On the similarity and apparent cycles of isotopic variations in East Antarctic snow-pits

29 Pages·2017·3.06 MB·English

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On the similarity and apparent cycles of isotopic variations in East
Antarctic snow-pits
ThomasLaepple1,ThomasMünch1,2,MathieuCasado3,MariaHoerhold4,AmaelleLandais3,and
SeppKipfstuhl4
1AlfredWegenerInstituteHelmholtzCentreforPolarandMarineResearch,TelegrafenbergA43,14473Potsdam,Germany
2InstituteofPhysicsandAstronomy,UniversityofPotsdam,Karl-Liebknecht-Str.24/25,14476Potsdam,Germany
3LaboratoiredesSciencesduClimatetdel’Environnement-IPSL,UMR8212,CEA-CNRS-UVSQ,GifsurYvette,France
4AlfredWegenerInstituteHelmholtzCentreforPolarandMarineResearch,AmAltenHafen26,27568Bremerhaven,
Germany
Correspondenceto:ThomasLaepple([email protected])
Abstract. Stable water isotopes in polar ice provide a wealth of information about past climate evolution. Snow pit studies
allowustorelateobservedweatherandclimateconditionstothemeasuredisotopevariationsinthesnow.Theythereforeoffer
thepossibilitytotestourunderstandingofhowisotopesignalsareformedandstoredinfirnandice.Asstablewaterisotopes
inthesnowfallarestronglycorrelatedtoairtemperature,isotopesinthenearsurfacesnowaresupposedtodepicttheseasonal
5 cycleatagivensite.Accordingly,variationbetweensitesinaccumulationrateisexpectedtobematchedbyvariationinthe
numberofseasonalcycles.However,snowpitstudiesfromdifferentaccumulationconditionsinEastAntarcticareportedsimilar
isotopicvariabilityandcomparableapparentcyclesintheδ18OandδDprofileswithtypicalwavelengthsof 20cm.These
∼
observations are unexpected as the accumulation rates strongly differ between the sites, ranging from 20 to 80mmw.e.yr 1
−
( 5–25cmofsnowperyear).Variousmechanismhavebeenproposedtoexplaintheisotopicvariationsindividuallyateach
∼
10 site; however, none of these is consistent with the similarity of the different profiles independent of the local accumulation
conditions.
Here,wesystematicallyanalyzethepropertiesandoriginsofisotopicvariationsinhigh-resolutionfirnprofilesfromeight
East Antarctic sites. First, we confirm the suggested cycle length (mean distance between peaks) of 20cm by counting
∼
theisotopicmaxima.Spectralanalysisfurthershowsastrongsimilaritybetweenthesitesbutindicatesnodominantperiodic
15 features.Finally,theapparentcyclelengthincreaseswithdepthformostEastAntarcticsites,whichisinconsistentwithburial
andcompressionofaregularseasonalcycle.Weshowthattheseresultscanbeexplainedbyisotopicdiffusionactingonanoise
dominated isotope signal. The firn diffusion length is rather stable across the East Antarctic and thus leads to similarpower
spectraldensitiesoftheisotopicvariations.Thisinturnimpliesasimilardistancebetweenisotopicmaximainthefirnprofiles.
Ourresultsexplainalargesetofobservationsdiscussedintheliterature,providingasimpleexplanationfortheinterpretation
20 ofapparentcyclesinshallowisotoperecords,withoutinvokingcomplexmechanisms.Finally,theresultsunderlineprevious
suggestionsthatisotopicsignalsinsingleicecoresfromlow-accumulationregionshaveasmallsignal-to-noiseratioandthus
likelydonotallowthereconstructionofinterannualtodecadalclimatevariations.
