity, volumeters utilized in the empirical formapproach is that the param

to-surface ratio, grain size, pore size) are generally first-order and are relatively easily

and inexpensively obtained from two-dimensional (2-D) thin or thick sections as well as

Matzl and Schneebeli,., 2006; Dominé et alnewly developed optical techniques [e.g.

2006;Painter et al., 2007; Gallet et al., 2009] for determining specific surface area.

Snow researchers have recently begun to employ more sophisticated and realistic models

of 3-D microstructural geometry in snow for use in heat transport models [Arons and

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Colbeck, 1998] and 3-D data obtained from micro-computed tomography (micro-CT)

imaging of snow for use in densification and heat and gas transport models in snow

[Lundy et al., 2002; Freitag et al., 2004; Kaempfer et al., 2005].Hörhold et al. [2009]

eability of polar firn based on is of anisotropy and permpresented the first 3-D analys

e, Antarctica. Hercules Domcro-CT data using samples fromim

be expressed by Darcy’s equation: eability of a material can The perm

Aqkp, (

)1

wherek is the permeability of the medium, q is the volumetric flow rate, A is the

cross-sectional area of the material, p is the pressure gradient through the material, and

is the fluid viscosity. The permeability of the medium can be expressed in terms of

porosity by equating Poiseuille’s law with Darcy’s equation. Poiseuille’s law for a

odel of a porous mconduit mcylindrical tubes of constant radius is: comprised of edium

2AqR8p (2)

whereR is the radius of the tubes making up the conduit model and  is the total

porosity of a material, or the total open space of the material, as determined by:

 = 1 - snow/ice (3)

wheresnow is the density of the snow and ice is the density of ice. The total

ents of density. The open measureined from laboratory mporosity is easily determ

roughout the sample without the contribution porosity, or the porosity open to air flow th

ane to of dead end or closed pores which do not contribute to air flow, is more germ

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determining the permeability, but also harder to determine. Solving for the permeability

, 1999]: Revil and Cathlesan equation [e.g. produces the Kozeny-Carm

22kcSVpcR2, (4)

whereVp/S, is the ratio of the pore volume to surface area, which equals

(R2L)/(2RL) = R/2when the pore geometry is assumed to be a bundle of cylindrical

tubes.R is the radius of the tubes, L is the length of the tubes, and c is dependent on the

cross-sectional area of the tubes that make up the microstructure model; c = 2 for circular

has been found to be cpirically, pores, 1.67 for equilateral triangles, 1.78 for squares. Em

5 for many types of granular porous media [Carman, 1956; Dullien, 1992].

Snow, existing as a solid in a range of temperatures approaching its melting point,

is a unique porous medium in that surface layers undergo rapid metamorphism from

perature ation and condensation processes driven by diurnal and seasonal temsublim

gradients [Colbeck, 1983; Kaempfer et al., 2005; Pinzer and Schneebeli, 2009]. Snow

exists naturally in several complex forms, ranging from those best modeled as random

assemblages of nearly spherical particles for newly fallen, wind blown snow, or as

ely conduit bundles for compacted firn. The microstructure of snow can be extrem

pth hoar. Snow also exhibits a large eplex, as exhibited by faceted, cup-shaped dcom

variability of site-to-site permeability values [Rick and Albert, 2004] correlated to

variations in conditions, as well as large temporal variability related to metamorphism

re than oeability of polar firn, snow mperties. Permand seasonal variability in snow pro

one year old, has been measured at a number of sites, e.g. Albert et al., [2000],Albert

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105106107108109

110111112113114115116117

118119120

and Shultz [2002], Rick and Albert [2004], Albert et al., [2004], Courville et al., [2007],
., [2009]. Fujita et alnd ., [2009], aHörhold et al

Until recently, the only technique for imcrostructure of snow was iaging the 3-D m

to fill the pores with a fixative, perform serial thin sections of the encapsulated snow, and

cro-CT techniques have been developed is, mble the thin sections. In recent yearreassem

that permit the nondestructive imaging of snow samples. The micro-CT uses sequential

x-ray scans of a material to recreate 3-D images of snow samples taken from the field. It

cture of a variety of porous ine the struamis a well-developed tool that has been used to exmedia by several researchers [e.g. Auzerais et al., 1996; Coker et al., 1996; and Fredrich
., 2001; Coléou et al and recently by investigators examining snow structure [., 2006]et alFlin et al., 2001; Lundy et al., 2002; Freitag et al., 2004; Pieritz et al., 2004; Schneebeli,
2004;Kaempfer et al., 2005; Flin and Brzoska, 2008; and Hörhold et al., 2009].

