regional groundwater flow model for a glaciation scenario
TRANSCRIPT
Regional groundwater flow model for a glaciation scenario
Simpevarp subarea – version 1.2
O Jaquet, P Siegel
Colenco Power Engineering Ltd
October 2006
R-06-100
Svensk Kärnbränslehantering ABSwedish Nuclear Fueland Waste Management CoBox 5864SE-102 40 Stockholm Sweden Tel 08-459 84 00 +46 8 459 84 00Fax 08-661 57 19 +46 8 661 57 19
CM
Gru
ppen
AB
, Bro
mm
a, 2
006
Regional groundwater flow model for a glaciation scenario
Simpevarp subarea – version 1.2
O Jaquet, P Siegel
Colenco Power Engineering Ltd
October 2006
ISSN 1402-3091
SKB Rapport R-06-100
This report concerns a study which was conducted for SKB. The conclusions and viewpoints presented in the report are those of the authors and do not necessarily coincide with those of the client.
A pdf version of this document can be downloaded from www.skb.se
�
Contents
1 Introduction 5
2 Objectives 7
3 Modellingapproach 9�.1 Conceptualmodel 9�.2 Modeldomain 10�.� Deformationzones 10�.4 Phenomenology 11�.5 Numericalaspects 1��.6 Flowparameters 1��.7 Transportandrock-diffusionparameters 14�.8 Discretisation 15�.9 Stochasticsimulations 15
4 Groundwaterflowmodelling 214.1 Initialconditions 214.2 Timeperiodsandboundaryconditions 214.� Glaciationsimulation:thebasecase 244.4 Glaciationsimulation:50mmcase �54.5 Particletrackingcalculations 42
5 Conclusions,discussionandperspectives 45
6 References 47
Appendix 49
5
1 Introduction
IntheframeworkofthesafetyassessmentSR-Can,SKBneedstodemonstratethatarepositoryincrystallinerockwillmeetthelong-termsafetyrequirementssetforthbytheauthorities.Atthetimescaleofthesafetyassessment(i.e.105to106a),climaticchangesareexpectedthatwillmodifysubsurfaceconditions.Therefore,thepotentialimpactofclimaticchangeshastobeevaluatedwithrespecttorepositoryperformanceandsafety.
Inparticular,climaticchangeswithexpandingicesheetsarelikelytooccur.Thegrowthanddecayoficesheetswillaffectthegroundwaterflowfieldanditscomposition.Forthisreason,these(longterm)transientglacialeffectshavetobeconsideredwhenstudyinggroundwaterflowataregionalscale.Forassessmentpurposesitisnecessarytodevelopanumericalmodelofthegroundwaterflowforaglaciationscenario.Thisgroundwaterflowmodelisthesubjectofthisstudy.
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2 Objectives
ThepresentstudywasestablishedonthebasisofSKBtechnicalspecifications.Itsmainobjectiveistoevaluatethegroundwatervelocityandsalinityfieldsforthedifferentconditionsprevailingduringaglaciationperiod,includingspecificsensitivitycases.
Anotherspecificobjectiveistheevaluationofrepositoryperformanceforperiodsofglaciationanddeglaciation.Inparticular,theflowpathsfromrepositorydepthtothesurfaceneedtobeassessedfordifferentglacialconditionstoevaluaterelativedifferencesinsolutetravel-times.
Thereportbeginswithanaccountofthemodellingapproachapplied.Then,theresultsofthedifferentcasessimulatedaredescribed,analysedandinterpretedindetail.Finally,conclusionsaredrawnuptogetherwithsomerecommendationsrelatedtopotentialmodellingissuesforthefuture.
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3 Modellingapproach
3.1 ConceptualmodelTheconceptualmodelSimpevarp1.2(SimpevarpregionalmodelS1.2;/Hartleyetal.2005/)providesthegeologicalbasisfortheregionalgroundwaterflowmodel,i.e.theglaciationmodel.TheS1.2regionalmodelprovidesthedeterministicdeformationzonesaswellastherockdomainthatconstitutesthebasisforthegeometricalframeworkoftheglaciationmodel.Intermsofsize,theglaciationmodelextendsfarbeyondtheS1.2regionalmodelinthenortherlyandsoutherlydirections.
Astochasticequivalentporousmediumapproachwasselectedfortheglaciationmodel.Numericalmodellingofvariable-densitygroundwaterflowincludingrock-matrixdiffusionisperformedatregionalscaleforaglacialperiodofapproximately20,000yearswherebytheboundaryconditionsareprovidedbyadynamicicesheetmodel/SKB2006/.
Inicesheets,thesub-glaciallayerisawaterconductivelayerassumedtoexistattheice/bedrockinterfaceintheareaofbasalmelting.Thislayerplaysamajorhydraulicroleincarryingmeltwaterwhichcantheninfiltrateinthesubsurfacewheresignificantmodificationsoftheflowfieldaretobeexpected.Duethescarcityofdataastochasticapproachwaschosenforthedescriptionoftheconductivefeaturesinthesub-glaciallayer.
Themovement–involvingglacialbuild-upandretreat–oftheicesheetisspecifiedthroughtheuseoftransientboundaryconditions.TheexistenceoftheBalticSeaisneglected,i.e.therearenofluctuationsinsealevelaswellasnosupplyofsaltfromtheBalticSea.
Geomechanicaleffectsduetoiceloadinglikelytoinducemodificationsofthegroundwaterflowfieldwerenotconsideredaspartoftheconceptualmodel.Therefore,theimpactoftheicesheetloadingintermsofrockdeformationleadingtovariationsinporosity,hydraulicconductivityandporepressurewerenotincludedinthismodellingapproach.Inaddition,theprogressionoftheicesheetisassumedtobeisothermal;thismeansthatpermafrostareaslocatedinthesurroundingsoftheicesheetwereneglectedandthusnoreductioninhydraulicconductivitywastakenintoaccountfortheseareas(seeFigure�-1).
Figure 3-1. Glaciation conceptual model /after Lemieux 2006/: description of variable-density groundwater flow including rock-matrix diffusion using boundary conditions from a dynamic ice sheet model. Ice loading and permafrost effects were not considered.
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3.2 ModeldomainThelongestdimensionofthe�Ddomainoftheglaciationmodelextendsabout�00kmupstreamandca100kmdownstreamoftherepositorylocation(seeFigure�-2).
ThewidthoftheglaciationmodelisthesameasthatoftheS1.2regionalmodel(21.6km).TherepositoryisassumedtobelocatedinsidetheS1.2localmodeldomain(7.8�.2km).Thedepthoftheglaciationmodelwassetto2.�kmtomatchtheverticalextentoftheS1.2regionalmodel.
Themainorientationofthedomain,i.e.itslongaxis,coincideswiththemainiceflowdirectionduringtheglacialcycle.Accordingto/Näslund2004/,thisorientationrangespredominantlybetweenN180degreesandN170degreesEast.N180degreeswasthereforeascribedtothemainorientationoftheglaciation-modeldomain.
3.3 DeformationzonesThedeformationzones,i.e.thefracturezones,correspondingtotheHydraulicConductorDomains(HCD),ofkilometricextentweretakenfromtheS1.2regionalmodel(seeFigure�-�).Theyareassumedtointersecttheentirethicknessofthedomain.Forthedomainoftheglacia-tionmodelbeyondthe21.6×1�kmareaoftheS1.2regionalmodel,noexplicitinformationonthedeformationzoneswasavailableintermsofgeometricandhydraulicparameters.Therefore,weassumethatthespatial-variabilitycharacteristicsoftheequivalentpermeabilityandporosityfieldsoftheS1.2regionalmodelcanbeextrapolatedbystochasticsimulationfortheremainderoftheglaciationmodeldomain.Sincethehydrauliceffectsofthedeformationzonesareintegratedintotheseequivalentproperties,thismeansthattheentiredomainoftheglaciationmodelisconsideredtocontaindeformationzones.
Figure 3-2. Location of glaciation model (red line).
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3.4 PhenomenologyFortheglaciationmodel(conceptualisedasstochasticequivalentporousmedium),thedescrip-tionofdensity-drivengroundwaterflowinducedbyvariablesalinityofthegroundwaterinthepresenceofrock-matrixdiffusionisobtainedusingthefollowingequationsimplementedinConnectFlow8.1/HochandJackson2004/.