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1 Introduction
Stablewaterisotoperecordsfromicecorescanbeusedtoinferpastlocaltemperaturevariations(Dansgaard,1964)andassuch
areanimportantclimateproxyatinterannualtoglacial-interglacialtimescales(Jouzeletal.,2007;Johnsenetal.,2001).The
depthandaccumulationrateofanicecoreaffectsthetemporalscaleandresolutionoftheclimatereconstructionthatcanbe
5 obtained.IncentralEastAntarctica,lowaccumulationratesanddeepicecoresallowclimatereconstructionstobemadethat
coverthelast800000years(EPICAcommunitymembers,2004),whilethehigheraccumulationratesincoastalareasallow
forhigherresolutionreconstructionsinwhichtheseasonalclimatesignalcanberecoveredfromtheiceisotopiccomposition
(Morgan,1985;Masson-Delmotteetal.,2003;vanOmmenandMorgan,1997;Kütteletal.,2012).
High-resolutionisotopedata,thoughttocorrespondtosub-seasonalvariationsarenowroutinelymeasuredatdeepicecore
10 sites(Gkinisetal.,2011);however,itisuncleartowhichextentisotopicsignalsontimescalesshorterthanmultidecadalcan
beinterpretedasindicatingclimate(Ekaykinetal.,2002;Baronietal.,2011;Poletal.,2014;Münchetal.,2016),especially
forthelow-accumulationregionsthataretypicalontheEastAntarcticPlateau(<100mmw.e.yr 1).Asthelinkiscomplex
−
betweenisotopiccompositionandtheclimaticconditionscreatingthem(Jouzeletal.,1997),numerousstudieshavesampled
the upper meters of firn in order to compare the isotopic variations with instrumental climate data (Masson-Delmotte et al.,
15 2008;Fernandoyetal.,2010;Steen-Larsenetal.,2014).Manyofthesehavereportedoscillationsinsnowpitrecordsfromthe
EastAntarcticPlateau,includingatVostok,DomeC(EDC),DomeA,DomeF(DF),SouthPole(SP)andKohnenStationat
thetheEPICADronningMaudLanddrillingsite(EDML)(Jouzeletal.,1983;Petitetal.,1982;Ekaykinetal.,2002;Hoshina
et al., 2014, 2016; Münch et al., 2016). Interestingly, despite the very different annual snow layer thicknesses at these sites,
whichrangefrom6cmto21cm,theirisotopeprofilesappeartohaveverysimilarpeak-to-peakdistances(Fig1)andarecent
20 systematic counting effort of isotopic maxima in firn profiles (Casado et al., 2016) suggested a characteristic wavelength of
15–25cmacrossallanalysedEast-Antarcticsites.
ForsitessuchasEDMLandSouthPole,theirapparentcyclelengthsmatchwellwiththeirannualsnowlayerthicknesses
andconsequentlytheircycleshavebeenexplainedasreflectingseasonalclimatevariation(Oerteretal.,2004;Münchetal.,
2016;Jouzeletal.,1983;Whitlowetal.,1992).However,thisexplanationisnotconsistentwiththesamecyclelengthbeing
25 observed at lower accumulation sites, where the annual snow layer thickness is often less than 10 cm (Petit et al., 1982).
Instead, a range of alternative explanations have been proposed for the oscillations at individual sites. At Vostok, Ekaykin
etal.(2002)attributedtheoscillationstohorizontallymovingdunes(Frezzottietal.,2002)leadingtoisotopiccyclesduring
burial.However,similarcyclesarefoundatcoresiteswithdifferentdunefeatures,windspeedsandaccumulationrates,and
thus a varying speed of dune movement and burial. At EDC, Petit et al. (1982) explained the mismatch between seasonal
30 andisotopiccyclesasbeingduetomissingyearsresultingfromthecombinedeffectsofsuccessiveprecipitationfreemonths,
erosionassociatedwithblowingsnow,andfirndiffusion.Inamulti-sitestudy,Hoshinaetal.(2014,2016)suggestedthatthe
multi-yearoscillationscouldbeformedbythecombinationofvariableaccumulationandpost-depositionalmodifications,such
asventilation.Finally,thecoarsesamplingresolutioninsomestudies(5cmorlonger)wouldnotresolvetheseasonalcycle,
butsimilarcharacteristicswerefoundforprofilessampledatarangeofresolutions(Ekaykinetal.,2002).Thus,noneofthe
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0 EDML profile T1P2
‰) 1

(
5

.
