Estimating Source Strength Functions of Dense Non-Aqueous Phase Liquids from Historical Field Datasets

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Title:
Estimating Source Strength Functions of Dense Non-Aqueous Phase Liquids from Historical Field Datasets
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1 online resource (151 p.)
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english
Creator:
Wood,Brandon T
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University of Florida
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Gainesville, Fla.
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Thesis/Dissertation Information

Degree:
Master's ( M.E.)
Degree Grantor:
University of Florida
Degree Disciplines:
Environmental Engineering Sciences
Committee Chair:
Annable, Michael D
Committee Members:
Hatfield, Kirk
Jawitz, James W

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Subjects / Keywords:
dnapl -- flux -- genetic -- groundwater -- hydrology -- mass -- optimization -- parameterization -- solute
Environmental Engineering Sciences -- Dissertations, Academic -- UF
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Environmental Engineering Sciences thesis, M.E.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

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Abstract:
Dense non-aqueous phase liquids (DNAPLs) pose a number of challenges in groundwater remediation design as well as prediction of contaminant fate. Previousiresearch has suggested that flux based analysis may more closely relate a contaminant source zone to plume evolution and analysis of risk to human health and the environment. Several mathematical models have been developed to relate DNAPL mass and spatial distribution to contaminant mass flux. These functions were coupled with plume evolution models in order to assess their applicability to field settings using historical field data sets. These coupled solutions were used in an optimization framework in order to assess the applicability of source strength functions to field sites and the feasibility of characterizing a DNAPL source zone with historical data, mainly in the form of contaminant plume information both temporally and spatially. An efficient optimization technique, evolutionary optimization or genetic algorithm optimization was used to parameterize source strength functions for both known (synthetically generated data with known conditions) and unknown (field sites) historical datasets of various temporal record duration and resolution. This allowed for effective and accurate parameterization of source information for synthetically generated data, but due to the limitations of the analytical solutions to describe solute transport at field sites, failed to accurately parameterize certain cases. It is suggested that transport solutions that more accurately describe field settings are required for this type of analysis.
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In the series University of Florida Digital Collections.
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Includes vita.
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Includes bibliographical references.
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Description based on online resource; title from PDF title page.
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This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Brandon T Wood.
Thesis:
Thesis (M.E.)--University of Florida, 2011.
Local:
Adviser: Annable, Michael D.
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RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2012-02-29

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lcc - LD1780 2011
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UFE0043477:00001


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ESTIMATINGSOURCESTRENGTHFUNCTIONSOFDENSENON-AQUEOUSPHASELIQUIDSFROMHISTORICALFIELDDATASETSByBRANDONT.WOODATHESISPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFMASTEROFENGINEERINGUNIVERSITYOFFLORIDA2011

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c2011BrandonT.Wood 2

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Formyfriendsandfamily 3

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ACKNOWLEDGMENTS Iwouldliketoacknowledgemyadvisor,Dr.MichaelAnnableforhisguidance,directionandhelpfulsuggestionsthroughouttheproject,Dr.JimJawitzforhiswit,constructivecriticismandtechnicaluency,andDr.KirkHateldforhisuniqueperspectiveandsuggestionsfortheproject.Dr.RafaelMunoz-Carpenaofferedsoundcontextandphilosophicalviewofgroundwaterhydrologyandscienceingeneral.Dr.WendyGrahamwasinvaluableinherhelpinunderstandingstochasticsubsurfacehydrology.Additionally,IwouldliketoacknowledgetheUniversityofFloridaHigh-PerformanceComputingCenterforprovidingcomputationalresourcesandsupportthathavecontributedtotheresearchresultsreportedwithinthispaper.FundingforthisprojectwasprovidedbytheStrategicEnvironmentalResearchandDevelopmentProgram(SERDP),ProjectER-1613:PredictingDNAPLSourceZoneandPlumeResponseUsingSite-MeasuredCharacteristics. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 9 ABSTRACT ......................................... 12 CHAPTER 1INTRODUCTION ................................... 13 2BACKGROUND ................................... 15 2.1SourceStrengthFunctions .......................... 16 2.1.1PowerFunctionSourceStrengthModel ............... 18 2.1.2EquilibriumStreamtubeModel .................... 20 2.2SoluteTransport ................................ 21 2.2.1AnalyticalSolutions ........................... 21 2.2.2NumericalSolutions .......................... 25 3HISTORICALFIELDDATASETS .......................... 26 3.1DataPreparation ................................ 26 3.2FieldSiteData ................................. 28 3.2.1JointBaseLewis-McChord,FortLewis,Washington ........ 28 3.2.1.1Samplingnetwork ...................... 29 3.2.1.2Temporalhistory ....................... 31 3.2.2HangarK,CapeCanaveralAirForceStation,CapeCanaveral,Florida .................................. 32 3.3SyntheticData ................................. 32 3.3.1StochasticConductivityRealizations ................. 33 3.3.2FlowSimulation ............................. 33 3.3.3SoluteTransport ............................ 37 3.3.3.1Powerfunctionsourcestrengthmodel ........... 37 3.3.3.2Equilibriumstreamtubemodel ............... 37 4SOURCEPARAMETERIZATIONANDOPTIMIZATION .............. 45 4.1InverseModelingfromHistoricalData .................... 45 4.1.1PlumeEvolutionMethods ....................... 46 4.1.1.1Globalttoalltimeseriesdatasimultaneously ...... 47 4.1.1.2Individualttotimeseriesdata ............... 47 4.1.2TransectMethods ............................ 47 4.1.2.1Transectsintime ....................... 48 5

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4.2ParameterizationandOptimizationMethods ................. 49 4.2.1ExhaustiveSearch ........................... 49 4.2.2GeneticAlgorithm ........................... 49 4.3Validation .................................... 51 4.4OptimizationandParameterizationofSourceStrengthFunctionsonHistoricalDataSets .................................... 52 4.4.1IndividualWellFits ........................... 52 4.4.2GeneticAlgorithmResults ....................... 55 4.4.3FortLewisResults ........................... 56 4.4.4HangarK ................................ 59 4.4.5SyntheticData ............................. 59 5SUMMARYANDFUTUREWORK ......................... 67 APPENDIX ARESULTSFROMGENETICALGORITHMOPTIMIZATION,POWERFUNCTIONSOURCESTRENGTHMODEL ........................... 70 BRESULTSFROMGENETICALGORITHMOPTIMIZATION,EQUILIBRIUMSTREAMTUBEMODEL ............................... 82 CEXAMPLEGENETICALGORITHMOPTIMIZATIONPROGRESSIONSUSINGFORTLEWIS,WADATA ............................... 94 DADDITIONALMASSDISCHARGERESULTSFROMSYNTHETICDATA .... 98 D.1PFSSM ..................................... 98 D.2ESM ....................................... 104 ECOMPUTERCODES ................................ 110 E.1GeneticAlgorithmImplementation,PFSSMandGuyonnetandNeville(2004) ...................................... 110 E.2GeneticAlgorithmImplementation,PFSSMandDomenico(1987) .... 124 E.3ExampleGeneticAlgorithmCongurationFile,fastga.inc ......... 140 E.4CalculationofEquation3 .......................... 141 E.5ConversionofMT3DMSUCNtoCSV .................... 143 REFERENCES ....................................... 146 BIOGRAPHICALSKETCH ................................ 150 6

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LISTOFTABLES Table page 3-1Coefcientsforequivalentconversion ....................... 27 3-2SelectionofESMparametersforMT3Dsimulation ................ 40 4-1Summaryofmethods ................................ 45 4-2VariablesusedwithminimumandmaximumvaluesforFortLewis,Washington 55 4-3Sourcestrengthfunctionparameterranges .................... 55 4-4Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=1,usinga40year,untruncatedtemporalrecord ....... 62 A-1Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=1,full40yearrecord ...................... 70 A-2Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=2,full40yearrecord ...................... 71 A-3Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=3,full40yearrecord ...................... 72 A-4Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=1,usinga5yeartemporalrecord ............... 73 A-5Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=2,usinga5yeartemporalrecord ............... 74 A-6Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=3,usinga5yeartemporalrecord ............... 75 A-7Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=1,usinga5yeartemporalrecordbetween10and15yearspostinitialrelease .................................. 76 A-8Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=2,usinga5yeartemporalrecordbetween10and15yearspostinitialrelease .................................. 77 A-9Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=3,usinga5yeartemporalrecordbetween10and15yearspostinitialrelease .................................. 78 A-10Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=1,usinga5yeartemporalrecordbetween20and40yearspostinitialrelease .................................. 79 7

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A-11Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=2,usinga5yeartemporalrecordbetween20and40yearspostinitialrelease .................................. 80 A-12Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=3,usinga5yeartemporalrecordbetween20and40yearspostinitialrelease .................................. 81 B-1Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.4,full40yearrecord ............... 82 B-2Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.7,full40yearrecord ............... 83 B-3Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=1.0,full40yearrecord ............... 84 B-4Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.4,usinga5yeartemporalrecord ........ 85 B-5Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.7,usinga5yeartemporalrecord ........ 86 B-6Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=1.0,usinga5yeartemporalrecord ........ 87 B-7Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.4,usinga5yeartemporalrecordbetween10and15yearspostinitialrelease .......................... 88 B-8Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.7,usinga5yeartemporalrecordbetween10and15yearspostinitialrelease .......................... 89 B-9Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=1.0,usinga5yeartemporalrecordbetween10and15yearspostinitialrelease .......................... 90 B-10Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.4,usinga5yeartemporalrecordbetween20and40yearspostinitialrelease .......................... 91 B-11Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.7,usinga5yeartemporalrecordbetween20and40yearspostinitialrelease .......................... 92 B-12Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=1.0,usinga5yeartemporalrecordbetween20and40yearspostinitialrelease .......................... 93 8

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LISTOFFIGURES Figure page 2-1ConceptualizationofDNAPLcontamination .................... 16 2-2DiagramshowingDNAPLsourcezoneandconceptofcontrolplaneacrosswhichsolubilizedNAPLtravels ........................... 17 2-3Comparisonof)]TJ /F1 11.955 Tf 10.1 0 Td[(valuestomassdischargeovertimewiths=0 ........ 19 2-4Comparisonoflnvaluestomassdischargeovertime ............. 20 3-1LocationofwellsinthesamplingnetworkatJointBaseLewis-McChord .... 30 3-2ExampletemporalrecordsofthreewellsatFortLewis,Washington,partofthelargerdataset ................................... 31 3-3Movementofinformationbetweensoftwareused.GeostatisticslibraryGSLIB(DeutschandJournel,1998)containedsequentialGaussiansimulationpackagetogeneratehydraulicconductivityeld.ThiseldwasusedinthenitedifferencegroundwaterowcodeMODFLOW,theresultsofwhichwerecoupledwithaknownsourcestrengthfunctionboundarycondition.ThisinformationwasusedforsolutetransportsimulationinthenitedifferencesolutetransportsoftwareMT3DMS 34 3-4Comparisonofstochasticrealizationofhydraulicconductivityeldswithh=10m .......................................... 35 3-5Comparisonofstochasticrealizationofhydraulicconductivityeldswithlnk=1.0 ........................................... 36 3-6Comparisonofpotentiometricheadbetweenvaryingheterogeneity,allwithh=10m,headsinmeters ............................... 38 3-7Comparisonofpotentiometricheadwithvaryingcorrelationlength,allwithlnk=1.0,headsinmeters ............................. 39 3-8PlotofthethreesourcestrengthfunctionsusingthePFSSMthatwereusedasboundaryconditionsfornumericaltransportsimulationwithMT3DMS .... 40 3-9Comparisonofplumecenterlinebetweenlowandhighheterogeneitycasesatvarioustimes .................................... 41 3-10EquivalentDNAPLsaturationofESMbasedonlnandln ........... 42 3-11PlotofthethreesourcestrengthfunctionsusingtheESMthatwereusedasboundaryconditionsfornumericaltransportsimulationwithMT3DMS ..... 42 3-12PlumecenterlineswithESMboundaryconditionwithln0.4 ......... 44 9

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4-1ComparisonofGuyonnetandNeville(2004)andDomenico(1987)tonumerical(MT3D)solutionusing)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,lnk=0.5,h=5mandq0.01m/day .... 53 4-2Optimum)]TJ /F1 11.955 Tf 10.1 0 Td[(valueforindividualwellhistoriesatFortLewis,showingclusteringofcertainvaluesof)]TJ /F1 11.955 Tf 10.1 0 Td[(nearsourcelocation.Allparameterswereheldconstantpersitemeasuredcharacteristics .......................... 54 4-3Comparisonofoptimumvaluesof)]TJ /F1 11.955 Tf 10.1 0 Td[(andlnatFortLewis,consideringalldataavailable ........................................ 57 4-4Comparisonofoptimumvaluesof)]TJ /F1 11.955 Tf 10.1 0 Td[(andlnatFortLewis,consideringdatalessthan500mfromplumecenterlineandlessthan1kmfromsourcelocation 58 4-5ResultsofgeneticalgorithmoptimizationusingdatafromHangarK ...... 60 4-6Spatiallocationofsamplesfromsyntheticdatausedforparameterizationingeneticalgorithm ................................... 61 4-7ProgressionofgeneticalgorithmusingdatasampledasshowninFigure4-6inanaquiferwithcorrelationlengthh=5m,varianceofhydraulicconductivityoflnk=0.5,powerlawsourcestrengthfunctionwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,and40yearsoftemporalrecord .................................... 63 4-8Valueandstandarddeviationof)]TJ /F1 11.955 Tf 10.1 0 Td[(formultiplecasesofvarianceandcorrelationlengthscaleofhydraulicconductivityeld ..................... 64 4-9Standarddeviationoflnformultiplecasesofvarianceandcorrelationlengthscaleofhydraulicconductivityeld ......................... 65 4-10Massdischargeintimeforboundarycondition,actualMT3DMSresult,andoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.0,h=10mandlnk=1.0 .. 65 4-11Massdischargeintimeforboundarycondition,actualMT3DMSresult,andoptimizedparameterresultforthecaseofln=0.7,h=10mandlnk=1.0 66 C-1Comparisonofoptimumvaluesof)]TJ /F1 11.955 Tf 10.1 0 Td[(andlnatFortLewis,consideringalldataavailable ........................................ 95 C-2ComparisonofoptimumvaluesofVpatFortLewis,consideringalldataavailable 96 C-3Comparisonofoptimumvaluesoft0atFortLewis,consideringalldataavailable 97 D-1Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.0,h=05mandlnk=0.5 ........ 98 D-2Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.0,h=05mandlnk=1.5 ........ 99 D-3Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.0,h=05mandlnk=2.5 ........ 99 10

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D-4Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.0,h=10mandlnk=0.5 ........ 100 D-5Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.0,h=10mandlnk=1.5 ........ 100 D-6Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.0,h=10mandlnk=2.5 ........ 101 D-7Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.0,h=20mandlnk=0.5 ........ 102 D-8Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.0,h=20mandlnk=1.5 ........ 102 D-9Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.09 0 Td[(=1.0,h=20mandlnk=2.5 ........ 103 D-10Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=05mandlnk=0.5 ....... 104 D-11Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=05mandlnk=1.5 ....... 105 D-12Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=05mandlnk=2.5 ....... 105 D-13Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=10mandlnk=0.5 ....... 106 D-14Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=10mandlnk=1.5 ....... 107 D-15Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=10mandlnk=2.5 ....... 107 D-16Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=20mandlnk=0.5 ....... 108 D-17Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=20mandlnk=1.5 ....... 109 D-18Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=20mandlnk=2.5 ....... 109 11

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AbstractofThesisPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofMasterofEngineeringESTIMATINGSOURCESTRENGTHFUNCTIONSOFDENSENON-AQUEOUSPHASELIQUIDSFROMHISTORICALFIELDDATASETSByBrandonT.WoodAugust2011Chair:MichaelAnnableMajor:EnvironmentalEngineeringSciencesDensenon-aqueousphaseliquids(DNAPLs)poseanumberofchallengesingroundwaterremediationdesignaswellaspredictionofcontaminantfate.Previousresearchhassuggestedthatuxbasedanalysismaymorecloselyrelateacontaminantsourcezonetoplumeevolutionandanalysisofrisktohumanhealthandtheenvironment.SeveralmathematicalmodelshavebeendevelopedtorelateDNAPLmassandspatialdistributiontocontaminantmassux.Thesefunctionswerecoupledwithplumeevolutionmodelsinordertoassesstheirapplicabilitytoeldsettingsusinghistoricalelddatasets.ThesecoupledsolutionswereusedinanoptimizationframeworkinordertoassesstheapplicabilityofsourcestrengthfunctionstoeldsitesandthefeasibilityofcharacterizingaDNAPLsourcezonewithhistoricaldata,mainlyintheformofcontaminantplumeinformationbothtemporallyandspatially.Anefcientoptimizationtechnique,evolutionaryoptimizationorgeneticalgorithmoptimizationwasusedtoparameterizesourcestrengthfunctionsforbothknown(syntheticallygenerateddatawithknownconditions)andunknown(eldsites)historicaldatasetsofvarioustemporalrecorddurationandresolution.Thisallowedforeffectiveandaccurateparameterizationofsourceinformationforsyntheticallygenerateddata,butduetothelimitationsoftheanalyticalsolutionstodescribesolutetransportateldsites,failedtoaccuratelyparameterizecertaincases.Itissuggestedthattransportsolutionsthatmoreaccuratelydescribeeldsettingsarerequiredforthistypeofanalysis. 12

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CHAPTER1INTRODUCTIONCommonlyusedinindustrialapplications,non-aqueousphaseliquids(NAPLs)aredenedtobeliquidsthatformanimmisciblephasewithwater(e.g.oil,gas).WiththousandstotensofthousandsoflocationsintheworldthatuseNAPLs,poordisposalpracticesorotherwiseunknownreleaseofNAPLsintothenaturalenvironmenthasculminatedinalastingandunfortunatelycommonenvironmentalissue.OfparticularconcernisgroundwatercontaminationwithNAPLs,whichpresentsanumberofengineeringandriskassessmentchallenges.ThesechallengesarefoundinthearguablyinnitecomplexityofNAPLbehaviorinporousmedia.Signicantefforthasbeeninvestedintheunderstandingofhowimmiscibleuidsbehaveinthesubsurface,whichhasprogressedthepetroleumindustryinadditiontocontaminanthydrologyandseeminglyunrelatedeldssuchasbiomedicalengineering( Elootetal. 2002 ).Whilethisunderstandinghasallowedinvestigatorstobetterdeneandmodelimmiscibleuidbehaviorinporousmedia,applicationofthisinformationateldsitesrequiressitespecicmeasurementsofmediacharacteristicsthatwouldbecostprohibitiveorotherwiseimpossible(e.g.anaccuratemapofthemediaporenetwork).TheseproblemsareexacerbatedbydensitycontrastsbetweenNAPLandwater.TwoclassicationsofNAPLarethatoflightNAPLs(LNAPLs)anddenseNAPLs(DNAPLs),wheretheformerhaveadensitylessthanthatofwater(e.g.oil)andthelaterhaveadensitygreaterthanthatofwater(e.g.TCE).LNAPLstendtoaccumulateatopwatertablesandtheDNAPLstendstomigratebeyondthewatertableandaccumulateonlowpermeabilitylensorlayers.FocusingontheDNAPLproblem,thisthesisexploresthepreviouslydenedabstractionsofDNAPLcontaminatedsoilsandtheirrelationshipbetweensiteinformationwithinaframeworktomaximizesiteunderstandingusingpre-existingknowledge. 13

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SourcestrengthfunctionshavebeendevelopedtodescribechangesinmassuxleavingaDNAPLcontaminatedzone,subjecttoregionalgroundwaterowsandlocalhydrogeology.Twoofthesefunctions,thepowerfunctionsourcestrengthmodel( Faltaetal. 2005a b )andtheequilibriumstreamtubemodel( Jawitzetal. 2005 ),wereconsideredforthepurposesofthisanalysis.ThesefunctionswerelinkedtoplumeresponsesolutionsbothnumericallywithMT3DMSandanalyticalsolutionsinordertoexplorethelinkbetweencommonlymeasuredplumeinformationandmoredifcultlymeasuredsourcestrengthfunctionparameters. 14

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CHAPTER2BACKGROUNDInordertobetterunderstandandcontextualizetheproblem,abriefdescriptionofthespecicsoftheDNAPLproblem,thesourcestrengthfunctionschosentodescribeDNAPLsourcezones,andthecouplingofthesefunctionstosolutetransportsolutionsisprovided.DNAPLs,duetoadensitygreaterthanwater,tendtomigratefurtherbelowthegroundsurfacesubsequenttoreleaseintotheenvironment.ConceptualizedinFigure 2-1 ,thismigrationresultsincomplexspatialdistributionsofDNAPLcontaminantsastheimmisciblephaseencountersdifferentformationsintheporousmedia(e.g.reacheslensesoflowerpermeability,highlyconductivechannels,fractures)whilebecomingmoredifculttomeasureandremediate.Furthermore,becauseDNAPLsexhibitlowwatersolubility,thesecontaminantstendtoactasacontinuingsourceofsolutewhichchangesspatiallylocallyandtemporallyasregionalgroundwaterowscarrysolubilizedDNAPLoutofthesourcezone.DNAPLcontaminatedsitestypicallyexhibitbothasourcezoneanddissolvedcontaminantplume.ThesourcezoneischaracterizedasthevolumeofsoilinwhichthemajorityoftheDNAPLcontaminantmassexistsorexistedasbothgangliaandfreeproducttypicallyintheformofDNAPLlensesatoplowpermeabilityunits.Regionalgroundwaterowcarriessolubilizedcontaminantawayfromofthissourcezoneintopreviouslyuncontaminatedareas,creatingthecontaminantplume(seenasadashedlineinFigure 2-1 ).Ofparticularconcerntoregulatoryagenciesisthebehaviorandfateofthedissolvedcontaminantplume,whichhastheabilitytomigratebeyondpropertyboundaries.Asmentionedpreviously,DNAPLsarecommonlyfoundinindustrialapplications,mostlycommonlyintheformofchlorinatedsolvents,creosoteandcoaltar.Anumberofchlorinatedsolventshavebeenorcontinuetobeusedinindustry,includingtetrachloroethene(PCE),trichloroethene(TCE),and1,2-dichloroethene(DCE).These 15

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q GroundSurface DNAPL PlumeFront Figure2-1.ConceptualizationofDNAPLcontamination solventsarespecicallyusedbydrycleaningfacilities(commonlyPCE)andenginedegreasingoperations(commonlyTCE)relatedtomilitaryorcivilianindustry.Whilelesscommon,DNAPLshavebeenusedinotherseveralinterestingways,suchasathermalconductinguidinasolarthermalcollector.ExposuretochlorinatedsolventsorothercertainDNAPLshasbeenlinkedtoanarrayofhealthproblems,includingnumerousformsofcancer( Blairetal. 1979 ),liverproblems( Wrightetal. 1994 )andotherhealthcomplications( Blairetal. 1979 ; Changetal. 2003 ; Seoetal. 2008 ). 2.1SourceStrengthFunctionsInanefforttounderstandordescribetheDNAPLsourcezonesdiscussedinSection 2 ,massuxwasemployedinordertodescribethedissolutionkineticsofthesourcezoneaswellasenhanceremediationdesign.Denedastherateatwhichmassiscarriedfromthesourcezone,massdischargeisanappropriatemeanstodetermine 16