In conjunction with the improved ability to image 3-D microstructures, numerical
odels to calculate heat gital mitechniques have been developed that use high resolution dne of these is the lattice-crostructures. Oiconduction and gas flow through 3-D model viscous flow through porous thod (LBM), which is well suited to meann mBoltzmmedia. Lattice-Boltzmann models were developed from lattice gas models in which
e at . The particles are allowed to collidove on a lattice networkdiscrete gas particles mnodes, with collisions governed by a simplified collision operator. After collision, the
particles bounce back in the direction opposite the original path. The movement and

collision of the particles is governed by kinetic gas theory. After a collision, the
rs by one of several collision operatorium equilibdistribution is allowed to relax intowhich have been developed. The Navier-Stokes equations can be recovered from the

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lattice-Boltzmann algorithm through the collision operator [Succi, 2002]. Lattice-

pute the input have been used to comcro-CT 3-D data asiann models using mBoltzm

permeability of several types of porous media [Chen and Doolen, 1998] including

sandstone [e.g. Auzerais et al., 1996; Manwart et al., 2002;Arns et al., 2004; White et al.,

2006; and Kemeda et al., 2006], sand [e.g. Ahrenholz et al., 2006; Lehmann et al., 2008],

and metallic foams [e.g. Gerbaux et al., 2010].Freitag et al. [2002] used 3-D data

odels of air ann mles in lattice-Boltzmpobtained from serial sectioning of snow sam

bined 3-D m In this work, we com and gas diffusivity.eabilitypermcro-CT i

odeled pared the mdel of air flow and comoann mreconstructions and a 3-D lattice-Boltzm

of permentsresults to measurem firn with a wide range of grain and pore eability for polar

scale characteristics.

2. Methods

ples 2.1 Field sites and sam

We examined two sets of firn samples as part of this work. The first set of

samples is taken from the megadunes region of East Antarctica (81°S, 125°E). We chose

eight sam of one another, eas, located within 3 km two different megadunes arples from

the windward face with two different accumulation rates. Four samples were taken from

of a dune, in an area of low accumulation (2 to 3 cm w.e. a-1) and four samples were

taken from the leeward face of the dune, in an area that experienced no snow

accumulation (hiatus) [Courville et al., 2007]. The samples were taken from depths of 0.1

,m, 0.4 m gadunes areaeulation rates in the m The different accum. and 10 m, 8 m, 9 m

ulation rates eral, low accumresulted in varying grain and pore sizes; in polar areas in gen

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perature es spent in near-surface temresult in large grains due to longer residence tim

ples were gradients. The second set of sam an area experiencing relatively taken from

higher accumulation, Hercules Dome, Antarctica (86°S, 105°W), with an accumulation

-1. w.e. aated to be 18 to 22 cmrate estim

We obtained the core samples from the megadunes area using both an

eter and ples were 8 cm in diamechanical drill and a hand drill. These samelectrom

inally 1 mnome firn cores were taken during the 2004 US in length. The Hercules Dom

ITASE traverse using a smaller electromechanical drill and were 5 cm in diameter and 1

m in length.

2.2 Laboratory Methods

The core samples were shipped to CRREL in Hanover, NH, where stratigraphy,

density, permeability, grain size, gas diffusivity, and thermal conductivity measurements

were made in a cold room laboratory. From the 1-m long cores retrieved in the field, we

ogeneous layers based on visual stratigraphy. These cut sections of relatively hom

samples varied from 4- to 10-cm in length. The density of each sample was determined

e. ents of mass and volumeasurem mfrom

ined from pressure and flow rate meability is determThe permeasured with a

custom-designed permeameter [Albert et al., 2000]. The permeameter is based on

[1970]’s design, which incorporates a double-head flow samShimizuinates pler that elim

ler has two concentric regions in which flow and pressure are pmedge effects. The sa

tched to ensure that aeasured through the sample. The pressure in the two regions is mm

the flow is the sample. A ents are read through the center of the sameasureme, and m

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flexible rubber membrane is inflated around the core sample to create an air-tight seal.

The rubber membrane accommodates a wide range of sample diameters and lengths. We

make ten pressure measurements at incremental flow rates, and ensure that the pressure

ents follow Darcy’s equation, i.e. are linear. Any asuremeversus flow rate m

measurement values that are not linear are repeated or discarded. The ten values of

ple are generally within 3% of at the different flow rates for any given sameabilityperm

one another. Replicate permeability values from tests on the same samples are on

ples from the ility values from tests on sameabaverage within 6% of one another. Perm

same layer in a snow pack vary less than 10% [Albert and Perron, 2000]. The minimum

length of a sample that can accurately be measured in the permeameter is 3 cm. It is

layers are present in one bulk sample due to the hic rapoften the case that several stratig

inhomogeneous nature of most firn, especially near-surface firn from high accumulation

areas.

