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Tephra transport, sedimentation and hazards

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Title:
Tephra transport, sedimentation and hazards
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Book
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English
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Volentik, Alain C. M
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University of South Florida
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Tampa, Fla
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Subjects / Keywords:
Tephra fall
Plinian eruptions
Sedimentation models
Inversion techniques
Terminal velocity
Dissertations, Academic -- Geology -- Doctoral -- USF   ( lcsh )
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non-fiction   ( marcgt )

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Summary:
ABSTRACT: Tephra deposits are one of the possible outcomes of explosive volcanic eruptions and are the result of vertical settling of volcanic particles that have been expelled from the volcanic vent into the atmosphere, following magma fragmentation within the volcanic conduit. Tephra fallout represents the main volcanic hazard to populated areas and critical facilities. Therefore, it is crucial to better understand processes that lead to tephra transport, sedimentation and hazards. In this study, and based on detailed mapping and sampling of the tephra deposit of the 2450 BP Plinian eruption of Pululagua volcano (Ecuador), I investigate tephra deposits through a variety of approaches, including empirical and analytical modeling of tephra thickness and grain size data to infer important eruption source parameters (e.g. column height, total mass ejected, total grain size distribution of the deposit).I also use a statistical approach (smoothed bootstrap with replacement method) to assess the uncertainty in the eruptive parameters. The 2450 BP Pululagua volcanic plume dynamics were also explored through detailed grain size analysis and 1D modeling of tephra accumulation. Finally, I investigate the influence of particle shape on tephra accumulation on the ground through a quantitative and comprehensive study of the shape of volcanic ash. As the global need for energy is expected to grow in the future, many future natural hazard studies will likely involve the assessment of volcanic hazards at critical facilities, including nuclear power plants. I address the potential hazards from tephra fallout, pyroclastic flows and lahars for the Bataan Nuclear Power Plant (Philippines) posed by three nearby volcanoes capable of impacting the site during an explosive eruption.I stress the need for good constraints (stratigraphic analysis and events dating) on past eruptive events to better quantify the probability of future events at potentially active volcanoes, the need for probabilistic approaches in such volcanic hazard assessments to address a broad range of potential eruption scenarios, and the importance of considering coupled volcanic processes (e.g. tephra fallout leading to lahars) in volcanic hazard assessments.
Thesis:
Dissertation (Ph.D.)--University of South Florida, 2009.
Bibliography:
Includes bibliographical references.
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by Alain C. M. Volentik.
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Title from PDF of title page.
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Document formatted into pages; contains 194 pages.
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Includes vita.

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oclc - 437010636
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ABSTRACT: Tephra deposits are one of the possible outcomes of explosive volcanic eruptions and are the result of vertical settling of volcanic particles that have been expelled from the volcanic vent into the atmosphere, following magma fragmentation within the volcanic conduit. Tephra fallout represents the main volcanic hazard to populated areas and critical facilities. Therefore, it is crucial to better understand processes that lead to tephra transport, sedimentation and hazards. In this study, and based on detailed mapping and sampling of the tephra deposit of the 2450 BP Plinian eruption of Pululagua volcano (Ecuador), I investigate tephra deposits through a variety of approaches, including empirical and analytical modeling of tephra thickness and grain size data to infer important eruption source parameters (e.g. column height, total mass ejected, total grain size distribution of the deposit).I also use a statistical approach (smoothed bootstrap with replacement method) to assess the uncertainty in the eruptive parameters. The 2450 BP Pululagua volcanic plume dynamics were also explored through detailed grain size analysis and 1D modeling of tephra accumulation. Finally, I investigate the influence of particle shape on tephra accumulation on the ground through a quantitative and comprehensive study of the shape of volcanic ash. As the global need for energy is expected to grow in the future, many future natural hazard studies will likely involve the assessment of volcanic hazards at critical facilities, including nuclear power plants. I address the potential hazards from tephra fallout, pyroclastic flows and lahars for the Bataan Nuclear Power Plant (Philippines) posed by three nearby volcanoes capable of impacting the site during an explosive eruption.I stress the need for good constraints (stratigraphic analysis and events dating) on past eruptive events to better quantify the probability of future events at potentially active volcanoes, the need for probabilistic approaches in such volcanic hazard assessments to address a broad range of potential eruption scenarios, and the importance of considering coupled volcanic processes (e.g. tephra fallout leading to lahars) in volcanic hazard assessments.
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Inversion techniques
Terminal velocity
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TephraTransport,SedimentationandHazards by AlainC.M.Volentik Adissertationsubmittedinpartialfulllment oftherequirementsforthedegreeof DoctorofPhilosophy DepartmentofGeology CollegeofArtsandSciences UniversityofSouthFlorida Co-MajorProfessor:CharlesB.Connor,Ph.D. Co-MajorProfessor:CostanzaBonadonna,Ph.D. DianaC.Roman,Ph.D. JereyG.Ryan,Ph.D. PaulH.Wetmore,Ph.D. DateofApproval: March31,2009 Keywords:Tephrafall,Plinianeruptions,sedimentationmodels,inversiontechniques, terminalvelocity,Pululagua,volcanichazards,probabilisticmodels,criticalfacilities, BataanPeninsulaPhilippines c Copyright2009,AlainC.M.Volentik

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DEDICATION TomywifeJasmine, myparentsChristianeandJacques,DanyandElda&Micoul, mybrothers,Kevin,Pierre-Antoine&Frederic,andsister,Julie, andmyinvaluablefriends,Remo,LoycandBecs. InmemoryofStephanie

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ACKNOWLEDGMENTS Iwouldliketothankmyco-advisorsDr.CharlesConnorandDr.CostanzaBonadonna forgivingmetheopportunitytojointheDepartementofGeologyatUSFandtoworkon excitingresearchtopicssuchastephrafalloutmodelingandvolcanichazards.Ialsowould liketothanktherestofmycommitteemembers,Dr.DianaRoman,Dr.JeRyanandDr. PaulWetmorefortheirsupportthroughoutthesefouryears.MauroRosi'sguidanceinthe eldwascrucialinthesuccessofthisstudy.Iherebythankhimverymuchforsharinghis knowledgeofPululaguadepositsandabouttephrafalloutprocessesingeneral.Aspecial thankstoLauraConnorforherinvaluablehelpandadvicewithcomputationalproblems. IamverythankfultotheIstitutoGeosicoinQuito,especiallyPathyMothes,Minard Hall,GorkyRuiz,DiegoBarba,andDanielAndradefortheirlogisticsupportduringmy eldwork.AdditionaleldsupportfromMartinJutzeler,JohnPetriello,RebeccaCarey andBruceHoughtonisalsoacknowledged.IamalsoverygratefultoJohnScottforhis precioushelpinthelabwithgrainsizeandgrainshapeanalysis.Myocematesand friendsfromthevolcanologygroup,Heather,Mandie,Sophie,JohnP.,Armando,Koji, WayneandJohnO.,havealwaysbeenverysupportiveaswell.Itwasapleasuresharing ideas,discussingproblemsandhangingoutwithyouguys.AspecialthankstoMikelwho provedtobemorethananocemateandcolleague,butalsoagreatfriend.Irecall countlesshoursoftennischallenges,litersofbeersandendlessphilosophicaldiscussions. Paoloandhiscrewatthe"GrottoMadonnadellaFontana"inAsconaSwitzerlandarealso acknowledgedforhostingmetwosummersinarow.AspecialthanksalsotoMaryHaney andMandyStuckfortheirhelpandguidancethroughthemeandersofadministration. IamalsogratefultotheNationalScienceFoundationNSFforpartiallyfundingmy researchGrantEAR-0130602andtoUSFforaGraduateAssistantScholarship.Last butnotleast,thankstoyou,Jasmine,forallthesupport,patienceandloveyougaveme inthislongjourneythatisthePh.D.Tiamotantissimo.