m
o
n 0
a

O
5
8 -
1
δ
0
1
-
0 EDC DCoxy80
1
)
‰
( 5 depth (cm)

.
m
o 0
n
a
O 5
-
8
1
δ 0
1
-
0 0.50 1.00 1.50 2.00
snow depth (m)
Figure1.ExampleisotopeprofilesfromEDMLandEDC.Bothprofilesarevisuallysimilardespitethedifferingtimeperiodscovered, 10
∼
yrforEDMLand 25yrforEDC,andannualsnowlayerthicknesses, 21cmforEDMLand 8cmforEDC.Alsoshownisanexample
∼ ∼ ∼
oftheautomaticestimationofisotopiccyclelength.Redandblackdotsshowtheidentifiedmaximaandminima.Theshorthorizontallines
underneaththesedotsindicatethe 6cmregionamaximum(minimum)mustbeabove(below)tobeidentifiedasanextremum.Thelonger
±
blackandredhorizontallinesatthebottomofthefigureindicatetheidentifieddistancesbetweensubsequentmaximaorminima.
existing interpretations explain why the apparent observed cycles are so similar across sites and largely independent of the
accumulationrateandrelatedclimaticconditions.
HerewecombineastatisticalanalysisofisotopeprofilesfromeightEastAntarcticPlateausiteswiththeoreticalconsidera-
tionsandnumericalsimulationsofthefirnsignal.Wesuggestthatthepresenceofapparentcyclesinthefirn,andtheirlargely
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Annual mean surface
air temperature (°C) 0o
-5 30o W 30oE
-10
-20-15 6o0W EDMLMDPK 60Eo
DF
-25
o90W South Pole 90Eo
-30 Vostok
S2
EDC
80oS
-35
-40 120Wo 70oS 12o0E
-45
-50 150oW 150o E
180oW
Figure2.Locationofthesamplingsitesusedinthisstudy(solidsquares).The2500ma.s.l.,elevationcontourismarkedbyagreyline,
coloursindicatetheannualmeansurfaceairtemperature(NicolasandBromwich,2014).
invariant length, can be explained by a combination of deposition-related noise in the surface isotope signal and isotopic
diffusion(Johnsenetal.,2000),whichisratherconstantacrosstheEastAntarcticPlateau.
2 DataandMethods
We first introduce the dataset and the method used to compare the power spectral density of observed isotope profiles with
5 those from a null model of diffused noise. We then provide an analytic solution for the expected distance between isotopic
maxima (’cycle length’) and a method to estimate this cycle length from the observed firn profiles. Finally we provide a
minimalnumericalforwardmodelfortheisotopicvariations.
2.1 Data
WeanalysedatafromeightsitesontheEastAntarcticPlateau,forwhichverticalisotopeprofilesofδ18OorδDareavailable
10 with lengths of at least 2m and minimum resolutions of 3.5cm per sample (Fig. 2 and Table 1). We focus our analysis on
theupper4moffirnwithinwhichcycleshavebeendescribedandinterpreted.FortheSouthPoleandEDML,acombination
ofsnowpitandshallowfirncoredataallowsustoextendtheanalysisdowntoasnowdepthof18m.Allrecordshavebeen
published (Table 1), except those for EDML for which we use 22 3.4m deep profiles sampled from snow trenches (T15) as
describedandpartlyanalysedinMünchetal.(2017),togetherwithnewisotopedatafromthefirncoresB41andB50.These
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two cores were drilled close to Kohnen Station in 2012/13, approximately 1 km apart (Alfred-Wegener-Institut Helmholtz-
ZentrumfürPolar-undMeeresforschung,2016).Isotoperatioswereanalysedataresolutionof3cm,usingalaserinstrument
attheAlfredWegenerInstitute(AWI)inBremerhavenandfollowingtheprotocoldescribedinMasson-Delmotteetal.(2015).