2.3 Micro-tomography

We shipped the core samples in insulated boxes as received, with no pore-filler, to

the Alfred Wegener Institute (AWI) in Bremerhaven, Germany for micro-CT imaging.

d to odifie available Skyscan 1074SR mI micro-CT scanner is a commerciallyThe AW

, as described in operate in a -25°C cold room [2002]. The CT scanner has Freitag et al.

crofocus X-ray tube that operates at 40 kV and 1000 A. A charge-ian integrated m

X-ray detector with a total range of 256 era is used as the coupled device (CCD) cam

a ice and pore space differ by as mgreyscale units. The mean grey levels of 100 ny as

o >120, which allows the two phases to begreyscale units, with a signal-to-noise rati

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distinguished from one another. The snow sample is placed on a turntable which rotates

ple. A ages make up one 180° rotation of the samat intervals of 0.9°. 210 shadow im

ages into a series of horizos the shadow im transformdigital convolution algorithmntal

cross-sectional images that are used to construct the 3-D structure of the final image. 490

horizontal scans at 40 micron spacing make up one three dimensional image. The

resolution of one voxel is 40 microns. The maximum size of sample that can fit in the

CT-scanner is 25mm in diameter and 20mm in height. Each original bulk sample was

cut into three to five subsamples 2 cm in length in order to fit in the CT-scanner. A hole

saw was used to cut a 2.5-cm diameter core out of the center of the original larger core

sample. The 2.5-cm diameter grey value images from the CT-scanner are then cropped to

a 1.6-cm cube, segmented and filtered, and used as the input in the lattice-Boltzmann

model.

We determined the threshold value between air (white) and ice (black) pixels for

each sample using two different methods. The first method involved choosing a

threshold value for each subsample so that the average overall porosity of the modeled

subsamples equaled the original measured sample porosity. The threshold for each of the

individual subsamples was chosen so that 2-D slices of the binary image matched the

geometry of the greyscale image based on visual inspection. The second method, as

outlined in Freitag et al., 2004 and Hörhold et al., 2009, is to choose the threshold value

as the mid-point of the maxima for the pore space and ice particle values in the greyscale

histogram from several of the 2-D slices. Threshold values for each individual subsample

awere chosen in this mnner, as opposed to picking a universal threshold value for all

ples with porosities near the thods result in reconstructed digital sameples. Both msam

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easured porosities of the origmable 2 for a summary of the porosity inal samples (see T

values).Freitag et al., 2004 compare the density calculated from the micro-CT data to

ll. eeasured by gamma absorption and found that they agreed whigh-resolution density m

 = 1.2 ages were processed either using a 3x3x3 Gaussian filter with ple imThe sam

(megadunes samples) or a 3-D median filter with a 3x3x3 mask (Hercules Dome

samples) in order to remove image artifacts. The binary, filtered images were

reassembled into a 3-D reconstruction and used as input for the 3-D LBM permeability

model. Samples of the 3-D micro-CT digital reconstructions of firn from each megadunes

the 3-D racterization fromarea are shown in Figure 1. Microstructural cha

ined using MAVI reconstructions of the micro-CT data for the samples was determ

ercially-available,ages), a specialized, comme Ims for Volum(Modulated Algorithm

micro-CT software package. Microstructure data represent mean values of a volume of

~4.096 cm3 of firn. Porosity, , is the fraction of air voxels in the volume, or the total

ple is calculated from the mhe density of the snow samporosity. Tcro-CT data as (1-i

)ice, where ice is the density of ice, equal to 0.917 g/cm3. The specific surface of the

snow matrix, SSA, is defined as the surface density per mass, and is determined from the

cro-CT data as: im

SSA = total surface area of snow/ total unit volu(5)em

The effective diameter, deff, or optical grain size is then calculated from the SSA [Warren,

, 2000]: , Nolin and Dozier, 1993Nolin and Dozier1982,

= 6/SSA (6) deff

We report the effective grain diameter, deff, as proposed by Dominé et al., 2008 and

others. The volume-to-surface-ratio of the pores, Vp/S, is calculated by dividing the total