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DNAPL CP Figure2-2.DiagramshowingDNAPLsourcezoneandconceptofcontrolplaneacrosswhichsolubilizedNAPLtravels risktohumanhealthandhasrecentlygainedinterestedforuseinregulation.FollowingFigure 2-2 ,weconsideracontrolplane(CP)downgradientofthesourcezone,therateatwhichcontaminantleavingthesourcezonetravelsthroughtheCPonamassbasiswouldbedenedasthemassux[M=L2=T]. KreftandZuber ( 1978 )deneduxmorespecicallyastheratioofthesolutemassandwateruxdensities,emphasizingdifferencesbetweenresidentanduxdetectionandinjectionmodesandtheimplicationsoftheseinsolvinganalyticalsolutionstogroundwaterequations. Daganetal. ( 1992 )derivedageneralframeworkforsoluteuxinheterogeneousformationswhile Cvetkovicetal. ( 1992 )exploreduncertaintywhenusingthisframework.Thereafter, Feenstraetal. ( 1996 )exploredtheconceptofDNAPLuxhasameansofriskassessment,while Raoetal. ( 2001 )wasamongthersttosuggestthatcontaminantuxratherthanconcentrationshouldbeusedtomeasure 17

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remediationeffectiveness. Faltaetal. ( 2005b )demonstratedameansbywhichtomodelDNAPLuxandtheimplicationsofsourcezoneremediationtoaproposedDNAPLuxmodel,oneoftwosourcestrengthfunctionmodelsexaminedhere.Therefore,bycalibratingsourcestrengthfunctionstohistoricaldatasets,DNAPLsourcezonesateldsitescanbebetterunderstoodwithreducedeffortbyutilizingexistinginformationtofullestextentpossible.Sourcestrengthfunctionshavebeendevelopedbyvariousresearchers( Faltaetal. 2005b ; Jawitzetal. 2005 ; ParkerandPark 2004 )inordertodescribemassuxchangesovertime.Thisprovidesasimpledescriptionofahighlycomplexsystem.Previousworksby Annableetal. ( 2005 )andothers( Bockelmannetal. 2003 ; Hateldetal. 2004 )haveyieldedtheabilitytomeasurecontaminantmassuxineldscalesettings,howeverlittleefforthasbeenmadeinusinghistoricalsitedatatopredictanappropriatesourcestrengthfunctioncapableofdescribingtheDNAPLcontaminatedsitesourcezoneandplumedata.Thesesourcestrengthfunctionsincludethepowerfunctionsourcestrengthmodel( Faltaetal. 2005b )andanequilibriumstreamtubemodel( Jawitzetal. 2005 ).Althoughothermodelsexist( ParkerandPark 2004 ),thesetwoweretheprimaryfocusofthisstudyinordertoreducecomputationandanalysisrequirementswhilesurveyingtwodistinctlydifferentsourcestrengthfunctions. 2.1.1PowerFunctionSourceStrengthModelDevelopedby Faltaetal. ( 2005b ),thepowerfunctionsourcestrengthmodel(PFSSM)relatessourcemassandregionalgroundwaterowtomassuxbyanempiricalpowerfunction.ThisformulationcanbeseenasEquation 2 andplottedasFigure 2-3 Cs(t) C0=M(t) M0)]TJ /F1 11.955 Tf 162.35 -14.18 Td[((2) Cf(t)=C0 M)]TJ -.94 -7.14 Td[(0)]TJ /F7 11.955 Tf 9.3 0 Td[(VdAC0 sM)]TJ -.94 -7.14 Td[(0+M1)]TJ /F8 7.97 Tf 6.59 0 Td[()]TJ -11.96 -7.97 Td[(0+VdAC0 sM)]TJ -.94 -7.14 Td[(0e(1)]TJ /F8 7.97 Tf 6.59 0 Td[()]TJ 4.82 -.11 Td[()st)]TJ ET q .359 w 369.73 -610.61 m 382.43 -610.61 l S Q BT /F13 5.978 Tf 369.73 -615.73 Td[(1)]TJ /F13 5.978 Tf 5.76 0 Td[()]TJ /F1 11.955 Tf 61.29 -11.06 Td[((2) 18

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00.20.40.60.810510152025303540 M(t)=M0 t )]TJ /F2 11.955 Tf 10.1 0 Td[(0.0)]TJ /F1 11.955 Tf 10.09 0 Td[(=0.2)]TJ /F1 11.955 Tf 10.09 0 Td[(=0.5)]TJ /F2 11.955 Tf 10.1 0 Td[(1.0)]TJ /F1 11.955 Tf 10.09 0 Td[(=3.0 Figure2-3.Comparisonof)]TJ /F1 11.955 Tf 10.1 0 Td[(valuestomassdischargeovertimewiths=0 Wheretistimesincerelease,C0istheinitialconcentrationleavingacontrolplane,M0istheinitialsourcemass,VdistheDarcyvelocity,Aistheareaofthecontaminantcontrolplane,andsabiodegradationratewithinthesourcezone.Inherentinthepowerfunctionsourcestrengthmodelareexponentialandlineardecay.Exponentialdecayoccurswhen)]TJ /F1 11.955 Tf 10.1 0 Td[(=1inEquation 2 whilelineardecayoccurswhen)]TJ /F1 11.955 Tf 10.1 0 Td[(=0.5( Faltaetal. 2005b ).TheseformsofEquation 2 arepresentedasEquations 2 and 2 ,respectively. Cs(t)=C0exp)]TJ /F7 11.955 Tf 10.49 8.09 Td[(VdAC0 M0t,)-277(=1.0(2) Cs(t)=C0)]TJ /F7 11.955 Tf 13.15 8.08 Td[(VdAC20 2M0t,)-277(=0.5(2)Inadditiontothesecases,ifbioticorabioticdestructionofcontaminantisnegligible,onecanderiveEquation 2 fromEquation 2 Cs(t)=C0 M)]TJ -.93 -7.14 Td[(0()]TJ /F2 11.955 Tf 14.31 0 Td[()]TJ /F3 11.955 Tf 11.96 0 Td[(1)VdAC0 M)]TJ -.94 -7.14 Td[(0t+M1)]TJ /F8 7.97 Tf 6.58 0 Td[()]TJ -11.95 -7.97 Td[(0)]TJ ET q .359 w 329.87 -587.28 m 342.57 -587.28 l S Q BT /F13 5.978 Tf 329.87 -592.39 Td[(1)]TJ /F13 5.978 Tf 5.76 0 Td[()]TJ /F1 11.955 Tf 101.14 -11.06 Td[((2)ForamoredetailedderivationofEquations 2 through 2 ,see Faltaetal. ( 2005b ). 19

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InherentinallformsofthePFSSMarebothgroundwaterowandDNAPLsourceparameters.Itisimportanttonotethatfortheparticularinstanceofeldsiteswherecontinuousmassdisposalhasoccurredforasignicantperiodoftime,thetimeofreleasebecomesanoptimalvaluebetweentwoextremesratherthanadenitetime.Duetothischangeintime,othervariablessuchassourcemasshadtobeconsideredasavariableaswell.Anotherexampleisthatofsourcearea,whichcannothaveatruevalueandmustbesomeoptimalvalueratherthanaparameterbasedsolelyonmeasurement.Thisconceptwillbeexploredmoreinsubsequentchapters. 2.1.2EquilibriumStreamtubeModelDevelopedby Jawitzetal. ( 2005 ),theequilibriumstreamtubemodel(ESM)statisticallyrelatesDNAPLsaturationandlocationtoadistributionofstreamtubes,whichproducevariableamountsofsoluteuxbasedonanassumedormeasuredreactivetraveltimedistributionacrossallstreamtubes.ThisrelationshipcanbeseenEquation 2 whileaplotofEquation 2 canbeseenasFigure 2-4 .TheESMcanbeadesirablefunctiontodescribeasourcezoneinthattheparametersoftheESMcanbemeasuredinaeldsetting(e.g.atracertest)ratherthanbeingempiricallydetermined(asrequiredwiththePFSSM). Cf(t)=fcCs1)]TJ /F10 11.955 Tf 11.95 16.86 Td[(1 2+1 2erflnT)]TJ /F4 11.955 Tf 11.95 0 Td[(ln lnp 2(2)WhereTisthenumberofporevolumespassthroughthesourcezone,fcisthefractionofstreamtubescontaminatedwithNAPL,Csisthesolubilitylimitofthecontaminantinwater,lnisthemeanofthereactivetraveltimedistributionandlnisthestandarddeviationaboutthatmeaninthelognormallydistributedreactivetraveltimedistribution. 2.2SoluteTransportInordertodeterminetheapplicabilityofthesesourcestrengthfunctionstoeldsettings,anassessmentoftherelationshipbetweensourcestrengthfunctionsandsolutetransportorplumeresponseneededtobeperformed.Sourcestrengthfunction 20

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00.20.40.60.8105101520 M()=M0 ln0ln=0.3ln=0.8ln=1.2ln=1.9 Figure2-4.Comparisonoflnvaluestomassdischargeovertime applicabilityisdenedhereasthefunction'sabilitytoaccuratelymodelmassux(andthereforeplumeresponse)fromthesourcezone.Becausemanyhistoricaldatasetsdonothavedirectinformationonmassux,datasetsconsideredherecontaintime,location,andconstituentconcentrationatnumerouswellslocatedthroughouttheplumeandnearthesourcezone.Bothanalyticalandnumericalsolutionswereusedtodescribesolutetransportinthisanalysis. 2.2.1AnalyticalSolutionsTodescribecontaminanttransportfromthesourcezone(orzones), Bear ( 1979 )presentedthegoverning3-Dadvection-dispersiongoverningequation,seenasEquation 2 R@C @t=)]TJ /F7 11.955 Tf 9.3 0 Td[(v@C @x+xv@2C @x2+yv@2C @y2+zv@2C @z2)]TJ /F4 11.955 Tf 11.95 0 Td[(pC(2)Equation 2 canbesimpliedintoonedimensionwithnodecayasEquation 2 R@C @t=)]TJ /F7 11.955 Tf 9.3 0 Td[(v@C @x+xv@2C @x2(2) 21

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Clearyetal. ( 1978 )deriveda1-DanalyticalsolutiontoEquation 2 todescribecontaminanttransportwithdecay(Equation 2 ). A1(x,t)=v v+Uexpx(v)]TJ /F7 11.955 Tf 11.96 0 Td[(U) 2DerfcRx)]TJ /F7 11.955 Tf 11.96 0 Td[(Ut 2p DRt+v v)]TJ /F7 11.955 Tf 11.96 0 Td[(Uexpx(v+U) 2DerfcRx+Ut 2p DRt (2) +v2 2DR(p)]TJ /F4 11.955 Tf 11.96 0 Td[(x)expnvx D+(x)]TJ /F4 11.955 Tf 11.95 0 Td[(p)toerfcRx+vt 2p DRtWhere, U=p v2+4DR(p)]TJ /F4 11.955 Tf 11.96 0 Td[(x)(2)WhileEquation 2 describes1-Dcontaminanttransportwithoutbioticoraboticdestructionofcontaminant(p=0). A2(x,t)=1 2erfcRx)]TJ /F7 11.955 Tf 11.95 0 Td[(vt 2p DRt+r v2t DRexp")]TJ /F3 11.955 Tf 10.5 7.92 Td[((Rx)]TJ /F7 11.955 Tf 11.96 0 Td[(vt)2 4DRt#)]TJ /F3 11.955 Tf 10.5 8.09 Td[(1 21+vx D+v2t DRexpvx DerfcRx+vt 2p DRt (2) Domenico ( 1987 )presentedanapproximatesolutiontoEquation 2 ,whichhasbeenusedinseveralgroundwatercontaminanttransportmodelssuchasBIOCHLOR,BIOSCREEN,andREMChlor.The Domenico ( 1987 )solutionforsolutetransporthasbeensubjecttosomecriticismintheliterature( Srinivasanetal. 2007 ; Westetal. 2007 ).Nevertheless,thissolutionisusedinvarioussoftwaresuchasBIOCHLOR( Azizetal. 2000 ),BIOSCREEN( Newelletal. 1996 ),andREMChlor( Faltaetal. 2005a ).Forthepurposesofcontinuityandreproducibility,the Domenico ( 1987 )solutionwasoriginallyusedintheseanalyses. Faltaetal. ( 2005a )coupledamodiedversionofthe Domenico ( 1987 )solutiontothepowerfunctionsourcestrengthmodeltoderiveEquation 2 C(x,y,z,t)=fy(x,y)fz(x,z)Zt0Cs(t)]TJ /F4 11.955 Tf 11.95 0 Td[()@A(x,) @d(2) 22

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WiththepartialofAbeingdenedasthepartialderivativewithrespecttotimeofeitherEquation 2 or 2 ,shownasEquations 2 and 2 ,respectivelyandisadummyvariableofintegration. @A1(x,t) @t=v v+uRx+ut 2tp xvRtexp v)]TJ /F7 11.955 Tf 11.95 0 Td[(u 2xv)]TJ /F3 11.955 Tf 13.15 7.92 Td[((Rx)]TJ /F7 11.955 Tf 11.95 0 Td[(ut)2 4xvRt!+v v)]TJ /F7 11.955 Tf 11.96 0 Td[(uRx)]TJ /F7 11.955 Tf 11.96 0 Td[(ut 2tp xvRtexp v+u 2xv)]TJ /F3 11.955 Tf 13.15 7.92 Td[((Rx+ut)2 4xvRt!+v 2pxRx)]TJ /F7 11.955 Tf 11.95 0 Td[(vt 2tp xvRtexp x x)]TJ /F4 11.955 Tf 13.15 8.09 Td[(pt R)]TJ /F3 11.955 Tf 13.15 7.93 Td[((Rx+vt)2 4xvRt!)]TJ /F10 11.955 Tf 11.29 16.86 Td[(v 2Rxexpx x)]TJ /F4 11.955 Tf 13.15 8.09 Td[(pt RerfcRx+vt 2p xvRt (2) Whereuisdenedas, u=r 1+4px v(2)WherevisDarcyvelocityinthex-direction,Risaretardationfactor,xisthedistanceawayfromthesourcezoneinthedirectionoftheplumecenterline,tistimesincereleaseofcontaminant,xislongitudinaldispersivity,andpisthebiodegradationratewithintheplume.Examiningthenegligibledecaycase,thepartialderivativeofEquation 2 withrespecttotimeisshownasEquation 2 @A2(x,t) @t=1 p exp)]TJ /F3 11.955 Tf 9.3 0 Td[((Rx)]TJ /F7 11.955 Tf 11.96 0 Td[(vt)2 4DRt" v 2p DRt)]TJ /F7 11.955 Tf 13.15 8.09 Td[(DR(Rx)]TJ /F7 11.955 Tf 11.95 0 Td[(vt) 4(DRt)3 2!+ (Rx)]TJ /F7 11.955 Tf 11.96 0 Td[(vt)2 4DRt2+v(Rx)]TJ /F7 11.955 Tf 11.95 0 Td[(vt) 2DRt!r v2t DR+v2 2Dq v2t DR35+ v 2p DRt)]TJ /F7 11.955 Tf 13.15 8.09 Td[(DR(Rx+vt) 4(DRt)3 2!exp vx D)]TJ /F3 11.955 Tf 13.15 7.93 Td[((Rx+vt)2 4DRt!1+vx D+v2t DR)(2) 23

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WhenusingeitherEquation 2 orEquation 2 ,functionsfy(x,y)andfz(x,z)aredenedasEquations 2 and 2 ,respectively. fy(x,y)=1 2erfy+Y=2 2p yx)]TJ /F10 11.955 Tf 11.95 16.86 Td[(y)]TJ /F7 11.955 Tf 11.95 0 Td[(Y=2 2p yx(2) fz(x,z)=1 2erfz+Z 2p zx)]TJ /F10 11.955 Tf 11.96 16.86 Td[(z)]TJ /F7 11.955 Tf 11.96 0 Td[(Z 2p zx(2)Subsequentworks( Srinivasanetal. 2007 ; Westetal. 2007 )haveexaminedthesignicanceoftheerrorinthe Domenico ( 1987 )approximatesolutiontoEquation 2 Westetal. ( 2007 )arguedthattheassumptionsmadeintheDomenicosolutionresultinerrorsinapproximationthatarenotinsignicantinsomecases. Westetal. ( 2007 )alsoarguedthatbecauseonecannotdeterminethesignicanceoftheseerrorswithoutalsosolvingtheproblemwithanexactanalyticalsolutiontoEquation 2 ,ittheinvestigatorshoulduseanexactanalyticalsolutioninadditiontoapproximatesolutionsforcomparativepurposes.WhileexactanalyticalsolutionsEquation 2 havebeenpresentedintheliterature( Clearyetal. 1978 ; Sagar 1982 ; Wexler 1992 ),difcultiesarisewhenusingthesesolutions.Thesedifcultiesstemmostlyfromcomputationalcomplexitiesinnumericalintegration.WhilecreatingBIOSCREEN-AT,acloneoftheBIOSCREENsoftwarewithanexactanalyticalsolutiontothegoverningtransportequation, Karanovicetal. ( 2007 )derivedanexactanalyticalsolutionsubjecttoanexponentialdecayconcentrationboundarycondition,shownasEquation 2 C(x,y,z,t)=C0x 8p D0xexpf)]TJ /F4 11.955 Tf 15.27 0 Td[(tgZt01 3=2exp(()]TJ /F4 11.955 Tf 11.95 0 Td[())]TJ /F3 11.955 Tf 13.15 7.92 Td[((x)]TJ /F7 11.955 Tf 11.95 0 Td[(v0)2 4D0x)"erfc(y)]TJ /F7 11.955 Tf 11.96 0 Td[(Y=2 2p D0y))]TJ /F7 11.955 Tf 11.95 0 Td[(erfc(y+Y=2 2p D0y)#"erfc(z)]TJ /F7 11.955 Tf 11.95 0 Td[(Z 2p D0z))]TJ /F7 11.955 Tf 11.96 0 Td[(erfc(z+Z 2p D0z)#d(2) 24

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Whereisthesourcedecayrate,Yisthesourcewidth,Zisthesourceheight,D0x,D0y,andD0zareretardationadjusteddispersioncoefcients(e.g.xq=(R)),v0isretardationadjustedvelocity(q=(R)),andisadummyvariableofintegration.Duringvalidation,Equation 2 wasfoundtomatchalmostexactlyEquation 2 atlowvaluesforplumedegradation(106)andmatchedperfectlyconstantconcentrationtransportfoundinBIOCHLOR.ComparingthesolutionofBIOCHLORtoBIOCHLOR-ATyieldedsomewhatsignicanterrorbetweensolutions.Itwasforthisreasonoriginallythatanexactanalyticalsolutionsuchasthatof Wexler ( 1992 )wasconsideredtomodelsolutetransportinsubsequentanalysis. GuyonnetandNeville ( 2004 )derivedanexactanalyticalsolutiontoEquation 2 withmultipleboundaryconditions.Equation 2 isactuallyasolutiontoEquation 2 withanexponentiallydecayingboundarycondition.Therefore,Equation 2 showsamoregeneralsolutionswithatransientconcentrationboundarycondition(Cs()). C(x,y,z,t)=x 8p D0xZt0Cs()1 (t)]TJ /F4 11.955 Tf 11.96 0 Td[()3=2exp)]TJ /F4 11.955 Tf 9.3 0 Td[((t)]TJ /F4 11.955 Tf 11.96 0 Td[())]TJ /F7 11.955 Tf 13.15 8.08 Td[(x)]TJ /F7 11.955 Tf 11.96 0 Td[(v0(t)]TJ /F4 11.955 Tf 11.95 0 Td[()2 4D0x(t)]TJ /F4 11.955 Tf 11.96 0 Td[()"erfc(y+Y=2 2p D0y(t)]TJ /F4 11.955 Tf 11.95 0 Td[()))]TJ /F7 11.955 Tf 11.95 0 Td[(erfc(y)]TJ /F7 11.955 Tf 11.96 0 Td[(Y=2 2p D0y(t)]TJ /F4 11.955 Tf 11.96 0 Td[())#"erfc(z+Z=2 2p D0z(t)]TJ /F4 11.955 Tf 11.95 0 Td[()))]TJ /F7 11.955 Tf 11.95 0 Td[(erfc(z)]TJ /F7 11.955 Tf 11.95 0 Td[(Z=2 2p D0z(t)]TJ /F4 11.955 Tf 11.96 0 Td[())#d(2)Alloftheanalyticalsolutionstosolutetransportequationsusedinthisstudyassumeasemi-inniteisotropicaquifer.AftercomparingsolutionsusingEquation 2 and 2 (exploredindetailinChapter 4 ),Equation 2 presentedby GuyonnetandNeville ( 2004 )wasused.Thesetechniquesforcouplingsourcestrengthfunctionsasauxboundaryconditionallowformodelingofconcentrationtimeseriesdata,suchasthosefoundinhistoricalelddatasets. 2.2.2NumericalSolutionsFornumericalsolutionstoEquation 2 ,MODFLOW-2005( McDonaldandHarbaugh 2005 )wasusedforowsimulationandMT3DMS( Zhengetal. 1999 ) 25

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wasusedforsolutetransport.Foranextensiveexplanationofthenumericalmethodsusedinthesepackages,theMODFLOW-2000orMODFLOW-2005usermanualforowandMT3DMSusermanualfortransportarerecommended.BecausenumericalsolutionstoEquation 2 arecomputationallyintensive,particularlywhencomparedtotheanalyticalsolutionspresentedpreviously,numericalsolutionswereusedasasourceofdataratherthanameansbywhichtestthemethodsoutlinedinChapter 3 .ItisinChapter 3 thatthedetailsofhownumericalsolutionswereusedashistoricaldataaregiven. 26