2.2 Spectralanalysis
5 Spectra are estimated using Thomson’s multitaper method with three windows (Percival and Walden, 1993). The depth pro-
files are linearly detrended before analysis. For profiles with non-equidistant sampling, the data is interpolated to the lowest
resolutionafterlow-passfilteringtoavoidaliasingeffectsasdescribedinLaeppleandHuybers(2013).Inthecaseofmultiple
profilesatasinglesiteweshowthemeanoftheindividualspectra.
Significancetestingofthepowerspectraldensityisperformedagainstanullhypothesisofnoiseaffectedbyfirndiffusion.
10 Morespecifically,weassumethesumofwhite(temporallyindependent)noisesubjecttoisotopicdiffusionwithadepthvarying
diffusionlengthandadditivewhitemeasurementnoise.Themodelingoftheisotopicdiffusionandthesitespecificparameters
aredescribedlaterindetail.
Thereisnosimpleclosedformexpressionforthepowerspectrumofadiffusedsignalundervaryingdiffusionlengths.We
thusresorttoaMonteCarloprocedurebysimulatingdiffusedwhitenoiseprofilesona2mmresolution,resamplingthemto
15 the actual resolution of the observed profiles to include the effect of discrete sampling, adding measurement noise and then
estimating the spectra on these surrogate datasets using the same method as for the observed profiles. The variance of the
diffusedwhitenoisesignalandthemeasurementnoisearefreeparametersandarechosentominimizetherootmeansquare
deviationoftheobservedandthenull-hypothesisspectrum.
Finally,wescalethenull-hypothesisspectrumbythe95%percentquantilesofaχ2distributiontoobtaincriticalsignificance
20 levels.Thesemarktherangeofspectralpowerexpectedifthetime-serieswerediffusednoise.Thislevelhastobeovercomefor
apeaktobelocally(thusatagivenfrequency)significant.Thedegreesoffreedom(DOF)oftheχ2distributionaretheproduct
oftheDOFfromthespectralestimatorandtheeffectivenumberofindependentprofiles.Weassumeindependencebetween
profilesforallsitesexceptfortheEDMLtrenchdata.Forthisdatasetconsistingof22nearbyprofilesthatweresampledina
singleseason,weassumefiveeffectivedegreesoffreedom.
25 2.3 Rice’sformulafortheexpectednumberoflocalextrema
The’wiggliness’oftimeseries,assumingastationaryrandomprocess,isdeterminedbythefirstmomentsofthespectralden-
sity.ThisrelationshipknownasRice’sformula(Rice,1944,1945)wasshowntohaveimportantimplicationsforinterpreting
paleoclimaterecords(Wunsch,2006)andcanbeusedtoderivetheexpectednumberµoflocalextremes(maximaandminima)
perunittime.Specifically,forastationaryGaussianprocess(e.g.Lindgren,2012),µis
1 Ω
4
30 µmax=µmin= 2π Ω , (1)
r 2
whereΩ andΩ denotethesecondandthefourthmomentofthespectraldensityoftheGaussianprocess.