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volumr can be rtuosity factoace. The toe of the pores (air fraction) by the total surf

calculated by MAVI geometrically. The value is obtained by an arithmetic mean of all

pathways.

ann Model 2.4 Lattice-Boltzm

The LB model uses a 19-direction D3Q19 lattice [Succi, 2002]. The middle node

represents the rest particle, with the remining nodes representing 18 possible non-zero a

velocities. The 3-D data from micro-CT scans are used as the input geometry for the

model. Each voxel in the 3-D image represents one node in the lattice-Boltzmann model

so that the resolution of the model is also 40 microns. The model uses a force at each

the pressure gradient across the sample. satepore node to drive the flow that approxim

(BGK) collision operator which employs k utilizes the Bhatnagar-Gross-Krooodel The m

a single relaxation time parameter. The 3-D cubic model snow samples have a 40 micron

ple periodic in the flow ke the samaresolution that results in 320x320x320 nodes. To m

ple is reflected about the plane perpendicular to the flow and joined direction a cubic sam

to its mirror image. The final sample has 320x320x640 nodes. Simple on-site bounce-

back is used at pore-solid interfaces as well as at the solid boundary at the sample sides.

evergence in about 5000 timple reaches reasonable conThe flow through the model sam

steps, which takes approximbers, less ately 10 hours to run on a PC. Low Reynolds num

ined ber is determinar flow. The Reynolds numthan 0.1, were used in order to insure lam

byVL/, where V is the fluid velocity per unit cross-sectional area, as calculated by the

LBM;L is an arbitrary length, equal to 10 lattice units; and  is the kinematic viscosity,

which is set to a constant value. The permeability of the sample is computed from

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around consolidated periodic testing flowDarcy’s equation. The model was validated by

arrays of spheres compared to published results [dos Santos et al., 2005; Larson and

, 1989]. The results of the test of Stokes flow around consolidated spheres (i.e. Higdon

t area between spheres) are shown in Table 1, thespheres with non-zero contac

ensions are in lattice units. dim

For the megadunes samples, the LBM composite permeability, kCOMP,for three to

five subsamples were combined by adding the reciprocal of each subsample weighted by

the subsample length to estimate the bulk permeability of the original sample:

LkCOMPmLikii

(7)

whereL is the total length of the sample, Li is the length of the subsample, i, and

(k)i is the permeability of the ith subsample. For the Hercules Dome samples, we chose

eability using the LBM. del permoone representative subsample to m

The REV (representative elementary volume) of the both coarse and fine grained

sample types was determined by running the LB model for cubic volumes of

100x100x100 voxels at 125 different starting voxel locations, 150x150x150 at 27

different starting locations, 200x200x200 at eight different starting locations and

ples are m250x250x250 at eight starting locations. The results for two different types of sa

3) is a ple, the 200 unit voxel cube (0.5 cmshown in Figure 2. For the fine-grained sam

stable result, with the permeability values calculated for the 250 unit cube (1 cm3) having

3ple, the 250 unit cube (1 cma standard deviation of +/-7%. For the course-grained sam)

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281282283284285286287288289290291292293294295296297298299300301302303

odel using the result of the me average deviation fromgives a reasonable result, with th +/-5%, and the standard deviation of the results of the eight em0 cubic voluthe entire 32250 cubic units being +/-7%. This is within the limit of the error of our permeability
measurements. Examination of the REV model runs for the coarse-grained samples
portions having ratified, with top and bottomple were ste of these subsamreveal that somdifferent permeability values, i.e. volumes sampled from different portions of the entire
sample revealed systematic, geometrically based differences. The result of the
stratification of the coarse-grained subsample is that a larger REV is required to produce
eability value. able perma reason

ent Validation 3. Model and MeasuremWe determined the permeability of a 10-cm diameter, 10-cm height cylinder
randomly packed with 4-mm diameter glass beads using the permeameter [Albert et al.,
2007]. The measured permeability for the beads was k = 9.97 x 10-9 m2+/- 0.50 x 10-9 m2
for 20 replicate tests, which compares well to the Kozeny-Carman (KC), kKC = 10.12 x
10-9 m2,and the Kozeny-Blake (KB), kKB = 12.15 x 10-9 m2,predictions for
unconsolidated granular media of the same diameter and porosity. The lattice-Boltzmann
e geometry was ple of glass beads with the samputer generated sammodel value of a com10.70 x 10-9 m2, with a relative error of 7% compared to the average measured value for
the bead packs, and reasonably close to the precision of the permeameter, approximately
5%.ples 4. Results for Firn Sam4.1 Microstructure characterization

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Results for the microstuctural properties of the micro-CT data are summarized in