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CHAPTER3HISTORICALFIELDDATASETSAtmanyeldsites,historicaldatasetsexistintheformofconcentrationtimehistoriesatvariousmonitoringwelllocations.Thefrequencywithwhicheachofthesewellsissampledandtheamountofmassdissolutionhistorycapturedbyeachwellcanbehighlyvariablewithinagivendatasetandmore-sobetweendatasetsatdifferentmanagedsites.Historicaldatasetscannevercapturetheentiretyofthesystem,butcanstilldescribesolutetransportprocessesatausefulscale.Forexample,itisnotuncommonforahistoricalrecordtohaveinformationonthecontaminantplumeorsourcezonewellaftertheDNAPLreleasehasoccurred.Inadditiontotemporalresolutionandcontinuityissues,seasonalshiftsingroundwaterowdirection,anisotropyintheporousmedia,sinks,etc.canallcreate`noise'inthedata,whichmakesformoredifcultmodeloptimization.Theeffectofthisnoisehasrecentlybeenexploredintheliterature( Parkeretal. 2010 ). 3.1DataPreparationThemaincomponentofmostelddatasetscomprisesconcentrationtimeseriesdataintheformofperiodicallymonitoredwellsinstalledatthesite.ThesewellsaretypicallylocatedonadenedcoordinatesystemsuchasNorthAmericanDatum(NAD)orastateplanecoordinatesystem.Becausetheequationsusedtopredictplumeevolutionfromavariableuxboundarybasex,yandzparametersonthedistancedowntheplumecenterline,perpendiculardistancefromtheplumecenterline,andthedepthbelowtheuxplanerespectively,itisnecessarytoalignconcentrationtimeseriesdataphysicallocationswiththeplumecenterline.ThiscanbedonebyrotatingthepointsaboutthelocationofthesourcezonesothatwellsarephysicallyalignedwiththeplumecenterlineusingEquations 3 and 3 .Whileothermeansbywhichtotranslatetheselocationsarepossible,thismethodwasfoundtobethemostsimplisticandleast 27

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Table3-1.Coefcientsforequivalentconversion ParentPCETCE1,2)]TJ /F5 7.97 Tf 6.59 0 Td[(DCEVC PCE1.000001.262161.710622.65341TCE-1.000001.355312.102271,2-DCE--1.000001.55114VC---1.00000 pronetoerrorincalculation. x0=xcos)]TJ /F7 11.955 Tf 11.96 0 Td[(ysin(3) y0=xsin+ycos(3)Wherex0andy0arethex-andy-locationofawellafterrotation.Becausechlorinatedsolventshavethetendencytodegradethroughbiologicalprocessesorabioticallyovertime,theobservedconcentrationsofchlorinatedsolventsarenotreectingtheinitialconditionsorinitialmassreleaseofthecontaminant.Inordertohaveamorecompleteunderstandingoftheinitialconditionsonwhichsourcestrengthfunctionsrely,thedaughterproductsoftheparentproduct(intheeldsitesconsideredhere,TCE)wereconvertedintomolarequivalentsofTCEsothattheeffectsofbiodegradationcouldbeneglected.Thistechniqueassumes,therefore,thatthereexistrecordsofdaughterproductsalongwithparentproductsinsamplingandthattheamountofcontaminantcompletelylosttobiodegradation(i.e.toethene,chloride)isnegligible.ThisassumptionwassupportedbylowconcentrationsofDCEandVCattheeldsitesconsideredhere.CoefcientsfromTable 3-1 canbeusedinEquation 3 toachieveequivalentconcentrationsofparentcontaminant. Cparent=PCECPCE+TCECTCE+1,2)]TJ /F5 7.97 Tf 6.59 0 Td[(DCEC1,2)]TJ /F5 7.97 Tf 6.59 0 Td[(DCE+VCCVC(3)WhereCrepresentsconcentrationofcontaminantandrepresentstherespectivecoefcientfromthetableabove. 28

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Afterconvertingalldatatotheequivalentparentproduct,plumedegradationuncertaintiescouldbereduced.Itisworthconsideringtheimplicationsonretardationthatthismayhave.Duetothehighlyuncertainkineticsofbiodegradationineachareaofthecontaminantplume,asingleretardationfactorfoundduringoptimizationshouldallowinaccuraciesinthisparametertobereducedbymeansofamathematicallyoptimalvalue. 3.2FieldSiteDataFieldsiteswerechosenbasedontheiravailabilityofdatasetsthatarebothlargeenoughtoperformsomeofthemoredemandinganalysespresentedinChapter 4 andclosetothoseobservationsthatmaybemadeatmosteldsites.Fieldsitesmusthavebeenstudiedthoroughlyenoughinpreviousinvestigationssothatowandtransportparameterscouldbeestimatedwithinareasonablerange.Inadditiontothesetraits,siteswereselectedthatalsohadarichhistoricalrecordofplumeand/orsourcezoneconcentrations.Twoeldsiteswereconsideredhere,JointBaseLewis-McChordnearTacoma,WashingtonandHangarKatCapeCanaveralAirForceStation,CapeCanaveral,Florida. 3.2.1JointBaseLewis-McChord,FortLewis,WashingtonJointBaseLewis-McChord(hereaftersimplyFortLewis),isaUnitedStatesArmypostlocatedinthePugetSoundlowlandwithsignicantTCEgroundwatercontamination.From1946throughthemid1960s,wastechlorinatedsolventsweredisposedintoanon-sitelandllknownastheEastGateDisposalYard(EGDY).ThedisposalactivitiesresultedinthreeprimaryTCEsourcezonescontributingtoalargecontaminantplumeapproximatelytwomilesinlength(USGS,1998).ThePugetSoundlowlandgeologyiscomprisedprimarilyofVashonDriftwithunderlyingcomplexlayersofglacialoutwashandnon-glacialdeposits(BordenandTroost,2001).ThishighlyheterogeneouscompositionyieldshighlyvariablemeasurementsforhydraulicconductivityandDarcyvelocity. 29

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Tracertestshavereportedhydraulicconductivitiesrangingfrom70to3,100ft/daywhereascalibratedhydrologicmodelsandaquifertestsbyotherinvestigatorshavereportedvaluesbetween80to300ft/day(Prych,1999).UsingthetransectmethodasdescribedinAPI(2003),depthaveragedgroundwateruxqvalueswerereportedat2719cm/daypriortoremediationand1612cm/dayafterremediationasdescribedinBrooksetal(2008).Chlorinatedvolatileorganiccompounds(CVOCs)concentrationsgreaterthanregulatorylevelswererstdetectedin1985beneaththeFt.LewisLogisticsCenter.In1986,theU.S.EnvironmentalProtectionAgency(EPA)foundsimilarcontaminationinatownapproximatelyonemiledowngradient.In1989,theFt.LewisLogisticsCenterwasdesignatedaSuperfundsite.Remediationeffortsbeganthereafterandin1995apump-and-treatsystemwasfullyoperationaltotreatthecontaminatedshallowaquifer.Studiespublishedin1998examinedthesuitabilityofothertreatmenttechnologiessuchasphytoremediationandbioremediation(USGS,1998).The1995pumpandtreatsystemcontinuestoremoveapproximately500kgTCEperyear.Between2001and2002,anestimated20,000kgofmasswasremovedviadrumremovalfromthesourcezones.In2004,thermalremediationremovedapproximately3,000kg.TCEfromtheEGDYsourcezoneandcontinuedthereaftertofurtherremovesourcemass. 3.2.1.1SamplingnetworkSince1990,longtermmonitoringhasperformedatFortLewis,yieldingslightlymorethan200wellsandover2000measurementsofTCEanditsdegradationbi-products(DCE,VC).ThelocationofthesewellshasbeenmodiedviaEquations 3 and 3 andisshowninplanandproleasFigure 3-1 .ForthedatashowninFigure 3-1 ,xpositionwasnormalizedtotheeasternmostwellavailableinthedatasetandisnotnecessarilywherethesourcezoneCPisbelievedtobelocated.Theplumecenterlinewasassumedbasedonobservedconcentrationsandwellswerenormalized 30

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-1000-500050010001500200005001000150020002500300035004000 Northing(m) Easting(m) APlanviewofwelllocations 02040608010012005001000150020002500300035004000 DepthBGS(m) Easting(m) BProleviewofwelllocationswheredepthbelowgroundsurfaceistakentobethescreeningintervalmidpointofeachsamplingwell Figure3-1.LocationofwellsinthesamplingnetworkatJointBaseLewis-McChord 31

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tothiscenterline(y=0).Thedepthofeachwellisbasedonscreeningintervalmidpointanddepthbelowgroundsurfacenormalizedtothegroundelevationneartheassumedsourcezone.TheimplicationsoftheseassumptionsareexploredinChapter 4 3.2.1.2TemporalhistoryThetemporalrecordatFortLewisspansasmuchas20yearsforsomewells,thoughdatawerenotconsistentlyrecordedatregularintervals.Figure 3-2 showsthatwhiletemporalrecordsthatareavailablecanhavelonghistories,certainwellsdonottrendsignicantlyorarestronglyaffectedbyshiftsingroundwaterdirection,remediationactivitiesifnearthesourcezone,orotherprocessesforwhichitcanbedifcultorimpossibletoadjust. 11010010001992199419961998200020022004200620082010 Concentration(g/L) t(year) LC-064BLX-12LX-02 Figure3-2.ExampletemporalrecordsofthreewellsatFortLewis,Washington,partofthelargerdataset BecausedatasuchasthoseseeninFigure 3-2 donotalwayshaveacleartrendoraresubjecttosignicant`noise',additionalinformationfromallwelllocationsmayimproveor`smoothout'thisinformation.TheimplicationsofnoiseandthechoiceofdatatobeusedisexaminedfurtherinChapter 4 32

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3.2.2HangarK,CapeCanaveralAirForceStation,CapeCanaveral,FloridaLocatedinCapeCanaveral,Florida,HangarKattheCapeCanaveralAirForceStation(CCAFS,hereaftersimplyHangarK)isTCE-contaminatedsitewitharelativelylarge(180acre)contaminantplume.Originallyconstructedinthelate1950's,HangarKwasusedforalargemechanicalmaintenanceandcleaningoperationwhichusedsignicantamountsofTCE.Groundwaterowmeasurementssuggestthatthenaturalgradientisbetween0.001to0.003ft/ft.RemediationofHangarKbeganin1999withabiospargeinstallationwhichwasrepurposedayearlaterasanairspargeforimprovedperformance. 3.3SyntheticDataTheproblemremainsthatonedoesnotknowthe`correct'solutiontodescribetheDNAPLsourcestrengthfunctionateldsites.TotestthemethodologypresentedinChapter 4 ,syntheticdatamustbegeneratedandsubsequentlycalibratedtoinordertocomparetoaknownsourcebehavior.Thisuseofsyntheticdatawillbecriticaltohelpdetermineuncertaintyinthemethods'abilitytoestimatemodelparameters.Syntheticdataweregeneratedwithsixsignicantlydifferentknownsourcestrengthfunctionconcentrationboundaryconditions.Intheinterestoftime,asinglerealizationofeachcasewereevaluated.AowchartofthemovementofinformationbetweensoftwareusedcanbefoundasFigure 3-3 .HydraulicconductivityeldsweregeneratedviasequentialGaussiansimulationfollowedbyanitedifferencegroundwaterowcodetosolveforowineachhydraulicconductivityrealization.Thereafter,asourcestrengthfunctionandtheowresultswerecoupledinanitedifferencesolutetransportcodewhichthenyieldedthesyntheticdatasetsusedforparameterestimation.Withthevariableamountofheterogeneityinhydraulicconductivityelds,thelimitofthemethodscanbeevaulated.Itishypothesizedthatthisteststhelimitationofananalyticalsolutiontotplumedataforheterogeneous/anisotropicporousmedia.Ifan 33

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aquiferismorecomplexthanthisanalyticalsolutioncanmodel,amorecomplexnitedifference/niteelementeffortwouldberequired. 3.3.1StochasticConductivityRealizationsHydraulicconductivityeldsweregeneratedbysequentialGaussiansimulation(SGS)usingtheGSLIB( DeutschandJournel 1998 )software.Thestochasticrealizationsofaquiferswerecreatedwithlnk=0.5,1.0,1.5,2.0,and2.5withh=5,10,and20metersandav=0.5,1.0,and2.0meters.Anexponentialcovariancefunctionwasusedtodescribethecovarianceoflags.Figure 3-4 showsrealizationsofconstantcorrelationlengthandvaryingheterogeneity.Increasingheterogeneitysignicantlyincreasesthevariabilityofhydraulicconductivity.AdditionalrealizationsforasinglelayerinplanviewcanbefoundintheAppendices.Figure 3-5 comparesasinglecaseofheterogeneityandvariouscorrelationlengthscales.Theresultssuggestthatthecorrelationlengthscaleissignicantwhenusedforowandtransportsimulations,whichisconrmedinthesubsequentanalysis.Whenconsideringwhichcasemaybeclosertotherealityateldsites,itisdifculttosayatbest.Becausecorrelationlengthsaredependentonthescaleofthesystemobserved,itmightbebesttosimplyobserveallrealizationsratherthanndingthe`closesttoeldsettings'heterogeneitycase. 3.3.2FlowSimulationForallaquiferrealizationsproducedbyGSLIB,MODFLOW-2005wasusedtosimulategroundwaterow.Inordertocaptureinformationcomparabletothatofawell,agridsizeof1m3wasusedinthe500x250x50blockdomain,makingfor6.5x106gridblocksforeachMODFLOWsimulation.BecauseallrealizationscouldberunsimultaneouslyattheUniversityofFloridaHighPerformanceComputingCenter,MODFLOWsimulationtimeswerenotsignicantlymorethanseveralhoursatthisscale.Foreachrealization,aconstantheadboundarywassetontheeastandwestendsoftheaquiferwithadifferenceof5moccurringacross500mofaquifer,producing 34

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GSLIBMODFLOWMT3DMSKFieldFlowFieldC(x,y,z,t)SubsetsDatasetADatasetBDatasetnSourceStrengthFunctionBoundary Figure3-3.Movementofinformationbetweensoftwareused.GeostatisticslibraryGSLIB( DeutschandJournel 1998 )containedsequentialGaussiansimulationpackagetogeneratehydraulicconductivityeld.ThiseldwasusedinthenitedifferencegroundwaterowcodeMODFLOW,theresultsofwhichwerecoupledwithaknownsourcestrengthfunctionboundarycondition.ThisinformationwasusedforsolutetransportsimulationinthenitedifferencesolutetransportsoftwareMT3DMS 35

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0100200300400500Easting(m)050100150200250 Northing(m) 0.1110100Ah=10m,v=1.0m,lnk=0.5 0100200300400500Easting(m)050100150200250 Northing(m) 0.1110100Bh=10m,v=1.0m,lnk=1.5 0100200300400500Easting(m)050100150200250 Northing(m) 0.1110100Ch=10m,v=1.0m,lnk=2.5 Figure3-4.Comparisonofstochasticrealizationofhydraulicconductivityeldswithh=10m 36

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0100200300400500Easting(m)050100150200250 Northing(m) 0.1110100Ah=5m,v=0.5m,lnk=1.0 0100200300400500Easting(m)050100150200250 Northing(m) 0.1110100Bh=10m,v=1.0m,lnk=1.0 0100200300400500Easting(m)050100150200250 Northing(m) 0.1110100Ch=20m,v=2.0m,lnk=1.0 Figure3-5.Comparisonofstochasticrealizationofhydraulicconductivityeldswithlnk=1.0 37

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agradientof0.01m/m.Headsforeachboundaryweresettohigherthanthatoftheheightoftheaquifersothatalllayerswerefullysaturatedatalltimes.Thispreventeddryingofcellswhichmightaffectsolutetransport.Figure 3-6 showspotentiometricheadatlowandhighlog-varianceofhydraulicconductivitywhileFigure 3-7 comparestheeffectofcorrelationlengthofthehydraulicconductivityeldonow. 3.3.3SoluteTransportSolutetransportwassimulatedwithMT3DMScoupledwiththeowsolutionfoundusingMODFLOW-2005.Usingthegeneralizedconjugategradientmethod,nostabilityconstraintswerenecessaryforsolutetransportsimulation.Inthisway,anarbitrarysourcestrengthfunctionstressperiod(i.e.periodsofconstantconcentrationleavingapatchsourcezoneorCP)couldbeusedwitha10daysstressperiodstep.Thisstressperiodstepwaschosentolessentheeffectsofdiscretizationofthesourcestrengthfunctionboundaryconditionthatwerefoundtobesignicantatstressperiodsofonemonthorgreater. 3.3.3.1PowerfunctionsourcestrengthmodelBecausesourcezoneswithshortlifetimeswereconsideredtobeunlikelyateldsites,only)]TJ /F1 11.955 Tf 10.09 0 Td[(valueslargerthan1wereconsidered.Threevaluesof)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,2.0,and3.0wereusedasboundaryconditions.TheresultingSSFsareplottedinFigure 3-8 3.3.3.2EquilibriumstreamtubemodelSimilartothesolutetransporteffortperformedforthepowerfunctionsourcestrengthmodel,theESMwasusedasatransientconcentrationboundaryconditionforagivensourcedimensionof10by5meters.BecausetheESMhasnoinherentinitialmass(M0),caremustbetakenwhenconsideringparameterstousefortheESMastonotdrasticallyover-orunder-estimatethesourcemass.Equation 2 wasintegratedandadjustedtorecoverthetotalmassinthesystem,shownasEquation 3 M Vsz=Z10fcCs1)]TJ /F10 11.955 Tf 11.95 16.86 Td[(1 2+1 2erflnT)]TJ /F4 11.955 Tf 11.96 0 Td[(ln lnp 2dT(3) 38

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50.049.549.048.548.047.546.546.045.50100200300400500Easting(m)050100150200250 Northing(m) Ah=10m,v=1.0m,lnk=0.5 50.049.549.048.548.047.546.546.045.50100200300400500Easting(m)050100150200250 Northing(m) Bh=10m,v=1.0m,lnk=2.5 Figure3-6.Comparisonofpotentiometricheadbetweenvaryingheterogeneity,allwithh=10m,headsinmeters 39

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50.049.549.048.548.047.546.546.045.50100200300400500Easting(m)050100150200250 Northing(m) Ah=5m,v=0.5m,lnk=1.0 50.049.549.048.548.047.546.546.045.50100200300400500Easting(m)050100150200250 Northing(m) Bh=20m,v=2.0m,lnk=1.0 Figure3-7.Comparisonofpotentiometricheadwithvaryingcorrelationlength,allwithlnk=1.0,headsinmeters 40

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00.10.20.30.40.50.60.70.80.910510152025303540455055 C=C0 t(years) )]TJ /F1 11.955 Tf 10.09 0 Td[(=1.0)]TJ /F1 11.955 Tf 10.09 0 Td[(=2.0)]TJ /F1 11.955 Tf 10.09 0 Td[(=3.0 Figure3-8.PlotofthethreesourcestrengthfunctionsusingthePFSSMthatwereusedasboundaryconditionsfornumericaltransportsimulationwithMT3DMS Table3-2.SelectionofESMparametersforMT3Dsimulation lnDesiredlnUsedlnM(kg) 0.400.3902.9210003.20.700.7022.7510006.71.000.9962.5010002.8 WhereMisthetotalmassinthesourcezone[M]andVszisthevolumeofaquiferconsideredtobethesourcezone[L3],whileallotherparametersaredenedinEquation 2 .BecauseaclosedformsolutionforEquation 3 couldnotbefound,Equation 3 wasintegratednumericallyviaa61pointGaussianquadrature( Calvettietal. 2000 ).TheresultsofthisintegrationforagivensourcedimensionisshownasFigure 3-10 .TheFORTRANcodeusedtocalculateEquation 3 isprovidedinAppendix E.4 .TheresultingsourcestrengthfunctionsusingtheparametersgiveninTable 3-2 areshowninFigure 3-11 .UsingtheESMsourcestrengthfunctionsasaboundaryconditioninMT3DMS,transportinvariablyheterogeneousaquiferswassimulatedandshowninFigure 3-12 .Onecanseeinthisgurethatthehigher 41

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1e-050.00010.0010.010.11050100150200250300350400450500 C=C0 Easting(m) 5yrs10yrs20yrs40yrsA)]TJ /F15 9.963 Tf 8.41 0 Td[(=1.0,lnk=0.5,h=10m 1e-050.00010.0010.010.11050100150200250300350400450500 C=C0 Easting(m) 5yrs10yrs20yrs40yrsB)]TJ /F15 9.963 Tf 8.41 0 Td[(=1.0,lnk=2.5,h=10m Figure3-9.Comparisonofplumecenterlinebetweenlowandhighheterogeneitycasesatvarioustimes 42

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00.511.522.53ln00.511.522.53 ln 1001000100001000001e+06 Figure3-10.EquivalentDNAPLsaturationofESMbasedonlnandln 00.10.20.30.40.50.60.70.80.9105101520253035404550 C=C0 t(years) ln0.4ln0.7ln1.0 Figure3-11.PlotofthethreesourcestrengthfunctionsusingtheESMthatwereusedasboundaryconditionsfornumericaltransportsimulationwithMT3DMS 43

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heterogeneitycaseresultsinaslightlyincreasedvelocityand,similartoFigure 3-9 ,increased`noise'inthedata. 44

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0.00010.0010.010.11050100150200250300350400450500 Concentration(g/L) Easting(m) 5yrs10yrs20yrs40yrsAUsingESMwithlnk0.5 0.00010.0010.010.11050100150200250300350400450500 Concentration(g/L) Easting(m) 5yrs10yrs20yrs40yrsBUsingESMwithlnk2.5 Figure3-12.PlumecenterlineswithESMboundaryconditionwithln0.4 45

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CHAPTER4SOURCEPARAMETERIZATIONANDOPTIMIZATIONDuetotheinherentlimitationsofanalyticalsolutionstoaccuratelydescribeeldsettingsandtheassumptionsmadeofthesourcearchitectureandbehavior,optimizationmaybefoundasamathematicallyaccurateabstractionofeldsettingsthatismostcapableofdescribingthesourcebehavior.Forthisreason,itmaybearguedthatcertainsiteparameters,evenwhenmeasured(e.g.velocity),maynotaccuratelydeneananalyticalmodeloftheeldsite.Becausesourcestrengthfunctionsarebydenitionsimplicationsofsourcezonebehavior(andinthisway,desirable),atleastsomeparameterizationwillbenecessarywhenattemptingtousehistoricaldatasetstodeterminetheoptimumorbestsourcestrengthfunctions.Becausetherearenumerouswaysinwhichmassuxcanbeapproximatedorthesourcefunctionsanalyzed,vedifferentmethodsareproposedtoanalyzesourcestrengthfunctionapplicability,tabulatedinTable 4-1 .Thesemethodsattempttoutilizecommonlyrecordedhistoricalelddata,includingspatiallydistributedtemporalconcentrationhistories,welltransects,andextractionwellconcentrationhistoriesandarecoveredindetailinsubsequentsections.Whileallofthesemethodsare Table4-1.Summaryofmethods IdentierDescriptionType 1ModeltotallC(x,y,z,t)welldataGlobal2IndividualwelltforC(t)at(x,y,z)Local3Transectsapproach,MD(x)Spatial4Transectsapproach,MD(t)Temporal5ExtractionwelldataMassFlux summarizedhere,itisimportanttonotethatonlytheresultsofmethods1and2inTable 4-1 arespecicallycoveredinthisdocument. 4.1InverseModelingfromHistoricalDataTabulatedinTable 4-1 ,severalmethodsbywhichtoparameterizesourcestrengthfunctionshavebeendevelopedbasedaroundtheconceptofinversemodeling.This 46