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TABLEOFCONTENTS LISTOFTABLESiv LISTOFFIGURESv ABSTRACTxiii CHAPTER1INTRODUCTION1 CHAPTER2MODELINGTHECLIMACTICPHASEOFTHE2450BPPLINIAN ERUPTIONOFPULULAGUAVOLCANO,ECUADOR7 2.1Introduction7 2.2Geologicalsetting8 2.3Newstratigraphy11 2.4Empiricaldeterminationoferuptiveparameters15 2.4.1Samplegrainsizeandtotalgrainsizedistribution15 2.4.1.1Grainsize15 2.4.1.2Totalgrainsizedistribution22 2.4.2Eruptedvolume25 2.5Analyticaldeterminationoferuptiveparameters28 2.5.1Eruptedmass29 2.5.2Columnheight33 2.5.3Totalgrainsizedistribution37 2.5.4Uncertaintyanalysis37 2.6Massdischargerateanderuptionduration38 2.7Particlepath39 2.8Forwardmodeling41 2.9Plumedynamics41 2.9.1Cornerposition41 2.9.2Strongplumemodel48 2.10Discussion50 2.10.1Statisticalvs.numericaldeterminationoferuptiveparameters50 2.10.2Plumedynamics54 2.10.3Diusioncoecient55 2.10.4Windornowind?56 2.11Conclusions57 i

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CHAPTER3INFLUENCEOFPARTICLESHAPEONTEPHRADISPERSAL60 3.1Introduction60 3.2Methodology63 3.3Particleshape65 3.3.1Bulkresultsforeach class65 3.3.2Resultsasafunctionofeach classanddistancefromthe vent66 3.4Terminalvelocity73 3.4.1Comparisonbetweendierentmodels73 3.4.2 V WH / V KL vs AR 77 3.5Sedimentation80 3.6Discussion84 3.7Conclusions88 CHAPTER4ASPECTSOFVOLCANICHAZARDSASSESSMENTFORTHE BATAANNUCLEARPOWERPLANT,PHILIPPINES90 4.1Introduction90 4.2Volcanicsetting93 4.3Assessmentofvolcanocapability96 4.4Estimatingscreeningdistancevalues99 4.4.1Hazardsfromtephrafallout100 4.4.1.1Deterministicanalysis101 4.4.1.2Probabilisticanalysis109 4.4.2Laharsourceregions113 4.4.3Hazardsfrompyroclasticdensitycurrents118 4.5Concludingremarks120 4.5.1Furtherreading123 REFERENCES124 APPENDICES134 AppendixAGrainsizedistributionandcharacteristicsoftheBF2layer144 AppendixBPerlcodetocalculatethehorizontaldisplacementofvolcanic particlesduetowindadvection144 AppendixCPerlcodetoassesstheuncertaintyonthemassandcolumn heightusingtheTEPHRA2model150 AppendixDShapeparameters:aspectration,shapefactorandroundness withtheir1-sigmastandarddeviation158 AppendixEPerlcodetocalculatetheterminalvelocityofvolcanicparticles followingthethreemodelsdescribedinChapter3158 AppendixFPerlcodetocalculatethediameteroftheequivalentshpere fallingatthesameterminalvelocitythanthemeasuredparticle163 ii

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AppendixGPerlcodestocalculatethetephrasedimentationusingthe modelofBonadonnaandPhilippsandthethreedierentapproachesdiscussedinthetextincomputingtheterminal velocity168 AppendixHBootstrapwithreplacementprocedureinPerltocalculate therecurrenceintervalandthereforetheprobabilityofan eruptionofagivenvolcano181 AppendixIPerlandGMTcodesforlaharanaylsislaharsourceregion, totalvolumeandpotentialareaofinundationaroundMt. NatibvolcanoBataanPeninsula,Philippines187 ABOUTTHEAUTHOREndPage iii

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LISTOFTABLES Table2.1Compilationofgrainsizecharacteristicsforthedierenttechniqueof TGSDcalculations.Dataonthe1980eruptionofMountSt.Helens MSHarefromDurantetal..23 Table2.2Exampleofinputparameterrangesfortheinversionandoutputexamplefromtheinversion.31 Table2.3Outputfromtheinversionongrainsize,andtheuncertaintyanalysis. GS:grainsize,H t :columnheight,DC:DiusionCoecient,FTT:Fall TimeThreshold.35 Table2.4InputparametersforaforwardsolutionfortheBF2layerusingthe TEPHRA2model.SeeFigurerefg2-1bforabbreviations.41 Table3.1Mean ,1 standarddeviationStdandnumber N ofparticlesanalyzedfordierentshapeparameters:aspectratio AR ,convexity C roundness R anddiameteroftheequivalentsphere ED .GSstands forgrainsize.69 Table4.1Eruptioncolumnheightandtotalmassinputsfordeterministictephra modelsarebasedonanalogeruptionsandVolcanoExplosivityIndex VEI.104 Table4.2TephrafalloutthicknesscmattheBNPPsiteforeacheruptionscenariointhedeterministicanalysis.106 iv

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LISTOFFIGURES Figure2.1aLocationmapofEcuador,withthemainvolcanoestrianglesand localitiescircles.PululaguaislocatednorthofQuitoandisshownas abigwhitetriangle.TheblacksquarearoundPululaguarepresentsthe areaofinterestshowninbandthroughoutthedierentmapsinthis paper.bRegionofinterestaroundPululagua,withthethreeaxes usedinthisstudy:1,theESEaxisinred;2,theSEaxisinblueand3, theSWaxisingreen.Numbersrefertosamplelocations.Citiesabbreviationsareasfollows,A:Atahualpa,C:Calacali,G:Guayllabamba, N:Nanegal,Ng:Nanegalito,No:Nono,P:Perucho,SA:SanAntonio, SJM:SanJosedeMinas.Thedarkgreyarearepresentstheextent ofQuito;cZoomonthePululaguavolcaniccomplex,showingthe irregular-shapedcaldera.10 Figure2.2Pictureanddetailedstratigraphyoftheoutcropforthreelocations atvariousdistancesfromthevent.aProximal:PL40locatedat 4.5kmsoutheastfromtheinferredvent.bMedial:PL19locatedat 13kmeast-southeastfromtheinferredvent.cDistal:PL24located at 21kmsoutheastfromtheinferredvent.Wedenedtheinferred ventasbeinginthecenterofthecaldera,inthecurrentpositionofthe centralpost-calderadomes.Notethealmost-constantthicknessofthe WhiteAshinanylocationawayfromthevent.12 Figure2.3GrainsizedistributionfortheBF2layerforproximaltomoredistal locationsforvedierentlocalities.Md isthemediangrainsize, isthesortingandSkGistheskewnessofthedeposit.aisthegrain sizedistributionforPL40,bforPL10,cforPL19,dforPL24and eforPL55.16 Figure2.4GrainsizecharacteristicsoftheBF2layer.aPlotofthemedian diameterMd vs.distancefromthevent.bPlotofthestandard deviation vs.distancefromthevent.cPlotof vs.Md .Red dotsarefordatafromaxis1ESE,bluedotsarefordatafromaxis 2SE,greendotsarefordatafromaxis3SW,andblackdotsare fortherestofthedataset.Solidlinesareregressionsthroughthedata fromthedierentaxescolorschemesameasbefore.Thepyroclastic owandfalleldsaredenedafterWalker.17 v