Table 2.Hörhold et al., [2009] presents many more details on the Hercules Dome data.

site were large, with an effective grainThe near surface snow grains at the hiatus

ulpared to the accumeter of 1.5 mm on average, comdiamation site, with an effective

grain diameter of 1.0 mm in the near surface, as determined from micro-CT data. The

average effective grain diameter of the Hercules Dome samples in the near surface was

ents, vary easuremined from density msamples, determ1.5 mm. The porosities of the

from 0.4 to 0.6. The average pore sizes, determined from the micro-CT data, vary from

0.86 mm for the fine-grained, accumulation samples to 1.12-1.39 mm for the coarse-

e egadunes region and 0.6 mm for the Hercules Domgrained, samples from the m

sam of 15 nodes per pore, above the 4 nodes per pore needed umples. This allows a minim

, 2002].Succito insure that the LBM produces Poiseuille flow in the pores [

ann model 4.2 Lattice-Boltzm

For the megadunes samples, the comparison between the calculated permeability

eability values is shown in Figure easured perminal mvalues from the LBM and the orig

3. The composite permeability calculated from the subsample permeabilities, determined

using Equation 7, is indicated by the open circles in the figure. The results are

summarized in Table 2. For the Hercules Dome modeling runs, one representative

subsample of each sample was modeled and used to represent the composite value of the

original sample, as the Hercules Dome samples tended to be shorter, more homogeneous,

gadunes sameand less layered than the mples. These results are shown in Figure 4 along

with the composite values of permeability for the megadunes samples. In order to

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examine the performance of the model in comparison to the experimental results, we

examined the variability of the permeability values from modeled megadunes subsamples

r between the mposite value, as well as the erroparison to the comin comodeled and

measured results. For the Hercules Dome samples, only one subsample was taken from

each bulk original sample, and only the total error between measured and modeled results

is reported in Table 2.

gadunes subsamples e4.3 Variability of m

The stratigraphy of the megadunes site is quite complex, with areas experiencing

.,Albert et altamorphosed firn [ehiatus having coarse bands of large-grained, highly m

ulation areas with near-surface layering as seen in other 2004] alternating with accum

polar regions, and the beginning of a paleo-dune hiatus surface at depth. This variability

in the firn structure is seen in our measurements of both permeability and microstructure.

For three of the megadunes samples, the modeled subsamples show considerable spread

in permeability values, caused by inhomogeneous layering within the samples. The

ples for Samindividual subsame-to-surface ratio stance, had values of volumple C, for in

(Vp/S) of the pore space varying from 0.14 mm to 0.22 mm. Sample G had individual

mples A and B, in /S values varying between 0.27 mm and 0.40 mm. Saple Vsubsamp

/S values which had no significant variation and variation parison, had subsample Vcomp

in the range between 0.18 and 0.21 mm, respectively, and also smaller variability in the

permeability values. The largest variability occurs in samples near the surface (C and F)

es would not be pluently the original samore natural layering occurs, and conseqwhere m

les from the accumpogeneous. Coarse-grained samas homulation area at depth (D and

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G) also have high variability. This depth (approximately 10 m) at the accumulation site

marked a transition between snow that had been accumulating and a hiatus dune surface

buried below, which accounts for some of the variability in permeability and Vp/S ratio

ples. The rest of the samsambetween suballer grained and with less layering, ples, sm

have coefficient of variation (CV) values of calculated permeability between subsamples

8 to 13%. that range from

4.4 Error

The average composite modeled permeability values are within 25% (average

absolute relative error of modeled values compared to measured values) of the measured

ally 18%, and is not norme uncertainty ofbulk values. The 25% error has a larg

all error around +/- 0.3 x lations showed a relatively smumdistributed. About half of the si

10-9 m2, Figure 5. The other half showed much larger errors, up to +/- minus 2 x 10-9 m2,

almost a factor of ten. We could not find a sufficient explanation of this large variation.

ples which have by larger grain size. The samy be partially explained aThe large errors m

the greatest error between the modeled and measured results are in general coarse-

grained, deeper samples (samples B, D, and G) from the megadunes site, or shallow

samples (sample K and M) from Hercules Dome. The higher error in the Hercules Dome

easured results can be attributed to the use of one subsample to ples compared to msam

represent the original sample instead of finding a composite model result. The high

eay be partly due to megadunes site merrors from the mtamorphic changes induced in

gadunes eodeled mtransport, which is supported by the general trend of the m

permeability values to be higher than the measured results. It is likely that some