TheflowequationsaregovernedbyDarcy’slaw:
( )0( )Rp= kq g (1)
where:
q:Darcyvelocity
k:intrinsicpermeabilitytensor
μ: fluidviscosity
pR:residualpressurewith
p: pressure(total)
ρ: fluiddensity
ρ0:referencedensityoffluid(freshwater)
z: elevation
z0:referenceelevation
g: gravitationalacceleration.
andthecontinuityequation:
( )ft+ =( ) 0q (2)
where:
φf:fractureporosity.
Figure 3-3. Location and geometry of deformation zones in the S1.2 regional model area of Simpevarp /after Hartley et al. 2005/. Verified deformation zones of high confidence (red) and lineaments of low confidence (green).
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Aspecificstoragecoefficientofzeroisassumed.Thishypothesisisjustifiedgiventherangeofhydraulicconductivity,thevaluetakenforthespecificstorage(10–6m–1;after/JaquetandSiegel2004/)andthetimestepsconsidered(cfpart�.5)fortheglaciationmodel.
Therepresentationofsalttransportwithrock-matrixdiffusionisgivenby:
0'( ) wcc c c
t w =+ = +f f int( ) ( D ) Dq (�)
where:
c: concentrationofsoluteflowingthroughthefractures(expressedasamassfraction)D : hydrodynamicdispersiontensor
ζ: flowwettedsurface
Dint: effectivediffusioncoefficient
c’: concentrationofsoluteintherockmatrix(expressedasamassfraction)
w: coordinateintotherockmatrix.
Andthehydrodynamicdispersiontensorisdefinedasfollows:
vvv
v= + + i jm
ij T ij L TDD ( ) (4)
where:
Dm: moleculardiffusioncoefficient
τ: tortuosity
αL,αT: longitudinalandtransversedispersivity
v: porewatervelocity(with = qv and v= v v ).
Finallyfortherock-matrixdiffusion,thefollowingequationisused:
'( )mcc
t w w= intD (5)
where:
φm: rock-matrixporosity
Dint: effectivediffusioncoefficient.
Forequation(5),theboundaryconditionsarethefollowing:(a)thematrixconcentrationatthefracturesurfaceisequaltothelocalconcentrationinthefractures:
'( 0)c w c= = (6)
and(b)thefluxofconcentrationinthematrixiszeroatthemaximumdepthofpenetrationintothematrix:
( )' 0c w dw
= =intD (7)
where:
d: matrixdiffusionlength(2bd = wherebisthefracturespacingand
2b
= ).
1�
3.5 NumericalaspectsConsideringthesizeoftheglaciationmodel,itwasdecidedtoapplyanumericalschemefortransientsalttransportwhichismoreefficientintermsofCPUtimethantosolvethefullycoupledformoftheseequations.ThisschemecorrespondstotheapproachusedfortheregionalhydrogeologicalsimulationsofSimpevarp/Hartleyetal.2005/.Itinvolvesadecouplingofthesolutionsforpressureandsalttransportbylinearisingtheequations/Marsicetal.2002,Hartleyetal.2004/.Ateachtimestepthegroundwaterflowcalculationsaresolvedintwostages:(a)solveforflow,accountingforvariabledensityand(b)resolvewithadvection-dispersion-matrix-diffusionequationsforsalinityinthenewflowfield.
TheGMRES(GeneralizedMinimalResidual)iterativesolverofNAMMU/Marsicetal.2001/isusedtosolvetheflowandtransportequations.GMRESisaKrylov-basediterativemethodforthesolutionoflinearsystemsassociatedtounsymmetricmatrices.Forthetimediscretisa-tion,afullyimplicitCrank-Nicholsontransientschemeisused.Thematrixdiffusionequationissolvedusinganumericalapproachbasedonamethoddevelopedby/Carreraetal.1998/.ThenumericalparametersselectedforsimulationarelistedinTable�-1.
3.6 FlowparametersTheequivalentpropertiesoftheHydraulicConductorDomains(HCD),HydraulicRockDomains(HRD)andHydraulicSoilDomains(HSD)aretakenfromtheSimpevarpregionalmodel(S1.2:/Hartleyetal.2005/)andcorrespondtothebasecasewithreferencewatercalibration(case:SReg_4Component_IC2).
TheHCDpropertiesareassumedconstantforeachdeformationzone.ThedeformationzonesweredownscaledonthegridoftheSimpevarpmodelandthenanumericalup-scalingofbedrockfracturingincludingdeformationzoneswasperformedtoobtaintheequivalentpropertiesforeachelementofthemodel.TheresultsareequivalenthydraulicconductivitytensorsandporosityvaluesfortheSimpevarpareawhichaccountforthehydrauliceffectsofthedeformationzones(detailscanbefoundin/Hartleyetal.2005/).
Fortheremainderoftheglaciation-modeldomainbeyondtheSimpevarparea,theequivalentpermeability(diagonal)tensorandporosityfieldswereextrapolatedbystochasticsimulationusingparametersofspatialvariability(suchasmean,standarddeviationandcorrelationlength)estimatedfromtheSimpevarparea(seeTable�-2).
ThepropertiesoftheHSDwhichdescribelayersofsiltytillareconsideredasconstantoverthewholetopsurfaceoftheglaciationmodel.TheirvaluesweresetequaltothoseoftheSimpevarparea/Hartleyetal.2005/.
Thegeometryofconductivefeatures(oricetunnels)inthesub-glaciallayerwasdescribedusingastochasticmodel.ThegeometryoftheconductivefeatureswasthenprojectedintotheglaciationmodelwithaverticalextentcorrespondingtothethicknessoftheHSD.TheproportionofmeltwaterlikelytoflowintheconductivefeaturesandintheHSDdependsonthetransmissivitycontrastbetweenthesetwounits.Finally,thehydraulicconductivityoftheconductivefeatureswascalibratedinsuchawaythatliftingoftheiceisavoided.Thespecificstoragewasassignedbasedonpreviousstudies(seealsopart�.4):auniformvalueofzerofortheresultingup-scaledfracturedrockdomain(HRD+HCD),HSDandsub-glaciallayer.
Table3-1. Numericalparameters.
GMRESconvergencecriterion
Timestepping Accuracyparameterformatrixdiffusion
10–6 100 a 10–4
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Table3-2. Flowparameters.
Domain(thickness)
Hydraulicconductivity[m/s]
Standarddeviation[log10]
Correlationlength[m]
Specificstorage[m–1]
HSD_1 (0–1 m)
10–5 Uniform Uniform 0.0
HSD_2 (1–3 m)
10–7 Uniform Uniform 0.0
HRD+HCD (3–2,100 m)
1) Kxx = 1.7·10–8 1) Kyy = 1.9·10–8 1) Kzz = 1.4·10–8
0.69 0.65 0.75
2) 300+(800, 400, 15,000) 0.0
Bottom (2,100–2,300)
5.0·10–10 Uniform Uniform 0.0
1) Geometric mean of diagonal component.2) Variogram = isotropic exponential model + anisotropic exponential model.
3.7 Transportandrock-diffusionparametersThetransportandrock-diffusionparametersappliedfortheglaciationmodelaregiveninTable�-�andinTable�-4.
Themoleculardiffusioncoefficientissetequalto10–9m2·s–1andthetortuosityisidenticalto1.
Table3-3. Transportparameters.
Domain Porosity[–]
Standarddeviation[log10]
Correlationlength[m]
αL[m]
αT
[m]
HSD_1 5·10–2 Uniform Uniform 3) 80, 160 3) 20, 80HSD_2 5·10–2 Uniform Uniform 3) 80, 160 3) 20, 80
HRD+HCD 1) 4.2·10–5 0.85 2) 300+(800, 400, 15,000) 3) 80, 160 3) 20, 80Bottom 5.0·10–5 Uniform Uniform 3) 80, 160 3) 20, 80
1) Geometric mean of fracture porosity.2) Variogram = isotropic exponential model + anisotropic exponential model.3) Values for Simpevarp area.
Table3-4. Rock-matrixdiffusionparameters.