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Figure2.5Isomassmapsforeachindividualgrainsizeclassfrom-5 to-2 of theBF2layer.SeeFigure2.1bforabbreviations.Dashedlineswhere isomasscontoursareextrapolated.19 Figure2.6Isomassmapsforeachindividualgrainsizeclassfrom-1 to2 of theBF2layer.SeeFigure2.1bforabbreviations.Dashedlineswhere isomasscontoursareextrapolated.20 Figure2.7aIsopachmapfortheBF2layerofthe2450BPPlinianeruption ofPululaguaVolcano.Individuallocationthicknessesandcontours areshown.Valuesareincentimeters.Notethecircularshapeofthe isopachs.Dashedlineswhereisopachcontoursareextrapolated.b MapshowingthedistributionoftheMd valuesoftheBF2layer.Note thatthecircularshapeislesspronouncedthanfortheisopachmap, andthatthedistributionofMd isslightlytowardthewest.Dashed lineswhereiso-Md contoursareextrapolated.SeeFigure2.1bfor abbreviations.21 Figure2.8ResultsoftotalgrainsizedistributionsTGSDcalculationsusingdifferenttechniques.aTechniqueAwiththetwosetsofdatapoints; bTechniqueBwiththetwosetsofdatapoints;cTechniqueC;d TechniqueDwiththerstsetofdatapoints;eTechniqueDwith thesecondsetofdatapoints;fFromtheinversionongrainsize,includingandexcludingthe-7 sizefraction;gTechniqueDwitha zeroaccumulationlineat100kmforthetwodatasets;hTechnique Dwithazeroaccumulationlineat100and200kmwiththerstdata set.24 Figure2.9Semi-logarithmicplotsoflogofthicknesscmagainstthesquareroot oftheareaenclosedbyanisopachmapcontourfortheBF2tephra deposit.aFielddataarettedaccordingtotheexponentialdecay proposedbyPyle,excludingthe1and2cmisopachs.bField dataarettedaccordingtotheexponentialdecayproposedbyPyle ,includingthe1and2cmisopachs.cFielddataaretted usingthepower-lawtechniqueproposedbyBonadonnaandHoughton ,excludingthe1and2cmisopachs.dFielddataaretted usingthepower-lawtechniqueproposedbyBonadonnaandHoughton ,includingthe1and2cmisopachs.26 Figure2.10Comparisonbetweentheobservedtephraaccumulationontheground andthecalculatedtephraaccumulationfromoneofthebest-tinversionresultsontheBF2thicknessateachlocality.Thediagonalblack linerepresentstheoptimalcase,whenthemodelequalstheactualaccumulation.30 vi

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Figure2.112-DspaceofinputparametersfortheinversionontheBF2thickness. Plotshowingthecolumnheightvs.logmass.Theblackdotrepresents solutionswitha RMSE> 100.32 Figure2.12Comparisonbetweentheobservedtephraaccumulationontheground andthecalculatedtephraaccumulationfromtheimproved-inversion resultsontheBF2grainsizeateachlocality.Resultsshownarefor threedierentgrainsizesateachlocation:athe-3 grainsize;b the0 grainsizeandcthe2 sizefraction.34 Figure2.13Reconstructionofthemodeledgrainsizedistributionaccumulationin kgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 inredandcomparisonwiththeactualgrainsizedistribution fromelddata,inblack,forlocalitiesfromproximaltomedial,along axis1.36 Figure2.14Windrosediagramfromtheinversiononindividualgrainsizeclasses fromthe-7 ato4 lsizeclasses,indicatingthedirectiontowhich thewindisblowingateachatmosphericlevel.Unitbarsrepresentthe windvelocityms )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 .40 Figure2.15Particlepathsfromtheheightofreleaseabovetheventredtriangle downtosedimentationontheground,calculatedfromwindadvection usingtheresultsfromtheinversionongrainsize.Particlepathsfrom thea-7 to-5 ,b-4 to0 andc1 to4 sizeclasses.Wepresent twodierentparticlepathsforthe4 fraction,withtwodierentrelease heights:10and20km42 Figure2.16IsomassmapfortheBF2layerfromaforwardmodelingusingthe TEPHRA2modelandinputparametersresultingfromtheanalysis presentedinthisstudyseeTable2.4.Notetheslightdispersaltoward thesouth-west.43 Figure2.17Massaccumulationperunitdistancekgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 ofparticlesingrainsize classesfrom64mmto63 m-6 to4 ,respectivelyforaxis1ESE axisdenedinFigure2.1b.45 Figure2.18Massaccumulationperunitdistancekgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 ofparticlesingrainsize classesfrom64mmto63 m-6 to4 ,respectivelyforaxis2SE axisdenedinFigure2.1b.46 Figure2.19Massaccumulationperunitdistancekgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 ofparticlesingrainsize classesfrom64mmto63 m-6 to4 ,respectivelyforaxis3SW axisdenedinFigure2.1b.47 vii

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Figure2.20Resultsofthestrongplumemodelforaplumeheightof20km.Trianglesareelddata.Thethicksolidlineisthethinningtrendpredicted bythemodelusingtheTGSDfromtheVoronoimethodwithazero accumulationlineat200km;thesolidlineistheexponentialdecay model;thedashedlineisthepower-lawmodel;thethinsolid,dottedanddashedlinesrepresenttheproportionofparticlesfallingfrom theumbrellacloudintheturbulent,intermediateandlaminarregime, respectively.49 Figure2.21Comparisonbetweentheobservedaccumulationonthegroundblack trianglesandthepredictedaccumulationonthegroundfromthe strongplumemodel,using i theTGSDfromtheVoronoianalysis andazeroaccumulationlineat50kmwhitetriangles, ii theTGSD fromtheVoronoianalysisandazeroaccumulationlineat200kmgrey trianglesand iii theTGSDfromtheinversionongrainsizedata lightgreycircles.Forfurthercomparison,weusedtheTGSDfrom the1980eruptionofMountSt.Helensgreysquares.Thethreeplots representatheESEaxis,btheSEaxisandctheSWaxisof Figure2.1b.51 Figure3.1RepresentationofahypotheticalvolcanicparticleandsomeofthemorphologicalparametersmeasuredbythePVS.Meandiameter:theradius r fromthecenterofthemasstotheparticleperimeterismeasuredateverypixelontheperimeter.Themeandiameteristhen calculatedfromthemeanvalueofthosemeasurements.Diameter:the diameterisdeterminedbythediameterofacirclewiththesamearea astheparticle.64 Figure3.2Frequencydistributionsoftheaspectratio AR ,convexity C and roundness R fordierentgrainsizeclassesfrom0 to5 .Atruncatedlognormaldistributionhasbeenttedtotheaspectratio AR dataandatruncatednormaldistributionhasbeenttedthroughthe convexity C androundness R dataforeachgrainsizeclasses.67 Figure3.3Frequencydistributionsoftheaspectratio AR ,convexity C and roundness R fordierentgrainsizeclassesfrom6 to10 .Atruncatedlognormaldistributionhasbeenttedtotheaspectratio AR dataandatruncatednormaldistributionhasbeenttedthroughthe convexity C androundness R dataforeachgrainsizeclasses.68 Figure3.4Variationsofshapeparameters AR C and R asafunctionofgrain sizeleftcolumnanddistancefromtheventrightcolumnforthe ESEaxisaxis1,seeFigure2.1b.70 Figure3.5Variationsofshapeparameters AR C and R asafunctionofgrain sizeleftcolumnanddistancefromtheventrightcolumnfortheSE axisaxis2,seeFigure2.1b.71 viii

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Figure3.6Variationsofshapeparameters AR C and R asafunctionofgrain sizeleftcolumnanddistancefromtheventrightcolumnforthe SWaxisaxis3,seeFigure2.1b.72 Figure3.7Comparisonsbetweenparticleterminalvelocitiescalculatedfromdifferentmodels: V KL ,approximatingvolcanicparticleassphereKunii andLevenspiel,1969; V WH blueeldandbluetrianglecalculated fromWilsonandHuang1979.Thediameteroftheparticleisthe equivalentdiameterofasphere.76 Figure3.8Cumulativefrequencydistributionofterminalvelocitiescalculatedwith thedierentmodelsexplainedinthetext V KL inred, V WH inblue with F calculatedassuming c = b and V WH indashed-bluewith F calculatedassuming c =0.Notethejumpin V KL valuesforterminal velocitiesofabout5.5ms )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 inthe0 fraction.78 Figure3.9Comparisonbetweenmeasureddiametersofvolcanicparticlesanddiametersofspheresfallingatthesameterminalvelocity.Resultsfor the0 inblack,1 inred,2 inblue,3 inyellow,4 ingreen,5 in orangeand6 inpurple.79 Figure3.10Relationshipbetweenthemeanvaluesof V WH / V KL and AR forparticlegroupedin0.1 AR binsandforeachgrainsizefractionfrom0 to8 .The1standarddeviationisshownastheverticalerrorbar. Equationsandcorrelationcoecientforeachlinearrelationshipare alsoshown.81 Figure3.11Inuenceofthedierentmodelofterminalvelocitycalculationsonthe sedimentationoftephradepositfordierentgrainsizeclassesfrom0 to4 .Inred,sedimentationcalculatedusing V KL andinblue V WH Thedashedblacklinesaresedimentationcalculatedwithatruncated normaldistributionfor F .ThesimulationsarefortheBF2layerof PululaguavolcanoseeChapter2,withacolumnheightof20kmand atotalmassvaryingforeachgrainsizeaccordingtothetotalgrainsize distributioncalculatedfora"zeroaccumulationline"at200kmfrom theventseeFigure2.7andTable2.1.85 Figure4.1LocationmapshowingtheBataanPeninsula,formingthesouthern partoftheLuzonPeninsulawithinthePhilippinesarchipelago.Black trianglesindicateactivevolcanoes.WhitetrianglesindicateactivevolcanoesclosesttotheBataanNuclearPowerPlantBNPP.TheBataan Peninsulaismainlyformedfromtwolargevolcanoes,Mt.Natibtothe northandMt.Marivelestothesouth.ThelocationoftheBNPPis markedwithablacksquare.92 ix