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requiresunderstandingofacertainprocess(e.g.plumeevolutioncoveredinChapter 2 )andusingthisunderstandingtolearnmoreaboutsourcebehavior. 4.1.1PlumeEvolutionMethodsInherentinmosteldsitesareascatterofwelllocationsatvaryingdepthsthroughouttheplumeandsourcezone(s).Inordertotakeadvantageofthesedatatocharacterizesourcezonebehavior,aplumematchingtechniquecanbeemployedbycouplingadvection-dispersionwithasourcestrengthfunctionasaconcentrationboundarycondition.DetailsofthecoupledexactanalyticalsolutionwithvariableuxboundarycanbefoundinSection 2.2.1 whiledataconsiderationsforthesemethodscanbefoundinSection 3.1 .Ideally,thismethodmightbeusedinconcertwithanadvanced,calibratednitedifferencesitemodelsuchasMODFLOW.Usingsuchamodelmightnecessitateoptimizingforanunmanageablenumberofparametersandthus,forthepurposesofthisanalysis,thecoupledanalyticalsolutionshownasEquation 2 wasusedtotplumedata.Duetothelimitationsoftheanalyticalsolutiontomatchcomplexgroundwaterowsateldsites,thedistanceoftheconcentrationmeasurementpoint(i.e.welllocation)fromthesourcezonehadtobeconsidered.Assolutemigratesawayfromthesourcezoneintothecontaminantplume,thecontaminantconcentrationcanbeaffectedbyotherprocessesotherthansourcezonebehavior(e.g.biodegradation,sorption,volatilization).Forthisreason,thosewellsnearerofthesourcezonewereconsideredtobemoreindicativeofthesourcezonebehaviorthanthosefurtherfromthesourcezone.Thedistancethatmeasuringpointcouldbefromthesourcezonebeforesignicantdeviationfromsourcezonebehaviorcouldbeobservedremainsanunknownquantitywhenthesourcezonebehavioritselfisundened.Therefore,themaximumspatialdistancefromthesourcezonethatameasuringpointcouldbewasconsideredanadditionalunknownoptimizationparameteralongwiththemodelparameters.Itshouldbenotedthatwhenapplyingthistypeofdatalimitation,thenumberofconcentration 47

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measurementsshouldbeashighaspossiblesothatmodeloptimizationeffortsarenotdominatedordictatedbyafewmeasurements.Sowhilethemaximumdistancefromthesourcezoneshouldbeconsidered,onemustalsoconsidertheminimumnumberofdatapointstobeusedinoptimization. 4.1.1.1GlobalttoalltimeseriesdatasimultaneouslyWhencalculatingthecoupledsourcestrength-advectiondispersionequationswith10to16parametersandassociateduncertainties,optimizationcanquicklybecomedifcultbothinimplementationandexecutiontime.Itwasfoundthatforthepurposesofthisanalysis,anexhaustivesearchapproachwouldrequirefartoomuchcomputationtime(insomecases,overseveralCPU-years).Afterexaminingtherelativeeaseofimplementationandlikelihoodofeffectiveoptimization,ageneticalgorithmwasimplementedtosolvethecoupledequationsforbothsourcestrengthfunctions( Faltaetal. 2005b ; Jawitzetal. 2005 ).TheparametersandrangesofvaluesusedforFortLewisareoutlinedinTable 4-2 whilesourcestrengthfunctionparameterrangesareoutlinedinTable 4-3 4.1.1.2IndividualttotimeseriesdataOnceoptimumsiteparametershavebeencalculatedasoutlinedinSection 4.1.1.1 ,optimumsourcestrengthfunctionparameterscanbeobtainedforindividualwells.Becauseoptimizationateachindividualwellwillbeononlyonetothreeparameters,exhaustivesearchcanbeeffectiveandlesscomputationallyintensiveforthisanalysis.Afterthisanalysishasbeenperformed,variousvisualizationsoftherelationshipsbetweensourcestrengthfunctionsandareasoftheplumecanbeexamined.Ofparticularusemaybethecomparisonofoptimumsourcestrengthfunctionparametersanddistancefromtheproposedsourcezone. 4.1.2TransectMethodsTransectmethodsareofuseinthattheyhavetheabilitytomorecloselyfollowthesourceandplumearchitecturescalculatedbysourcestrengthfunctions.Moreover, 48

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transectmethodstendtoreducetheaffectsofnoiseinconcentrationdata,butideallyrequiresthatwellsarearrangedperpendiculartotheowelddown-gradientofthesourcezone. MD=qnXi=1CiAi(4)Transectscanbecalculatedusinganumberofmethods.Thesetransectmassuxescanbemeasureddirectlyusingpassiveuxmeters(PFM)( Annableetal. 2005 ),multi-levelsamplers( KubertandFinkel 2006 ),stochasticmethods(SchwedeaandCirpka,2009),screenedwellsandcombinationsofthesetechniquesinadditiontoothers.Forthepurposesofthesite(s)presentedhere,asimpleconcentrationwithanassumedareaofinuencecoupledwithgroundwateruxwasusedtodeterminemassuxthroughtheplane,shownasEquation 4 .ThiswasperformedbysupplementinganexistingPFMtransect(capturingasinglepointintime)withnearbywellsthathadmeasuredconcentrationsintime. 4.1.2.1TransectsintimeBecausewelltransectshavetheabilitytocoupleplaneaveragedconcentrationwithgroundwaterowtoproducemassuxvalues,observingthechangeintheseuxvaluesintimecanproducemeaningfuluxtimeserieswhichcanbedirectlyttosourcestrengthfunctions.Intheapplicationofthismethod,itisassumedthatthetransectcapturingthemassuxisnearenoughtothesourcezonetoreduceerrorintroducedbyprocessesoccurringineld(e.g.changeinowelddirection).Oneexampleofthiscanbefoundinthedenitionofsourcearea.Throughoutthetimethatthesourcestrengthfunctionissaidtobedescribedbyoneofthemathematicalmodelsconsideredhere,itisassumedthatthesourceareadoesnotchangewithtime.Asmassisremovedfromthesourcezoneintothedissolvedcontaminantplume,thesourceareathroughwhichwaterowsmustconsequentlyreduceinsizeinreality.Whilethisphenomenaisdescribedmostlybychangesinconcentrationleavingthesourcearea,itisunknownexactlywhichsourceareawouldcorrespondtothebestdescription 49

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ofthesourcezoneandsourcezonebehavior.Thisproblem,coupledwithinherentuncertaintiesofsourcezonelocationthatarecommonofmanyeldsitesisnotlimitedonlytothisparameter.Forthesereasons,itcouldbearguedthatallparametersintheanalyticalsolutionare,toacertaindegree,subjecttosomevariability.Therefore,inordertoreducethecomputationtimeandndgloballyoptimumanswersamidstuncertaintyofmultipleparameters,differentoptimizationtechniquesandalgorithmswereconsidered. 4.2ParameterizationandOptimizationMethods 4.2.1ExhaustiveSearchOneofthemostsimplisticandcomputationallyinefcientoptimizationmethodsisthatofexhaustivesearch.Thismethodinvolvescyclingthroughvaluesofvariablesandcalculatingmodeltateachvalue.Thiscanbebestdescribedbythepsuedocodebelow: dogamma=0.01,3.0,0.01dosource_width=10,20,1result=calculate_value(gamma,source_width)fit=calculate_fit(result)printgamma,source_width,result,fitenddoenddoThismethod,whileamongtheeasiesttoimplement,alsoinvolvesthegreatestamountofcomputationtimetocomplete.Whilethismethodmaybereasonableforsmallerproblemssuchastheonepresentedabove,whenmoreuncertaintyinvariablesisintroduced,theproblemincreasessizemultiplicativelywiththeadditionofvariablesandsmallerchangesinvariablevalues. 50

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4.2.2GeneticAlgorithmSimilaroptimizationproblemswithalargenumberofparametershavebeensolvedusingageneticalgorithmmethod( Changetal. 2005 ; Wang 1997 ; Yapoetal. 1998 )whileothersanarticialneuralnetwork( DawsonandWilby 2001 ; Hsuetal. 1995 ).Basedontherelativeeaseofimplementation,ageneticalgorithmwasusedtooptimizemodelparametersforthisparticularmethod.Thismethodinvolvesencodingparameterrangesintobinaryrepresentationsandgeneratinganinitialrandom`population'ofsolutions.Thesepopulationsareactuallyanarrayofvariablevalueswhichallhaveacertain`tness'orparameter(s)onwhichtheproblemistobeoptimized.Oncethisarrayofanswers'tshavebeencalculated,theyaresortedbybesttandselectedfor`crossover'.Thisprocessinvolvesassigningprobabilityofselectiontoeachsolutionbasedontheirtness,sothattheprobabilityofselectionincreaseswithgoodnessoftortness.Twosolutionsarethenpickedatrandombasedontheprobabilitydistributionoftheindividualsolutionsassignedearlier.Thetwosolutionsthenexchangevariablesatrandompointsalongthebinarystringthatrepresentsthesolutionsofeachparameter.Followingthis,eachanswerissubjecttomutationsothattheproblemdoesnoteasilyapproachalocaloptimum.Thisprocessisrepeatedforanarbitrarynumberof`generations'oruntilthetnessstopcriteriahasbeenmet,suchasacoefcientofefciencyvaluenear1.Simpliedpsuedocodeofthisalgorithmcanbefoundbelow. population=get_initial_population()dowhile((generationerror_criteria))callfitness_of(population)callsorting_of(population)callcrossover(population)callmutate(population) 51

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calloutput(population)error=get_min_error(population)generation=generation+1enddoTheprecisionwithwhichavariablemaybedenediscontrolledbythenumberofbitsassignedtorepresenteachvariable.Following Wang ( 1997 ),variablesaredenedbymultiplyingadiscretechangeinvariable(e.g.)]TJ /F1 11.955 Tf 15.14 0 Td[()byascalarrepresentedinbinary.ThisdiscretechangeisdenedinEquation 4 =max)]TJ /F4 11.955 Tf 11.95 0 Td[(min 2n)]TJ /F3 11.955 Tf 11.96 0 Td[(1(4)Whereisanarbitraryvariableandnisthenumberofbitsusedforthesolution.ForthepurposesoftheanalysisatFortLewis,8bitswereusedyielding255uniquevaluesforeachvariableconsideredintheanalysis.Itwasfoundduringtheanalysisthatusingfewerbitswouldresultinalackofdiversitywhereasusingmorebitswouldnecessitateimpracticallylargepopulationstocapturethemajorityoftheso-calledanswerlandscape.Tocalculatethevalueofavariable,Equation 4 wasused. =min+nXi=12(i)]TJ /F8 7.97 Tf 6.58 0 Td[(1)bi(4)Wherebisdenedtobeasinglebitinthen-lengthbitarrayrepresentingthevariablevalueandisthevaluecalculatedwithEquation 4 4.3ValidationInordertovalidatetheFORTRANcodetocalculatethecoupledsourcestrengthfunctionandadvectiondispersionequationswithnoplumedecay(p=0),thecodewastestedagainstBIOCHLOR( Azizetal. 2000 )usingparametersfoundatFortLewis,Washington.ItwasfoundthatthecodeperformedverywellmatchingBIOCHLORoutputsbutbehaveddifferentlycomparedtoREMChloroutputs.Duetotheinherent 52

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differencesofthehandlingofvelocityprolesinREMChlor,comparisonbetweenthecodeswasfoundtobedifcult;possiblyrequiringmodifyingthecodebeyondwhatwasrequiredforpurposesoftheanalysispresentedhere.Atnearlyalleldsites,groundwatervelocitycanvarybothintimeandspace( Gelharetal. 1992 ).Whilethenearlyallanalyticalsolutionstogroundwatertransportassumeahomogeneousmedia,excludingcertainrecentliterature(e.g. NiandLi 2009 ),thesolutionpresentedby Domenico ( 1987 )isuniqueinthatsignicanterroroccursatPecletnumberslessthan6( GuyonnetandNeville 2004 ).Figure 4-1 comparesanumericalsolution(MT3DMS)tothecoupledpowerfunctionsourcestrengthfunction-solutetransportanalyticalsolution()]TJ /F1 11.955 Tf 10.09 0 Td[(=1.0).Whiletheexactanalyticalsolutionpresentedby GuyonnetandNeville ( 2004 ),the Domenico ( 1987 )solutionwasalmostentirelyincorrect.DuringoptimizationwhenparametersthatcanaffectthePecletnumberofasystemareunknown(e.g.R,Vp),itwouldbeconsideredunwiseifthesolutionlostaccuracyforcriticalcaseswhereinthecorrectsolutionmaylie.Itisinagreementwithotherauthors( GuyonnetandNeville 2004 ; Srinivasanetal. 2007 )thatanexactanalyticalsolutioninthiscasewouldbenecessaryandsupportedbytheresultsplottedinFigure 4-1 .Afterhavingevidencethatthe Domenico ( 1987 )solutionwouldresultinincorrecttransportforthegivenconditionsofnumericalandeldsiteanalysis,particularlywhenconsideringdatathatismosttellingofthesourcebehavior,the GuyonnetandNeville ( 2004 )solutionwasultimatelyusedforallanalyses. 4.4OptimizationandParameterizationofSourceStrengthFunctionsonHistoricalDataSets 4.4.1IndividualWellFitsCoveredindetailinSection 3.2.1 ,FortLewisisalargeTCEcontaminatedsitenearTacoma,Washington.Usingdatafromtheextensivemonitoringnetworkpresentatthe 53

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1e-050.00010.0010.010.110100200300400500 C=C0 Easting(m) MT3DMS5yrs10yrs20yrs40yrsAAnalyticalsolutionpresentedby GuyonnetandNeville ( 2004 ) 1e-050.00010.0010.010.110100200300400500 C=C0 Easting(m) MT3DMS5yrs10yrs20yrs40yrsBAnalyticalsolutionpresentedby Domenico ( 1987 ) Figure4-1.Comparisonof GuyonnetandNeville ( 2004 )and Domenico ( 1987 )tonumerical(MT3D)solutionusing)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,lnk=0.5,h=5mandq0.01m/day 54

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11.21.41.61.822.22.405001000150020002500300035004000 Optimum)]TJ ET Q BT /F1 11.955 Tf 182.91 -247.18 Td[(DistancefromSource(m) Figure4-2.Optimum)]TJ /F1 11.955 Tf 10.1 0 Td[(valueforindividualwellhistoriesatFortLewis,showingclusteringofcertainvaluesof)]TJ /F1 11.955 Tf 10.1 0 Td[(nearsourcelocation.Allparameterswereheldconstantpersitemeasuredcharacteristics site,sourceandowparameterswerecalculatedviageneticalgorithmoptimizationusingparameterrangesshowninTable 4-2 and 4-3 .Inanattempttounderstandanyspatialtrendingof)]TJ /F1 11.955 Tf 6.78 0 Td[(,individualwellhistoriesweretbychangingoptimum)]TJ /F1 11.955 Tf 10.1 0 Td[(valuesusingEquation 2 coupledwiththePFSSM.TheresultsofthiseffortareplottedinFigure 4-2 .Whileideallytheentireplumeresponsewouldbetoasinglesetofsourcestrengthfunctionparameters,inrealitythereislikelytobeadistributionofparametersthatbestdescribestheplumeresponseataeldsite.Thisislikelytoholdespeciallytrueforeldsitesthatareheavilyagedorhaveparticularlylargecontaminantplumes.Clusteringorgroupingofoptimum)]TJ /F1 11.955 Tf 10.1 0 Td[(valuesforeachwellhistorycanbeseennearthesourceandtrendingasdistancefromthesourceincreases.Thismightsuggestthatoptimumvaluesof)]TJ /F1 11.955 Tf 10.1 0 Td[(liebetween1.2and2.0,thoughbecauseothersourcestrengthfunctionandtransportcharacteristicsareheldconstant,theeffectsofinaccuraciesintheseparameterscannotbemeasured.Moreover,becausealteringotherparameters 55

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Table4-2.VariablesusedwithminimumandmaximumvaluesforFortLewis,Washington ParameterDescriptionMinimumMaximumUnits VdDarcyvelocity0.011.0meters/dayC0Initialconcentration11100mg/LM0Initialsourcemass60,000120,000kgSwidthSourcewidth10100metersSheightSourceheight550meterst0Timeofrelease19501975RRetardationfactor14xLongitudinaldispersivity1100metersx0x-locationofsourcezone-5050metersy0y-locationofsourcezone-5050metersz0z-locationofsourcezone010meters Table4-3.Sourcestrengthfunctionparameterranges FunctionParameterMinimumMaximumUnits Power-Law,eq. 2 )]TJ /F1 11.955 Tf 67.16 0 Td[(0.0110Vd0.011.0meters/dayC011100mg/LM060,000120,000kgSwidth10100metersSheight550meterst019501975 Streamtube,eq. 2 fc0.011.0ln0.0110ln0.01100Slength10100meters (e.g.M0,Vp)affectstheoptimumvalueof)]TJ /F1 11.955 Tf 6.77 0 Td[(,theseresultscanbeconsideracoarserepresentationofwhatmaybepresentatagiveneldsitesuchasFortLewis.Inreality,thesewellhistorieswouldrequireexaminationchangingmultipleparameters,arguablyallparametersinvolvedintransportandsourcebehaviorchangesovertime.Asthenumberofparametersusedincreases,theabilitytoobserveanyclusteringorgroupingofparametersbecomesanimpossibletask,leadingtothemotivationbehindotheroptimizationtechniques. 56

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4.4.2GeneticAlgorithmResultsThreesubsetsofthedatawereusedinthisanalysis:onethatcontainedallavailabledata,onethatlimitedthemaximumdistancefromtheapparentplumecenterlineto500metersandonethatlimitedthemaximumdistancedowngradientto1000metersandmaximumdistancefromtheapparentplumecenterlineof500meters. 4.4.3FortLewisResultsWhileusingallavailableinformationmayseemdesirable,thismaynotnecessarilybethecase.Whenusingallavailableinformation,wellconcentrationmeasurementsfrommultiplestratigraphicunitsmaybeused.Thiscreatesanissueinthatthereisagreaterdivergenceofsitedatafromtheassumptionsoftheanalyticalsolutionsusedhere(homogeneous,isotropic).Thisissuecanbeseeninalmostallresultsusingelddatafailstoconvergetoauniquesolutionforanydatasetusingdatainthismanner.AsseeninFigure 4-3 ,asthegeneticalgorithmprogresses,thecoefcientofefciency(E)failstoreachavaluehigherthanzero,meaningthatnosetofparametersmodelsallthedatabetterthanthemean.Thispoortisduetotheanalyticalsolution'sinabilitytoaccountforchangesinstratication,temporalshiftsingroundwaterowdirection,orotherphenomenanotspecicallydenedinEquation 2 .Therefore,toimprovethist,thedataweretruncatedspatiallytoallowforconditionsatthesitetomatchmorecloselytheassumptionsoftheanalyticalsolution.Moreover,becausesignicantremediationbeganin1998,thesourcestrengthfunctioncouldnotaccuratelyaccountforthechangeinsourcearchitecturewithoutsignicantlyincreasingthenumberofttingparametersrequired.Itisforthisreasonthatonlydatapriorto1998wereconsideredinfurtheranalysis.Fromthistruncationspatiallyandtemporally,approximately75%oftheavailabledatawereremoved.TheresultsfromthisanalysiscanbeseeninFigure 4-4 .AdditionalparametersplottedsimilarlytoFigures 4-3 and 4-4 canbeseeninAppendix C 57

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1.41.61.822.22.42.62.8050100150200250-0.01-0.0095-0.009-0.0085-0.008-0.0075-0.007 )]TJ /F5 7.97 Tf 6.78 -1.79 Td[(opt E Generation )]TJ /F5 7.97 Tf 6.77 -1.79 Td[(optEAOptimumvalueof)]TJ /F15 9.963 Tf 8.42 0 Td[(andCoefcientofEfciency(E) 11.21.41.61.822.22.42.62.83050100150200250-0.0084-0.0082-0.008-0.0078-0.0076-0.0074-0.0072-0.007-0.0068 ln E Generation lnEBOptimumvalueoflnandCoefcientofEfciency(E) Figure4-3.Comparisonofoptimumvaluesof)]TJ /F1 11.955 Tf 10.1 0 Td[(andlnatFortLewis,consideringalldataavailable 58

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11.21.41.61.822.22.4050100150200250-0.1-0.08-0.06-0.04-0.0200.020.040.06 )]TJ /F5 7.97 Tf 6.78 -1.8 Td[(opt E Generation )]TJ /F5 7.97 Tf 6.77 -1.79 Td[(optEAOptimumvalueof)]TJ /F15 9.963 Tf 8.42 0 Td[(andCoefcientofEfciency(E) 11.21.41.61.822.22.42.62.83050100150200250-0.1-0.08-0.06-0.04-0.0200.020.04 ln E Generation lnEBOptimumvalueoflnandCoefcientofEfciency(E) Figure4-4.Comparisonofoptimumvaluesof)]TJ /F1 11.955 Tf 10.1 0 Td[(andlnatFortLewis,consideringdatalessthan500mfromplumecenterlineandlessthan1kmfromsourcelocation 59

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Withthetruncationofthedatainspaceandtime,thecoefcientofefciencybecomespositive,butfarfromconvergence(E=1).BecauseFortLewisisasiteofimmensesizeandcomplexity,itmaybethattheplumeevolutionsolutionspresentedinChapter 2 areinsufcienttodescribetheeldsettings. 4.4.4HangarKSimilartotheresultsofFortLewis,HangarK(east)wasfoundtobeequallydifculttomodel,withanaveragecoefcientofefciencyof0.05.Theresultsof)]TJ /F1 11.955 Tf 10.1 0 Td[(andM0areplottedinFigure 4-5 4.4.5SyntheticDataInordertotesttheabilityofthemethodologypresentedhere,syntheticdataasdescribedinChapter 3 wascreatedforavarietyofsourcestrengthfunctionsandowelds.Forconsistency,thesameparameterrangeswereusedinthegeneticalgorithmforsyntheticdataaswasusedforFortLewisdata,tabulatedinTables 4-2 and 4-3 .Lessmasswasusedinthesyntheticdataandintheconsideredrangeofinitialmass(10,000kgascomparedto100,000kg).ThiswasdonesothatdomainmodeledinMODFLOW-2005andMT3DMScouldbeofareasonablesize,thusreducingcomputationtime.SamplesfromthedatasetsshowninChapter 3 werechosenspatiallyinordertosimulateasamplingnetworkaeldsite.Thelocationsofthese`wells'canbeseeninFigure 4-6 .UsingthesamplingnetworkshowninFigure 4-6 ,thegeneticalgorithmwasusedtoparameterizeallsyntheticdatasets,usingvariableamountsoftemporalinformation.Theresultsofmostoftheseanalysesweresuccessfulinthatinalmostallcases,thegeneticalgorithmwascapableofparameterizingtheoweldandsourcezonecorrectlywithhighcoefcientsofefciencyinnearlyallcases(E1).Using40yearsoftemporalrecord(a`bestcase'scenario),theresultsforasingleparameterfromasingleaquifer 60

