Table Of ContentSPATIALCHARACTERIZATIONOFAHYDROGEOCHEMICALLY
HETEROGENEOUSAQUIFERUSINGATHREE-DIMENSIONAL
DISTRIBUTEDPARAMETEREXTENDEDKALMANFILTER
By
YANZHANG
ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL
OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT
OFTHEREQUIREMENTSFORTHEDEGREEOF
DOCTOROFPHILOSOPHY
UNIVERSITYOFFLORIDA
1997
ACKNOWLEDGEMENTS
Thecompletionofthisworkwouldnothavebeenpossibleifitwerenotfor
the help and support ofmany individuals; their assistance is therefore cheerfully
acknowledged.
First,IwouldliketothankDr. P.S.C.Raoforhisinvaluablehelpandguidance
throughoutthecourseofthisresearch. Dr. Raohasprovidedmewithopportunities
toparticipateininterestingscientificandengineeringprojects. Iappreciatethemany
intellectualandchallengingdiscussionswehadovertheyears.
SpecialthanksalsogotoDr. KirkHatfield,Dr. MichaelD.Annable,andDr.
KennethL.Campbellforservingasmycommitteemembers,andfortheirinsightful
commentsprovidedduringmanyresearchmeetings.
IwouldalsoliketothankDr. AndyI.JamesandDr. AshieAkpojifortheir
valuableinputtothisresearch. Inaddition,mygratitudegoestomyfellowgraduate
studentsintheHydrologicalSciencesAcademicClusterfortheirhelpandfriendship;
inrandomorder,GeorgeG.Demmy,LiyongLi,XavierFoussereau,RandyK.Sillan,
JamesW.Jawitz,DongpingDai,andHeonkiKim.
Iwouldliketothankmyfamilyandfriends,whoseloveandsupporthavebeen
essential.
Finally,Iamdeeplyindebtedtomyadvisor,Dr. WendyD.Graham,forher
guidance,support,encouragement,andconstantenthusiasm. Iamgratefulforthe
patienceandconfidenceshehasshowninme. Ifeelmyselfveryfortunatenotonly
ii
tohavebenefitedfromheracademicguidancebutalsotohaveenjoyedthefreedom
shehasgivenmeduringmyPh.D.
FinancialsupportforthisresearchwasprovidedinpartbytheAirForceOffice
ofScientificResearchandtheUniversityofFloridaCollegeofAgriculture-Hydrologic
SciencesAcademicClusterResearchAssistantshipProgram.