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Figure4.2Thetotalgrain-sizedistributionusedinthetephramodelsisderived fromtheanalysisoftheclimacticPlinianeruptionofMt.Pinatuboin June1991ClassIIfragments.ModiedfromKoyaguchiandOhno .105 Figure4.3Hazardsassociatedwithtephrafalloutarestronglydependentonmeteorologicalconditions.Here,acompilationofreanalysisdataforthe BNPPsiteillustratestheaveragedarklineandonestandarddeviationhorizontalbarsofwindconditionsin2006,forathedirection towardwhichthewindisblowingandbwindspeedms )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 ,asa functionofheightabovesealevel.ThesedataareusedasinputparametersforTEPHRA2toestimatetephraaccumulationinthesite region.cTephradepositionattheBNPPsiteismaximumwhenthe windblowsfromthevolcanotowardthesite.Thepercentageofthe timethewindblewtowardthesite 15 fromMt.Natibcircles, Mt.PinatubodiamondsandMt.Marivelestrianglesisgraphedas afunctionofheightabovesea-level.106 Figure4.4ExplosiveeruptionsofaMt.Pinatubo,bMt.Natib,andcMt.Marivelesvolcanoesmayresultinsubstantialaccumulationoftephraatthe BNPPsite.Theseexamples,basedonoutputfromTEPHRA2,show isomassmapsforeruptionsofvariousmagnitudesandwindconditions. InaaVEI6eruptionofMt.Pinatuboduringaveragewindconditions for2006resultsinanisomassmapthatisverysimilartotheactual tephradistributionfollowingthe1991eruptionofMt.Pinatubo.In thisexample,tephraaccumulationatthesiteis 100kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(2 ,amass loadsucienttocausedamagetosomestructures,andtoadverselyaffectelectricalandwaterltrationsystems.Incontrast,amuchsmaller magnitudeeruption,VEI4,fromMt.Natibwouldpotentiallyresultin muchlargertephraaccumulationatthesite, > 1000kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(2 b.Inthis simulationwindisassumedtoblowfromMt.Natibtowardthesiteat averagespeedasafunctionofelevationfortheregion.Similarly,the modelsuggeststhataVEI5eruptionofMt.Mariveleswouldresult in > 1000kgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 tephraaccumulationatthesite,ifwindsblewfrom thevolcanotowardthesite.Contoursareinmassoftephraaccumulationperunitareakgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 ,dry,wherekgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 isroughlyequivalent to10cmtephrathickness.108 Figure4.5Log-normallydistributedvaluesfortotalamountoftephraerupted kg.Theprobabilisticassessmentoftephrafalloutrandomlychooses totaleruptionmassvaluesfromthislog-normaldistribution.Therange ofpossiblevaluesisinitiallycalculatedfromarangeofprobableeruptioncolumnheightsanderuptiondurations.110 x

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Figure4.6Hazardcurvesshowtheconditionalprobabilityofexceedingdierent thicknessesoftephraatthelocationoftheBNPP,givenavolcanic eruption.GraphacomparestephrathicknessesmodeledforNatib ,Mariveles,andPinatubo.Thecurvesweregeneratedfrom TEPHRA2output,basedon1000simulationsusingwindvaluesrandomlyselectedfromreanalysisdatafor2006anderuptionparametersrandomlyselectedfromarangeofexplosiveeruptionconditions. Thisgraphindicatesthatgivenaneruption,tephraaccumulationat theBNPPfromeruptionsofMt.NatibandMt.Marivelesaresimilar,andwouldlikelyexceedtephraaccumulationsassociatedwitha Mt.Pinatuboeruptionbyoneorderofmagnitude.Graphbcompares theEBASCOhazardcurve,basedonthe1912eruptionofMt.KatmaiinAlaska,withtwohazardcurvesgeneratedby1000simulationsusingTEPHRA2:curve2isidenticaltocurve1ingrapha, curve3isbasedoneruptionparameterssimilartothe1991eruptionof Mt.Pinatuboandarandomwindeld,alsobasedon2006reanalysis data.Thisgraphindicatesthatusingthe1912Katmaieruptionasan analogfortephraaccumulationoverestimatesthehazardatthesiteby approximatelyoneorderofmagnitude.111 Figure4.7Mapcontourstheprobabilityoftephraaccumulationexceeding10cm 100kgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 ,givenanexplosiveeruptionofMt.Natib.Notethat thesesimulationsindicatethattephraaccumulationismostlikelyon theWandSWanksofMt.Natib,suggestingtheseareasarepotential sourcesforlaharsfollowingexplosivevolcanicactivity.112 Figure4.8aPotentiallaharsourceregionsdarkshadedareasresultingfrom ahypotheticalVEI5eruptionfromMt.Natibwindblowingtoward thesite,identiedasthoseareaswheretheFactorofSafety, FS 1. ArrowshighlightmaindrainagesontheSSWpartofMt.Natibwhere laharshavethepotentialtooccurandaecttheNPPsiteregion.Black starindicatesthelocationforthehazardcurveshowninb.bExceedanceprobability,basedontheVEI5eruptionusedina,andsurfaceruno% waterandsedimentrunodividedbytheamount ofrainfallplottedasafunctionoftephrathickness.Thisplotindicatesthatlaharpotentialincreaseswithhighertephraaccumulation andhigherruno.Surfacerunovs.tephrathicknessvaluessolid trianglesareforne-grainedtephraonMiyakejimavolcanoJapan, modiedafterYamakoshietal..RunoisdiminishedforcoarsegraineddepositsopentriangleonMiakejimavolcano.Forexample, givenanexplosiveeruptionVEI5ofMt.Natib,theTEPHRA2model indicatesthattheprobabilityoftephraexceeding17cmis50%.EmpiricalobservationsonMiyakejimavolcanosuggestthatforthisthickness oftephra, 25%ofrainfallandsedimentbyvolumewillrunointo drainages,forminghyper-concentratedows.115 xi

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Figure4.9aThreepotentialpyroclasticowrunoutsfromthecalderaoorof Mt.Natib,estimatedusingtheenergyconemodel.The3gray-shaded regionsrepresentpossibleareasinundatedbypyroclasticowsoriginatingfromthecollapseofa100m-highdome.Thedierentshaded regionsrepresentareasinundatedbypyroclasticowsofincreasing potentialenergy,representedbytheratioofdomeheighttorunout length: H=L =0 : 2darkestgrayarea, H=L =0 : 15mediumgray area, H=L =0 : 1lightgrayarea.Uncertaintyintheappropriate valueof H=L resultsinuncertaintyinthetotalrunoutoftheow. Inallofthesecases,thepyroclasticowsdonotovertopthecaldera wall,andthusowawayfromtheBNPPsite.bIncontrast,higher releaseheightse.g.,1000mabovethecalderaoorassociatedwith eruptioncolumncollapseandhigherintensityeruptionsresultininundationoftheBNPPsite.Shadedareasshowinundationbypyroclastic densitycurrentsfor H=L =0 : 15closesttothevent,darkestshading, H=L =0 : 1,and H=L =0 : 075farthestfromthevent,lightestshading.119 xii