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1.31.41.51.61.71.81.922.12.22.3050100150200250-0.08-0.06-0.04-0.0200.020.040.06 )]TJ /F5 7.97 Tf 6.78 -1.8 Td[(opt E Generation )]TJ /F5 7.97 Tf 6.77 -1.79 Td[(optEAParameter)]TJ ET BT /F1 11.955 Tf 94.52 -533.8 Td[(45005000550060006500700075008000850090009500050100150200250-0.08-0.06-0.04-0.0200.020.040.06 M0 E Generation M0EBParameterM0 Figure4-5.ResultsofgeneticalgorithmoptimizationusingdatafromHangarK 61

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05010015020025030035040060801001201401601801520253035z(m) x(m)y(m)z(m) Figure4-6.Spatiallocationofsamplesfromsyntheticdatausedforparameterizationingeneticalgorithm realizationareplottedinFigure 4-7 whiletheresultsfromallrealizationsofmediacanbeseeninTable 4-4 .Forcasesofhighvarianceofhydraulicconductivity,themeanhydraulicconductivityandthelikelihoodofapreferentialowbeingavailabletosoluteleavingthesourcezonewereincreased.Forthesereasonsitissuggestedthathigheroptimumvelocitiesfromthegeneticalgorithmarestillaccuratetothemediathroughwhichthesolutetravels.Notethateachcasewasrunthreetimes,theaverageoftheseresultsandstandarddeviationofthesethreerunsbeingshowninTable 4-4 .TheresultsfromallanalysesaretabulatedinAppendix A and B .Inadditiontothetabulatedvalues,onecanviewthegivenoutputsoftheoptimizationandvarianceofoutputvaluefortwocasesinFigures 4-8 and 4-9 .Whilethetabulatedandplottedvaluesdeviatefromthegiven(correct)values,theresultantoutputoftheseparametersintheformofmassdischargeshowsthatanaccuratemeasurementofmass 62

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Table4-4.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.09 0 Td[(=1,usinga40year,untruncatedtemporalrecord OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE11.000.001.000.001.000.00)]TJ /F1 11.955 Tf 46.85 0 Td[(11.250.191.090.041.060.01M0(104kg)1.00.930.230.920.130.980.21C=C011.120.031.110.031.130.05Vsrc(m/day)0.030.020.010.020.010.020.00Vp(m/day)0.030.020.010.020.010.020.00R1.01.160.051.200.151.220.10Sw(m)1011.810.6914.762.6114.010.90Sh(m)57.400.486.272.405.230.15X0(m)0.01.670.301.730.112.530.71Y0(m)-125-0.820.97-0.162.212.010.30Z0(m)-25-0.461.420.291.480.830.20 10mE11.000.001.000.001.000.00)]TJ /F1 11.955 Tf 46.85 0 Td[(11.130.101.150.051.040.02M0(104kg)1.01.050.040.990.251.160.10C=C011.140.041.080.011.120.03Vsrc(m/day)0.030.020.000.020.010.020.00Vp(m/day)0.030.020.000.020.010.020.00R1.01.230.061.100.081.180.10Sw(m)1011.470.8911.810.6213.181.35Sh(m)57.220.757.700.836.351.11X0(m)0.02.060.600.960.382.811.28Y0(m)-125-0.090.770.600.52-1.041.46Z0(m)-25-0.571.190.571.53-0.631.23 20mE11.000.001.000.001.000.00)]TJ /F1 11.955 Tf 46.85 0 Td[(11.150.031.170.151.220.21M0(104kg)1.01.030.121.140.060.930.20C=C011.120.041.120.061.100.05Vsrc(m/day)0.030.020.000.020.000.020.01Vp(m/day)0.030.020.000.020.000.020.01R1.01.150.101.210.111.200.13Sw(m)1013.851.0613.002.3714.642.15Sh(m)56.031.165.911.005.881.19X0(m)0.02.171.281.320.771.570.55Y0(m)-1250.960.90-0.652.35-2.012.18Z0(m)-25-1.230.290.380.84-1.040.67 63

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1.21.41.61.822.22.4050100150200250-0.4-0.200.20.40.60.81 )]TJ /F5 7.97 Tf 6.78 -1.79 Td[(opt E Generation )]TJ /F5 7.97 Tf 6.78 -1.79 Td[(optE Figure4-7.ProgressionofgeneticalgorithmusingdatasampledasshowninFigure 4-6 inanaquiferwithcorrelationlengthh=5m,varianceofhydraulicconductivityoflnk=0.5,powerlawsourcestrengthfunctionwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,and40yearsoftemporalrecord dischargeispossibleevenwheninputparametersarenotentirelyaccurate.AdditionalplotsofmassdischargescanbefoundintheAppendix.Becauseinmostcasesthecorrectmassdischargetemporalrecordcouldbefoundusingsyntheticdata,evenwithinaccuraciesininputparameters,itisarguedthatthetechniquesoutlinedhereworkedwellinapracticalway.Moreover,thiswayofviewingthetofparameterscanbeobservedwithasingleparameterofmassdischarge. 64

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68101214161820h(m)0.511.522.5 lnk 11.051.11.151.21.25AValueofCalculated)]TJ /F15 9.963 Tf 8.42 0 Td[(forcaseof)]TJ /F15 9.963 Tf 8.42 0 Td[(=1forallrealizationsofaquifer 68101214161820h(m)0.511.522.5 lnk 00.020.040.060.080.10.120.140.160.180.20.22BStandarddeviationof)]TJ /F15 9.963 Tf 8.42 0 Td[(forcaseof)]TJ /F15 9.963 Tf 8.42 0 Td[(=1forallrealizationsofaquifer Figure4-8.Valueandstandarddeviationof)]TJ /F1 11.955 Tf 10.1 0 Td[(formultiplecasesofvarianceandcorrelationlengthscaleofhydraulicconductivityeld 65

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68101214161820h(m)0.511.522.5 lnk 00.050.10.150.20.250.30.35 Figure4-9.Standarddeviationoflnformultiplecasesofvarianceandcorrelationlengthscaleofhydraulicconductivityeld 00.511.522.533.5051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC Figure4-10.Massdischargeintimeforboundarycondition,actualMT3DMSresult,andoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,h=10mandlnk=1.0 66

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00.511.522.533.5051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC Figure4-11.Massdischargeintimeforboundarycondition,actualMT3DMSresult,andoptimizedparameterresultforthecaseofln=0.7,h=10mandlnk=1.0 67

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CHAPTER5SUMMARYANDFUTUREWORKTheintentionofcharacterizingDNAPLsourcezoneswithsourcestrengthfunctionswasoriginallytoreducetheseeminglyinnitecomplexityfoundateldsiteswithDNAPLcontamination.Thedifcultyinthiseffortliesincreatingareliablemodelorparameterizinganexistingmodeltodescribeobservedphenomena.Thisdifcultyiscompoundedbythelackofinformationontheeldsettings(e.g.changesinow,`adequate'representationofstratication,etc.)andmissingspatio-temporalcontaminantinformation(i.e.newlydiscoveredagedsitescannotbemeasuredatorneartheinitialreleasetime).Inordertocombatthislackofinformation,varioustechniques(outlinedinChapter 4 )weredevelopedtouseallavailableinformationateldsites.Usingsyntheticdata,itwasshownthatusingcoupledsourcestrengthfunctionsandplumeevolutionmodelswithinanoptimizationframeworkallowedforaccurateparameterizationofsourceboundaryconditions(i.e.sourcestrengthfunctionparameters),quantiedbycoefcientofefcienciesclosetoone.Aeldsitewasfoundtobemoredifculttomodelinthisway,butthisdifcultycanbeattributedtotheinabilityoftheplumeevolutionsolutionsand/orsourcestrengthfunctionstoaccuratelymodeleldsettingsathighlyheterogeneoussiteswithcomplexowsandsourcestrengthfunctions.ItisimportanttonotethatcomputationaltechniquessuchasthegeneticalgorithmusedinChapter 4 requirealargenumberofevaluationsofanobjectivefunctioninordertoconvergetoaglobaloptimumresult.Whileusingtheanalyticalsolutionstodescribeplumeevolutionallowedforquickevaluationoftheobjectivefunction,difcultiesarosewhenusingthesesolutionsateldsites.Theresultsindicatethat,atleastconceptually,thetechniquesusedhereworkwellincasesthatfollowcloselytheassumptionsoftheanalyticalsolutionsdemonstratedinChapter 2 andeventhosecasesthatdivergegreatlyfromtheseassumptions,suchasthehighheterogeneitycasesseeninChapter 4 withconstantheadboundaries.However,thelimitationliesmostlyintheinabilityof 68

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analyticalplumeevolutionsolutionstodescribetheavailabledataincaseswheremediaheterogeneityandunaccountablechangesinowandtransportoccur.Foreldsitesthathavesignicantremediationorothermajorperturbationsinsourcebehaviorforwhichanalyticalsolutionsand/orsourcestrengthfunctionscannotaccount,theabilitytoapplyanysimplisticmodeltodescribesourcebehaviorreducessignicantly.Otherunaccountablephenomena,suchasshiftinggroundwaterowdirection,tidalinuence,orwelldrawdowninuencefurtherdivergeeldsettingsfromtheassumptionsmadebytheanalyticalsolutionsmadehereandthereforemustbealtered,asmanyauthorshavedone(e.g. Clearyetal. 1978 ; ZhanandCao 2000 ).ThisrequirementofspecicanalyticalsolutionstomoreaccuratelydescribeaeldsettingcouldnecessitatearevisitingofspecicanalyticalsolutionsthathavesincebeenreplacedbynitedifferenceorniteelementsolutionssuchasthoseusedinChapter 3 .Computationalconstraintscouldalsomeanthatparameterizingsourcestrengthfunctionsforeldsitesthathaveintricateowandtransportcannotyetbemodeledwiththistechnique.Itcanbeinferredthatacalibratedowandtransportmodelcouldbeusedtoparameterizesourcestrengthfunctionstodescribesourcezonesateldsitesusinganoptimizationschemesuchasthegeneticalgorithm,butatgreatcomputationalexpense.Forexample,eachgeneticalgorithmoptimizationeffortonsyntheticdatarequired2.5105objectivefunctionevaluations.Usingthismetric,thiswouldrequireroughly15CPUyearsofcomputationforanMT3DMSsimulationthattook30minutesonaverage.Whilethismayseemlikealargegure,highperformancecomputingcouldmakethispossibletobeperformedinasmallamountofrealtime(e.g.usersofthemodestfacilitiesattheUniversityofFloridahighperformancecomputingcenteruse15CPUyearsonaweeklybasis).Asaccesstohighperformancecomputingresourcesbecomeslessexpensivetoengineersandsitemanagers,thetechniquesoutlinedherecouldbeatoolbywhichtoreducecostwhilemaximizingtheuseofavailable 69

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information,evenatsiteswhereanalyticalsolutionsfailtodescribeeldsettingsordataisinsufcienttocaptureallimportantprocessespresent.ItbecomesclearthatmodelingDNAPLbehaviorinthesubsurfaceisachallengingproblem,evenwhenconsideringsimpliedabstractionsofthemorecomplexreality. 70

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APPENDIXARESULTSFROMGENETICALGORITHMOPTIMIZATION,POWERFUNCTIONSOURCESTRENGTHMODEL TableA-1.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=1,full40yearrecord OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE11.000.001.000.001.000.00)]TJ /F1 11.955 Tf 46.85 0 Td[(11.250.191.090.041.060.01M0(104kg)1.00.930.230.920.130.980.21C=C011.120.031.110.031.130.05Vsrc(m/day)0.030.020.010.020.010.020.00Vp(m/day)0.030.020.010.020.010.020.00R1.01.160.051.200.151.220.10Sw(m)1011.810.6914.762.6114.010.90Sh(m)57.400.486.272.405.230.15X0(m)0.01.670.301.730.112.530.71Y0(m)-125-0.820.97-0.162.212.010.30Z0(m)-25-0.461.420.291.480.830.20 10mE11.000.001.000.001.000.00)]TJ /F1 11.955 Tf 46.85 0 Td[(11.130.101.150.051.040.02M0(104kg)1.01.050.040.990.251.160.10C=C011.140.041.080.011.120.03Vsrc(m/day)0.030.020.000.020.010.020.00Vp(m/day)0.030.020.000.020.010.020.00R1.01.230.061.100.081.180.10Sw(m)1011.470.8911.810.6213.181.35Sh(m)57.220.757.700.836.351.11X0(m)0.02.060.600.960.382.811.28Y0(m)-125-0.090.770.600.52-1.041.46Z0(m)-25-0.571.190.571.53-0.631.23 20mE11.000.001.000.001.000.00)]TJ /F1 11.955 Tf 46.85 0 Td[(11.150.031.170.151.220.21M0(104kg)1.01.030.121.140.060.930.20C=C011.120.041.120.061.100.05Vsrc(m/day)0.030.020.000.020.000.020.01Vp(m/day)0.030.020.000.020.000.020.01R1.01.150.101.210.111.200.13Sw(m)1013.851.0613.002.3714.642.15Sh(m)56.031.165.911.005.881.19X0(m)0.02.171.281.320.771.570.55Y0(m)-1250.960.90-0.652.35-2.012.18Z0(m)-25-1.230.290.380.84-1.040.67 71

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TableA-2.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=2,full40yearrecord OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE11.000.001.000.001.000.00)]TJ /F1 11.955 Tf 46.85 0 Td[(21.160.091.170.061.050.01M0(104kg)1.00.910.010.960.150.940.23C=C011.100.021.120.031.120.06Vsrc(m/day)0.030.020.000.020.000.020.01Vp(m/day)0.030.020.000.020.000.020.01R1.01.160.081.200.041.110.03Sw(m)1012.461.1513.312.3714.161.42Sh(m)57.231.045.971.285.600.73X0(m)0.01.550.252.030.311.901.19Y0(m)-125-0.571.44-0.311.931.531.42Z0(m)-25-0.351.35-0.860.141.190.38 10mE11.000.001.000.001.000.00)]TJ /F1 11.955 Tf 46.85 0 Td[(21.100.111.080.051.120.06M0(104kg)1.01.070.091.120.150.970.10C=C011.100.041.090.041.130.03Vsrc(m/day)0.030.020.000.020.000.020.00Vp(m/day)0.030.020.000.020.000.020.00R1.01.290.031.170.091.220.12Sw(m)1012.200.5012.911.5614.472.60Sh(m)56.010.306.481.085.891.71X0(m)0.01.120.591.310.702.490.89Y0(m)-125-1.651.00-0.380.660.871.24Z0(m)-250.221.27-0.671.30-0.071.20 20mE11.000.001.000.001.000.00)]TJ /F1 11.955 Tf 46.85 0 Td[(21.190.051.230.141.200.21M0(104kg)1.01.150.091.040.050.810.22C=C011.110.031.130.011.090.05Vsrc(m/day)0.030.020.000.020.000.010.01Vp(m/day)0.030.020.000.020.000.010.01R1.01.200.151.270.051.210.12Sw(m)1014.401.2414.741.8813.982.62Sh(m)55.661.365.240.986.641.87X0(m)0.01.750.812.461.381.050.20Y0(m)-1250.092.12-1.720.68-2.231.92Z0(m)-25-1.050.350.041.170.121.45 72

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TableA-3.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=3,full40yearrecord OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE11.000.001.000.001.000.00)]TJ /F1 11.955 Tf 46.85 0 Td[(31.130.061.160.071.050.02M0(104kg)1.00.950.260.920.190.930.22C=C011.130.041.130.021.120.06Vsrc(m/day)0.030.020.000.020.010.020.00Vp(m/day)0.030.020.000.020.010.020.00R1.01.100.061.160.051.110.03Sw(m)1013.872.6912.512.1512.671.79Sh(m)56.401.476.981.586.531.29X0(m)0.02.050.362.080.241.741.07Y0(m)-1250.792.190.650.861.061.29Z0(m)-250.311.21-1.270.700.411.22 10mE11.000.001.000.001.000.00)]TJ /F1 11.955 Tf 46.85 0 Td[(31.060.051.050.021.120.06M0(104kg)1.01.070.091.070.090.970.10C=C011.100.041.060.021.130.03Vsrc(m/day)0.030.020.000.020.010.020.00Vp(m/day)0.030.020.000.020.010.020.00R1.01.220.121.230.111.220.12Sw(m)1012.500.8611.810.2314.472.60Sh(m)56.090.376.421.135.891.71X0(m)0.01.490.841.090.702.490.89Y0(m)-125-1.161.53-1.160.570.871.24Z0(m)-250.261.23-0.481.21-0.071.20 20mE11.000.001.000.001.000.00)]TJ /F1 11.955 Tf 46.85 0 Td[(31.150.031.230.141.100.05M0(104kg)1.01.130.081.040.050.890.18C=C011.100.021.130.011.080.01Vsrc(m/day)0.030.020.000.020.000.010.00Vp(m/day)0.030.020.000.020.000.010.00R1.01.120.091.270.051.080.04Sw(m)1014.031.0614.741.8811.270.45Sh(m)56.251.155.240.988.290.37X0(m)0.01.700.762.461.381.260.34Y0(m)-1250.351.74-1.720.680.090.42Z0(m)-25-1.300.320.041.170.471.38 73

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TableA-4.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=1,usinga5yeartemporalrecord OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE11.000.000.990.000.940.04)]TJ /F1 11.955 Tf 46.85 0 Td[(11.840.561.130.052.140.25M0(104kg)1.01.030.131.340.081.300.08C=C011.200.001.150.071.140.08Vsrc(m/day)0.030.020.000.030.000.010.01Vp(m/day)0.030.020.000.030.000.010.01R1.01.430.271.000.001.130.18Sw(m)1012.381.118.731.719.290.99Sh(m)53.110.578.442.219.610.40X0(m)0.00.000.000.000.000.160.22Y0(m)-125-123.893.75-126.430.91-128.900.87Z0(m)-25-25.130.65-26.650.16-27.650.29 10mE10.970.040.970.010.940.00)]TJ /F1 11.955 Tf 46.85 0 Td[(11.950.631.170.111.240.03M0(104kg)1.01.260.181.370.011.180.23C=C011.190.010.980.120.860.03Vsrc(m/day)0.030.030.030.020.000.010.00Vp(m/day)0.030.030.030.020.000.010.00R1.01.570.161.000.001.000.00Sw(m)108.581.5514.001.1719.210.39Sh(m)55.101.138.512.0910.000.00X0(m)0.00.010.010.000.000.000.00Y0(m)-125-124.383.30-126.361.43-126.780.42 Z0(m)-25-25.030.02-24.491.46-22.600.1020mE11.000.000.970.000.960.00)]TJ /F1 11.955 Tf 46.85 0 Td[(12.350.472.190.401.340.08M0(104kg)1.00.960.310.960.230.810.22C=C011.050.111.070.131.200.00Vsrc(m/day)0.030.010.010.010.010.010.01Vp(m/day)0.030.010.010.010.010.010.01R1.01.370.141.070.091.000.00Sw(m)1013.060.9412.670.249.211.39Sh(m)54.150.825.000.965.030.91X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.290.14-128.051.48-121.430.32Z0(m)-25-25.660.93-24.980.02-26.170.37 74

PAGE 75

TableA-5.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=2,usinga5yeartemporalrecord OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE11.000.000.980.010.960.02)]TJ /F1 11.955 Tf 46.85 0 Td[(22.050.522.070.432.220.32M0(104kg)1.01.130.290.910.181.270.04C=C011.000.141.170.041.100.14Vsrc(m/day)0.030.040.020.020.010.020.00Vp(m/day)0.030.040.020.020.010.020.00R1.01.530.191.010.001.000.00Sw(m)1012.310.157.871.4612.154.30Sh(m)53.660.648.232.487.833.07X0(m)0.00.000.000.000.000.000.00Y0(m)-125-126.801.85-126.341.37-128.952.53Z0(m)-25-25.040.07-25.511.40-26.691.21 10mE11.000.000.980.000.940.00)]TJ /F1 11.955 Tf 46.85 0 Td[(21.520.311.100.071.470.35M0(104kg)1.01.180.181.390.000.910.32C=C010.900.000.900.000.990.15Vsrc(m/day)0.030.050.010.030.000.010.01Vp(m/day)0.030.050.010.030.000.010.01R1.01.270.031.000.001.000.00Sw(m)1012.251.4713.700.4916.953.19Sh(m)53.820.4210.000.0010.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-124.730.39-125.380.00-127.851.26Z0(m)-25-24.990.00-25.951.58-22.620.08 20mE11.000.000.980.000.960.00)]TJ /F1 11.955 Tf 46.85 0 Td[(21.600.282.040.562.020.46M0(104kg)1.01.100.210.970.290.940.12C=C011.170.041.140.091.030.12Vsrc(m/day)0.030.030.010.020.010.020.00Vp(m/day)0.030.030.010.020.010.020.00R1.01.560.091.000.001.000.00Sw(m)1011.622.6011.671.387.350.37Sh(m)55.052.477.331.908.041.45X0(m)0.00.000.000.000.000.000.00Y0(m)-125-124.553.64-126.651.64-124.331.85Z0(m)-25-25.600.94-25.511.87-26.870.59 75

PAGE 76

TableA-6.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=3,usinga5yeartemporalrecord OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE11.000.000.980.000.970.00)]TJ /F1 11.955 Tf 46.85 0 Td[(31.800.431.570.261.230.07M0(104kg)1.00.840.170.860.131.220.07C=C011.200.001.100.140.950.06Vsrc(m/day)0.030.030.010.040.010.040.00Vp(m/day)0.030.030.010.040.010.040.00R1.01.270.181.000.001.000.00Sw(m)109.870.8113.882.349.860.84Sh(m)55.171.274.180.539.990.01X0(m)0.00.000.000.000.000.000.00Y0(m)-125-124.682.80-126.392.04-126.650.86Z0(m)-25-25.651.52-25.960.63-27.800.10 10mE11.000.000.970.010.940.01)]TJ /F1 11.955 Tf 46.85 0 Td[(32.170.471.300.261.370.44M0(104kg)1.01.250.111.320.091.180.15C=C010.920.030.990.151.080.16Vsrc(m/day)0.030.050.000.040.010.030.01Vp(m/day)0.030.050.000.040.010.030.01R1.01.510.121.010.011.000.00Sw(m)1014.611.2214.972.2615.703.54Sh(m)54.180.957.492.3410.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.190.07-125.800.59-126.414.07Z0(m)-25-25.060.13-26.051.28-22.700.02 20mE11.000.000.960.020.950.00)]TJ /F1 11.955 Tf 46.85 0 Td[(32.390.531.830.831.470.26M0(104kg)1.01.100.181.170.171.190.16C=C011.030.131.100.141.200.00Vsrc(m/day)0.030.050.030.030.020.050.01Vp(m/day)0.030.050.030.030.020.050.01R1.01.570.361.060.051.000.00Sw(m)1010.102.5211.012.938.831.93Sh(m)54.150.836.952.215.341.25X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.680.68-128.122.48-126.173.50Z0(m)-25-25.030.03-25.791.08-26.190.32 76