Domain Effectivediffusioncoefficient[m2·s–1]
Flowwettedsurface[m2·m–3]
Rockmatrixporosity[–]
Matrixdiffusionlength[m]
HRD+HCD 5·10–13 2 5·10–3 0.5Bottom 5·10–13 2 5·10–3 0.5
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3.8 DiscretisationTheglaciationmodelwasdiscretisedusinga�Dfinite-elementmeshwithcuboidelements(8nodes)ofnon-uniformsize.DuetoConnectFlowlimitationsonlyonenestedlevelcouldbedefinedwhichcorrespondstotheSimpevarparea.Thegridresolutioninthehorizontaldirectionis100mfortheSimpevarpmodelareaand�00mfortheremainderoftheglaciationmodel.
Intheverticaldirection,thediscretisationoftheglaciationmodelisthesameasthatoftheS1.2regionalmodelandcorrespondstoaglobaldiscretisationof100mwithmetricrefinementsfortheHydraulicSoilDomains.
Thefinite-elementmeshoftheglaciationmodelwasgeneratedwithColencotoolsandcontainsatotalof�,265,920elements.
Forthetopography,auniformelevationofzerowasappliedtotheentireareaoftheglaciationmodel.ThissimplificationwasrequiredbecausenumericalproblemswereencounteredwithConnectFlowwhenapplyingaprescribedrechargeonaspatiallyvariabletopography.
3.9 StochasticsimulationsFractured rock domain
Theequivalenthydraulicpropertiesforthefracturedrockdomain(HRD+HCD)oftheglaciationmodelbeyondtheSimpevarpareawereextrapolatedwithstochasticcosimulationusingtheturn-ingbandsmethod/ChilèsandDelfiner1999/.TheparametersforthecosimulationwereestimatedusingtheequivalenthydraulicconductivityandporosityfieldsfromtheSimpevarparea.
Variogramsandcrossvariogramswerecalculatedtoparameteriseallspatial(cross)correlation(seeFigure�-4)betweenthediagonalcomponentsofthehydraulicconductivitytensorandtheporosityusingaconsistentmultivariatemodelcomposedofasumofexponentialvariograms(cfTable�-2).Inaddition,thecosimulationoftheequivalenthydraulicpropertiesfortheglaciationmodeldomainwasperformedtomatchthehistogramsofthehydraulicpropertiesfortheSimpevarparea.
Ultimately,everyelementofthefinite-elementmeshdiscretisingthefracturedrockdomainbeyondtheSimpevarpareawasassigneda“stochastic”equivalenthydraulicconductivityandporosity(seeFigure�-5).
Sub-glacial layer
Icesheetsproducelargeamountsofsubglacialmeltwaterevenwhengrowing.Inthiscase,meltwaterisduetofrictionattheice/bedrockinterfaceandtothegeothermalgradient/Paterson1994/.
ThecharacteristicsoficesheethydrologywerebasedonconceptualinformationprovidedbySKB(seeFigure�-6).Inicesheets,thesub-glaciallayerisawaterconductivelayerassumedtoexistattheice/bedrockinterfaceintheareaofbasalmelting.UpstreamoftheELA(Equilibriumlinebetweenaccumulationandablationareas),thesub-glaciallayercarriesthebasalmeltwatergeneratedatthebottomoftheicesheet.Intheablationarea,downstreamoftheELA,thesub-glaciallayerreceivesbothbasalandsurfacemeltwater.Duetothelargeamountofmeltwateratspecificlocations,erosionalconductivefeatures(oricetunnels)areformedwithinthesub-glaciallayer.
Intheablationarea,thepatternofcatchmentareaswasassignedusingrecentobservationsoficesheetsinGreenland.Eachcatchmentareahasamoulinthroughwhichsurfacemeltwaterisassumedtobetransferredinstantaneouslytothesub-glaciallayer.
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Figure 3-4. Multivariate anisotropic variogram model (thick curve) fitted to the experimental variograms and cross variograms (light curve) applied for the stochastic cosimulation of equivalent hydraulic properties for the glaciation model domain. Dashed curves correspond to the validity bounds for the fitted cross variograms. The dashed horizontal line represents the variance (or covariance) of the transformed (Gaussian) data.
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Figure 3-5. Cosimulation of equivalent hydraulic conductivity (Kxx) and porosity for a part of the glaciation-model domain (at a depth of 1,000 m) with the Simpevarp area (of 13 km extent in the South part) showing the discretised deformation zones.
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Figure 3-6. Sub-glacial layer concept /after SKB 2006/.
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Theminimumdistancebetweenconductivefeatureswasestimatedbasedontheaveragedistance(measuredperpendiculartothedirectionoficeflow)betweenmoulins(seeFigure�-7).ThemaximumdistancewassetequaltothedistancebetweeneskerstypicallyencounteredinSweden.Therefore,theseparationdistancefortheconductivefeatureswasconsideredtorangebetween�and10km.
Informationonthelocationofconductivefeaturesinasub-glaciallayercurrentlyremainsspeculative.Therefore,thegeometryofconductivefeatureswassimulatedforthesub-glaciallayerusingastochasticmodelbasedontheseparationparameter(seeFigure�-8).Themethodchosenwasstochastic,andithasallowedthesimulationofnetworksofdiscreteconduitsoccurringinheterogeneousgeologicalmedia/Jaquetetal.2004/.
Inordertoavoidpotentiallyadversenumericaleffects,twoconductive(deterministic)featureswereaddedalongbothsideedgesofthemodel.Asimilardefinitionofconductivefeatureshadbeenadoptedinthepreviousglaciationmodellingstudy/JaquetandSiegel200�/.Conductivefeaturesweregeneratedfortheentiremodeldomainalthough,conceptuallyspeaking,theyshouldappearonlydownstreamoftheELA.Ineffect,thesmallbasalmeltratesresultingupstreamoftheELArenderedthehydrauliceffectoftheconductivefeaturesnegligibleformodellingpurposes.
Finally,thehydraulicconductivityfortheconductivefeatureswascalibratedsuchthatthewaterpressureonaveragedoesnotexceedthepressureoftheice;i.e.theliftingoftheiceisavoidedgloballybutlocalexceptionsarepermitted.Ahydraulicconductivityof2m/swasobtainedascalibratedvaluefortheconductivefeatures.Higherhydraulicconductivitieswerenotconsidered,becausesuchvalueswoulddiminishbedrockinfiltrationandpotentiallyleadtoanunderestimationofflowfieldmodificationsduetoglaciation.
Figure 3-7. Map of catchment areas in Greenland showing moulins on the surface of the ice sheet. The flow of ice is towards the West /After Thomsen et al. 1989/.
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Figure 3-8. Stochastic simulation of conductive features for the sub-glacial layer in three stages (top to bottom). Stage I: creation of the potential location of conductive features using truncated Gaussian simulations constrained with separation distance. Stage II: stochastic simulation of the geometry of conductive features conditioned with potential and ice flow direction. Stage III: downscaling of the conductive features to the glaciation model using the IFZ method /Marsic et al. 2001/.
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4 Groundwaterflowmodelling
Groundwaterflowduringaperiodofglaciationismodelledforthebasecasewiththeparametersdefinedintheprecedingchapters.Theinitialandboundaryconditionsforthebasecasearedefinedbelow.
4.1 InitialconditionsSalinity initial conditions
Forthebasecase,thefollowinginitialconditionsforsalinityareselected:
• Betweengroundsurfaceand–500m:freshgroundwaterconditions.
• Between–500mand–2,100m:thesalinityincreaseslinearlyfrom0%to10%byweight.
• Below–2,100m:thesalinityisconstantat10%byweight.Thisvaluecorrespondstoadensityof1,074kg/m�usingtherelationof/Svensson1999/:ρ=ρ0(1+as)withthesalinity, s,andthecoefficient,a,equalto7.41·10–�.
FlowinitialconditionsTheinitialconditionsforflowweretakenfromasimulationperformedundersteady-stateconditionswithafixedsaltprofile(cfabove)intheabsenceoftheicesheet.
4.2 TimeperiodsandboundaryconditionsRatherthancorrespondingtothefullperiodoftheWeichselianglaciation,theglaciationperiodmodelledisthatrelevanttothemodelleddomainintermsoficebeingpresent.Withintheglaciationperiod,thefollowingtransienteffectsofglaciationareconsidered:(a)glacialbuildup,(b)glacialcompletenessand(c)glacialretreat.
Intermsofboundaryconditions,theglaciationperiodfrom–�0,900to–11,400a(expressedinyearsbeforepresent)isdividedintofivephases:
• P0(–30,900a).Pre-glacialbuildup:initially,noicesheetispresent.