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TephraTransport,SedimentationandHazards AlainC.M.Volentik ABSTRACT Tephradepositsareoneofthepossibleoutcomesofexplosivevolcaniceruptionsand aretheresultofverticalsettlingofvolcanicparticlesthathavebeenexpelledfromthe volcanicventintotheatmosphere,followingmagmafragmentationwithinthevolcanic conduit.Tephrafalloutrepresentsthemainvolcanichazardtopopulatedareasandcriticalfacilities.Therefore,itiscrucialtobetterunderstandprocessesthatleadtotephra transport,sedimentationandhazards. Inthisstudy,andbasedondetailedmappingandsamplingofthetephradepositofthe 2450BPPlinianeruptionofPululaguavolcanoEcuador,Iinvestigatetephradeposits throughavarietyofapproaches,includingempiricalandanalyticalmodelingoftephra thicknessandgrainsizedatatoinferimportanteruptionsourceparameterse.g.column height,totalmassejected,totalgrainsizedistributionofthedeposit.Ialsouseastatistical approachsmoothedbootstrapwithreplacementmethodtoassesstheuncertaintyinthe eruptiveparameters.The2450BPPululaguavolcanicplumedynamicswerealsoexplored throughdetailedgrainsizeanalysisand1Dmodelingoftephraaccumulation.Finally,I investigatetheinuenceofparticleshapeontephraaccumulationonthegroundthrough aquantitativeandcomprehensivestudyoftheshapeofvolcanicash. Astheglobalneedforenergyisexpectedtogrowinthefuture,manyfuturenatural hazardstudieswilllikelyinvolvetheassessmentofvolcanichazardsatcriticalfacilities, includingnuclearpowerplants.Iaddressthepotentialhazardsfromtephrafallout,pyroclasticowsandlaharsfortheBataanNuclearPowerPlantPhilippinesposedbythree nearbyvolcanoescapableofimpactingthesiteduringanexplosiveeruption.Istressthe xiii

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needforgoodconstraintsstratigraphicanalysisandeventsdatingonpasteruptiveevents tobetterquantifytheprobabilityoffutureeventsatpotentiallyactivevolcanoes,theneed forprobabilisticapproachesinsuchvolcanichazardassessmentstoaddressabroadrangeof potentialeruptionscenarios,andtheimportanceofconsideringcoupledvolcanicprocesses e.g.tephrafalloutleadingtolaharsinvolcanichazardassessments. xiv

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CHAPTER1 INTRODUCTION Volcaniceruptionscanvarydramaticallyinstyle,sizeandtypeoferuptedproducts, fromlow-volumeextrusionofviscouslavaatthesurfaceoftheEarthtolargevolumesof volcanicasheruptedexplosivelyandaectingwideareasaroundthevolcanoSigurdsson etal.,2000.Tephraarepyroclaststhatareeruptedintotheatmosphereandfallbacktothe Earth'ssurface.Usuallythetermisappliedtoparticlesthataretransportedprimarilyin theeruptioncolumnandbyverticalsettlingthroughtheatmosphere,ratherthanprimarily bylateralow,whichoccursduringpyroclasticdensitycurrents. Asmagmarisesintheconduitofthevolcano,bubbleformationandexpansionresultsin disruptionofthemagma.Asbubblesformandgrow,theascendingmixturebecomesdispersed,characterizedbyanessentiallycontinuousgasphase,withisolatedmagmadroplets. Thedropletscooltoformpumiceorscoria-knownaspyroclasts.Pyroclastsresultingfrom thisprocesshaveawiderangeofsizesfrommicrontodecimetric.Thesizes,shapesand densitiesoftheseparticlesarefundamentalcontrolsontheirsettlingvelocity,andhence theirpatternofdeposition.Thevelocitywithwhichthismixtureleavestheconduitand enterstheatmosphere,formingavolcanicplume,isanadditionalcontrolontheeventual patternoftephradeposition.Thismixtureisexpelledintotheatmosphereandwilldevelop avolcanicplumeiftheconditionsforbuoyancyareachievedi.e.densityofthevolcanic mixture < densityofthesurroundingatmosphere.Oncetheeruptivecolumnreachesthe levelofneutralbuoyancy,itwillcontinuetoriseduetomomentumforcesbeforelaterallyspreadingintheatmospherearoundthelevelofneutralbuoyancy,formingagravity current,termedan umbrellacloud Sparks,1986;Sparksetal.,1997. 1

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Volcanicparticlessettleoutoftheumbrellacloudaccordingtotheirterminalvelocity andfalltotheground.Astheyfall,pyroclastsaredispersedbythewind.Largerclasts mightalsosettleoutoftherisingplumethroughtheeruptivecolumnmargins.Thus, thephysicalprocessesthatresultinexplosivevolcaniceruptions,magmafragmentation, heightoftheeruptioncolumn,andsizedistributionofpyroclastsallplayimportantroles intheeventualdepositionoftephra.Inordertounderstandtephradeposits,andforecast volcanichazardsassociatedwithtephrafallout,wemustlearnasmuchaspossibleabout theseprocesses. Volcanologistsstudytheseprocessesfromavarietyofperspectives.Forexample,itis notpossibletoobservedirectlytheascentandfragmentationofmagmaduringexplosive volcaniceruptions.Geophysicalobservationsgatheredduringvolcaniceruptionsprovide someinsightintothenatureofmagmaascentandowinconduitsNeuberg,2006.Study ofthephysicsofmagmaascenthasledtothedevelopmentofnumericalsimulationsof conduitowandfragmentationofmagmae.g.Dobran,1992;Woods,1995;Papale,1999; Melnik,2000;LlewellinandManga,2005.Ourunderstandingofthephysicsoferuption columnsgreatlyimprovedthroughthestudiesofSparks,WoodsandSparks etal.,amongothers.Throughfutureimprovementsinknowledgeandmodelingof volcanicprocesses,wewillbeabletoreneandfurtherdevelopmodelsoftephradispersion andsedimentation. Inthisstudy,Iuseinformationavailablefromthedeposite.g.totalthicknessand grainsizedatatoexploredierentaspectsoftephraanalysis.Empiricaland2Danalyticalmodelingoftephradepositswereusedtoinferimportanteruptiveparameterssuchas totaleruptedmass,columnheightandtotalgrainsizedistributionofthedeposit.Through astatisticaltechniqueasmoothedbootstrapwithreplacementmethod,proposedbyEfron andTibshirani,1991Iassesstheuncertaintyinthedeterminationofcolumnheightand totaleruptedmass.Detailedgrainsizeanalysiscombinedwith1Dmodelingoftephra accumulationwereusedtoinvestigateplumedynamics.Finally,throughadetailedquantitativeandcomprehensivestudyofvolcanicclastmorphology,Iexaminetheinuenceof 2