PAGE 77

TableA-7.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=1,usinga5yeartemporalrecordbetween10and15yearspostinitialrelease OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.990.010.950.000.920.01)]TJ /F1 11.955 Tf 46.85 0 Td[(11.190.131.710.541.900.09M0(104kg)1.01.170.221.190.140.990.20C=C011.050.120.980.201.160.03Vsrc(m/day)0.030.020.010.020.000.010.00Vp(m/day)0.030.020.010.020.000.010.00R1.01.290.061.000.001.000.00Sw(m)1010.101.8610.982.369.430.37Sh(m)57.631.008.701.2410.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-123.992.33-126.630.37-127.050.82Z0(m)-25-26.210.33-26.481.05-27.900.32 10mE11.000.000.940.010.870.01)]TJ /F1 11.955 Tf 46.85 0 Td[(11.540.341.780.831.280.11M0(104kg)1.01.260.100.990.201.180.06C=C011.050.121.160.051.200.00Vsrc(m/day)0.030.010.000.010.010.010.00Vp(m/day)0.030.010.000.010.010.010.00R1.01.270.051.000.001.000.00Sw(m)109.671.1610.081.8414.822.40Sh(m)59.800.2810.000.019.061.33X0(m)0.00.000.000.000.000.000.00Y0(m)-125-126.701.11-128.491.63-130.122.18Z0(m)-25-25.930.08-25.930.66-22.590.51 20mE10.990.000.960.010.930.00)]TJ /F1 11.955 Tf 46.85 0 Td[(11.070.061.060.011.160.16M0(104kg)1.01.320.091.340.031.180.25C=C010.850.071.000.141.050.15Vsrc(m/day)0.030.020.000.020.000.030.01Vp(m/day)0.030.020.000.020.000.030.01R1.01.130.111.000.001.000.00Sw(m)1012.890.339.340.4210.572.00Sh(m)57.920.559.141.226.360.59X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.510.09-126.291.90-122.140.61Z0(m)-25-26.560.00-27.020.07-26.700.20 77

PAGE 78

TableA-8.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=2,usinga5yeartemporalrecordbetween10and15yearspostinitialrelease OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.990.000.950.000.910.00)]TJ /F1 11.955 Tf 46.85 0 Td[(21.940.451.750.231.720.46M0(104kg)1.00.980.181.110.110.970.23C=C011.200.001.110.131.190.00Vsrc(m/day)0.030.020.000.020.000.020.01Vp(m/day)0.030.020.000.020.000.020.01R1.01.170.071.000.001.000.00Sw(m)1010.312.467.240.888.110.22Sh(m)56.191.569.610.299.830.12X0(m)0.00.000.000.000.000.000.00Y0(m)-125-127.881.55-127.730.16-128.390.43Z0(m)-25-26.700.19-27.320.17-27.600.03 10mE10.990.000.930.010.870.01)]TJ /F1 11.955 Tf 46.85 0 Td[(21.670.471.420.111.510.21M0(104kg)1.00.930.171.020.231.060.32C=C011.200.001.100.151.190.02Vsrc(m/day)0.030.020.010.020.000.010.00Vp(m/day)0.030.020.010.020.000.010.00R1.01.180.121.000.001.000.00Sw(m)109.923.1512.152.7512.731.07Sh(m)57.312.159.830.2310.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-127.701.40-127.291.19-130.320.81Z0(m)-25-26.520.40-26.550.52-22.940.10 20mE10.990.000.950.010.940.01)]TJ /F1 11.955 Tf 46.85 0 Td[(21.480.151.690.241.400.11M0(104kg)1.00.990.281.100.241.280.04C=C011.170.041.120.111.030.13Vsrc(m/day)0.030.020.010.020.010.040.00Vp(m/day)0.030.020.010.020.010.040.00R1.01.250.101.000.001.000.00Sw(m)107.370.818.470.477.972.11Sh(m)58.851.018.900.808.601.98X0(m)0.00.000.000.000.000.000.00Y0(m)-125-128.190.73-123.851.40-122.501.17Z0(m)-25-26.520.09-27.400.31-26.910.32 78

PAGE 79

TableA-9.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=3,usinga5yeartemporalrecordbetween10and15yearspostinitialrelease OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.990.000.940.010.900.00)]TJ /F1 11.955 Tf 46.85 0 Td[(32.040.721.610.342.020.03M0(104kg)1.01.020.251.180.161.180.19C=C011.200.001.160.031.030.07Vsrc(m/day)0.030.020.010.040.010.020.00Vp(m/day)0.030.020.010.040.010.020.00R1.01.110.101.000.001.000.00Sw(m)109.151.938.393.359.360.43Sh(m)56.121.028.591.999.870.10X0(m)0.00.000.000.000.000.000.00Y0(m)-125-127.971.42-125.362.47-128.970.00Z0(m)-25-26.790.33-26.310.94-27.440.09 10mE10.990.000.930.000.880.00)]TJ /F1 11.955 Tf 46.85 0 Td[(31.600.301.580.151.380.13M0(104kg)1.01.340.061.050.141.080.13C=C010.890.231.170.041.200.00Vsrc(m/day)0.030.030.000.020.000.020.00Vp(m/day)0.030.030.000.020.000.020.00R1.01.390.081.000.001.000.00Sw(m)1013.702.949.130.7312.500.00Sh(m)57.092.8910.000.0010.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.650.03-128.930.07-130.050.14Z0(m)-25-26.350.32-25.780.16-23.010.05 20mE10.990.000.950.000.930.00)]TJ /F1 11.955 Tf 46.85 0 Td[(31.180.091.490.341.830.59M0(104kg)1.01.250.031.090.081.340.06C=C011.190.011.040.130.990.25Vsrc(m/day)0.030.040.010.030.010.050.01Vp(m/day)0.030.040.010.030.010.050.01R1.01.340.211.000.001.000.00Sw(m)107.340.397.290.3012.061.03Sh(m)57.870.469.210.715.231.46X0(m)0.00.000.000.000.000.000.00Y0(m)-125-128.320.61-124.602.66-121.400.97Z0(m)-25-26.630.12-27.010.15-26.480.54 79

PAGE 80

TableA-10.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=1,usinga5yeartemporalrecordbetween20and40yearspostinitialrelease OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.990.000.950.01)]TJ /F1 11.955 Tf 46.85 0 Td[(11.110.101.190.08M0(104kg)1.01.150.111.040.05C=C011.070.131.140.09Vsrc(m/day)0.030.020.000.020.00Vp(m/day)0.030.020.000.020.00R1.01.230.061.000.00Sw(m)1010.141.6910.641.73Sh(m)58.340.349.181.16X0(m)0.00.000.000.000.00Y0(m)-125-126.751.17-126.650.03Z0(m)-25-26.040.03-27.100.24 10mE10.990.010.940.000.900.01)]TJ /F1 11.955 Tf 46.85 0 Td[(11.080.121.150.081.070.07M0(104kg)1.01.180.101.180.271.110.05C=C011.200.001.010.131.080.03Vsrc(m/day)0.030.020.000.010.000.010.00Vp(m/day)0.030.020.000.010.000.010.00R1.01.220.031.000.001.000.00Sw(m)108.950.7313.931.6915.901.63Sh(m)59.200.6110.000.0010.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-127.660.98-126.830.79-128.561.95Z0(m)-25-25.780.04-25.020.03-22.900.12 20mE10.980.000.960.000.940.01)]TJ /F1 11.955 Tf 46.85 0 Td[(11.090.121.070.091.100.11M0(104kg)1.01.190.131.180.091.230.15C=C011.190.011.130.101.180.02Vsrc(m/day)0.030.020.000.020.000.030.01Vp(m/day)0.030.020.000.020.000.030.01R1.01.220.101.000.001.000.00Sw(m)109.391.639.692.039.422.11Sh(m)58.720.619.840.227.681.89X0(m)0.00.000.000.000.000.000.00Y0(m)-125-122.991.54-123.361.36-122.451.53Z0(m)-25-26.170.23-26.670.13-26.900.48 80

PAGE 81

TableA-11.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=2,usinga5yeartemporalrecordbetween20and40yearspostinitialrelease OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.980.000.950.000.920.01)]TJ /F1 11.955 Tf 46.85 0 Td[(21.600.221.920.181.850.07M0(104kg)1.01.270.041.110.141.240.10C=C011.190.011.160.031.110.06Vsrc(m/day)0.030.030.000.020.000.020.00Vp(m/day)0.030.030.000.020.000.020.00R1.01.160.041.000.001.000.00Sw(m)107.680.739.352.289.901.95Sh(m)57.700.749.061.338.201.43X0(m)0.00.000.000.000.000.000.00Y0(m)-125-128.780.28-126.830.30-128.781.20Z0(m)-25-25.820.60-26.850.09-27.260.12 10mE10.980.010.940.000.900.00)]TJ /F1 11.955 Tf 46.85 0 Td[(21.500.111.820.601.480.08M0(104kg)1.01.280.061.040.171.100.21C=C011.200.001.200.001.150.07Vsrc(m/day)0.030.020.000.010.000.010.00Vp(m/day)0.030.020.000.010.000.010.00R1.01.190.031.000.001.000.00Sw(m)107.250.4010.451.559.371.17Sh(m)59.230.7010.000.0010.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-128.190.55-128.390.83-129.560.48Z0(m)-25-25.890.05-25.000.01-22.830.13 20mE10.980.010.950.000.940.01)]TJ /F1 11.955 Tf 46.85 0 Td[(22.000.561.450.091.570.03M0(104kg)1.00.950.111.230.131.240.07C=C011.190.021.170.020.960.20Vsrc(m/day)0.030.020.000.020.000.040.00Vp(m/day)0.030.020.000.020.000.040.00R1.01.250.031.000.001.000.00Sw(m)108.260.386.951.007.711.26Sh(m)58.880.909.160.347.382.31X0(m)0.00.000.000.000.000.000.00Y0(m)-125-127.800.96-123.552.65-122.841.56Z0(m)-25-26.330.15-26.700.19-26.690.48 81

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TableA-12.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofpowerlawmodelwith)]TJ /F1 11.955 Tf 10.1 0 Td[(=3,usinga5yeartemporalrecordbetween20and40yearspostinitialrelease OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.980.000.950.000.920.01)]TJ /F1 11.955 Tf 46.85 0 Td[(32.050.062.000.101.800.21M0(104kg)1.01.240.041.140.101.170.27C=C011.180.011.200.001.030.11Vsrc(m/day)0.030.030.000.030.000.030.01Vp(m/day)0.030.030.000.030.000.030.01R1.01.150.031.000.001.000.00Sw(m)107.710.746.460.566.831.40Sh(m)57.690.7010.000.009.181.16X0(m)0.00.000.000.000.000.000.00Y0(m)-125-126.213.11-127.340.42-127.800.99Z0(m)-25-26.210.01-26.730.11-27.360.03 10mE10.970.000.940.000.890.01)]TJ /F1 11.955 Tf 46.85 0 Td[(31.980.171.970.201.720.23M0(104kg)1.01.210.181.300.051.190.12C=C011.140.011.140.021.120.06Vsrc(m/day)0.030.020.000.020.000.020.00Vp(m/day)0.030.020.000.020.000.020.00R1.01.190.061.000.001.000.00Sw(m)109.981.8710.810.8711.045.15Sh(m)56.881.7710.000.008.162.60X0(m)0.00.000.000.000.000.010.01Y0(m)-125-127.921.49-128.321.20-128.530.75Z0(m)-25-26.350.64-24.980.03-22.810.05 20mE10.980.000.950.010.930.00)]TJ /F1 11.955 Tf 46.85 0 Td[(31.890.262.110.301.830.48M0(104kg)1.01.280.091.300.101.130.04C=C011.190.021.170.031.100.14Vsrc(m/day)0.030.030.000.030.010.040.00Vp(m/day)0.030.030.000.030.010.040.00R1.01.200.091.000.001.000.00Sw(m)108.900.588.601.737.111.06Sh(m)56.620.859.041.314.570.48X0(m)0.00.000.000.000.000.000.00Y0(m)-125-127.701.80-122.581.33-122.411.02Z0(m)-25-26.890.47-26.650.09-26.790.42 82

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APPENDIXBRESULTSFROMGENETICALGORITHMOPTIMIZATION,EQUILIBRIUMSTREAMTUBEMODEL TableB-1.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.4,full40yearrecord OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.990.000.950.020.870.10ln0.40.400.040.390.060.620.15ln2.922.360.072.770.123.000.00fc10.860.040.770.180.880.05Vp(m/day)0.030.030.000.050.000.080.00R1.01.220.091.000.001.070.10Sl(m)1018.011.0818.011.6319.960.06Sw(m)1015.032.3113.213.7611.271.93Sh(m)56.700.439.450.199.930.09X0(m)0.00.000.000.000.000.080.11Y0(m)-125-125.360.03-125.560.15-127.441.46Z0(m)-25-25.640.52-26.870.51-26.392.08 10mE10.990.000.960.000.910.00ln0.40.370.010.400.040.580.07ln2.922.430.122.840.103.000.00fc10.870.030.790.030.960.02Vp(m/day)0.030.030.000.060.000.090.00R1.01.060.051.000.001.000.00Sl(m)1016.732.3618.370.4020.000.00Sw(m)1014.861.1416.350.1019.820.13Sh(m)57.620.5810.000.0010.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.510.24-125.750.06-127.220.52Z0(m)-25-25.320.46-26.480.30-22.630.06 20mE10.990.000.970.000.930.01ln0.40.330.040.430.040.540.08ln2.922.530.212.810.083.000.00fc10.950.050.880.050.750.07Vp(m/day)0.030.030.000.050.000.080.00R1.01.260.091.000.001.000.00Sl(m)1015.343.1117.470.9420.000.00Sw(m)1014.381.5313.771.7813.600.80Sh(m)56.830.308.240.787.430.53X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.340.12-125.040.03-124.240.19Z0(m)-25-26.210.14-26.960.19-26.690.18 83

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TableB-2.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.7,full40yearrecord OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.990.000.970.000.950.00ln0.70.770.070.840.010.830.00ln2.752.210.242.660.302.950.05fc10.980.030.950.060.850.07Vp(m/day)0.030.030.000.050.000.090.01R1.01.190.041.030.041.000.00Sl(m)1016.653.9615.454.2019.890.15Sw(m)1012.550.0510.552.1413.441.32Sh(m)57.050.579.660.429.720.13X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.510.09-125.700.30-126.650.37Z0(m)-25-26.010.33-26.700.47-27.770.15 10mE10.990.000.960.000.930.00ln0.70.700.090.770.100.860.01ln2.752.420.092.760.132.990.01fc10.900.010.850.020.960.01Vp(m/day)0.030.030.000.060.010.100.00R1.01.290.181.000.001.000.00Sl(m)1014.051.3316.002.5020.000.00Sw(m)1014.711.2015.640.8919.210.11Sh(m)57.330.499.990.0110.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.410.03-125.820.10-127.440.22Z0(m)-25-26.170.32-26.660.06-22.540.08 20mE10.990.000.970.000.940.00ln0.70.770.080.760.090.860.04ln2.752.130.032.570.162.940.04fc11.000.000.950.060.790.03Vp(m/day)0.030.030.000.050.000.090.00R1.01.250.011.000.001.000.00Sl(m)1018.101.1818.151.3419.990.01Sw(m)1012.510.0112.190.4512.530.03Sh(m)57.930.168.690.477.740.33X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.780.61-124.990.15-124.290.10Z0(m)-25-26.520.04-27.130.14-27.090.37 84

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TableB-3.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=1.0,full40yearrecord OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE11.000.000.970.000.950.00ln1.01.020.081.300.181.200.02ln2.502.220.342.220.162.570.03fc10.940.050.970.030.830.00Vp(m/day)0.030.030.000.050.000.090.00R1.01.190.061.010.011.000.00Sl(m)1013.834.4114.803.3219.370.89Sw(m)1012.780.2512.040.6614.380.00Sh(m)57.180.199.010.709.920.05X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.360.09-125.730.25-126.560.00Z0(m)-25-26.280.17-27.180.44-27.620.01 10mE10.960.050.960.000.930.00ln1.01.330.481.340.191.310.17ln2.502.580.402.330.102.850.02fc10.920.110.910.050.960.03Vp(m/day)0.030.040.000.060.000.110.00R1.01.280.091.000.001.000.00Sl(m)1013.953.8316.152.1518.001.13Sw(m)1012.703.0816.500.3519.840.22Sh(m)57.691.009.990.0110.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-126.831.93-125.920.52-127.240.56Z0(m)-25-25.560.48-26.580.03-22.580.02 20mE10.990.000.970.000.940.01ln1.01.030.151.050.101.380.24ln2.502.540.342.720.192.840.04fc10.940.080.930.050.910.03Vp(m/day)0.030.030.000.050.000.100.00R1.01.460.061.000.001.000.00Sl(m)1010.324.3212.514.5218.491.08Sw(m)1013.180.9912.060.6310.831.36Sh(m)57.530.439.430.457.861.53X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.210.07-125.210.12-124.380.24Z0(m)-25-26.220.18-26.830.25-27.010.40 85

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TableB-4.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.4,usinga5yeartemporalrecord OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE11.000.000.950.050.960.01ln0.40.200.070.790.381.090.87ln2.922.960.002.950.063.000.00fc10.960.050.810.200.920.05Vp(m/day)0.030.030.000.040.010.090.00R1.01.500.181.060.051.000.00Sl(m)1018.370.8019.700.0819.990.02Sw(m)1014.053.4813.515.0112.571.54Sh(m)54.380.779.460.689.710.41X0(m)0.00.000.000.000.000.000.00Y0(m)-125-127.142.95-125.530.47-126.390.63Z0(m)-25-24.720.43-24.450.70-27.700.29 10mE11.000.000.980.000.940.00ln0.40.890.540.780.800.520.21ln2.922.940.082.990.013.000.00fc11.000.000.920.080.910.03Vp(m/day)0.030.030.000.050.010.100.01R1.01.230.221.000.001.000.00Sl(m)1019.230.8319.680.3319.370.88Sw(m)1013.130.6415.001.7719.170.28Sh(m)56.252.039.960.0610.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.140.07-125.870.54-126.850.63Z0(m)-25-26.200.87-25.921.75-22.430.03 20mE11.000.000.980.010.960.00ln0.40.390.090.310.180.150.00ln2.922.600.402.990.012.980.03fc10.990.000.930.050.790.03Vp(m/day)0.030.030.000.040.010.090.00R1.01.750.111.010.011.000.00Sl(m)1017.731.4119.350.9120.000.01Sw(m)1012.982.6814.451.5710.971.09Sh(m)54.180.538.640.899.061.32X0(m)0.00.000.000.000.000.000.00Y0(m)-125-124.900.50-126.781.76-124.600.28Z0(m)-25-25.160.21-24.432.27-25.782.20 86

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TableB-5.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.7,usinga5yeartemporalrecord OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE11.000.000.990.000.960.00ln0.71.060.491.560.151.140.30ln2.752.630.522.990.003.000.00fc10.950.041.000.010.850.07Vp(m/day)0.030.030.000.040.010.080.01R1.01.350.111.000.001.000.00Sl(m)1019.840.1219.610.3620.000.00Sw(m)1011.700.9210.650.7914.680.46Sh(m)56.680.309.530.389.610.06X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.240.39-125.700.31-127.480.37Z0(m)-25-25.071.27-27.620.13-27.880.06 10mE11.000.000.980.000.940.00ln0.71.490.201.380.620.490.19ln2.752.980.022.870.172.960.03fc10.970.020.980.020.900.03Vp(m/day)0.030.030.000.050.000.120.01R1.01.270.211.000.001.000.00Sl(m)1018.481.6518.391.9417.881.28Sw(m)1014.110.4714.402.2118.890.53Sh(m)56.320.699.980.0210.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.360.14-125.800.28-126.830.38Z0(m)-25-26.210.36-27.350.13-22.470.02 20mE11.000.000.980.000.960.01ln0.70.790.161.060.290.430.28ln2.752.830.052.920.023.000.00fc10.990.010.980.010.850.11Vp(m/day)0.030.030.000.040.000.090.00R1.01.290.271.000.001.000.00Sl(m)1014.244.0519.150.5916.983.65Sw(m)1012.331.2611.501.1710.411.84Sh(m)54.380.419.430.388.810.50X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.380.26-125.210.09-124.190.31Z0(m)-25-25.170.17-27.500.13-27.530.28 87

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TableB-6.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=1.0,usinga5yeartemporalrecord OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.970.040.970.020.940.03ln1.01.610.991.760.032.270.57ln2.502.890.082.800.163.000.00fc10.990.010.920.100.870.08Vp(m/day)0.030.040.000.050.000.100.00R1.01.690.141.000.001.000.00Sl(m)1018.051.8915.863.0619.280.97Sw(m)1012.500.2811.841.1115.012.34Sh(m)55.680.859.300.149.740.21X0(m)0.00.010.010.000.000.000.00Y0(m)-125-125.460.36-124.920.51-126.630.45Z0(m)-25-26.321.35-27.250.49-27.710.27 10mE11.000.000.980.000.940.00ln1.02.110.272.030.101.250.29ln2.502.900.122.870.053.000.01fc10.990.011.000.000.910.04Vp(m/day)0.030.040.000.060.010.120.01R1.01.420.101.000.001.000.00Sl(m)1018.491.3218.331.4719.660.47Sw(m)1011.970.7613.400.6919.510.32Sh(m)56.511.8510.000.0010.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.700.97-125.480.09-127.120.45Z0(m)-25-26.100.89-27.130.06-24.112.28 20mE11.000.000.980.000.950.01ln1.01.640.101.920.261.370.26ln2.502.680.032.800.123.000.00fc11.000.010.990.010.740.05Vp(m/day)0.030.030.000.050.000.090.00R1.01.330.161.000.001.000.00Sl(m)1016.311.2017.191.7620.000.00Sw(m)1014.001.0711.850.9213.051.77Sh(m)55.210.809.640.288.201.74X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.750.63-125.340.45-124.510.27Z0(m)-25-24.550.81-27.260.08-26.711.22 88