• P1(–30,900to–25,100a).Glacialbuild-up:theicesheetprogressivelycoversthemodeldomain.
• P2(–25,100to–14,100a).Glacialcompleteness:theicesheetcoversthefulldomainofthemodel.
• P3(–14,100to–11,400a).Glacialretreat:theicesheetprogressivelywithdrawsfromthemodeldomain.
• P4(–11,400a).Post-glacialretreat:theicesheethascompletelydisappearedfromthemodeldomain.
Top surface: periods P1, P2 and P3
Themovementoftheglacierissimulatedwithtransientboundaryconditionsprovidedbyadynamicicesheetmodel/SKB2006/.Aspecificrunoftheicesheetmodelwasperformedwithahighspatialresolution(10×10km)toobtaintheicethicknessandthebasalandsurfacemeltwaterratesneededasinputforthegroundwaterflowmodel(seeFigure4-1).Theicesheet
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datawereavailablefrom–40,000to–9,000a(expressedinyearsbeforepresent)withatimestepof100a/NäslundandFastook2005/.
Allsurfacemeltwaterisassumedtoreachthesub-glaciallayerinthesamegridcellinwhichitisgenerated.Fortheglaciationmodelthetotalmeltrate(includingbasalandsurfacemeltrate)isimplementedasaprescribedtransientflowboundary.Onthebasisofthedisplacementvelocityoftheicesheet,theareacoveredbytheglaciationmodelwasdividedinto16zonesof25×25km.Foragivenzone,theaverage(total)meltratewasestimatedusingtheneighbouringdatavaluesprovidedbytheicesheetmodel.Cokriging/Wackernagel200�/wasappliedtoestimateanaveragemeltrateforeachofthe16zonesoftheglaciationmodelandforeachtimestep.Thisprocedurewasselectedinordertotakeintoaccountthecorrelationbetweenmeltrateandicethicknesswhenestimatingtheflowboundaryconditionsusingicesheetdata.
Themeltratesofuptoseveralm/aaretoolargetocorrespondphysicallytothegroundwaterrecharge(Figure4-�).Basedonresultsfrom/Walkeretal.1997/,itwasdecidedtoselectamaximumvalueof200mm/afortherecharge.
Atmosphericpressureisprescribedinfrontoftheicesheetaswellastheconcentration(withavalueequaltozero).Alsotheconcentrationoftheinfiltratingglacialwaterissettozero.
Figure 4-1. Results of ice sheet modelling at time step –30,000 a /after Näslund and Fastook 2005/: the blue points indicating the presence of ice. Projected into the ice sheet model are the 16 zones discretised for the glaciation model to implement the ice-sheet boundary conditions. For each zone, an average meltrate was estimated by cokriging using the nearest data points. The green zone comprises the Simpevarp model area.
7000000
Y (m
)
X (m)
6900000
6800000
6700000
6600000
6500000
6400000
6300000
6100000
1400000 1500000 1600000 1700000 1800000
6200000
2�
Figure 4-3. Evolution of the total meltrate at repository location /after Näslund and Fastook 2005/.
Figure 4-2. Evolution of the thickness of the ice sheet at repository location /after Näslund and Fastook 2005/.
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Top surface: periods P0 and P4
Atmosphericpressureisprescribedeverywhereaswellastheconcentrationwhichissetequaltozero.
Top surface: period P2
Inordertoenablewatertoleavethemodelduringglacialcompleteness,thelast5kmoftheSoutherntopsurfaceofthemodelweresettoatmosphericpressure.
Bottom surface: periods P0, P1, P2, P3 and P4
Thebottomsurfaceboundaryconditionistakenasanoflowconditionwithaspecifiedsaltconcentrationof10%byweight.
Lateral surfaces: periods P0, P1, P2, P3 and P4
No-flowconditionsareappliedonallfourlateralsides.
4.3 Glaciationsimulation:thebasecaseTheglaciationsimulationwasperformedforthebasecaseforaperiodof19,500a(from–�0,900to–11,400a,expressedinyearsbeforepresent).Thefollowingfivetimestepswereselectedastheyareparticularlyrepresentativeofcertainstagesofglacialadvanceorretreat(seeFigure4-4):
I.Glacialbuildupat–26,800a: ThefrontoftheicesheetmeetstheedgeoftheSimpevarparea.
II.Glacialbuildupat–26,500a: TheicesheetcoverstheSimpevarparea.
III.Glacialcompletenessat–17,900a: Theicesheetfullycoverstheglaciation-modelarea.
IV.Glacialretreatat–1�,900a: TheicesheetcoverstheSimpevarparea.
V.Glacialretreatat–1�,800a: TheicesheetfrontislocatedontheedgeoftheSimpevarparea.
Anoverviewofthesimulationresultsfortheglaciationperiod(seeFigure4-5)demonstratestheglacialeffectsongroundwaterflowfordifferentglacialphases(5,800afortheglacialbuild-up,11,000afortheglacialcompletenessand2,700afortheglacialretreat).Thephasesofbuild-upandretreatoftheicesheetareaccompaniedbylargeamountsofmeltwaterwhichdrasticallymodifytheflowpatternandthusstronglyinfluencethesaltconcentration.Inparticular,up-coningeffectsoccuratthemarginoftheicesheet,i.e.duetothemeltwaterinputthatgovernsgroundwaterflow,thesalinityfrontismovedupwards.Thiseffectcanbeseenattimestep4,400a(cfFigure4-5).
Thesimulationresultsforthetimestep–26,800a(glacialbuild-up),expressedintermsofrelativeconcentration,displaythestrikingeffectoftheicesheetontheflowfield(seeFigure4-6).Duetotheconsistentmeltingoftheicesheetandtheheterogeneityrelatedtotheconductivefeaturesandthefracturedrockdomain,theconcentrationdevelopsaspikypattern.InFigure4-6,theicecoverstheupperleftportionofthemodelillustrationwiththeicemarginlocatedatpositionca100,000malongtheYaxis.Thehorizontalcutdemonstratesthemarkeddifferencebetweenthedomainsoneithersideoftheicemargin.Intheareadownstreamoftheglacierthevariabilityofthesaltconcentrationismainlysubjectedtodiffusiveeffects,i.e.therearenoeffectsyetoftheicesheet.
25
Figure 4-4. The five selected time steps (expressed in years before present) corresponding to specific glacial conditions. The location of the Simpevarp (repository) area at depth is indicated with a black box.
26
Duringphasesofbuildupandretreat,belowtheicesheet,theconcentrationofthesaltwithintherockmatrixissimilartotheconcentrationwiththeflowingfractures(seeFigure4-6andFigure4-7).Thisobservationmeansthattheconcentrationoftherock-matrixandtheconcentrationwithinthefracturesareclosetoequilibrium.Thehighvalueconsideredforflowwettedsurface(2m2·m–�),enablerock-matrixdiffusiontotakeplaceeffectivelyforaccessingamatrixblockwithatimescaleofafewtensofyears/Hartleyetal.2005/.Inaddition,theicesheetprovideslargeamountofmeltwaterwithvelocitylikelytofavourexchangesbetweenrockmatrixandfractures.
Figure 4-5. Base case: simulation of 14 time steps, along a horizontal North – South cut (located in the middle of the model) displaying the (relative) concentration with glacial build-up (0–5,800 a), glacial completeness (5,800–16,800 a) and glacial retreat (16,800–19,500 a). The time steps are expressed in relative time (underlined values = selected time steps) and the concentration scale is identical in the following figures.
27
Figure 4-7. Simulation of the base case (relative matrix concentration) at time step –26,800 a. The ice margin is located at Y ≈ 100,000 m.
Figure 4-6. Simulation of the base case (relative concentration) at time step –26,800 a. The ice margin is located at Y ≈ 100,000 m. The horizontal cut is at a depth of 500 m below the ground surface.
Infrontoftheicesheet,theconcentrationofthesaltwithintherockmatrixexhibitsasmoothervariabilitythantheconcentrationassociatedwiththeflowingfractures(seeFigure4-7).Thisisrelatedtothediffusioneffectsoccurringbetweenthelessmobilewaterintherockmatrixandthemobilewaterflowingthroughthefractures.Diffusionrelatedconcentrationpatternstendtobemoreblurredthanflowrelatedconcentrationpatterns.