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395

metamorphism of the snow samples from the megadunes occurred during shipment of the

any fromples to Germsam the the U.S., as evidenced by condensation on the inside of

plastic bags used to ship the samples and the disappearance of markings made on the

sam the ent. No temperature data-loggers had been placed withples before shipm

shipment to determine if the temperatures during transport were high enough (i.e. greater

ents, including the than -10ºC) to induce changes as was done with all later shipm

Hercules Dome samples. The temperature logs during the Hercules Dome shipment

show that temperatures stayed below -20C, and metamorphism was likely minimized.

reduced size of the CT samples, as ethodological errors are 1) the Other m

ple size; 2) the destruction of the interface between easured sampared to the mcom

subsamples caused by cutting the sample, which we are not able to reconstruct in the

modeling; 3) errors introduced by the segmentation process and filtering; and 4) error due

to the volume modeled for the coarse-grained subsamples being close to the REV. This

last effect is observable in a plot of the statistical error of the measured permeability

values compared to the modeled permeability values versus the effective grain diameter

e grain size forle increase in error as thple in Figure 5. There is an observabof the sam

ple increases. the sam

It should be noted that the coarse-grained samples examined are end-members in

for polar fieabilitys of both grain sizes as well as permtermrn, due to the fact that they

are from an accumulation hiatus region. For most types of firn will have REV’s for the
3.ined here of ~1 to 1.5 cmaller end of the REV values determLBM on the sm

eability correlations rison to traditional permpa4.5 Com

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397398399400

401

402

403

404405406

407

408409

410411

412

413414415

416

417

We com ships for pirical relationpared the results from the LBM to em

permeability (Figure 6). Shimizu (1970) related permeability to grain size, dgrain, for
several types of season snow: kshimizu = 0.077dgrain2e(-7.8*) (8)
where* is the specific gravity of snow. For comparison, we calculated * for

each sample based on density measurements. We compared the LBM results to the

= 5.can (KC) relationship (Equation 4) with Kozeny-Carm

In previous work examining the permeability of polar firn, Rick and Albert [2004]

andHörhold [2006] developed relationships for permeability following Revil and Cathles
(1999) utilizing the concept of the formation factor, F, which is equal to-m according the
empirically based Archie relationship, where is porosity and m is the “cementation

an relationship to include (2004) modified the Kozeny-CarmRick and Albertexponent.”

: a pore size termkRA = (dpore/4)(Vp/S)2 (9)

Here we use the pore size as determined from micro-CT data for dpore.Hörhold
[2006] further added a term for the tortuosity of the firn, , following Walsh and Brace

[1984], as well as a term defining the anisotropy, dl, as described in Hörhold et al.,

[2009]:khörhold = (dpore/4)(Vp/S)2(/)dl (10)
Here we use the geometrical tortuosity,, as determined by the micro-CT, and

ow pathway to that of a straight line. It should be the deviation of the flsputed acom

noted that this tortuosity is not the same as the tortuosity factor, which relates such

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420

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424

425

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427

428

429

430

431

432

433

434

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436

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438

439

440

material properties of the porous medium as electrical conductivity, diffusivity, etc. to

those in free air.

ining the e LBM is much better at determAs can be seen in Figure 6, th

permizu’s relationship and the KC equation, which are traditionally eability than the Shim

used to predict snow permeability. The model does moderately better at predicting the

permeability than the newer formulations of Rick and Albert [2004] and Hörhold [2006]

which incorporate more details on the microstructure of snow.These microstructural

idetails, namely the pore size, tortuosity, and anisotropy, require data from the mcro-CT

that are not as easily determined as porosity, grain size, and SSA. The microstructural

on the mvalues used in these relationships are based cro-CT data and are subject to many i

or the LBM. e errors and uncertainties as underlying structure fof the sam

5. Conclusions

cro-CT reconstructions irough 3-D mann modeling of flow thLattice-Boltzm

croscale details of pressure-driven air flowiise in understanding mshows great prom

ining snowodel is a useful tool for determann mthrough firn. The lattice-Boltzm

permeability, reproducing measured results and able to model permeability values at a

much smaller scale than is possible with measurements. This will be especially useful

when examining the permeability of single stratigraphic layers on the order of 1 cm.

Measured results across a range of porosities and grain sizes are reproduced by the

model, and the model is better at predicting permeability than traditional permeability

relationships for snow. While computationally intensive, lattice-Boltzmann modeling

can provide insight, by modeling the entire flow field in the snow matrix, into the nature

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of the flow around the com

plex m

crostructure of the firn, without having to mi

plifications to the snow or firn geomsim

etry.