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TableB-7.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.4,usinga5yeartemporalrecordbetween10and15yearspostinitialrelease OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.990.000.960.000.900.00ln0.40.510.070.740.131.550.00ln2.922.520.272.800.172.980.02fc10.900.070.930.080.990.01Vp(m/day)0.030.030.000.050.000.090.00R1.01.130.081.000.001.000.00Sl(m)1014.682.1616.262.3019.740.18Sw(m)1013.470.6812.191.1716.250.00Sh(m)58.440.459.210.569.490.06X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.510.03-125.730.25-126.870.07Z0(m)-25-26.260.02-27.140.16-27.430.06 10mE10.990.010.940.010.880.00ln0.40.770.560.910.460.710.08ln2.922.390.212.750.023.000.00fc10.910.100.920.071.000.00Vp(m/day)0.030.030.000.050.000.090.00R1.01.070.051.000.001.000.00Sl(m)1016.053.2717.990.8820.000.00Sw(m)1015.241.8615.940.9820.000.00Sh(m)58.950.579.980.0310.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.340.17-126.020.03-126.610.07Z0(m)-25-26.100.22-26.550.03-23.300.11 20mE10.990.000.960.000.910.00ln0.40.410.090.350.131.240.37ln2.922.830.172.880.043.000.00fc10.930.070.840.051.000.00Vp(m/day)0.030.030.000.050.000.100.00R1.01.190.051.000.001.000.00Sl(m)1010.651.9617.130.8020.000.00Sw(m)1014.381.5312.660.2212.820.45Sh(m)57.930.679.210.067.440.18X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.360.09-125.020.06-124.310.19Z0(m)-25-26.490.08-27.010.09-26.530.07 89

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TableB-8.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.7,usinga5yeartemporalrecordbetween10and15yearspostinitialrelease OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.990.010.950.000.850.08ln0.70.720.150.860.051.990.62ln2.752.420.232.690.242.690.09fc10.880.160.820.090.980.03Vp(m/day)0.030.030.000.050.000.100.00R1.01.300.161.000.001.000.00Sl(m)1014.803.5217.272.4318.510.14Sw(m)1011.882.3411.481.5215.000.88Sh(m)58.190.8410.000.0010.000.00X0(m)0.00.000.000.000.000.130.19Y0(m)-125-125.460.06-126.090.07-129.123.00Z0(m)-25-25.710.53-26.910.25-26.990.67 10mE10.990.000.940.000.890.00ln0.70.720.191.190.250.940.01ln2.752.540.402.620.183.000.00fc10.790.090.990.011.000.00Vp(m/day)0.030.030.000.050.000.110.00R1.01.130.111.000.001.000.00Sl(m)1012.633.8414.072.1620.000.00Sw(m)1014.750.4915.980.4719.640.09Sh(m)59.340.2810.000.0010.000.00X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.430.03-126.240.28-126.850.21Z0(m)-25-25.980.13-25.810.58-23.030.01 20mE10.990.000.960.000.920.00ln0.71.130.300.980.422.030.17ln2.752.590.282.850.153.000.00fc10.950.040.840.111.000.00Vp(m/day)0.030.030.000.050.000.160.03R1.01.150.101.000.001.000.00Sl(m)1012.201.4515.693.6519.990.01Sw(m)1013.380.8412.550.0611.591.32Sh(m)58.930.769.730.319.010.69X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.430.03-125.040.09-124.140.06Z0(m)-25-26.470.11-26.850.21-27.150.16 90

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TableB-9.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=1.0,usinga5yeartemporalrecordbetween10and15yearspostinitialrelease OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.990.000.950.000.860.07ln1.01.020.131.160.141.960.36ln2.502.250.142.540.072.480.26fc10.780.040.730.050.920.11Vp(m/day)0.030.030.000.050.000.100.00R1.01.160.091.000.001.000.00Sl(m)1014.922.0516.252.1518.070.57Sw(m)1013.281.1112.500.0015.270.77Sh(m)58.010.609.900.099.980.02X0(m)0.00.000.000.000.000.120.17Y0(m)-125-125.510.09-126.190.31-129.022.66Z0(m)-25-26.350.14-26.930.27-27.170.40 10mE10.990.000.940.000.820.09ln1.01.070.341.310.171.110.12ln2.502.450.412.330.172.860.10fc10.760.180.910.071.000.00Vp(m/day)0.030.030.000.060.000.110.01R1.01.160.031.000.001.000.00Sl(m)1013.303.1017.071.4317.750.65Sw(m)1013.441.3215.370.7819.520.35Sh(m)59.780.0110.000.0010.000.00X0(m)0.00.000.000.000.001.672.36Y0(m)-125-125.600.16-126.390.09-126.610.33Z0(m)-25-25.910.10-25.640.47-23.540.51 20mE10.990.010.960.000.920.00ln1.01.050.391.050.212.080.33ln2.502.370.332.850.102.800.14fc10.740.190.730.100.920.05Vp(m/day)0.030.030.000.060.000.170.01R1.01.130.101.000.001.000.00Sl(m)1015.740.3415.812.2118.340.19Sw(m)1013.811.7312.190.4412.820.44Sh(m)59.310.509.950.078.190.69X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.360.15-124.920.09-123.550.33Z0(m)-25-26.440.18-26.800.17-26.800.35 91

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TableB-10.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.4,usinga5yeartemporalrecordbetween20and40yearspostinitialrelease OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.980.010.880.050.860.03ln0.40.370.070.840.350.890.09ln2.922.660.222.530.102.430.24fc10.820.070.780.160.990.01Vp(m/day)0.030.040.000.060.010.070.00R1.01.190.091.000.001.000.00Sl(m)1016.001.8217.093.2418.530.64Sw(m)1010.550.4717.032.1016.071.60Sh(m)59.110.9610.000.0010.000.00X0(m)0.00.000.000.000.000.040.05Y0(m)-125-127.951.56-127.922.41-128.532.64Z0(m)-25-26.110.34-26.190.09-26.390.32 10mE10.960.010.910.040.860.05ln0.40.530.220.500.040.760.09ln2.922.330.362.660.172.630.15fc10.740.160.820.051.000.00Vp(m/day)0.030.040.000.060.010.070.00R1.01.310.031.000.001.000.00Sl(m)1019.120.6018.860.9017.580.86Sw(m)1015.712.2318.061.4019.530.66Sh(m)58.631.6910.000.009.990.01X0(m)0.00.000.001.672.361.672.36 Y0(m)-125-126.020.44-126.260.24-126.560.16Z0(m)-25-26.521.15-24.970.07-24.040.2820mE10.930.050.910.01ln0.40.760.570.770.09ln2.922.300.452.650.20fc10.880.160.890.16Vp(m/day)0.030.040.000.060.00R1.01.290.141.000.00Sl(m)1015.544.0717.371.52Sw(m)1014.363.9315.400.66Sh(m)59.030.739.160.61X0(m)0.00.000.000.000.00Y0(m)-125-127.412.87-124.140.26Z0(m)-25-26.350.15-26.370.27 92

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TableB-11.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=0.7,usinga5yeartemporalrecordbetween20and40yearspostinitialrelease OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.980.010.890.020.890.02ln0.70.690.181.410.191.220.28ln2.752.440.292.180.082.320.26fc10.760.001.000.000.980.03Vp(m/day)0.030.040.000.070.010.070.00R1.01.280.031.000.001.000.00Sl(m)1017.080.9414.983.2015.541.69Sw(m)1011.561.3315.710.9716.221.75Sh(m)58.581.449.960.059.400.82X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.120.64-126.140.39-127.310.74Z0(m)-25-26.560.86-26.780.32-27.070.29 10mE10.930.020.870.02ln0.70.820.011.130.31ln2.752.700.162.660.19fc10.990.010.990.01Vp(m/day)0.030.060.000.070.00R1.01.000.001.000.00Sl(m)1016.703.4715.454.72Sw(m)1015.110.2816.712.51Sh(m)59.690.449.690.43X0(m)0.00.000.000.000.00Y0(m)-125-127.952.38-128.102.30Z0(m)-25-24.900.04-23.480.14 20mE10.960.030.930.020.860.02ln0.70.770.170.820.081.500.09ln2.752.390.342.740.212.600.03fc10.960.051.000.001.000.00Vp(m/day)0.030.040.000.080.030.130.04R1.01.240.051.000.001.000.00Sl(m)1016.142.7919.131.0518.021.59Sw(m)1013.803.3616.272.6310.722.23Sh(m)57.501.778.301.329.800.27X0(m)0.00.000.000.000.000.000.00Y0(m)-125-127.292.85-123.381.08-124.210.16Z0(m)-25-26.181.06-26.400.26-26.670.25 93

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TableB-12.Resultsofgeneticalgorithmoptimizationonsyntheticdata,caseofequilibriumstreamtubemodelwithln=1.0,usinga5yeartemporalrecordbetween20and40yearspostinitialrelease OutputwithgivenhandlnkhTermInputlnk=0.5lnk=1.5lnk=2.5 5mE10.910.030.900.010.890.02ln1.01.280.451.550.001.670.17ln2.502.250.412.660.162.640.14fc10.770.151.000.001.000.00Vp(m/day)0.030.040.010.140.050.120.05R1.01.290.231.000.001.000.00Sl(m)1015.722.9914.632.8112.653.01Sw(m)1016.742.5217.371.3215.790.66Sh(m)56.751.649.960.069.340.94X0(m)0.00.000.000.000.000.000.00Y0(m)-125-125.700.09-127.360.42-127.140.58Z0(m)-25-26.520.53-27.000.34-27.710.34 10mE10.930.010.890.01ln1.01.220.301.250.09ln2.502.400.422.730.10fc10.920.110.990.01Vp(m/day)0.030.060.000.090.01R1.01.000.001.000.00Sl(m)1014.631.6416.360.76Sw(m)1017.731.3215.930.29Sh(m)59.221.119.750.36X0(m)0.00.000.000.000.00Y0(m)-125-126.410.27-129.191.65Z0(m)-25-24.161.17-23.500.06 20mE10.910.040.930.010.920.01ln1.01.490.481.520.101.490.09ln2.502.960.042.420.142.830.05fc10.940.081.000.001.000.00Vp(m/day)0.030.120.070.090.020.170.04R1.01.360.061.000.001.000.00Sl(m)1012.413.9214.621.5517.541.91Sw(m)1015.313.5015.071.7110.861.45Sh(m)59.220.809.990.019.410.56X0(m)0.00.000.000.000.000.000.00Y0(m)-125-126.631.86-124.090.17-124.260.03Z0(m)-25-26.400.06-26.650.11-27.000.33 94

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APPENDIXCEXAMPLEGENETICALGORITHMOPTIMIZATIONPROGRESSIONSUSINGFORTLEWIS,WADATA 95

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1.41.61.822.22.42.62.8050100150200250-0.01-0.0095-0.009-0.0085-0.008-0.0075-0.007 )]TJ /F5 7.97 Tf 6.78 -1.79 Td[(opt E Generation )]TJ /F5 7.97 Tf 6.77 -1.79 Td[(optEAOptimumvalueof)]TJ /F15 9.963 Tf 8.42 0 Td[(andCoefcientofEfciency(E) 11.21.41.61.822.22.42.62.83050100150200250-0.0084-0.0082-0.008-0.0078-0.0076-0.0074-0.0072-0.007-0.0068 ln E Generation lnEBOptimumvalueoflnandCoefcientofEfciency(E) FigureC-1.Comparisonofoptimumvaluesof)]TJ /F1 11.955 Tf 10.1 0 Td[(andlnatFortLewis,consideringalldataavailable 96

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012345678910050100150200250-0.01-0.0095-0.009-0.0085-0.008-0.0075-0.007 vplume E Generation vplumeEAOptimumvalueofVpandCoefcientofEfciency(E)usingPFSSM 00.10.20.30.40.50.6050100150200250-0.0084-0.0082-0.008-0.0078-0.0076-0.0074-0.0072-0.007-0.0068 vplume E Generation vplumeEBOptimumvalueofVpandCoefcientofEfciency(E)usingESM FigureC-2.ComparisonofoptimumvaluesofVpatFortLewis,consideringalldataavailable 97

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1000150020002500300035004000450050005500050100150200250-0.01-0.0095-0.009-0.0085-0.008-0.0075-0.007 t0 E Generation t0EAOptimumvalueoft0andCoefcientofEfciency(E)usingPFSSM -100-80-60-40-20020406080100050100150200250-0.0084-0.0082-0.008-0.0078-0.0076-0.0074-0.0072-0.007-0.0068 t0 E Generation t0EBOptimumvalueoft0andCoefcientofEfciency(E)usingESM FigureC-3.Comparisonofoptimumvaluesoft0atFortLewis,consideringalldataavailable 98

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APPENDIXDADDITIONALMASSDISCHARGERESULTSFROMSYNTHETICDATA D.1PFSSM 00.20.40.60.811.21.41.61.82051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-1.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,h=05mandlnk=0.5 99

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00.511.522.533.544.5051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-2.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,h=05mandlnk=1.5 00.20.40.60.811.21.41.61.822.2051015202530354045 MD(kg/day) t(yrs) OptimumParametersInputBC FigureD-3.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,h=05mandlnk=2.5 100

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00.20.40.60.811.21.41.61.822.2051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-4.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,h=10mandlnk=0.5 01234567051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-5.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,h=10mandlnk=1.5 101

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051015202530051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-6.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,h=10mandlnk=2.5 102

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00.20.40.60.811.21.41.61.822.2051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-7.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,h=20mandlnk=0.5 00.511.522.533.544.5051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-8.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,h=20mandlnk=1.5 103

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0123456789051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-9.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseof)]TJ /F1 11.955 Tf 10.1 0 Td[(=1.0,h=20mandlnk=2.5 104

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D.2ESM 00.20.40.60.811.21.41.61.82051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-10.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=05mandlnk=0.5 105

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00.511.522.533.544.5051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-11.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=05mandlnk=1.5 0246810121416051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-12.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=05mandlnk=2.5 106

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00.511.522.5051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-13.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=10mandlnk=0.5 107

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01234567051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-14.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=10mandlnk=1.5 051015202530051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-15.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=10mandlnk=2.5 108

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00.511.522.5051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-16.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=20mandlnk=0.5 109

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00.511.522.533.544.5051015202530354045 MD(kg/day) t(yrs) OptimumParametersMT3DMSSolutionInputBC FigureD-17.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=20mandlnk=1.5 00.20.40.60.811.21.41.61.8051015202530354045 MD(kg/day) t(yrs) OptimumParametersInputBC FigureD-18.Massdischargeintimeforboundarycondition,MT3DMSresultandoptimizedparameterresultforthecaseofln=0.4,h=20mandlnk=2.5 110

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APPENDIXECOMPUTERCODES E.1GeneticAlgorithmImplementation,PFSSMand GuyonnetandNeville ( 2004 ) programfastga useieee arithmetic implicitnone !constants real,parameter::isqpi=1.e+00/sqrt(3.14159265e+00) real,parameter::pi=3.14159265e+00 !modelparameters real::g,c0,v,m0,ax,sw,sh,r real::ay,az real::t,x,y,z real::xl,yl,zl,tl real::fxv,fyv,fzv !reqsandhashtablevars real::rand real::dx,dy,dz,dv,dx4 real::c1,c2,c3,c4,ctmp real::sqrtdy2,sqrtdz2,sqrtpidx,sqsqrtpidx real::hashdfz1,hashdfy1 real::hashdfz2,hashdfy2 !integrationvariables real::abserr real,parameter::epsabs=5.e)]TJ /F25 10.909 Tf 8.48 0 Td[(06 111

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real,parameter::epsrel=1.e)]TJ /F25 10.909 Tf 8.48 0 Td[(06 integer,parameter::key=6 integer::neval,ier !datavariables integer::ndata,ios,sbios,spios integer,parameter::solbin=2 integer,parameter::solpar=3 character512::line real,dimension(32000,5)::wcsv real,dimension(32000,5)::wdata real::wavg,watt integer,parameter::iwd=1 !dummyvariables integer::i,j,k,ii,jj,kk integer::seed real::res integer,dimension(3)::times character20::frmt !geneticparameters integer,parameter::pop=1250 integer,parameter::gen=50 integer,parameter::bit=12 integer,parameter::npr=8 typecell real::t 112

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logical,dimension(nprbit)::dna endtypecell type(cell),dimension(pop)::culture !min/maxformodelparams real,dimension(npr,2)::mmp real,dimension(npr,2)::mpp include'fastga.inc' mpp=mmp !seedrandomfunction callitime(times) callsrand(times(1)+times(2)+times(3)) !readwelldata ndata=0 open(unit=iwd,le='dat/wdata.csv') do read(unit=iwd,fmt='(a)',iostat=ios)line if(ios/=0)then exit else ndata=ndata+1 read(unit=line,fmt=)wcsv(ndata,1),wcsv(ndata,2),wcsv(ndata,3),& wcsv(ndata,4),wcsv(ndata,5) if(ieee is nan(wcsv(ndata,5)))print,ERROR:WCSV(NDATA,5)ISNAN:,ndata res=res+wcsv(ndata,5) endif enddo 113

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close(iwd) wdata=wcsv wavg=res/ndata res=0.e+00 watt=0.e+00 doi=1,ndata watt=watt+(wdata(i,5))]TJ /F25 10.909 Tf 11.52 0 Td[(wavg)2 enddo if(ieee is nan(watt))then print,ERROR:WATTISNAN,watt,res,ndata endif !generateinitialculture doi=1,pop doj=1,nprbit if(rand(0)>0.5e+00)then culture(i)%dna(j)=1 else culture(i)%dna(j)=0 endif enddo enddo open(unit=solbin,le='fastga)]TJ /F25 10.909 Tf 8.49 0 Td[(bin.dat') open(unit=solpar,le='fastga)]TJ /F25 10.909 Tf 8.49 0 Td[(par.dat') !doallgenerations doii=1,gen 114

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!calculatetness dojj=1,pop !translatednatoactualvalues dokk=1,npr dv=(mpp(kk,2))]TJ /F25 10.909 Tf 11.52 0 Td[(mpp(kk,1))/(2bit)]TJ /F25 10.909 Tf 11.51 0 Td[(1) res=0.0e+00 doi=1,bit res=res+culture(jj)%dna((kk)]TJ /F25 10.909 Tf 11.51 0 Td[(1)bit+i)2(bit)]TJ /F25 10.909 Tf 11.52 0 Td[(i) enddo selectcase(kk) case(1) g=mpp(kk,1)+dvres case(2) c0=mpp(kk,1)+dvres case(3) v=mpp(kk,1)+dvres case(4) m0=mpp(kk,1)+dvres case(5) ax=mpp(kk,1)+dvres case(6) sw=mpp(kk,1)+dvres case(7) sh=mpp(kk,1)+dvres case(8) r=mpp(kk,1)+dvres endselect 115

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enddo !calculatefastparams ay=ax0.1 az=ay0.1 dx=axv/r dx4=4dx dy=ayv/r sqrtdy2=sqrt(dy)2 dz=azv/r sqrtdz2=sqrt(dz)2 sqrtpidx=8sqrt(pidx) c1=c0/(m0g) c2=(g)]TJ /F25 10.909 Tf 11.52 0 Td[(1)vswshc1 c3=m0(1)]TJ /F25 10.909 Tf 11.52 0 Td[(g) c4=g/(1)]TJ /F25 10.909 Tf 11.52 0 Td[(g) !initializetness ctmp=0.e+00 x=)]TJ /F25 10.909 Tf 8.49 0 Td[(1 y=)]TJ /F25 10.909 Tf 8.49 0 Td[(1 z=)]TJ /F25 10.909 Tf 8.49 0 Td[(1 !cyclethroughwelldata dokk=1,ndata xl=x x=wdata(kk,1))]TJ /F25 10.909 Tf 11.51 0 Td[(0.999 yl=y y=wdata(kk,2))]TJ /F25 10.909 Tf 11.51 0 Td[(0.5 116

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zl=z z=wdata(kk,3) t=wdata(kk,4) if(xl/=x)then sqsqrtpidx=(x/sqrtpidx)2 endif if(yl/=y)then hashdfy1=(y+sw/2.e+00)/sqrtdy2 hashdfy2=(y)]TJ /F25 10.909 Tf 11.51 0 Td[(sw/2.e+00)/sqrtdy2 endif if(zl/=z)then hashdfz1=(z+sh/2.e+00)/sqrtdz2 hashdfz2=(z)]TJ /F25 10.909 Tf 11.51 0 Td[(sh/2.e+00)/sqrtdz2 endif !adddifftorunningttotalwhilecalculatingvalueasfx()fy()fz() ctmp=ctmp+(wdata(kk,5))]TJ /F25 10.909 Tf 11.52 0 Td[(f()sqsqrtpidx)2 if(ieee is nan(ctmp))then ctmp=0 print,NANDETECTED:(GENERATION,INDIVIDUAL),ii,jj doi=1,ndata ctmp=ctmp+wdata(i,5) enddo exit endif enddo 117

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!nishcoeffofeffcalculation culture(jj)%t=1.e+00)]TJ /F25 10.909 Tf 11.52 0 Td[((ctmp/watt) write(frmt,)nprbit write(solbin,'(2i6,'//adjustl(frmt)//'i2)')ii,jj,culture(jj)%dna write(frmt,)npr+1 write(solpar,'(2i6,'//adjustl(frmt)//'f18.6)')ii,jj,culture(jj)%t,g,c0,v,m0,ax,sw,sh,r enddo !sort callsort(1,pop) !outputbestt dokk=1,npr dv=(mpp(kk,2))]TJ /F25 10.909 Tf 11.52 0 Td[(mpp(kk,1))/(2bit)]TJ /F25 10.909 Tf 11.51 0 Td[(1) res=0.0e+00 doi=1,bit res=res+culture(1)%dna((kk)]TJ /F25 10.909 Tf 11.52 0 Td[(1)bit+i)2(bit)]TJ /F25 10.909 Tf 11.52 0 Td[(i) enddo selectcase(kk) case(1) g=mpp(kk,1)+dvres case(2) c0=mpp(kk,1)+dvres case(3) v=mpp(kk,1)+dvres case(4) m0=mpp(kk,1)+dvres case(5) ax=mpp(kk,1)+dvres 118

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case(6) sw=mpp(kk,1)+dvres case(7) sh=mpp(kk,1)+dvres case(8) r=mpp(kk,1)+dvres endselect enddo write(,'(a,i6,a)')[,ii,] write(,'(a,i6,a,f10.6,a)')[,ii,]E=,culture(1)%t write(,'(a,i6,a,f10.5,a)')[,ii,]g=,g write(,'(a,i6,a,f10.5,a)')[,ii,]v=,v,m/year write(,'(a,i6,a,f10.5,a)')[,ii,]c0=,c01000,mg/L write(,'(a,i6,a,f10.1,a)')[,ii,]m0=,m0,kg write(,'(a,i6,a,f10.3,a)')[,ii,]ax=,ax,m write(,'(a,i6,a,f10.3,a)')[,ii,]sw=,sw,m write(,'(a,i6,a,f10.3,a)')[,ii,]sh=,sh,m write(,'(a,i6,a,f10.6,a)')[,ii,]r=,r !crossover callcrossover() !mutation callmutate() enddo close(solpar) close(solbin) 119