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theshapeofvolcanicparticlesontheirterminalvelocityandthereforeontephradispersal models. Mystudybuildsonavastliteraturededicatedtotheinferenceofvolcanicprocessesfrom thestudyofvolcanicdepositse.g.Walker,1971;Walkeretal.,1971;Suzuki,1983;Carey andSparks,1986;WilsonandWalker,1987;Armientietal.,1988;Pyle,1989;Bursiketal., 1992b;Sparksetal.,1992;Bonadonnaetal.,1998;Connoretal.,2001;Bonadonnaetal., 2002;BonadonnaandPhillips,2003;Bonadonnaetal.,2005a;BonadonnaandHoughton, 2005;ConnorandConnor,2006.Thesestudiesfocusedmainlyonthetransportand sedimentationprocessesfromtheumbrellacloud,althoughsomealsodescribedthesedimentationfromtheplumemargins.Suzukiwasthersttoproposetheanalytical solutionoftheadvection-diusion-sedimentationequationtomodeltephradeposits,and hisapproachwaslaterrenedbyArmientietal.andBonadonnaetal.a amongothers.Myworkisbasedonthesemodelsoftephratransportandsedimentation fromtheumbrellacloudappliedtothe2450BPtephradepositofPululaguavolcano.I usenotonlythicknessdataorisomassdata,butalsograinsizedataderivedfromthe deposittobettercharacterizetheeruptiveprocessesofthe2450BPPlinianeruptionof Pululaguabutalsoofvolcaniceruptionsingeneralandtoassesstheuncertaintyinthe determinationofcrucialeruptiveparameters.Empiricalmodelsusedtodetermineeruptive parametersareoftensubjecttointerpolatione.g.interpolationsofisopachandisopleth contours.Theemergenceofnumericalmodelingreducestheneedforinterpolationbecausemassandthicknessareestimatedateachsamplepointusingatephrasedimentation model. Thetephradepositofthe2450BPPlinianeruptionofPululaguavolcanoEcuador providesaframeworkformyinvestigationofhowtephradepositscanbeusedtoinfer thecharacteristicsoflongpasteruptionsusingquantitative,numericalmodelsoftephra dispersionseeChapter2.Thiseruptionwasremarkablesinceitapparentlyoccurred inrelativelycalmatmosphericconditions,thereforeremovingmanyofthecomplexities ofatmosphericinteractionfromtheproblem.DuringtwoeldexpeditionstoEcuador, 3

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ImappedandsampledthedepositaroundPululagua,acquiringcrucialdatatobetter understandthedepositandtomodeltheeruption.Sampleswerebroughtbacktothe UniversityofSouthFloridaUSFforfurtheranalysisofthephysicalcharacteristicsofthe deposit,suchasgrainsizedistributionandgrainshapeanalysis.Throughempiricaland analyticalmodeling,combinedwithuncertaintyanalysis,Iwasabletobetterconstrain eruptionsourceparametersforthe2450BPPlinianeruptionofPululaguavolcanosee Chapter2.Grainsizedatawereusednotonlytoinfereruptiveparameters,butalsoto betterunderstandplumedynamics. Quantitativeparticleshapedatahavebeenobtainedfromthetephradepositbyusing anewdevicetostudygrainshapeandsizesofverysmalldownto1micronpyroclasts. Thisinstrument,thePharmaVisionopticaldevice,worksbyscanningaglassslideon whichthesamplehasbeendeposited,creatinganimageofeachsingleclastandextracting morphologicalparametersfromthisimage.Thesemorphologicalparametersarethenused toinvestigatevariationsinshapeparametersofvolcanicparticlesasafunctionofdistance fromtheventandofgrainsize.Basedonthesedata,Iexploretheinuenceofparticleshape onterminalvelocitythroughtheimplementationofthreedierentmodelsproposedinthe literatureandontephraaccumulationontheground,astheterminalvelocityofvolcanic clastsistheprimaryvariablecontrollingthesedimentationoftephraseeChapter3. Tephrafalloutisthemainvolcanichazardlikelytoaecthumaninfrastructuresbecausetephracanbetransportedtogreatdistancesfromeruptingvolcanoese.g.theMay 1980eruptionofMountSt.Helens,Durantetal.,2009andtheMay2008eruptionof ChaitenvolcanoChile,Folchetal.,2008;Wattetal.,2009.Currentlyandinthenear future,volcanichazardstudieswillinvolvetheassessmentofvolcanichazardsatcritical facilities,includingnuclearpowerplants.Formanynuclearpowerplants,noadequate volcanichazardassessmenthasbeenperformed.ConsequentlytheInternationalAtomic EnergyAgencyIAEAisdevelopingguidelinesforvolcanichazardassessmentHilletal., 2009,butthereisaneedforapracticalexampleofhowsuchanassessmentshouldbeconductedfromavolcanologicalperspective.Therefore,Iaddresstheissueoftephrahazard 4

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throughacomprehensivetephrahazardassessmentstudyfortheBataanNuclearPower PlantBNPPinthePhilippinesseeChapter4.Atthetimeofthesitingandconstructionofthenuclearpowerplantinthelate1970'sandearly1980's,thevolcanichazard assessmentconductedbyaU.S.consultingcompanyonbehalfofthePhilippineAtomic EnergyCommissionwasquitecontroversial.TheirconclusionsEBASCO,1977,1979 werequestionedbyU.S.scientistsNewhall,1979,expertsfromtheIAEAIAEA,1978 andotherpanelsinthePhilippines.Furthermore,theUnionofConcernedScientistscited theproximityofthesitetothepotentiallyactiveMt.Natibvolcanoasamajorsourceof concernD'AmatoandEngel,1988.Thiscontroversyisstillongoing,sincetheIAEAhas beenappointedtohelpassessthefeasibilityofrehabilitatingtheBataanNuclearPower Plant,andmorerecentlythere-commissioningoftheBataanNuclearPowerPlanthasbeen approvedJ.Cabato,personalcommunication.Inthesamestudy,Ialsoaddressotheraspectsofvolcanichazardsthatarelikelytoaectcriticalfacilities,namelypyroclasticows andlaharsseeChapter4.Myresultsemphasizetheneedforprobabilisticapproaches inforecastingtheamountoftephrathatmightreachtheBNPPfollowinganexplosive eruptionatoneofthreenearbyvolcanoesMt.Pinatubo,Mt.NatibandMt.Mariveles,in ordertoencompassallthepossiblevariationineruptiveparametersthatledtotephradepositiononthesite.Ifoundthatthesiteisvulnerabletopotentiallargevolcaniceruptions fromthenearbyMt.Natib.Ialsostresstheimportanceofcouplingvolcanicphenomena e.g.,tephrafalloutandlaharsinthevolcanichazardassessmentandhowtheanalysisof complexvolcanicphenomenacanbestudiedsystematicallyaspartofacharacterizationof thevolcanichazardsfacedbysuchcriticalfacilities. Thisdissertationincludesadescriptionofthephysicalcharacteristicsofthetephra depositresultingfromthe2450BPPlinianeruptionofPululaguavolcanoEcuadorand ofmodelingthetransportandsedimentationprocessesofthistephradepositthroughempiricalandanalyticalapproaches.Onlybyunderstandingthesebasicvolcanicprocesses canwedevelopanadequateunderstandingofvolcanichazards.Thisunderstandingisnec5

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essaryinordertoevaluatevolcanichazardsatnuclearfacilities,forsimilarinfrastructure, andforpopulationslivingnearvolcanoes. Thepronoun"we"isusedinchapter2andchapter4,but"I"inchapter3,reectingthe contributionsofcoauthorsonthesepapersthataresubmittedforpublication.Chapter2 issubmittedtothe JournalofGeophysicalResearch andchapter4issoontobepublished inthebook VolcanicandTectonicHazardAssessmentforNuclearFacilities editedby Connor,C.B.,Chapman,N.andConnor,L.J. 6

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CHAPTER2 MODELINGTHECLIMACTICPHASEOFTHE2450BPPLINIAN ERUPTIONOFPULULAGUAVOLCANO,ECUADOR 2.1Introduction Tephradispersalmodelsareimportantinvolcanology,notonlytoconstrainphysical processesleadingtotephratransportandsedimentationfollowinganexplosiveeruptionat agivenvolcanoArmientietal.,1988;Bursiketal.,1992b;BonadonnaandPhillips,2003; Costaetal.,2006,butalsotoassesstephrahazardsthatpotentiallythreatenpopulated areasConnoretal.,2001;Bonadonnaetal.,2005a;Houghtonetal.,2006;Macedonio etal.,2008andcriticalfacilitiesVolentiketal.,2009.Tephrasedimentationmodels areusuallybasedonanalyticalsolutionsoftheadvection-diusionequatione.g.Suzuki, 1983.Whilethephysicsoftephradiusionseemstobewell-capturedbythesemodels,the windeldatthetimeoftheeruptionisoftennoteasilyconstrained,exceptforobserved eruptions.Accuratewindelddataareoftendiculttoinferbecausewindeldsforpast eruptionsarederivedfromelddatathroughanempiricalmodelthatisbasedonaxed windproleCareyandSparks,1986.Thuswindadvectionaddsalevelofcomplexity inthestudyoftephradispersion.Onlythreeeruptionsareknowntohaveoccurredin approximatelystillatmosphericconditions,resultinginacircular-shapeddispersionof tephraaroundthevent:the 5,000BPFogoAeruptionWalkerandCroasdale,1971; Bursiketal.,1992b,the1210BPeruptionofCotopaxilayer9ofBarberietal.,1995 andthe2450BPPlinianeruptionofPululagua,EcuadorPapaleandRosi,1993.Wehave chosenthelattertoinvestigatesedimentationfromPlinianplumesandvalidateempirical andanalyticalmodelsforthedeterminationofcrucialeruptiveparametersPyle,1989; BonadonnaandHoughton,2005;ConnorandConnor,2006andanalyticalmodelsfor 7