28
Thestrongimpactoftheicesheetontheflowfieldiswelldemonstratedbylookingatthetopsurfaceofthedomainattimesteps–26,800and–26,500a(seeFigure4-8andFigure4-9).Thehighmeltrateclosetotheicemarginleadstoasubstantialincreaseintheequivalentenvironmentalhead.Theobservedpatternsoftheheaddistributionarerelatedtothespace-timevariationsinmeltrateaswellastothepositionsoftheconductivefeaturesinthesub-glaciallayerwhichoperateasdrainagestructures.Forthestageofglacialbuild-up,theattainedheadvaluesaregloballybelowtheobservedicethickness(uptoca2,800m)whichcomplieswiththeconceptualassumption(cfpart�.9).
Figure 4-9. Simulation of the base case (equivalent environmental head) at depth 0 m, for time step –26,500 a.
Figure 4-8. Simulation of the base case (equivalent environmental head) at depth 0 m, for time step –26,800 a.
29
Duringtheadvanceoftheicesheet,moremeltwaterisintroducedtothemodel.Asaconse-quence,theflushingfront(locatedattheicemargin)progresseswiththeicesheetasitgrowstowardstheSouth(seeFigure4-10).Thesaltconcentrationwithinthematrixfollowsasimilarpatternastheflowingconcentrationastheicesheetadvances(seeFigure4-11).Forthistimestep(–26,500a),remarkableup-coningeffectscanbeobservedattheicemargin.
Figure 4-11. Simulation of the base case (relative matrix concentration) at time step –26,500 a. The ice margin is located south of the Simpevarp area.
Figure 4-10. Simulation of the base case (relative concentration) at time step –26,500 a. The ice margin south of the Simpevarp area. The horizontal cut is at a depth of 500 m below the ground surface.
�0
Figure 4-12. Simulation of the base case (relative concentration) at time step –17,900 a. The horizontal cut is at a depth of 500 m below the ground surface.
Figure 4-13. Simulation of the base case (relative matrix concentration) at time step –17,900 a.
Duringglacialcompleteness,therateofmeltwaterproductionreacheslowvaluesastheicesheetisnotdisplaced.Thissituationleadstoastabilisationoftheconcentrationpatternsintheflowfield(seeFigure4-12andFigure4-1�aswellasFigure4-5).
�1
Figure 4-15. Simulation of the base case (relative matrix concentration) at time step –13,900 a. The ice margin is located south of the Simpevarp area.
Duringglacialretreataroundca–14,000a,theamountofmeltwaterincreasessignificantly;atthescaleofalmosttheentireglaciationdomain,therateofmeltwaterrechargereachesthemaximumvalueof200mm/aforashortperiodoftime.Asaconsequence,duetothisstrongfreshwatercontributionfromtheicesheet,theconcentrationfieldsarealmostcompletelyflusheduptothetopofthebottomlayer(withlowhydraulicconductivity)locatedbelow2,100m(seeFigure4-14andFigure4-15).
Figure 4-14. Simulation of the base case (relative concentration) at time step –13,900 a. The ice margin is located south of the Simpevarp area. The horizontal cut is at a depth of 500 m below the ground surface.
�2
Forthestageofglacialretreat,someoftheattainedheadvaluesareabovetheobservedicethickness(uptoca2,800m:seeFigure4-16andFigure4-17).Duetothehighrateofmeltwaterrecharge,calibrationofthehydraulicconductivityfortheicefeaturescouldnotbeachievedusingrealisticvalues.
Figure 4-17. Simulation of the base case (equivalent environmental head) at depth 0 m, for time step –13,800 a.
Figure 4-16. Simulation of the base case (equivalent environmental head) at depth 0 m, for time step –13,900 a.
��
Figure 4-19. Simulation of the base case (relative matrix concentration) for the time step –13,800 a. The ice margin is located at Y ≈ 100,000 m.
Astheretreatoftheicesheetcontinues,somemeltwaterisstillproduced,leadingtoanalmostuniformconcentrationfieldattheendofthesimulationattimestep–11,400a(seeFigure4-18,Figure4-19andFigure4-5).
Figure 4-18. Simulation of the base case (relative concentration) for time step –13,800 a. The ice mar-gin is located at Y ≈ 100,000 m.
�4
Theevolutionoftheflowpatternswasanalysedattherepositorylocationatadepthof500m.ThearrivalandtheretreatoftheicesheetatSimpevarpleadstoastrongincreaseintheDarcyvelocityduetohighratesofmeltwaterrecharge(cfthevelocitypeaksofFigure4-20).Thethicknessoftheicesheetgrowsprogressivelyduringthephasesofglacialbuild-upandglacialcompleteness.However,thephaseofglacialretreatseestheicesheetdisappearwithinafewcenturies(cfFigure4-2).
Rememberingtheinitialsalinityprofile,attimestep–�0,900a,theconcentrationat500miszero(cfpart4.1salinityinitialcondition).Thephaseofglacialbuild-upstartswithanincreaseinthefractureandmatrixconcentrationmainlybecauseofdiffusiveeffects.Theup-coningeffectsdescribedabove(cfFigure4-5,Figure4-10andFigure4-11)couldnotbecapturedattherepositoryscaleduetothespatialdiscretisationoftheicesheetdisplacement.Thatistosay,theicesheetprogressesinstepsof25kmandtherepositoryislocatedbetweentwosubsequentpositionsoftheicemargin.Asaresult,up-coningeffectsoccurringupstreamanddownstreamoftherepositoryremainimperceptible.
AsoonastheicesheetapproachestheSimpevarparea,around–26,800a,theconcentrationprofilesundergoasteepdecreaserelatedtotheadvectionoflargeamountsofmeltwaterpro-ducedbytheicesheet.Then,duringglacialcompletenessandglacialretreatnomorevariabilityisobservedinconcentration,sincemostofthesalinitywasflushedoutbythemeltwater.Theconcentrationvaluesremainlowuntiltheendofthesimulation.
Asmentionedearlier,similarconcentrationchangesareobservedintheflowingfracturesandinthematrix.Thecalculationofthecharacteristicdiffusiontimeφm/4Dintζ2;after/HochandJackson2004/givesavalueofca20a.Thiscorrespondstoatimeestimateforthesalinitytodiffuseintotherockmatrix.Atthescaleofthetimestepconsideredforthesimulation,thesalinityiscapableofaccessingmostoftherockmatrix.Therefore,differencesinconcentrationbetweenflowingfracturesandtherockmatrixarelesslikelytooccurwhencomparingselectedtimestep.
Figure 4-20. Base case: evolution of (relative) concentration and Darcy velocity module (expressed in m/a) at repository location (500 m depth) during glacial phases.
�5
4.4 Glaciationsimulation:50mmcaseForthe50mmcase,theglaciationsimulationwasperformedwithamaximummeltwaterrechargeequalto50mm/a.Thissensitivitycaseaimsatevaluatingtheeffectsofoneofthemostuncertainparametersofthemodel(recallingthatthemaximumrechargeforthebasecasevaluewassetto200mm/a).Thevaluechosenforthemaximumrechargecorrespondstotheconstantvalueusedforthepreviousglaciationmodel/JaquetandSiegel200�/.Forcomparisonpurposes,theresultsofthe50mmcasewereproducedatthesametimestepsasthoseforthebasecase(–26,800a,–26,500a,–17,900a,–1�,900aand–1�,800a).
Forthetimestep–26,800a(glacialbuildup),theeffectsofthemeltwaterontheflowfieldarestillconsiderable;however,incomparisontothebasecase,thedepthofpenetrationofthemeltwaterforthe50mmcaseseemslesspronouncedinsomepartsofthemodel(seeFigure4-21andFigure4-22).
Figure 4-21. Simulation of the 50 mm case (relative concentration) at time step –26,800 a. The ice margin is located at Y ≈ 100,000 m.
Figure 4-22. Simulation of the 50 mm case (relative matrix concentration) at time step –26,800 a. The ice margin is located at Y ≈ 100,000 m.
�6
Figure 4-23. Simulation of the 50 mm case (relative concentration) at time step –26,500 a. The ice margin is located south of the Simpevarp area.
Figure 4-24. Simulation of the 50 mm case (relative matrix concentration) at time step –26,500 a. The ice margin is located of the Simpevarp area.