2 4
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onding arenot 18δOo
corresp ntsthat vertedt
h e n
c m o
orea sure wasc
f a
deandelevationabovesealevel; eprofileshavesinglemissingme δDδDearregressionto.ForSP, Reference Ekaykinetal.(2002) Ekaykinetal.(2002) Ekaykinetal.(2002) Ekaykinetal.(2002) Touzeauetal.(2016) Casadoetal.(2016) Casadoetal.(2016) Touzeauetal.(2016) Hoshinaetal.(2014) Hoshinaetal.(2014) Touzeauetal.(2016) Hoshinaetal.(2014) Münchetal.(2017)+thisstudy thisstudy thisstudy Jouzeletal.(1983) Jouzeletal.(1983) Whitlowetal.(1992)
u m n
udy.Foreachsitewelistlatitude,longit dproxyandoriginaldatareference.So OsamplesinDCoxy80werefilledbyli DepthResolutionProxy mcm 182.52δOδD, 183.12δOδD, 183.12δOδD, 1832.03.5δOδD–, 1833δOδD, 18212δOδD–,† 182.53.33.6δOδD–, 1823δOδD, 1842δOδD, 1822δOδD, 1832.93.0δOδD–, 1842δOδD, 183.42.23.0δOδDs)–, ?18122δOδD, ?18122δOδD, 18102δOδD,‡ ??17.91.92.5δD– 1860.91.4δO– 9.6dataavailableforfirstm. mdepth.
SummaryofthedrillingandsnowpitsitesusedinthisstTable1. recorditsname,theanalyseddepth,samplingresolution,measure 18δincludedintheprovidedsamplingresolution.The35missing 18δOusingaslopeof8togetacompletedataset SiteLat.Lon.ElevationName °N°Ema.s.l. 78.5106.83488VostokVK14−ST61 ST73 ST30 VK56 75.1123.33233EDCDCoxy5−DCoxy80 Vanish12 77.339.73810DFDF− 76.831.83733DKDK− 76.3120.03229S2S2− 74.043.03656MPMP− 75.00.12892EDMLT15(22profile−B41 B50 90.00.02835SPSP78P−SP78C SP92 ???3Topmremovedfromanalysisduetobadcorequality.No 04.9Incomplete.Missingvalueslinearlyinterpolated.Only–†‡
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AdiffusedwhitenoiseprocesshasthepowerspectraldensityP exp( ω2σ2)(vanderWeletal.,2015a),whereP isthe
0 0
−
totalpoweroftheundiffusedwhitenoise,σthediffusionlengthandωangularfrequency.Thesecondandfourthmomentsare
Ω = √πσ 3andΩ = 3√πσ 5.Thus,fromEq.(1)theaveragedifferencebetweentwomaximais
2 4 − 4 8 −
2
∆z =1/µ =2π σ, (2)
max max 3
r
5 hencealinearfunctionofthediffusionlengthσ–aremarkablysimplerelationship.
2.4 Automaticestimationoftheisotopiccyclelengthandamplitude
To investigate the isotopic variations in a similar way as visual cycle counting (Casado et al., 2016), we use an automatic
proceduretoidentifytheminimaandmaximainisotopeprofiles.Forthesakeofsimplicitywecallthetypicaldistancebetween
subsequentmaxima(orminima)cyclelength,notingthatthisdoesnotimplyaperiodicitythatwouldappearasapeakinthe
10 powerspectrum.
Toimproverobustnessagainstmeasurementnoise,wedefinealocalmaximum(orminimum)asthatvalueofaprofilewhich
isabove(orbelow)allothervalueswithinawindowof 6cmcenteredatthegivenpoint.Thisnaturallylimitstheminimum
±
possiblecyclelengthto6cm;however,weexpectthatmostcyclesarelongerthanthisandtheresultsarethusinsensitivetothis
choice.Sinceweapplythesamemethodtotheobservationsaswellastothesimulations,theirintercomparisonisunbiased.