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thedescriptionofparticletransportanddepositioni.e.BonadonnaandPhillips,2003; Bonadonnaetal.,2005a;Connoretal.,2008. Thereisuncertaintyinthemodelingoftephradepositsandtheinferenceoferuptive parameters.Suchuncertaintiesareusuallynotwelldescribedintheliterature.Therefore, wedescribeaMonteCarloapproach,combinedwithasmoothedbootstrapmethod,to quantifytheuncertaintyinthedeterminationoftotaleruptedmassandcolumnheight. Weinvestigatethevariabilityoftheresultsi.e.columnheightandtotaleruptedmassin termsofthetotalaccumulationobservedandforeachgrainsize. 2.2Geologicalsetting PululaguaVolcanoispartoftheactiveWesternAndeanVolcanicFrontofEcuadorFigure2.1aHalletal.,2008andislocated15kmnorthofQuitoFigure2.1b.Papaleand RosiandAndradeandMolinadescribedthevolcanicstratigraphyandevolutionofPululaguavolcano.PululaguaVolcanoisa19km 2 daciticcalderaandissurrounded bytenolderlavadomes.ThemostrecentvolcanicactivityatPululaguastartedwiththe formationofdaciticlavadomeswiththeirassociatedblock-and-ashowdeposits,which arecappedbyanubiquitous,well-developedpalaeosoil.The2450BPPliniansequence overliesthispalaeosoilconformably.Theexplosiveactivityleadingtotheformationofthe irregularlyshapedcalderaFigure2.1coccurredasaseriesofvolcaniceruptionsduring which 5 )]TJ/F15 10.9091 Tf 8.485 0 Td [(6km 3 DREofhornblende-bearingdaciticmagmawaserupted.Papaleand RosiestimatedthatthemainbasalpumicefallBFdepositFigure2.2coversan areaofmorethan2 : 2 10 4 km 2 andhasavolumeof 1.1km 3 0.34km 3 DRE.ThegeneralstratigraphyofPululaguadeposits,aswellasthecircularisopachandisoplethmaps, werepresentedbyPapaleandRosi1993forthewholebasalfalloutdeposit.Thecircular patternoftheisopachandisoplethmapsindicatesemplacementinwind-freeconditions, whichisconrmedbyanubiquitous,normallygradedWhiteAshdepositWA,athinash bedthattopsthePliniansequencePapaleandRosi,1993.Thisashbed,alsodened asco-plinianashaccordingtothegeneraldescriptionofFiersteinandNathenson, 8

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isthoughttohaveoriginatedfromtheslowsettlingofnes < 1mmaftercessationof thesustainedPliniancolumn.Hadamoderatewindeldbeenpresentatthetimeofthe eruptionoftheBFlayer,theneWhiteAshparticleswouldhavebeenadvecteddownwindandwouldhavesedimentedawayfromthevent.PapaleandRosicalculated amaximumcolumnheightof36kmbasedonthe3.2,1.6and0.8cmlithicisoplethsand 21kmbasedonthe6.4cmlithicisopleth,usingthemodelofCareyandSparks thereafterreferredasCS.ThemodelofWilsonandWalkerappliedtothe4.9and 6.4cmlithicisoplethsyieldedacolumnheightof28kmPapaleandRosi,1993.Magma dischargeratewasestimatedtobe2 10 8 kgs )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 ,followingboththemodelsofSparks andWilsonandWalker. PallinirevisitedtheBFdepositandsubdivideditintoadditionallayerscompared tothestudyofPapaleandRosi,andproposedavolumefortheBFof 0 : 58km 3 basedonthemethodofPyle.TheeruptioncolumnheightwasestimatedusingCS andPylemodelsandyieldedheightsof36kmand28kmrespectively.Thus,Pallini proposedaprobablecolumnheightof32km,resultingfromtheaverageofthese twoestimates,andamagmadischargerateof2 10 8 kgs )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 basedonSparks,1986and 3 10 8 kgs )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 basedonWilsonandWalker,1987. ThiswholeBFtephrasequenceisoverlainbynumerouspyroclasticdensitycurrents pyroclasticowsandsurgesinthenear-ventregionintercalatedwithinotherminortephra falloutdepositsPapaleandRosi,1993;AndradeandMolina,2006;Petriello,2007.The lattertephradepositsshowaglobalwestwarddispersionPapaleandRosi,1993compared totheBFsequence. Padronetal.identieddiuseCO 2 emissionswithinthecalderaofPululagua. TheyestimatedatotalCO 2 emissionrateof9.8tkm )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 d )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 tonsperdaypersquare kilometer.ThisrelativelylowCO 2 emissionvalueandlackofothersignsofunrestindicate thatPululaguaisinaperiodofquiescenceandthereforeposesnoimmediatehazardsto thesurroundingarea. 9

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Figure2.1.aLocationmapofEcuador,withthemainvolcanoestrianglesandlocalities circles.PululaguaislocatednorthofQuitoandisshownasabigwhitetriangle.The blacksquarearoundPululaguarepresentstheareaofinterestshowninbandthroughout thedierentmapsinthispaper.bRegionofinterestaroundPululagua,withthethree axesusedinthisstudy:1,theESEaxisinred;2,theSEaxisinblueand3,theSW axisingreen.Numbersrefertosamplelocations.Citiesabbreviationsareasfollows,A: Atahualpa,C:Calacali,G:Guayllabamba,N:Nanegal,Ng:Nanegalito,No:Nono,P: Perucho,SA:SanAntonio,SJM:SanJosedeMinas.Thedarkgreyarearepresentsthe extentofQuito;cZoomonthePululaguavolcaniccomplex,showingtheirregular-shaped caldera. 10

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2.3Newstratigraphy WeusetheworkofPallinitodeneastratigraphicsubdivisionfortheeruption Figure2.2: i abasalgreyashBGA,resultingfromseveraldiscretephreatomagmatic eruptionscharacterizingtheonsetofexplosiveactivityatPululaguaPapaleandRosi, 1993; ii twoearlyPlinianfalloutdepositsBF1aandb,overlainby iii themain climacticphasefalloutlayerofthePlinianeruption,theBF2layer,thatisthefocusofthis study; iv BF3Plinianfalloutdeposit,and v theWhiteAshWAfalloutdeposit.The BF2,BF3andWAepisodesarethoughttohaveoccurredinstillatmosphericconditions, whereastheBGAandBF1aandbeventsdisplayaNEdispersalaxisPallini,1996.These vetephradepositsareconformableandarethoughttohavebeendepositedwithoutany signicantbreakintheexplosiveeruptionPapaleandRosi,1993.Distinguishingfeatures ofthesedierentfalllayersaredescribedbelow. TheBGAlayermarksthebeginningoftheexplosiveeruptionofPululaguaFigure2.2a PapaleandRosi,1993.TheBGAisane-grainedashdeposit,composedofmultiplethin layersofalternatingcoarseandnedepositsthataretheresultofseveralphreatomagmatic pulses.Theseareinterpretedtocharacterizethevent-openingphaseofthePlinianeruption. ThethicknessofBGAvariesfromafewmillimetersuptoalmost10cminthemostproximal sections. TheBasalFallBFdepositliesconformablyontheBGAlayerFigure2.2,without anysignofbreakinthesedimentationprocess.TheBF1aandBF1blayersarecomposed ofwhiteangularpumicesandupto10%lithicsbyvolumeFigures2.2aand2.2b.The BF1aandblayersareseparatedbysurgedepositsinproximalareasFigure2.2aandby athinbedofnelapillifurtherawayfromthevent.Theiraxesofdispersionaretoward theNNWforBF1aandNWforBF1bPallini,1996. TheBF2layerrepresentstheclimacticphaseoftheBFPlinianeruptionofPululagua. ThislayeristhethickestandcoversthewidestareaofalloftheBFlayersFigure2.2.The transitionbetweenBF1bandBF2ismarkedbyasharpincreaseingrainsize.Pumices arewhiteincolor,dacitic,angularandnelyvesiculated.Accidentalbasementlithicsare 11