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ents Acknowledgem

This work was supported by NSF OPP grants 0125276 and 9814676. The authors

the Alfred Wwould also like to thank Johannes Freitag of gener Institute for help with e

e gener Institute for helping to fund someodeling, and Heinz Miller of the Alfred Wthe m

the anonymous reviewers were greatly of the work. The helpful comments of

appreciated.

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, 22, 1-32. of Low Temperature Science, Series A

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198

ent simulations, ., 1, cta GeotechA

30

629

630

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633

634

635

636

637

638

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640

641

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643

644

645

646

647

648

649

650

651

Table Captions

ic array of consolidated spheres for the Table 1. Results of Stokes flow around period

lattice-Boltzmann model compared to the empirical results of Larson and Higdon [1989].

odel time step. d mits anUnits are lattice un

e-to-surface ratio /S is the volumples. VTable 2. Results and errors for the modeled samp

of the pore space (mm);  is the porosity, comparing the measured bulk porosity (meas)

cro-CT data (CT) obtained for the individual i the merage porosity fromto the av

subsamples as well as the total sample (in bold); for length, we report the total length of

the original bulk sam); k ples (2 cm) in bold, as well as the length for the subsample (cm

is permeability (m2); is the standard deviation of the permeability values for the

subsamples; CV is the coefficient of variation of the subsamples permeability for each

ean of the observations; ple, defined as the standard deviation divided by the mbulk sam

and the relative error is the percent value of the modeled composite results as obtained

easured result (in bold) shown with the lk mpared to the buusing Equation 7 (in bold) com

individual results for the subsame individual t the error of this is noples. Note that th

subsamples compared to the measured result. Samples A-H are samples from a

megadune accumulation area (MD a) and a megadune hiatus area (MD h). Samples I-M

ples, we chose one subsample to run in e (HD a). For these sam Hercules Domare from

the lattice-Boltzmcrostructural data from i and present the mann, as indicated in the table,

parison. ples for comcro-CT of the other subsamithe m

199

31

652

653

654

655

656

657

658

659

660

661

662

663

664

665

666

667

668

669

670

671

672

673

Figure Captions

(top) and 9 ulation megadunes site, left, at 0.4 m high accumomples frFigure 1. Firn sam

pared to coarse-g) depths, comm (bottomht, ulation hiatus site, rig accumed firn fromrain

ite is snow and black is pore space. he depths. Wat the sam

ination of the REV of a coarse-grained sample (diamFigure 2. Determonds) and a fine-

e are grained sample (crosses). The average values of the REV runs for a given volum

shown as open circles.

different types of snow easured results fromodel versus mFigure 3. Lattice-Boltzmann m

samegadunes site; subat a mpared to the eabilities modeled by the LBM are comple perm

ents for those subsamples. easuremeability m, not permeabilityple permbulk sam

Different colors represent the individual sam each sample ples fromles, with the subsamp

s of the eability value circles represent the bulk perm color. Openerepresented in the sam

cro-CT 3-i momodeled frt the subsections monds represenples. Closed diamoriginal sam

aging. Letters refer to different types of snow. A, B, F, and H are snow samD iples m

ulation. C, D, E, and G are w accum snocing hiatus inegadunes areas experien mfrom

re complete oulation. See Table 2 for a mcing low accumdunes area experiengae a mfrom

rks the value of the mation. The straight line mdescripeasured vs. meabilityodeled perm

. eabilityperm

200

32

674

675

676

677

678

679

680

681

682

683

684

685

686

687

688

689690691

gadunes and eFigure 4. Modeled permeability results versus measured results for m

ples is s samgaduneeodeled result for the mposite mles. The compme saHercules Dom

pared to the mcomple representative subsam oneodeled result fromeasured result. The m

rks the value of the aples is presented. The straight line me sam the Hercules Domfrom

eability.ermeasured peability vs. mmodeled perm

ieability modeled permr (mFigure 5. Statistical erroeability) vs. easured permnus m

eter.effective grain diam

of snow from eabilityFigure 6. Comparison of LBM to empirical relationships for perm

Shimizu [1970], the Kozeny-Carman relationship (with c = 5), Rick and Albert [2004],

Hörholdand

[2006]. The straight linarks the value of the me m201

eability. easured perm33

692

Table 1

diameter

22

44

66

112

138

cell length

21

42

63

107

131

k theoretical

0.671

2.7763

6.1671

17.978

25.114

202

k modeled

0.663

2.7699

6.1427

17.9515

25.0336

error (%)