iii
TABLEOFCONTENTS
ACKNOWLEDGEMENTS
ii
LISTOFTABLES vi
LISTOFFIGURES viii
ABSTRACT xiv
CHAPTERS
1 INTRODUCTION 1
1.1 ResearchBackground 1
1.2 StochasticSubsurfaceHydrology,InverseProblems 8
1.2.1 Flowandtransportprocesses 8
1.2.2 Stochasticapproachtoflowandtransportmodeling ... 10
1.3 OutlineoftheDissertation 16
2 INFERENCEOFUNCONDITIONALMOMENTS 17
2.1 IntroductionandLiteratureReview 17
2.2 Theory,UnconditionalMomentEquations 29
2.3 SolutionMethods 38
2.4 CaseStudies 38
2.4.1 Definitionoftheproblem 39
2.4.2 Unconditionalsimulationresults 44
2.5 Summary 54
3 INFERENCEOFCONDITIONALMOMENTS 69
3.1 IntroductionandLiteratureReview 69
3.2 Theory,KalmanFilteringEquations 78
3.2.1 Problemformulation 81
3.2.2 Momentpropagationequations 85
3.2.3 Momentupdateequations 92
3.2.4 Filterinitialization 94
3.2.5 Solutionmethods 96
3.3 SyntheticCaseStudies 97
3.3.1 Problemdefinition,boundaryconditions 100
3.3.2 Conditionalsimulationresults 101
3.4 Summary 113
iv
4 ANALYSISOFFIELDDATA 137
4.1 Introduction 137
4.2 OU-1SiteBackgroundandInstallation 141
4.3 OU-1TracerTests 145
4.4 ProblemFormulation 146
4.4.1 Descriptionofthestateandmeasurement 146
4.4.2 Initialization 150
4.5 DiscussionoftheResults 153
4.5.1 Estimatedparameterdistributions 153
4.5.2 NAPLdistributionbasedonsoilcoreandmomentanalysis 156
4.6 Summary 180
5 CONCLUSIONS 182
APPENDIXES
A DERIVATIONOFFLUXCOVARIANCES 187
B THESQUARE-ROOTDECOMPOSITIONMETHOD 193
C DEFINITIONOFPARAMETERSINTABLES3.3-3.6 200
D CHOLESKYDECOMPOSITION 201
E FORMULATIONOFTHEITERATIVELINE-SORSCHEME 202
REFERENCES 209
BIOGRAPHICALSKETCH 219
v
423
LISTOFTABLES
2.1 Inputparametersfortheunconditionalsimulations 42
2.2 Inputparametersforunconditionalcasestudies 44
3.1 Inputparametersforconditionalsimulations 100
3.2 Inputparametersfortheconditionalcasestudies 103
3.3 SummaryofthePriorandPosteriorstatisticsforsyntheticcaseNo.l
(p=0.0)conditionedwithconcentrationmeasurementsatfrequencies
0.3days,0.6daysand0.9days 109
3.4 SummaryofthePriorandPosteriorstatisticsforsyntheticcaseNo.
(p=0.25)conditionedwithconcentrationmeasurementsatfrequencies
0.3days,0.6daysand0.9days 110
3.5 SummaryofthePriorandPosteriorstatisticsforsyntheticcaseNo.
(p=—0.25)conditionedwithconcentrationmeasurementsatfrequen-
cies0.3days,0.6daysand0.9days Ill
3.6 SummaryofthePriorandPosteriorstatisticsforsyntheticcaseNo.l
s((yppnt—=he0—t,1i.cs0a,cmappsleeirnfNegoc.tnl5eyt(wnpoerg=katis0,vheoluwysnecoi4rn2r0eFlicagotunercdeen\3t.nr4Kabt),iaonsndynmltehnae#stniucrfieecmladessne),tNsaon.adt
time=0.5and1.0days) 112
4.1 Tracers used inInterwell PartitioningTracerTest (IWPT) at OU-1
testcell, includingpartitioningcoefficients (KN) andinjectedtracer
concentration ' 146
4.2 InputparametersforstochasticsimulationusingOU-1IWPTdata . 151
4.3 Locationsofmultilevelsamplersinexperimentalandsimulationdomain152
4.4 Colorcodescorrespondingtoelevationsaboveclayformulti-levelsam-
plermeasurementpointsinexperimentalandsimulationdomain. . . 153
4.5 TargetanalyteconcentrationinanLNAPLsamplecollectedfromOU-1
testcell 157
4.6 ComparisonofNAPLsaturationspredictedbythesoilcoreanalysis
andpartitioningtracers 157
4.7 Massrecovery,wellsweptvolume,andaverageNAPLsaturation(after
Annableetal. [3]) 158
vi
C.l DefinitionofthePriorandPosteriorstatisticsusedinTable3.3through
Table3.6 200
vii
LISTOFFIGURES
2.1 Schematic diagramofthe three-dimensional simulationdomain and
boundaryconditions 40
2.2 Finitedifferencemeshfortheexampleproblem 41
2.3 Unconditionalmeanconcentration isshown asdashed contour lines
superimposedonthesyntheticallysimulatedsinglereplicateconcen-
tlCarayaseterioNZno4.fil(e0ld(.p7s6=2hom0w)nabaosvseoltihdecboansteo)uratlitniesm.e0S.h1,ow0n.5,ab1.o0v,eainsdho1r.i5zdoanytsa.l 46
2.4 U(0n.c7o6n2dimtiaobnoavlectohnecebnatsrea)tiaotntismtean0d.a1,rd0.d5e,v1i.a0t,ioanndat1.h5o.riCzaosnetaNlol.alye(rpZ=40) 47
2.5 Plotofunconditionalconcentrationstandarddeviationversusxalong
c(opn=tro0l)lineY4Z4attime0.2, 0.5, 1.0, 1.5,and2.0days. CaseNo.l 48
2.6 PatloltocoaftiKonNse05.6-3|5[,Py1c.(3x9.,7,x,2£.)1]59v,erasnuds2t.i9m2e1amlofnrgomthtehecoinntfrloolwlbioneunYd4aZr4y
onthecontrollineY4Z4. CaseNo.l (p=0) 49
2.7 Plotof£ [P9lC(x,x,t)]versusxalongcontrollineY4Z4attime0.2,
0.5,1.0,1.5,and2.0days. CaseNo.l (p=0) 49
2.8 sUpneccotndtiotiroenfaerlenccoerreploaitnitonxsp(2?/j./1(5x9,x'm),,1p.Cj7/7(x8,xm',),0a.7n6d2pmcc)(xa,rxe')shwiotwhnraes-
sSohloidwncolaobrovceonitsouhrorliiznoenst,aslolliadyecronZt4ou(r0.l7i6ne2s,manadbodvaeshtehdebcaosnet)ouartltiniemse.