Infrontoftheicesheet,diffusioneffects–similartothebasecase–areobserved.Inparticular,diffusion-relatedconcentrationpatternstendtobesmootherthanflow-relatedconcentrationpatterns(seeFigure4-22).
Duringglacialbuild-up,increasingamountsofmeltwaterareintroducedtothemodelastheicesheetprogresses.Theoverallconsequencesfortheflowfieldaresimilartothebasecase;however,thedepthofpenetrationforthemeltwaterdecreasesincomparisontothebasecase,especiallywhengettingclosertotheicemargin(seeFigure4-2�).Thesaltconcentrationwithinthematrixfollowsasimilarpatternastheflowingconcentrationduringthisglacialphase(seeFigure4-24).Likeforthebasecase,up-coningeffectscanbeobservedattheicemargin.
�7
Figure 4-25. Simulation of the 50 mm case (relative concentration) at time step –17,900 a. The ice margin is located at Y ≈ 100,000 m.
Duringglacialcompleteness,therateofmeltwaterrechargedecreasesastheicesheetdoesnotmove.Comparedtothebasecase,thereismoresalinityinthemodel,sincelessmeltwaterwasproducedduringthebuild-upphase;i.e.thiscasebeingcharacterisedbyamaximumrechargeof50mm/a(seeFigure4-25andFigure4-26).
Figure 4-26. Simulation of the 50 mm case (relative matrix concentration) at time step –17,900 a.
�8
Figure 4-27. Simulation of the 50 mm case (relative concentration) at time step –13,900 a. The ice margin is located south of the Simpevarp area.
Figure 4-28. Simulation of the 50 mm case (relative matrix concentration) at time step -13,900 a. The ice margin is located south of the Simpevarp area.
Duringglacialretreat(aroundca–14,000a),themeltwaterratereachesthemaximumvalueof50mm/aforashortperiodoftimeatthescaleofalmosttheentiremodeldomain.Forthiscase,theflushingwithmeltwaterisstillimportantbuttoalesserextentthanforthebasecase;somesalinityremainswithinthemodeldomain(seeFigure4-27andFigure4-28).
�9
Figure 4-30. Simulation of the 50 mm case (equivalent environmental head) at depth 0 m, for time step –13,800 a.
Forthe50mmcase,theattainedheadvaluesarewellbelowtheobservedicethickness(uptoca2,800m)forthestagesofglacialretreat(seeFigure4-29andFigure4-�0).
Astheglacialretreatcontinues,themeltwaterproducednolongermodifiestheconcentrationpatternsoftheflowfield;i.e.at–1�,800a,theresultingconcentrationfieldissimilartothatoftheprevioustimestep(seeFigure4-�1andFigure4-�2).
Figure 4-29. Simulation of the 50 mm case (equivalent environmental head) at depth 0 m, for time step –13,900 a.
40
Figure 4-32. Simulation of the 50 mm case (relative matrix concentration) for the time step –13,800 a. The ice margin is located at Y ≈ 100,000 m.
Figure 4-31. Simulation of the 50 mm case (relative concentration), for time step –13,800 a. The ice margin is located at Y ≈ 100,000 m.
41
Forthe50mmcase,theevolutionoftheflowpatternswasalsoanalysedatrepositorylocationatadepthof500m.ThearrivalandtheretreatoftheicesheetatSimpevarpcauseamuchsmallerincreaseintheDarcyvelocitythaninthebasecase(seeFigure4-��andFigure4-20:forthebasecase,themaximumvaluesfortheDarcyvelocityareca7to8higherthanthemaximumvaluesofthe50mmcase).Thiseffectisalsorevealedwhencomparing,forselectedtimesteps,horizontalcutsatrepositorylevel(cfAppendix;FigureA1-1toFigureA1-10).
Theconcentrationprofilesofthe50mmcaseexhibitsimilarshapesasthebasecase.Thephaseofglacialbuild-upwithanincreaseintheconcentrations(dominatedbydiffusiveeffects)issimilartothebasecase.WhentheicesheetapproachestheSimpevarparea,thesmallerDarcyvelocitiescausesufficientadvectiveeffectstohavemeltwateratrepositorylevel.Finally,duringglacialcompletenessandglacialretreat,nomorevariabilityisobservedinconcentration.Concentrationremainsatalowleveluntiltheendofthesimulationsincemostofthesalinitywasflushedoutatrepositorylevel.
Figure 4-33. 50 mm case: evolution of concentration and Darcy velocity module (expressed in m/a) at repository location (500 m depth) during glacial phases.
42
4.5 ParticletrackingcalculationsParticletrackingcalculationswereperformedtoassessperformancemeasuresinrelationtoahypotheticalrepositorylocatedintheSimpevarplocalarea.Foreachofthefivespecifictimestepsoftheglaciationmodel(cfFigure4-4),severalthousandparticleslocatedintheSimpevarparea(cfFigure4-1)werestartedatadepthof500m.Performingparticletrackinginthesteadystatemodeisacceptablebecausemostoftheexpectedtraveltimesarelikelytobeshorterthanthetimestepsappliedfortheglaciationmodel(cfpart�.5).Forthestatisticalanalysis,particleswithlongtrajectorieslikelytotravelwithinconductivefeatureswereremovedinordertoavoidbiasedresults.
Forboththebasecaseandthe50mmcaseshorttraveltimeswereobservedwithaverages(aswellas50thpercentile)below10aduringstagesofglacialbuild-upandglacialretreat(seeTable4-1,Table4-2,Figure4-�4andFigure4-�5).Theresultsofparticletrackingshowsomecorrelationintermsofthelocationoftheicesheet.Infact,thesymmetricalpatternexhibitedbythetraveltimesandtheF-factorsreflectsthepositionoftheicemarginwithrespecttotherepositoryarea.TheF-factor/Hartleyetal.2005/, /
l
F l= q,whereδlisastepin
distancealongthepathoftheparticle,characterisestransportresistancealongthecalculatedtrajectories.
Bothduringglacialbuild-upandglacialretreat,whentheicestillcoverstherepositoryarea(i.e.attimesteps–26,500aand–1�,900a)thetraveltimesexhibitsimilarlylowvalues(forthebasecase,respectively:1.4aand1.5a;forthe50mmcase,respectively:5.2aand5.7a).Thesameobservationisvalidwhentheicemarginisbarelyupstreamoftherepositoryareaat–26,800and–1�,800a(forthebasecase,respectively:2.0aand1.8a;forthe50mmcase,respectively:7.4aand6.9a).Thereasonisthatcomparablylargeamountsofmeltwaterarereleasedastheicemarginholdsasimilarpositionduringadvanceandretreatand,accordingly,theparticlestravelalongsimilartrajectories.Inabsoluteterms,theaveragetraveltimesinTable4-1andTable4-2reflectthattheheaviestmeltingisassociatedwiththeperiodsofglacierbuild-upandretreat.
Table4-1. Statisticsforparticletrackingcalculationsforthe200mmcase(basecase):traveltimeandF-factor.
Performancemeasure
Timestep
Mean σ Q5 Q25 Q50 Q75 Q95 N_traj.1)
Traveltimelog [a]
–26,800b) 0.293 0.348 –0.223 0.074 0.257 0.460 0.888 3,644–26,500b) 0.143 0.381 –0.593 –0.083 0.110 0.411 0.780 650
–17,900c) 3.341 0.131 3.086 3.299 3.324 3.405 3.553 3,062–13,900r) 0.182 0.381 –0.494 –0.050 0.167 0.442 0.767 935–13,800r) 0.244 0.340 –0.260 0.047 0.211 0.405 0.844 3,645
F–factorLog [a/m]
–26,800b) 4.462 0.691 3.251 4.008 4.540 5.002 5.431 3,644–26,500b) 4.260 0.715 2.915 3.646 4.508 4.854 5.090 650–17,900c) 6.702 0.493 5.770 6.410 6.796 7.036 7.384 3,062–13,900r) 4.439 0.721 3.006 3.936 4.735 4.957 5.254 935–13,800r) 4.413 0.688 3.235 3.953 4.481 4.949 5.387 3,645
1) Maximum number of valid trajectories is 3,645.
b) Build-up.
c) Completeness.
r) Retreat.