15 Wedeterminealllocalextremesforeachobservedorsimulatedprofileinthedescribedmannerandrecordthedistancesbe-
tweensubsequentextremes(i.e.,thedistancesbetweentwoneighboringmaximaaswellasbetweentwoneighboringminima)
asafunctionofdepth(midpointofdepthbetweenthetwoextremes,Fig.1).Wesorttherecordeddistances(cyclelengths)into
depthrangebins,e.g.1.5–2mdepth,formingadistributionofdistancesforeachspecificbin.Forthesimulations,andalsofor
severalofourstudysites,multipleprofilesareavailable,allowingabetterestimateofthecycle-lengthasafunctionofdepthto
20 bemadebybinningthedistancesfrommultipleprofilestogether.Thebinwidthischosenasatrade-offbetweenmaximising
theresolutionandminimizingthevarianceoftheestimation.Specifically,wechoose1mforsiteswithoneortwoprofiles(S2,
DF,SK,MP,SP,EDMLbelow3.4msnowdepth)and0.5mforsiteswithmorethantwoprofiles(EDC,VostokandEDML
above3.4msnowdepth).Fortheresultingdistributions,wereportthemeanandtwostandarderrors(2 se).Toestimatethe
×
standarderror,weassumeindependenceoftheprofilesexceptforEDML,whereweassumefiveeffectivedegreesoffreedom
25 asinthespectralanalysis.
2.5 Minimalforwardmodelforisotopictimeseries
Asatooltounderstandtheobservations,weconstructthefollowingminimalisticmodeltosimulateartificialisotopeprofiles
intheuppermetersofAntarcticfirn.Weapproximatethelocalclimateconditionsbythelocalnear-surfaceairtemperatures,
T (t),andassumethattheseshapetheisotopesignaloffreshlyformedsnow,δ18O (t).Subsequently,thesnowistrans-
air snow
30 ported to the surface by precipitation where it is redistributed and mixed by wind, giving rise to the surface isotope signal
δ18O (t). Finally, the surface signal is buried in the firn column which is accompanied by diffusional smoothing of the
surface
signalanddensificationofthelayers(Münchetal.,2017).Analysingasnowpitorfirncoreduringthisprocessthenrepresents
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Vostok 0-4m mean
S2
0 EDC 8
4
DF
DK
gth (cm) 30 MESDPPML 6 O (cm)
en 18δ
ycle l ngth
c 0 4 e
Expected 2 Diffusion l
10 2
0
0 2 4 6 8 10
Snow depth (m)
Figure3.Estimateddiffusionlengthsforthedifferentsites.Thediffusionlengthsforδ18O(rightscale)areshownagainstdepth.Alsoshown
aretheimpliedcyclelengths(leftscale)assumingdiffusedwhitenoise.Formostsites,themeancyclelengthsinthetop4m(triangles)are
around20cm.
asnapshotofthefirnisotopesignalδ18O (z).Wedescribetheprocesshereforδ18Obuttheanalogousapproachalsoapplies
firn
toδD.Wewillnowdiscussthesestepsindetail.
Onmonthlytomulti-decadaltimescales,thelocaltemperaturesinAntarcticaaredominatedbytheseasonalcycle.Atour
studied sites, the seasonal cycle explains more than 90% of the variance in the temperature evolution of the last decades
5 (ERA-interimreanalysis,Deeetal.(2011))whenevaluatedonamonthlyresolutionandconsideringthefirsttwoharmonics
oftheseasonalcycle(Table2).Wethereforeapproximatethelocalclimateconditionsbyparameterizingtheseasonalcyclein
temperatureas
T (t)=T +A cos(ωt+φ )+A cos(2ωt+φ )+(cid:15) . (3)
air 0 1 1 2 2 T
Here, ω is angular frequency, t time, T annual mean temperature, and A , A and φ , φ denote amplitude and phase of
0 1 2 1 2
10 thefirsttwoharmonicsoftheseasonalcycleand(cid:15)T theremainingtemperaturevariability.Weestimatetheparametersfrom
temperatureobservationsofnearbyautomaticweatherstations(Table2).Forourstudysites,φ andφ aresmall(<5°)and
1 2
are for simplicity set to zero. For converting the near-surface air temperatures into oxygen isotope ratios, we use the mean
Antarcticspatialslopeofβ=0.8‰°C−1(Masson-Delmotteetal.,2008),
δ18O (t)=βT (t)+(cid:15) , (4)
snow air δ
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where(cid:15) reflectstheisotopicvariabilitynotcapturedbythelinearrelationship.Weneglecttheinterceptofthecalibrationsince
δ
the absolute isotope values have no influence on the results of our analyses and note that our results, except for the spectral
comparison(Figure8),areindependentoftheamplitudesandthusthechoiceofthecalibration.Astrongtemporalrelationship
hasbeenconfirmedbetweentheseasonalcycleoflocaltemperatureandthewaterisotopesmeasuredinprecipitationsamples
5 (Eq.4)atseveralsitesinEastAntactica(FujitaandAbe,2006;Touzeauetal.,2016)althoughtheestimatedslopesvaryfrom
0.3–1‰°C−1betweensites.