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contains !f x(params) realfunctionf() callqag(df,0.e+00,t,epsabs,epsrel,key,f,abserr,neval,ier) return endfunctionf !f y(params) realfunctiondfy(dt,sqrttdt) real::dt,sqrttdt dfy=ferfc(hashdfy1/sqrttdt))]TJ /F25 10.909 Tf 11.51 0 Td[(& ferfc(hashdfy2/sqrttdt) return endfunctiondfy !f z(params) realfunctiondfz(dt,sqrttdt) real::dt,sqrttdt dfz=ferfc(hashdfz1/sqrttdt))]TJ /F25 10.909 Tf 11.51 0 Td[(& ferfc(hashdfz2/sqrttdt) return endfunctiondfz !sourcestrengthfunction realfunctioncs(dt) real::dt cs=c1(c2dt+c3)c4 return endfunctioncs 120

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!partialoff x realfunctiondf(dt) real::dt,sqrttdt sqrttdt=sqrt(t)]TJ /F25 10.909 Tf 11.52 0 Td[(dt) df=cs(dt)dfx(dt,sqrttdt)dfy(dt,sqrttdt)dfz(dt,sqrttdt) endfunctiondf !partialoftransportequation realfunctiondfx(dt,sqrttdt) real::dt,sqrttdt dfx=exp()]TJ /F25 10.909 Tf 8.48 0 Td[(1(x)]TJ /F25 10.909 Tf 11.51 0 Td[(v(t)]TJ /F25 10.909 Tf 11.51 0 Td[(dt))2/(dx4(t)]TJ /F25 10.909 Tf 11.52 0 Td[(dt)))/sqrttdt3 return endfunctiondfx !errorfunctionwithabilitytohandlenegativevalues realfunctionferf(zp) real::zp if(zp>0.e+00)then ferf=erf(zp) else ferf=)]TJ /F25 10.909 Tf 8.49 0 Td[(1.e+00erf(abs(zp)) endif return endfunctionferf !complementaryerfwithabilitytohandlenegativevals realfunctionferfc(zp) real::zp 121

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ferfc=1)]TJ /F25 10.909 Tf 11.52 0 Td[(ferf(zp) return endfunctionferfc !quicksortofculture recursivesubroutinesort(lo,hi) integer::lo,hi,s,i,j,k real::pivot,tt logical,dimension(nprbit)::tdna s=nint((hi+lo)/2.e+00) pivot=culture(s)%t i=lo j=hi dowhile(i<=j) dowhile(culture(i)%t>pivot) i=i+1 enddo dowhile(culture(j)%t
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tt=culture(i)%t culture(i)%t=culture(j)%t culture(j)%t=tt i=i+1 j=j)]TJ /F25 10.909 Tf 11.52 0 Td[(1 endif enddo if(loi)callsort(i,hi) endsubroutinesort subroutinecrossover() logical,dimension(pop,nprbit)::tmpcel integer::p1,p2,k1,k2,i0,j0 doi0=2,pop p1=1 p2=1 dowhile(p1==p2) p1=min(ceiling(real(poprand(0))),ceiling(real(poprand(0)))) p2=min(ceiling(real(poprand(0))),ceiling(real(poprand(0)))) enddo k1=1 k2=1 dowhile(k1==k2) 123

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k1=ceiling((nprbit)rand(0)) k2=ceiling((nprbit)rand(0)) enddo doj0=1,nprbit tmpcel(i0,j0)=culture(p1)%dna(j0) enddo doj0=min(k1,k2),max(k1,k2) tmpcel(i0,j0)=culture(p2)%dna(j0) enddo enddo doi0=1,nprbit tmpcel(1,i0)=culture(1)%dna(i0) enddo doi0=1,pop doj0=1,nprbit culture(i0)%dna(j0)=tmpcel(i0,j0) enddo culture(i0)%t=0.e+00 enddo endsubroutinecrossover subroutinemutate() doi=2,nint(pop0.1) doj=1,nprbit if(rand(0)<0.25)then 124

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if(culture(i)%dna(j))then culture(i)%dna(j)=0 else culture(i)%dna(j)=1 endif endif enddo enddo doi=nint(pop0.1),pop if(rand(0)>0.5e+00)then culture(i)%dna(j)=1 else culture(i)%dna(j)=0 endif enddo endsubroutinemutate endprogramfastga E.2GeneticAlgorithmImplementation,PFSSMand Domenico ( 1987 ) programfastga useieee arithmetic implicitnone !constants real,parameter::isqpi=1.e+00/sqrt(3.14159265e+00) !modelparameters real::g,c0,v,m0,ax,sw,sh,r real::ay,az 125

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real::t,x,y,z real::xl,yl,zl,tl real::fxv,fyv,fzv !reqsandhashtablevars real::rand real::vsq,dr,d,rx,vx,extrm,vxod real::c1,c2,c3,c4,ctmp !integrationvariables real::abserr real,parameter::epsabs=5.e)]TJ /F25 10.909 Tf 8.48 0 Td[(06 real,parameter::epsrel=1.e)]TJ /F25 10.909 Tf 8.48 0 Td[(06 integer,parameter::key=6 integer::neval,ier !datavariables integer::ndata,ios,sbios,spios integer,parameter::solbin=2 integer,parameter::solpar=3 character512::line real,dimension(32000,5)::wcsv real,dimension(32000,5)::wdata real::wavg,watt integer,parameter::iwd=1 !dummyvariables integer::i,j,k,ii,jj,kk 126

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integer::seed real::dx,res integer,dimension(3)::times character20::frmt !geneticparameters integer,parameter::pop=1000 integer,parameter::gen=1000 integer,parameter::bit=8 integer,parameter::npr=8 typecell real::t logical,dimension(nprbit)::dna endtypecell type(cell),dimension(pop)::culture !min/maxformodelparams real,dimension(npr,2)::mmp real,dimension(npr,2)::mpp include'fastga.inc' mpp=mmp !seedrandomfunction callitime(times) callsrand(times(1)+times(2)+times(3)) !readwelldata ndata=0 open(unit=iwd,le='dat/wdata.csv') 127

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do read(unit=iwd,fmt='(a)',iostat=ios)line if(ios/=0)then exit else ndata=ndata+1 read(unit=line,fmt=)wcsv(ndata,1),wcsv(ndata,2),wcsv(ndata,3),& wcsv(ndata,4),wcsv(ndata,5) if(ieee is nan(wcsv(ndata,5)))print,ERROR:WCSV(NDATA,5)ISNAN:,ndata res=res+wcsv(ndata,5) endif enddo close(iwd) wdata=wcsv wavg=res/ndata res=0.e+00 watt=0.e+00 doi=1,ndata watt=watt+(wdata(i,5))]TJ /F25 10.909 Tf 11.52 0 Td[(wavg)2 enddo if(ieee is nan(watt))then print,ERROR:WATTISNAN,watt,res,ndata endif !generateinitialculture doi=1,pop doj=1,nprbit if(rand(0)>0.5e+00)then 128

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culture(i)%dna(j)=1 else culture(i)%dna(j)=0 endif enddo enddo open(unit=solbin,le='fastga)]TJ /F25 10.909 Tf 8.49 0 Td[(bin.dat') open(unit=solpar,le='fastga)]TJ /F25 10.909 Tf 8.49 0 Td[(par.dat') !doallgenerations doii=1,gen !calculatetness dojj=1,pop !translatednatoactualvalues dokk=1,npr dx=(mpp(kk,2))]TJ /F25 10.909 Tf 11.52 0 Td[(mpp(kk,1))/(2bit)]TJ /F25 10.909 Tf 11.51 0 Td[(1) res=0.0e+00 doi=1,bit res=res+culture(jj)%dna((kk)]TJ /F25 10.909 Tf 11.51 0 Td[(1)bit+i)2(bit)]TJ /F25 10.909 Tf 11.52 0 Td[(i) enddo selectcase(kk) case(1) g=mpp(kk,1)+dxres case(2) c0=mpp(kk,1)+dxres case(3) 129

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v=mpp(kk,1)+dxres case(4) m0=mpp(kk,1)+dxres case(5) ax=mpp(kk,1)+dxres case(6) sw=mpp(kk,1)+dxres case(7) sh=mpp(kk,1)+dxres case(8) r=mpp(kk,1)+dxres endselect enddo !calculatefastparams ay=ax0.1 az=ay0.1 d=axv dr=dr c1=c0/(m0g) c2=(g)]TJ /F25 10.909 Tf 11.52 0 Td[(1)vswshc1 c3=m0(1)]TJ /F25 10.909 Tf 11.52 0 Td[(g) c4=g/(1)]TJ /F25 10.909 Tf 11.52 0 Td[(g) vsq=v2 !initializetness ctmp=0.e+00 x=)]TJ /F25 10.909 Tf 8.49 0 Td[(1. 130

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t=)]TJ /F25 10.909 Tf 8.49 0 Td[(1. y=)]TJ /F25 10.909 Tf 8.49 0 Td[(10000. z=)]TJ /F25 10.909 Tf 8.49 0 Td[(10000. !cyclethroughwelldata dokk=1,ndata xl=x x=wdata(kk,1) yl=y y=wdata(kk,2)!)]TJ /F26 10.909 Tf 11.52 0 Td[(125 zl=z z=wdata(kk,3)!)]TJ /F26 10.909 Tf 11.52 0 Td[(25 tl=t t=wdata(kk,4) !calcsomefastparams if(xl
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endif if(zl/=z)then fzv=fz() endif !adddifftorunningttotalwhilecalculatingvalueasfx()fy()fz() ctmp=ctmp+(wdata(kk,5))]TJ /F25 10.909 Tf 11.52 0 Td[(fxvfyvfzv)2 if(ieee is nan(ctmp))then ctmp=0 doi=1,ndata ctmp=ctmp+wdata(i,5) enddo exit endif enddo !nishcoeffofeffcalculation culture(jj)%t=1.e+00)]TJ /F25 10.909 Tf 11.52 0 Td[((ctmp/watt) write(frmt,)nprbit write(solbin,'(2i6,'//adjustl(frmt)//'i2)')ii,jj,culture(jj)%dna write(frmt,)npr+1 write(solpar,'(2i6,'//adjustl(frmt)//'f18.6)')ii,jj,culture(jj)%t,g,c0,v,m0,ax,sw,sh,r enddo !sort callsort(1,pop) !outputbestt dokk=1,npr 132

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dx=(mpp(kk,2))]TJ /F25 10.909 Tf 11.52 0 Td[(mpp(kk,1))/(2bit)]TJ /F25 10.909 Tf 11.51 0 Td[(1) res=0.0e+00 doi=1,bit res=res+culture(1)%dna((kk)]TJ /F25 10.909 Tf 11.52 0 Td[(1)bit+i)2(bit)]TJ /F25 10.909 Tf 11.52 0 Td[(i) enddo selectcase(kk) case(1) g=mpp(kk,1)+dxres case(2) c0=mpp(kk,1)+dxres case(3) v=mpp(kk,1)+dxres case(4) m0=mpp(kk,1)+dxres case(5) ax=mpp(kk,1)+dxres case(6) sw=mpp(kk,1)+dxres case(7) sh=mpp(kk,1)+dxres case(8) r=mpp(kk,1)+dxres endselect enddo write(,'(a,i6,a)')[,ii,] write(,'(a,i6,a,f10.6,a)')[,ii,]E=,culture(1)%t write(,'(a,i6,a,f10.5,a)')[,ii,]g=,g write(,'(a,i6,a,f10.5,a)')[,ii,]v=,v,m/year 133

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write(,'(a,i6,a,f10.5,a)')[,ii,]c0=,c01000,mg/L write(,'(a,i6,a,f10.1,a)')[,ii,]m0=,m0,kg write(,'(a,i6,a,f10.3,a)')[,ii,]ax=,ax,m write(,'(a,i6,a,f10.3,a)')[,ii,]sw=,sw,m write(,'(a,i6,a,f10.3,a)')[,ii,]sh=,sh,m write(,'(a,i6,a,f10.6,a)')[,ii,]r=,r !crossover callcrossover() !mutation callmutate() enddo close(solpar) close(solbin) contains !f x(params) realfunctionfx() callqag(dfx,0.e+00,t,epsabs,epsrel,key,fx,abserr,neval,ier) return endfunctionfx !f y(params) realfunctionfy() fy=0.5e+00(ferf((y+(sw/2.e+00))/(2.e+00sqrt(ayx))))]TJ /F25 10.909 Tf 11.51 0 Td[(& ferf((y)]TJ /F25 10.909 Tf 11.52 0 Td[((sw/2.e+00))/(2.e+00sqrt(ayx)))) return endfunctionfy 134

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!f z(params) realfunctionfz() fz=0.5e+00(ferf((z+sh/2.e+00)/(2.e+00sqrt(azx))))]TJ /F25 10.909 Tf 11.51 0 Td[(& ferf((z)]TJ /F25 10.909 Tf 11.52 0 Td[(sh/2.e+00)/(2.e+00sqrt(azx)))) return endfunctionfz !sourcestrengthfunction realfunctioncs(tr) real::tr cs=c1(c2tr+c3)c4 return endfunctioncs !partialoff x realfunctiondfx(tr) real::tr dfx=cs(t)]TJ /F25 10.909 Tf 11.52 0 Td[(tr)db(tr) endfunctiondfx !partialoftransportequation realfunctiondb(tr) real::tr real::srdrtr,svdrt,drtr15 srdrtr=sqrt(drtr) svdrt=sqrt(vsqtr/dr) drtr15=4(drtr)1.5 db=isqpi& 135

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(& exp()]TJ /F25 10.909 Tf 8.48 0 Td[(((rx)]TJ /F25 10.909 Tf 11.52 0 Td[(vtr)2)/(4drtr))& (& )]TJ /F25 10.909 Tf 8.49 0 Td[(1(& ()]TJ /F25 10.909 Tf 8.48 0 Td[(v/(2srdrtr)))]TJ /F25 10.909 Tf 11.51 0 Td[(& (dr(rx)]TJ /F25 10.909 Tf 11.52 0 Td[(vtr))/drtr15& )& +(& svdrt& (& (rx)]TJ /F25 10.909 Tf 11.52 0 Td[(vtr)2/(4drtr2)+& (v(rx)]TJ /F25 10.909 Tf 11.52 0 Td[(vtr)/(2drtr))& )& +(vsq/(2drsvdrt))& )& )& +& (& v/(2srdrtr)& )]TJ /F25 10.909 Tf 11.52 0 Td[((dr(rx+vtr))/drtr15& )& exp((vxod))]TJ /F25 10.909 Tf 11.52 0 Td[((rx+vtr)2/(4drtr))& (1+(vxod)+(vsqtr/dr))& )& )]TJ /F25 10.909 Tf 11.52 0 Td[(extrmferfc((rx+vtr)/(2srdrtr)) return endfunctiondb !errorfunctionwithabilitytohandlenegativevalues 136

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realfunctionferf(zp) real::zp if(zp>0.e+00)then ferf=erf(zp) else ferf=)]TJ /F25 10.909 Tf 8.49 0 Td[(1.e+00erf(abs(zp)) endif return endfunctionferf !complementaryerfwithabilitytohandlenegativevals realfunctionferfc(zp) real::zp if(zp>0.e+00)then ferfc=erfc(zp) else ferfc=2.e+00)]TJ /F25 10.909 Tf 11.51 0 Td[(erfc(abs(zp)) endif return endfunctionferfc !quicksortofculture recursivesubroutinesort(lo,hi) integer::lo,hi,s,i,j,k real::pivot,tt logical,dimension(nprbit)::tdna s=nint((hi+lo)/2.e+00) pivot=culture(s)%t 137

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i=lo j=hi dowhile(i<=j) dowhile(culture(i)%t>pivot) i=i+1 enddo dowhile(culture(j)%t
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if(hi>i)callsort(i,hi) endsubroutinesort subroutinecrossover() logical,dimension(pop,nprbit)::tmpcel integer::p1,p2,k1,k2,i0,j0 doi0=2,pop p1=1 p2=1 dowhile(p1==p2) p1=min(ceiling(real(poprand(0))),ceiling(real(poprand(0)))) p2=min(ceiling(real(poprand(0))),ceiling(real(poprand(0)))) enddo k1=1 k2=1 dowhile(k1==k2) k1=ceiling((nprbit)rand(0)) k2=ceiling((nprbit)rand(0)) enddo doj0=1,nprbit tmpcel(i0,j0)=culture(p1)%dna(j0) enddo doj0=min(k1,k2),max(k1,k2) tmpcel(i0,j0)=culture(p2)%dna(j0) enddo enddo 139

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doi0=1,nprbit tmpcel(1,i0)=culture(1)%dna(i0) enddo doi0=1,pop doj0=1,nprbit culture(i0)%dna(j0)=tmpcel(i0,j0) enddo culture(i0)%t=0.e+00 enddo endsubroutinecrossover subroutinemutate() doi=2,pop)]TJ /F25 10.909 Tf 11.51 0 Td[(10 doj=1,nprbit if(rand(0)<0.25)then if(culture(i)%dna(j))then culture(i)%dna(j)=0 else culture(i)%dna(j)=1 endif endif enddo enddo doi=pop)]TJ /F25 10.909 Tf 11.52 0 Td[(10,pop if(rand(0)>0.5e+00)then culture(i)%dna(j)=1 else 140

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culture(i)%dna(j)=0 endif enddo endsubroutinemutate endprogramfastga E.3ExampleGeneticAlgorithmCongurationFile,fastga.inc !g mmp(1,1)=1.001 mmp(1,2)=3.00 !c0 mmp(2,1)=0.6 mmp(2,2)=1.2 !v mmp(3,1)=0.001 mmp(3,2)=1 !m0 mmp(4,1)=6000. mmp(4,2)=14000. !ax mmp(5,1)=1. mmp(5,2)=20. !sw mmp(6,1)=5. 141

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mmp(6,2)=20. !sh mmp(7,1)=2.5 mmp(7,2)=10. !r mmp(8,1)=1. mmp(8,2)=2. E.4CalculationofEquation 3 programfastga useieee arithmetic implicitnone !integrationvariables real::abserr real,parameter::epsabs=5.e)]TJ /F25 10.909 Tf 8.48 0 Td[(06 real,parameter::epsrel=1.e)]TJ /F25 10.909 Tf 8.48 0 Td[(06 integer,parameter::key=6 integer::neval,ier !esmparameters real::conc real::tau,fc,csol,slnt,ulnt !loopparameters integer::i,j,k real,parameter::sqrt2=sqrt(2.0) 142

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fc=1.0 csol=1.0 doi=1,800 doj=1,800 ulnt=i0.01 slnt=j0.01 callqagi(cs,0,1,epsabs,epsrel,conc,abserr,neval,ier) print,ulnt,slnt,conc,neval,ier enddo enddo contains !sourcestrengthfunction realfunctioncs(tr) real::tr cs=fccsol(1)]TJ /F25 10.909 Tf 11.51 0 Td[((0.5+0.5ferf((log(tr))]TJ /F25 10.909 Tf 11.52 0 Td[(ulnt)/(slntsqrt2)))) return endfunctioncs realfunctionferf(zp) real::zp if(zp>0.e+00)then ferf=erf(zp) else ferf=)]TJ /F25 10.909 Tf 8.49 0 Td[(1.e+00erf(abs(zp)) endif return endfunctionferf 143

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!complementaryerfwithabilitytohandlenegativevals realfunctionferfc(zp) real::zp if(zp>0.e+00)then ferfc=erfc(zp) else ferfc=2.e+00)]TJ /F25 10.909 Tf 11.51 0 Td[(erfc(abs(zp)) endif return endfunctionferfc endprogramfastga E.5ConversionofMT3DMSUCNtoCSV programucn2csv implicitnone integer,parameter::iucn=1 integer,parameter::iout=7 integer,parameter::ncol=500 integer,parameter::nrow=250 integer,parameter::nlay=50 real,parameter::zerobelow=5.e)]TJ /F25 10.909 Tf 8.48 0 Td[(06 real,dimension(ncol,nrow,nlay)::cnew integer::ntrans,j,i,k,nt0,ks0,kp0,kstp,kper,& nc,nr,ilay,itmp1,itmp2,itmp3,ioerr 144

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integer::ii,jj,kk real::time0,time2 character16::text1,fname logical::founded,ended open(iucn,FILE='MT3D001.UCN',FORM='UNFORMATTED',ACCESS='SEQUENTIAL',STATUS='OLD') !deneoutputformat 2format(1x,'Transportstep',i5,'Timestep',i3,'Stressperiod',i3,'Totalelapsedtime',g11.4) 3format(1x,a16,':Timestep',i3,'Stressperiod',i3,'Totalelapsedtime',g11.4) kk=0 do kk=kk+1 write(fname,'(a12,i4.4)')mt3ducn)]TJ /F25 10.909 Tf 8.48 0 Td[(step,kk open(iout,le=fname//.csv) dok=1,nlay read(iucn,iostat=ioerr)itmp1,itmp2,itmp3,time2,text1,nc,nr,ilay if(ioerr/=0)then exit endif ntrans=itmp1 kstp=itmp2 kper=itmp3 if(text1(1:13).ne.'CONCENTRATION'.and.text1(1:13).ne.'concentration')then kstp=itmp1 kper=itmp2 145

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nt0=)]TJ /F25 10.909 Tf 8.49 0 Td[(1 ntrans=)]TJ /F25 10.909 Tf 8.48 0 Td[(1 endif if(k==1.and.ntrans>0)write(,2)ntrans,kstp,kper,time2 if(k==1.and.ntrans<0)write(,3)text1,kstp,kper,time2 read(iucn)((cnew(j,i,k),j=1,ncol),i=1,nrow) dojj=1,nrow doii=1,ncol if((cnew(ii,jj,k)
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Zheng,C.,Wang,P.P.,Zheng,C.,Wang,P.P.,1999.MT3DMS:Amodularthree-dimensionalmulti-speciestransportmodelforsimulationofadvection,dispersion,andchemicalreactionsofcontaminantsinground-watersystems.Documentationanduser'sguide.In:ContractReportSERDP-99-1,U.S.ArmyEngineerResearchandDevelopment. 150

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BIOGRAPHICALSKETCH BorninStockton,California,BrandonWoodmovedtoFloridain1990andbeganattendingtheUniversityofFloridain2005.In2009,hereceivedaBachelorofSciencedegreeinenvironmentalengineeringsciences. 151