4�
Whencomparingthe200mmand50mmcases(seeTable4-1andTable4-2),theaveragetraveltimesforthephasesofglacialadvanceandglacialretreatincreasebyafactorofabout�to4forthe50mmcase.Thereductionofthemaximuminfiltrationto50mmleadstolowerDarcyvelocitiesandhencetothecaproportionaldifferencesobservedfortheaveragetraveltimes.
Thelongestaveragetraveltimes(2,19�aforthebasecaseand1,50�aforthe50mmcase)occurduringtheperiodofglacialcompleteness.Thedifferenceintheaveragetimesshouldnotbetakenasrelevantsincethenumberofvalidtrajectoriesobtainedforthe50mmcasewasratherlowincomparisontothebasecase.However,theresultsforglacialcompletenessmustbetakenwithsomecaution,asinthiscase,theonlyexfiltrationzonefortheparticlesislocatedintheSouthernpartofthemodel(seeFigureA1-11inAppendix).Thiszoneistheonlyoneholdingboundaryconditionswithprescribedatmosphericpressure.Everywhereelseonthetopsurfaceofthemodel,inthepresenceoftheicesheet,boundaryconditionsareprovidedas(transient)prescribedflow.Therefore,thetraveltimesforparticlesduringglacialcompletenessarelikelytobeoverestimated.
TheF-factorresultscorrespondingtophasesofglacialadvanceandretreat(–26,800a,–26,500a,–1�,900aand–1�,800a)aresignificantlylowerincomparisontothoseforthephaseofglacialcompleteness.ThisisduetotheincreasedDarcyvelocityandshortertraveldistanceduringthephasesofglacialadvanceandretreat.Duringtheseglacialphases,whencomparingthebasecasetothe50mmcase,thedecreaseinthemaximumrecharge(leadingtolowerDarcyvelocity)isfollowedbyanincreaseoftheaverageF-factortoaboutonehalforderofmagnitude.Foragiventimestep,whencomparingthebasecaseandthe50mmcase,thehistogramsoftheirrespectiveperformancemeasuresshowsimilarshapes(seeFigure4-�4andFigure4-�5).ThehistogramsoftheremainingtimestepsaregiveninAppendix.
WhencomparingtheperformancemeasuresofthebasecasecalibratedfortheSimpevarparea(seeTable4-�)andthebasecaseoftheglaciationmodel(seeTable4-1;phasesofglacialbuild-upandretreat),theaveragetraveltimearemorethantwoordersofmagnitudelargerandtheaverageF-factoratleastoneorderofmagnitudelargerintheSimpevarpmodelforthetemperateperiod.
Table4-2. Statisticsforparticletrackingcalculationsforthe50mmcase:traveltimeandF-factor.
Performancemeasure
TimeStep
Mean σ Q5 Q25 Q50 Q75 Q95 N_traj.1)
Traveltimelog [a]
–26,800b) 0.870 0.393 0.336 0.622 0.803 1.074 1.574 3,644–26,500b) 0.717 0.347 0.003 0.557 0.711 0.947 1.267 963
–17,900c) 3.177 0.065 3.089 3.144 3.164 3.197 3.293 329–13,900r) 0.758 0.374 0.071 0.514 0.739 1.030 1.363 854–13,800r) 0.840 0.339 0.329 0.642 0.805 1.005 1.442 3,645
F–factorLog [a/m]
–26,800b) 5.011 0.689 3.780 4.587 5.086 5.537 5.928s 3,644–26,500b) 4.901 0.685 3.558 4.392 5.104 5.445 5.727 963–17,900c) 6.639 0.408 5.881 6.329 6.743 6.936 7.161 329–13,900r) 4.962 0.716 3.596 4.372 5.287 5.501 5.804 854–13,800r) 5.015 0.688 3.835 4.555 5.087 5.445 5.987 3,645
1) Maximum number of valid trajectories is 3,645.
b) Build-up.
c) Completeness.
r) Retreat.
44
Table4-3. StatisticsforthebasecaseSReg4ComponentIC2/afterHartleyetal.2005/:traveltimeandF-factor.
Performancemeasure
Mean σ Q5 Q25 Q50 Q75 Q95
Traveltimelog [a]
2.662 0.768 1.616 2.044 2.518 3.249 4.034
F-factorLog [a/m]
6.061 0.752 4.973 5.503 5.939 6.612 7.390
Figure 4-35. Histograms at time step –26,500 a (glacial build-up) for Darcy velocity (module), path length, travel time and F-factor: base case (left group of 4 histograms) and 50 mm case (right group of 4 histograms).
Figure 4-34. Histograms at time step –26,800 a (glacial build-up) for Darcy velocity (module), path length, travel time and F-factor: base case (left group of 4 histograms) and 50 mm case (right group of 4 histograms).
45
5 Conclusions,discussionandperspectives
Agroundwaterflowmodel(glaciationmodel)wasdevelopedataregionalscaleinordertostudylongtermtransienteffectsrelatedtoaglaciationscenariolikelytooccurinresponsetoclimaticchanges.Theinfluenceofsuchglacialeffectsneedstobestudiedwithrespecttorepositoryperformanceandsafetyastheyarebelievedtoinduceprofoundmodificationsonthegroundwaterflowpatterns.
ConceptuallytheglaciationmodelwasbasedontheregionalmodelofSimpevarpandwasthenextendedtoamega-regionalscale(ofseveralhundredkilometres)inordertoaccountfortheeffectsoftheicesheet.Theseeffectsweremodelledusingtransientboundaryconditionsprovidedbyadynamicicesheetmodeldescribingthephasesofglacialbuild-up,glacialcompletenessandglacialretreatneededfortheglaciationscenario.
Theresultsdemonstratethestrongimpactoftheicesheetontheflowfield,inparticularduringthephasesofthebuild-upandtheretreatoftheicesheet.Thesephaseslastforseveralthousandyearsandmaycauselargeamountsofmeltwatertoreachtheleveloftherepositoryandbelow.Thehighestfluxesofmeltwaterarelocatedinthevicinityoftheicemargin.Astheicesheetapproachestherepositorylocation,theadvectiveeffectsgaindominanceoverdiffusiveeffectsintheflowfield.Inparticular,up-coningeffectsarelikelytooccuratthemarginoftheicesheetleadingtopotentialincreasesinsalinityatrepositorylevel.Forthebasecase,theentiresalinityfieldofthemodelisalmostcompletelyflushedoutattheendoftheglaciationperiod.
Theflowpatternsarestronglygovernedbythelocationoftheconductivefeaturesinthesub-glaciallayer.Theinfluenceoftheseglacialfeaturesisessentialforthesalinitydistributionasistheirimpactontheflowtrajectoriesand,therefore,ontheresultingperformancemeasures.
TraveltimesandF-factorwerecalculatedusingthemethodofparticletracking.Glacialeffectscausemajorconsequencesontheresults.Inparticular,averagetraveltimesfromtherepositorytothesurfacearebelow10aduringphasesofglacialbuild-upandretreat.IncomparisontothebasecasecalibratedfortheSimpevarpregionalmodel(version1.2;temperateperiod),averagetraveltimeandF-factorarereducedbyabouttwoordersandoneorderofmagnitude,respectively,forphasesoficesheetdisplacement.
Inordertoevaluatetheeffectsofthemaximumrecharge,asensitivitycasewasperformedwithamaximumrechargeequalto50mm/a,i.e.areductionbyafactor4withrespecttothebasecase.Thissensitivitycaseshowsperturbationsintheflowpatternsduetoglacialeffects,althoughtoalesserextentthaninthebasecase.Intermsofperformancemeasures,the50mm/acasepresentsincreasesintraveltime(cafactor�to4)andF-factor(aboutonehalforderofmagnitude)ascomparedtothebasecaseduringphasesofbuildupandretreat.Inotherwords,thepenetrationdepthofthemeltwaterisstillwellbelowtheleveloftherepository.Thus,atthislevel,up-coningeffectsareexpectedduringphasesoficesheetdisplacement.
Thefollowingrecommendationsregardingfurtherworkonopenissuesmaybepostulated:
1. Investigationsoftheconceptualuncertaintylinkedtothesub-glaciallayer.AlternativeconceptsarecurrentlyunderstudybySKBglaciologists.Oneconceptinparticularconsidersthereplacementofthetransientflowboundarywithatransientheadboundarywiththevaluesdependingontheicesheetthicknessandheaddrawdownsbeingspecifiedatthelocationsoftheconductivefeatures.Anotheroptionwouldbetoapplyamixoftime-dependentboundaryconditions;i.e.touseaprescribedfluxdynamicallyconstrainedbytheice-sheetthicknessfromonetimesteptothenext/Lemieux2006/.Thistypeofboundarywouldallowthecomputationofsubglacialinfiltrationinamorerealisticmanner.