0.1,0.2,0.5,1.0,1.5,and2.0days. CaseNo.l(p=0) 57
2.9 Uernecnocnediptoiionntalxco(r2r.e1l5a9timo,ns1p.y7y7(8x,mx,')0a.7n6d2pmcq)i(xa,rex')shwoiwtnhraesspseocltidtocorleofr-
cZNoo4n.tl(o0u.(r7p6=2linm0e)saabnodvesotlhiedbcaosnet)ouartltiinemse.0S.1h,ow0.n5,a1b.o0v,eanisdh1o.r5izdoanytsa.llCaayseer 58
2.10 Unconditionalmeanconcentrationisshownassolidcontourlinessu-
aaapsbenorddviaeCmsaphtsoehesdeeNdcbooa.osn3net)o(tupahrte=ltisn-iye0mns.te.2he50St.)h5i,coaw1l.nl0y,asbaionmvduel1ai.st5ehddoarycisoz.nocnetCanaltsrelaatyNieoor.n2Zf4i(epl(d0=.s7h06.2o2w5mn) 59
viii
2.11 Unconditionalcorrelationspyy(x,x'),pcy(x,x'),andpcc(x,x')withre-
specttoreferencepointx(2.159m, 1.778m,0.762m)areshownas
sS0.oh2l,oidw0n.c5o,laob1r.o0vc,eoanitnsoduhro1r.l5iizndoeansty,asslo.lliCadyaescroenZNt4oou.(r20.l(7ip6ne2=s,m0a.n2a5db)odvaeshtehdecbaosnet)ouartltiniemse. 60
2.12 Unconditionalcorrelationspyy(x,x'),pcy(x,x'),andpcc(x,x')withre-
specttoreferencepointx(2.159m, 1.778m,0.762m)areshownas
s0S.oh2l,oidw0n.c5o,laob1r.o0vc,eonaitnsoduhro1r.l5iizndoeansy,tsa.slollCiaadyseceronNZto4o.u3(r0{.lp7i6n=e2s,m-0a.na2db5o)dvaeshtehdecbaosnet)ouartltiniemse. 61
2.13 Unconditionalcorrelationspyy(x,x'),pcy(x,x'),andpcc(x,x')withre-
specttoreferencepointx(2.159m, 1.778m,0.762m)areshownas
s0S.oh2l,oidw0n.c5o,laob1r.o0vc,eoanitnsoduhro1r.l5iizndoeansy,tsa.slollCiaadyseceronNZto4o.u4(r0(.lp7i6n=e2s,m1)anadbodvaeshtehdecbaosnet)ouartltiniemse. 62
2.14 Unconditionalcorrelationspyy(x,x'),pcy(x,x'),andpcc(x,x')withre-
specttoreferencepointx(2.159m, 1.778m,0.762m)areshownas
sS0.oh2l,oidw0n.c5o,laob1r.o0vc,eoanitnsoduhro1r.l5iizndoeansyt,sa.slollCiaadyseceronNZto4o.u5(r0(.lp7i6n=e2s,m-a1)nadbodvaeshtehdecbaosnet)ouartltiniemse. 63
2.15 ComparisonofUnconditionalconcentrationstandarddeviationversus
xalongcontrollineY4Z4attime0.5days 64
2.16 vCeormspuasrxisaolnonogfucnocnotrnodlitliionneaYl4lZon4giattudtiinmael0m.a5crdoadyisspersivefluxP9iC(x,x) 65
2.17 ComparisonofunconditionalPyc(x,x)at(1.397m,1.778m,0.762m)
versustime 66
2.18 [A] ComparisonofUnconditionalpyc(x,x') withrespecttoreference
pointx'(2.159m,1.778m,0.762m)versusxalongcontrollineY4Z4at
time0.5days. [B]ComparisonofUnconditionalp9lC(x,x')withrespect
toreferencepointx(2.159m,1.778m,0.762m)versusxalongcontrol
lineY4Z4attime0.5days 67
2.19 Unconditionalcorrelationspyy(x,x'),pcy(x,x'),andpcc(x,x')withre-
specttoreferencepointx(2.159m, 1.778m,0.762m)areshownas
sSohloidwncolaobrovceonitsouhrorliiznoens,taslolliadyecronZt4ou(r0.l7i6ne2s,manadbodvaeshtehdecbaosnet)ouartltiniemse.