Goingfromtheisotopesignalinthesnowtothesurfacesignal,thevariabilityoftheseasonalcycleisaffectedbyaliasingdue
toprecipitationintermittency(Helsenetal.,2005;Simeetal.,2009;Laeppleetal.,2011;Perssonetal.,2011),byredistribution
ofsnow(Fisheretal.,1985;Münchetal.,2016;Laeppleetal.,2016),andbyinterannualvariationintheaccumulationrate
10 andtheaccumulationseasonality(CuffeyandSteig,1998).Wenotethatexchangebetweenatmosphericwatervaporandthe
snowmightfurtherinfluenceδ18O (Steen-Larsenetal.,2014;Touzeauetal.,2016;Casadoetal.,2016).However,even
surface
in this case, the variations in δ18O might still follow the temperature variations. To a first approximation, precipitation
surface
intermittency,snowredistributionandinterannualaccumulationvariabilitydonotaffectthetotalvarianceoftheinputsignal
butrathermainlyredistributeitsenergyacrossfrequencies,similartotheeffectofaliasing(Kirchner,2005).Thus,tosimplify
15 matters,wedescribethecombinationoftheseprocessestogetherwith(cid:15)T and(cid:15)δ bytemporallyindependent(=white)noise,
and set the variance of the total surface signal (seasonal cycle + noise) to the variance of the original seasonal cycle in the
snow(Eq.4).Thechoiceofwhitenoiseisthesimplestoptionhereandtheresultsareactuallynotsensitivetothisassumption
(AppendixA).
Ourmodelfortheisotopicsurfacesignalthenis
20 δ18Osurface(t)=β (1−ξ)1/2Tair(t)+ξ1/2σTair(cid:15)(t) , (5)
(cid:16) (cid:17)
whereσ isthestandarddeviationoftheseasonalcycleintemperature(Eq.3),and(cid:15)(t)areindependentnormallydistributed
Tair
randomvariables(whitenoise)withzeromeanandstandarddeviation=1.Theparameter0 ξ 1determinesthefraction
≤ ≤
ofnoiseinthesurfacesignal:ξ=1representingthecaseofpurenoise(completelyreshuffledseasonalcycle)andξ=0the
caseofafullypreservedseasonalcycle.Themodelalsoincludesoneimplicitparameter,theresolutionatwhichweevaluate
25 the variance of the noise (cid:15)(t). This is required as, in contrast to the seasonal cycle, white noise is not a band-limited signal.
Descriptively,theparameter(cid:15)(t)representsthesmallestspatialscaleonwhichisotopicvariationsarepossible.Weassume1
cmhere,thusimplyingthecompletemixingofanyvariationsoccurringonsmallerspatialscales.
Finally,theburialofthesurfacesnowtransfersthesurfacesignaltimeseriesintothedepthprofileδ18O (z).Weapprox-
firn
imatethisprocessassumingaconstantaccumulationrategivenbythepresent-dayobservations(Table2)astheintraseasonal
30 andinterannualvariationsinaccumulationarealreadyincludedin(cid:15)(t).Duringburial,theisotopesignalisinfluencedbyden-
sification,layerthinningbyiceflowandisotopicdiffusion.Thinningofthelayersisnegligibleinthetopmetersanalysedhere
and therefore neglected in our analysis. Densification is modeled using the Herron-Langway model (Herron and Langway,
1980)assumingconstantsurfacedensityandtemperatureforeachsitewhicharesettothemodernobservations(Table2).The
resultsarenotsensitivetothesesimplificationssincetheoveralleffectofdensificationissmallinthetopmetersoffirn.