46
2. Assessmentoftheimpactofalowervaluefortheflowwettedsurfacewithrespecttotheconcentrationfieldsandtheperformancemeasures.
Firstestimatesofthecharacteristicdiffusiontimerevealthatinstantaneousequilibriumbetweentheconcentrationoftheflowingfracturesandtherockmatrixisnolongerlikelytooccurwhichcouldleadtoadditionaltransportofsalinity.
�. Evaluationofgeomechanicaleffectsandpermafrostconditionsthroughtheapplicationoftemporallyvariablehydraulicparametersrelatedtothelocationoftheicesheet.
Geomechanicaleffectsduetoiceloadingarelikelytoinducemodificationsinthegroundwaterflowfield.Intermsofrockdeformation,theimpactoftheicesheetloadingleadstovariationsinporosity,hydraulicconductivityandporepressure.Themodellingofgroundwaterflow(withgeomechanicaleffects)shouldbeinitiatedwithscopingcalculationsofhydromechanicalcouplingfollowingtheapproachof/Lemieux2006/.
Duringtheprogressionoftheicesheet,permafrostisformedwithinseveralkilometresofitsperimeter.Thepermafrostgreatlyreducesthehydraulicconductivity.Theimportanceofthepermafrostrelatestothelocationoftheicesheetandneedstobeevaluatedwithrespecttorepositoryperformance.
4. Applicationofanovelmethodologyforthedeterminationofgroundwaterage,lifeexpectancyandtransittimedistributions.
Thismethodologydevelopedby/CornatonandPerrochet2005ab/allowstoavoidnumericalproblemsinherenttoparticletrackingmethodswhenusedincombinationwithfiniteelements.Itmaybeavaluablealternative,butitwouldfirstrequiresometesting,e.g.atthescaleoftheS1.2regionalmodel.
ThemodellingapproachappliedforthestudyofaglaciationscenarioatSimpevarphassuccessfullydescribedtheassumedconditionsandsomeoftherelevantprocesses.Itmaycertainlyserveasawellfoundedbaseforfuturemodellingtaskstoprovidesolutionstofurtherquestions.
47
6 References
CarreraJ,Sanchez-VilaX,BenetI,MedinaA,GalarzaG,GuimeraJ,1998.Onmatrixdiffusion:formulations,solutionsmethodsandquantitativeeffects,HydrogeologyJournal,6,1,178–190.
Chilès J P, DelfinerP, 1999.Geostatistics:modellingspatialuncertainty,WileySeriesinProbabilityandMathematicalStatistics,695p.
CornatonF,PerrochetP,2005a.Groundwaterage,lifeexpectancyandtransittimedistributionsinadvective-dispersivesystems:1.Generalisedreservoirtheory,AdvancesinWaterResources,inpress.
CornatonF,PerrochetP,2005b.Groundwaterage,lifeexpectancyandtransittimedistributionsinadvective-dispersivesystems:2.Reservoirtheoryforsub-drainagebasins,AdvancesinWaterResources,inpress.
HartleyL,WothD,GyllingB,MarsicN,HolménJ,2004.Preliminarysitedescription:groundwaterflowsimulations,Simpevarparea(version1.1)modelledwithConnectFlow,SKBR-04-6�,SvenskKärnbränslehanteringAB.
HartleyL,HochAR,HunterF,JacksonCP,2005.Regionalhydrogeologicalsimulations–NumericalmodellingusingConnectFlow,PreliminarysitedescriptionSimpevarpsubarea–version1.2,SKBR-05-12,SvenskKärnbränslehanteringAB.
HochAR,JacksonCP,2004.Rock-matrixdiffusionintransportofsalinity,SKBR-04-78,SvenskKärnbränslehanteringAB.
JaquetO,SiegelP,2003.Groundwaterflowandtransportmodellingduringaglaciationperiod,SKBR-0�-04,SvenskKärnbränslehanteringAB.
JaquetO,SiegelP,2004.Local-scalemodellingofdensity-drivenflowforthephasesofrepositoryoperationandpost-closureatBeberg,SKBR-04-46,SvenskKärnbränslehanteringAB.
JaquetO,SiegelP,KlubertanzG,BenabderrhamaneH,2004.Stochasticdiscretemodelofkarsticnetworks,AdvancesinWaterResources,27,751–760.
LemieuxJM,2006.ImpactoftheWisconsinianglaciationonCanadiancontinentalgroundwaterflow,PhDThesis,UniversityofWaterloo,Canada.
MarsicN,HartleyL,JacksonP,PooleMandMorvikA,2001.DevelopmentofhydrogeologicalmodellingtoolsbasedonNAMMU,SKBTR-01-49,SvenskKärnbränslehanteringAB.
MarsicN,HartleyL,Sanchez-FrieraP,MorvikA,2002.Embeddedregional/local-scalemodelofnaturaltransientsinsalinegroundwaterflowillustratedusingtheBebergsite,SKBR-02-22,SvenskKärnbränslehanteringAB.
NäslundJO,FastookJ,2005.Metadatafornestedhighresolution(10km)icesheetmodelrunof24thMarch2005,StockholmUniversity.
NäslundJO,2004.Personalcommunication.
PatersonWSB,1994.Thephysicsofglaciers,PergamonPress,Oxford,�rdedition.
SKB,2006.ClimateandclimaterelatedissuesforthesafetyassessmentSR-Can,SKBTR-06-2�,SvenskKärnbränslehanteringAB.
48
Svensson U, 1999.SubglacialgroundwaterflowatÄspöasgovernedbybasalmeltingandicetunnels,SKBR-99-�8,SvenskKärnbränslehanteringAB.
ThomsenHH,ThorningL,BraithwaiteR,1989.Appliedglacierresearchforplanninghydro-electricpower,Ilulissat/Jakobshavn,WestGreenland.AnnalsofGlaciology,1�:257–261.
WackernagelH,2003.MultivariateGeostatistics,�rdedition,Springer,Berlin.
WalkerD,RhénI,GurbanI,1997.SummaryofhydrogeologicconditionsatAberg,BeberbandCeberg,SKBTR-97-2�,SvenskKärnbränslehanteringAB.
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Appendix
Figure A1-1. Base case: Darcy velocity (module) field for time step –26,800 a, horizontal cut at depth of 500 m.
Figure A1-2. 50 mm case: Darcy velocity field (module) for time step –26,800 a, horizontal cut at depth of 500 m.
50
Figure A1-3. Base case: Darcy velocity (module) field for time step –26,500 a, horizontal cut at depth of 500 m.
Figure A1-4. 50 mm case: Darcy velocity (module) field for time step –26,500 a, horizontal cut at depth of 500 m.
51
Figure A1-5. Base case: Darcy velocity (module) field for time step –17,900 a, horizontal cut at depth of 500 m.
Figure A1-6. 50 mm case: Darcy velocity (module) field for time step –17,900 a, horizontal cut at depth of 500 m.
52
Figure A1-7. Base case: Darcy velocity (module) field for time step –13,900 a, horizontal cut at depth of 500 m.
Figure A1-8. 50 mm case: Darcy velocity (module) field for time step –13,900 a, horizontal cut at depth of 500 m.
5�
Figure A1-9. Base case: Darcy velocity (module) field for time step –13,800 a, horizontal cut at depth of 500 m.
Figure A1-10. 50 mm case: Darcy velocity (module) field for time step –13,800 a, horizontal cut at depth of 500 m.
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Figure A1-11. Histograms at time step –17,900 a (glacial completeness) for Darcy velocity (module), path length, travel time and F-factor: base case (left group of 4 histograms) and 50 mm case (right group of 4 histograms).
Figure A1-12. Histograms at time step –13,900 a (glacial retreat) for Darcy velocity (module), path length, travel time and F-factor: base case (left group of 4 histograms) and 50 mm case (right group of 4 histograms).
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Figure A1-13. Histograms at time step –13,800 a (glacial retreat) for Darcy velocity (module), path length, travel time and F-factor: base case (left group of 4 histograms) and 50 mm case (right group of 4 histograms).