0.2,0.5,1.0,and1.5days. Hydraulicconductivityisspatiallyinvariant. 68
3.1 Estimatepropagation. ConcentrationmeasurementsC*_jandC*be-
comeavailableattimet^xandtimeU,respectively 80
3.2 StructureofthesequentialKalmanfiltering 98
3.3 Schematicdiagramoftheunconditionalsimulationdomainandbound-
aryconditions. Twelvemultilevelsamplers (MLSs) generate60con-
centrationmeasurementsateachmeasuringtime 102
ix
3.4 Horizontalplanviewofthespatialplacement ofmultilevelsamplers
(MLSs). (a) 12 MLSsevenlydistributed; (b) 12-MLSconfiguration;
(c)84-MLSsnap-shotconfiguration 117
3.5 NaturalloghydraulicconductivityInKgeneratedbyaturning-band
a0.l5g4o4r,it0h.7m62i,sasnhdow0n.9a8t0mhoraibzoovntealthelaybearsse,Zr2e,spZe3c,tivZe4l,y)and Z5 (0.327, 118
3.6 NaturalloghydraulicconductivityInifgeneratedbyaturning-band
a2.l7g9o4rimthmfriosmshtohewnoraitgivneritnicya-ldisrleiccetsioYn2,,rYes4p,ecatnivdelYy6.)(0.762,1.778,and 119
3.7 Vhoercitzoorntpallotlayoefrsx-Zy2,coZ3m,poZn4e,natnd(q.Zx5y)(0o.f32t7h,e0s.5i4m4u,la0t.e7d62,Daarncdy0f.l9u8x0amt
abovethebase,respectively) 120
3.8 VveercttiocralpslloitcesofYx2-,zZc4o,mpaonndenYt6((q0x.z7)62,of1t.h7e78,siamnuldat2e.d794Damrcyfrfolmuxthaet
origininy-direction,respectively) 121
3.9 tVaelctloaryeprlsotZ2o,fZx3-,ycZ4o,mpaonndenZt5((q0x.y32)7o,f0e.s5t4i4m,at0.e7d62D,aracnydf0l.ux98a0tmhoraibzoovne-
thebase,respectively). SyntheticcaseNo.l: p=0 122
3.10 VsleicctesorY2pl,otZ4o,fxa-nzdcoYm6po(n0.e7n6t2,(q1.xz77)8o,faensdtim2a.t7e94dDmarfcryomflutxheatorviegritnicailn
y-direction,respectively). SyntheticcaseNo.l: p=0 123
3.11 Conditionalandunconditionalmeanconcentrationsareshownassolid
anddashedcontourlines,respectively,superimposedonthesyntheti-
ctSaayllnltlyhaesyteiirmcuZlc4aats(ee0d.Nc7o6o.2nlc:menptar=baotv0ieontfhieelbdass(ei)nactolotri)m.esSh0.o5w,n1.a0b,oavendis1h.o5rdiazyosn.- 124
3.12 Ct1.oo0un,rdialtniindoesn1a.al5tdchaooynrsci.zeonSntytranaltthileoatnyiecsrtcZaa4nsde(a0rN.do7.6ld2:evmipaat=bioo0vneisthpelobtatseed)aaststoilmiedsc0o.n5-, 125
3.13 tEhsetiomraitgiinoanlloyfslinm9unlaitsedshNoAwnPLasrsaonldidomcofnitelodur(inlinceoslors)u.peSrhiomwponseadbooven
0ar.e98f0oumrhaobroivzeontthaelblaasyee,rsreZs2p,ecZt3i,veZl4y,).anSdyntZh5et(i0c.3c27a,se0.N5o4.4l,:0p.7=62,0.an.d. 126
3.14 Estimationofln0„isshownassolidcontourlinessuperimposedonthe
originallysimulatedNAPLrandomfield(incolor). Shownaboveare
threeverticalslicesY2,Y4,andY6 (0.762, 1.778,and2.794mfrom
theorigininy-direction,respectively). SyntheticcaseNo.l: p=0. . . 127
3.15 Conditionalstandarddeviationofln9nisshownassolidcontourlines
a0t.9f8o0urmhaorbiozvoenttahlelbaayseer,srZe2s,peZc3t,iveZl4y,).anSdynZt5het(0i.c32c7a,se0.N5o4.4l,:0p.7=62,0.an.d. 128
3.16 aCtontdhirteieonvearltisctaalnsdlaircedsdYe2v,iaYt4i,onanofdlYn60n(0i.s7s62h,ow1n.77a8s,saolnidd2c.o7n9t4oumrflirnoems
theorigininy-direction,respectively). SyntheticcaseNo.l: p=0. . . 129
x