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Table 2. Meteorological conditions and model parameters at the study sites. Listed are the annual mean temperature (T0), amplitude of
thefirsttwoharmonicsoftheseasonalcycle(A1,A2),annualmassaccumulationrate(b˙),firnsurfacedensity(ρ0),averageatmospheric
pressure(P0)andfractionofvarianceinERA-interimmonthlysurfacetemperatureexplainedbytheseasonalcyclealone(Fseas).Ifborehole
temperaturemeasurementsexist,weusethe10mfirntemperatureforT0 insteadofairtemperatureobservations,astheyprovideamore
accurateestimateoftherelevanttemperatureforthediffusion.Ifnotemperatureobservationexists,thetemperaturefromthenearestsitewas
usedbyaddingthetemperatureanomalybetweenthesitesfromreanalysisdata(Deeetal.,2011)
Site T0 A1 A2 b˙ ρ0 P0 Fseas
°C °C °C kgm−2yr−1 kgm−3 mbar %
Vostoka 55.3 16.7 6.6 21 350 624 97
−
S2b 55.1 17.4 6.3 21 350 642 97
−
EDCc 51.4 17.4 6.3 27 350 642 95
−
DFd 54.4 16.4 6.6 27.3 368 592 95
−
DKe 53.1 16.7 6.6 35.5 368 592 94
−
MPf 48.6 15.5 6.6 40.9 372 592 93
−
EDMLg 44.5 13.2 4.9 72 345 677 93
−
SPh 49.9 15.7 6.4 83.5 350 682 95
−
aEkaykinetal.(2002). bTouzeauetal.(2016),A1,A2andP0fromEDC.
cTouzeauetal.(2016). dKamedaetal.(2008). eHoshinaetal.(2014),A1,A2andP0
adaptedfromDF. fHoshinaetal.(2014),A1,A2andP0adaptedfromDF.
gEPICAcommunitymembers(2006). hCaseyetal.(2014).
Theeffectoffirndiffusionontheoriginalisotopesignalδ18O ismodelledastheconvolutionwithaGaussiankernel
surface
(Johnsen et al., 2000) which leads to an overall smoothing of the input signal. The amount of smoothing is governed by the
width of the convolution kernel given by the diffusion length σ, which is sensitive to ambient temperature, pressure and the
densityofthefirn(WhillansandGrootes,1985).WetreatthedependencyondensityaccordingtoGkinisetal.(2014),with
5 diffusivity after Johnsen et al. (2000). The temperature dependency of the diffusion length is highly nonlinear, with warmer
temperaturesleadingtoastrongerchange.Thus,theseasonalcycleinfirntemperatureinthetopmetersincreasestheeffective
diffusionlength.Toapproximatethiseffect,wefollowtheapproachofSimonsenetal.(2011).Wemodeltheseasonalcyclein
firntemperatureaccordingtothegeneralheattransferequation,drivenbysurfacetemperaturesforconstantthermaldiffusivity
andnegligibleheatadvection(e.g.Paterson,1994).Wethencalculatethediffusionlengthforparcelsstartingineverymonthof
10 theyearandcomputetheaveragediffusionlengthoverallparceltrajectories.Forthesakeofsimplicity,weassumeaconstant
densityforthefirntemperaturemodeling,whichissettotheobservedsurfacedensities(Table2).
TheresultingeffectivediffusionlengthsforourstudysitesareshowninFig.(3).Interestingly,thecombinedeffectoflower
accumulationratesandcoldertemperatureslargelycompensateeachother,leadingtoaratherconstantdiffusionlengthacross
theEastAntarcticPlateau.
10