1.20

0.23

0.40

0.15

0.32

34

693

Table 2.samplesitedepthVp/S lengthdeffk, calc.k, meas. variability, ksubrel. err.
22(m)(mm)(meas)(calc)(cm)(mm)(m-9)(m-9)2-9CV
%%)x10(mx10x10AMD h9.70.160.400.408.31.711.791.5921212.6
A10.160.4021.811.840.52.6
A20.160.3921.672.022.212.4
A30.160.4021.641.582.112
BMD h8.50.200.410.417.21.732.461.6631348.2
B10.210.4121.742.732.610.7
BB320.180.210.410.412211.75.7122.12.633.41.713.96.9
CMD a0.10.190.560.5612.70.933.022.69398612.3
C10.140.5620.762.336.922.9
C20.150.5620.891.9510.735.5
C30.260.5621.033.5250.116.6
C40.220.5620.981.027.2239
DMD a9.20.260.510.5110.41.426.044.18152344.5
D3D20.280.270.510.512211.34.4875.86.9118.21.330.12.2
D40.230.5121.494.9910.517.3
EMD a0.40.220.590.5911.11.005.885.93611-0.8
E10.220.6021.026.465.89.9
E20.180.5820.985.266.210.5
EE340.220.250.620.572211.04.0156.50.503.86.26.410.6
FMD h 0.40.280.520.5212.61.705.416.292234-14.0
FF210.270.330.520.522211.80.4362.83.6214.227.926.252.5
FF430.260.290.520.532211.85.5277.78.7423.723.243.843
F50.260.5221.887.211833.3
GMD a10.40.340.510.509.51.7210.247.94292729.0
G20.340.5221.847.542726.4
G30.400.4821.6613.1028.527.9
G40.270.5121.7011.9016.816.4
HMD h0.20.240.580.5811.51.718.049.7078-17.1
H10.270.5821.558.423.84.8
H3H20.220.230.580.572211.69.5887.59.155.48.96.811.1
H40.250.5822.018.181.31.7
IHD a10.00.140.430.434.11.201.191.099.2
JHD a10.70.170.450.436.01.321.3622.8
1.3120.430.17J1J2J30.170.170.440.43221.331.311.67
KHD a0.30.130.570.565.70.631.54-26.6
K10.140.5820.591.13
K20.130.5320.67
LHD a1.10.170.590.573.80.832.602.84-8.5
MHD a1.20.150.530.523.90.804.06-59.1
M10.150.5320.791.66
0.8120.510.14M2

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35

694695

696

697

Figure 1. Firn samples from high accumulation megadunes site, left, at 0.4 m (top) and 9

m (bottom) depths, compared to coarse-grained firn from accumulation hiatus site, right,

ite is snow and black is pore space. he depths. Wat the sam

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36

698

699

700

701

702

703

704

ination of the REV of a coarse-grained sample (diamFigure 2. Determonds) and a fine-

e are grained sample (crosses). The average values of the REV runs for a given volum

shown as open circles.

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37

705

706707

708

709

710

711

712

713

714

715

716

717

718

different types of snow easured results fromodel versus mFigure 3. Lattice-Boltzmann m

at a megadunes site; subsample permeabilities modeled by the LBM are compared to the

bulk sample permeability, not permeability measurements for those subsamples.

each sample ples fromles, with the subsampDifferent colors represent the individual sam

represented in the same color. Open circles represent the bulk permeability values of the

original samples. Closed diamonds represent the subsections modeled from micro-CT 3-

ples maging. Letters refer to different types of snow. A, B, F, and H are snow samD i

from megadunes areas experiencing hiatus in snow accumulation. C, D, E, and G are

from a megadunes area experiencing low accumulation. See Table 2 for a more complete

description. The straight line marks the value of the modeled permeability vs. measured

. eabilityperm

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38

719720

721

722

723

724

gadunes and eFigure 4. Modeled permeability results versus measured results for m

Hercules Dome samples. The composite modeled result for the megadunes samples is

compared to the measured result. The modeled result from one representative subsample

from the Hercules Dome samples is presented. The straight line marks the value of the

modeled permeability vs. measured permeability.

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39

725726

727

Figure 5. Statistical error (modeled permeability minus measured permeability) vs.

eter.effective grain diam

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40

eability. easured permarks the value of the me m [2006]. The straight linand [2004], 732

an relationship (with 728

[1970], the Kozeny-Carm731

Hörhold

Shimizu

bertlRick and A = 5), c

of snow from eabilityFigure 6. Comparison of LBM to empirical relationships for perm

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