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Figure2.2.Pictureanddetailedstratigraphyoftheoutcropforthreelocationsatvarious distancesfromthevent.aProximal:PL40locatedat 4.5kmsoutheastfromthe inferredvent.bMedial:PL19locatedat 13kmeast-southeastfromtheinferredvent. cDistal:PL24locatedat 21kmsoutheastfromtheinferredvent.Wedenedthe inferredventasbeinginthecenterofthecaldera,inthecurrentpositionofthecentral post-calderadomes.Notethealmost-constantthicknessoftheWhiteAshinanylocation awayfromthevent. 12

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usuallyhighlyoxidizedandcompriseupto20%involumeofthedeposit.Inproximal areas,oneortwoashlayersoccurintheuppermostpartoftheBF2deposit.Theselayers representeitherapauseinthePlinianeruption,resultingintheaccumulationofslowsettlingneparticles,orsmallpyroclasticdensitycurrentspyroclasticsurgesresulting fromephemeralinstabilitiesinthePliniancolumn.Theseashlayersarenotubiquitous andthinquicklyawayfromthevent. ThetransitionbetweentheBF2andBF3layersisrepresentedbyaseriesofdilute pyroclasticdensitycurrentsinproximallocationsFigure2.2a.Apronounceddecreasein grainsizemarksthistransitioninmoredistalsections.Thenatureofthepumiceclasts inBF3arethesameasthoseofBF2andBF1:white,angularandnelyvesiculated pumices.Lithicfragmentsarestillpresent,butarelessabundantthanintheBF2 )]TJ/F15 10.9091 Tf 8.485 0 Td [(10% involume.Intheupperthirdpartofthedeposit,theBF3displaysadistinctincrease insizeofpumiceclasts,whichcanbeattributedtoanincreaseintheeruptionintensity resultinginahighercolumnheight. ThecontactbetweentheBF3layerandtheWhiteAshlayerisnotsharp,asisthecase withpreviouscontacts,butrathershowsagradationingrainsizefromtheBF3tothe WAlayersFigure2.2.Weusedtheappearanceofthedominantwhitecolorfromthene whiteashandthedisappearanceoflargeclasts 1mmtosubdividetheBF3andthe WAlayers.TheWAlayerisnormallygradedandubiquitouslycoverstheunderlyinglapilli falloutdepositsoftheBFeruption.Therefore,theWAmarkstheendoftherstPlinian phaseofPululagua.Wherepristine,theWAthicknessvariesfrom10cmclosetothevent to6cmindistallocations.TheareacoveredbytheWAlayerisgreaterthanthearea coveredbythepreviousBFlayers,astheWAhasbeenfoundasfaras63kmwestofthe calderaPallini,1996andevenatthecoastline 200kmwestfromthecalderaP.Mothes, personalcommunication.ThepresenceoftheWAontopoftheotherBFlayersnotonly guaranteestheintegrityoftheunderlyingunits,butalsogivesahintabouttheatmospheric conditionsatthetimeoftherstPlinianeruptionofPululagua.Theoccurrenceofsucha uniformnegrainedlayerrequiresanearlystillatmosphericcolumn,asneparticleshave 13

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suchlowterminalvelocitiesthattheywouldhaveformedanasymmetricdepositinwindy conditions. ThesePlinianfalloutdepositsfromPululaguaareoverlainbyasequenceofpyroclastic surgesandpyroclasticows,interlayeredwithadditionalminorPlinianfalloutdeposits fromPululaguaPapaleandRosi,1993;AndradeandMolina,2006;Petriello,2007. Inproximallocations,theBF2layerpresentsoneortwohorizonsofnerashFigure2.2a,thatcouldrepresentasmallpauseintheeruption,resultinginthesettlingof neparticles,orsmallpyroclasticdensitycurrentspyroclasticsurges,resultingfromlocalinstabilitiesintheeruptioncolumn.Furthermore,inthesameproximalareas,small densitycurrentdepositsverysmallvolumepyroclasticowsand/orsurgesareinterbeddedbetweentheBF2andBF3layersFigure2.2a,suggestingeitheranotherpauseinthe sustainedphaseofthePlinianeruptionbetweentheBF2andBF3layersor,again,some smallinstabilitiesoftheouterpartofthevolcanicplume.However,thesharptransition ingrainsizebetweentheBF2andBF3layersinalllocationsarguesinfavorofapausein thePlinianphaseoftheeruption. Inthepresentstudy,wefocusontheBF2layer,whichrepresentstheclimacticphase ofthe2450BPPlinianeruptionofPululagua.WemeasuredthicknessoftheBF2layers at73locations.BF2thicknessvariesfromabout40cminthemostproximallocationi.e. about4.5kmfromtheinferredventinthepresentcalderatolessthan1cminthemost distallocationwesampledabout35kmfromtheinferredvent.Sampleswerecollected at53locationsforgrainsizeanalysisFigure2.3andforeachlocation,wecalculatedthe medianclastdiameterMd andthegraphicalstandarddeviationorsorting, from InmanFigure2.4. 14

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2.4Empiricaldeterminationoferuptiveparameters 2.4.1Samplegrainsizeandtotalgrainsizedistribution 2.4.1.1Grainsize Wecollected53samplesanddry-sieveddownto4 mat1 intervals.Proximal depositsweresievedintheelddowntothe-3 meshandthefractionnerthan-3 was rstquarteredtoreducethetotalvolumeoftheremainderdeposit,andthencarriedbackto thelabforfurthersieving.Theashfractionnerthan4 mwasanalyzedforgrain sizecharacteristicsdownto12 withtheMalvernPharmaVision830PVSautomated opticaldevice.ResultsfromthePVSincludedierentmorphologicalparametersofthe particlesthatmayberelatedtosettlingvelocity,suchasthemaximumlength,themean diameter,orthewidthoftheparticles.Therefore,thegrainsizedistributioncanbe recalculatedusingeachmorphologicalparameter.Wedecidedtoconstrainthegrainsize distributionoftheneashbyusingtheparticlewidthparameter,asitgivesthebest resultcomparedtohand-sieveddata.ThemediangrainsizeMd andsorting of thedepositvaryfrom-4 to2.25 andfrom1.15 to3 respectively,withthemajority ofthesampleshavingaMd < 0 anda > 2.0 .Therefore,theBF2layeriscoarse grainedandpoorlysortedCasandWright,1987,whichcanbeattributedtothelack ofsignicantwindduringtheeruption.Figure2.3showsdierentgrainsizedistributions forsampleswithincreasingdistancefromtheinferredvent.AsexpectedSparksetal., 1992theMd andthe decreasewithdistancefromtheventFigure2.4,meaningthat theoverallgrainsizedecreasesawayfromthevolcanicventandthesortingofthedeposit improves. Figures2.5and2.6showtheisomassmapsoftheindividualgrainsizeclassesfrom -5 downto2 .Samplelocationsshowinggrainsizeclasseslargerthan-5 arenot sucienttotraceisomassmaps,whilethe3 and4 grainsizeclassesdisplaysuchalow accumulationthatcontouringtheelddataisnotanobjectivetask.Isomassmapsfor clastfractions-5 to-2 displayadispersioncomponenttowardthesouthandthewest. 15

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Figure2.3.GrainsizedistributionfortheBF2layerforproximaltomoredistallocations forvedierentlocalities.Md isthemediangrainsize, isthesortingandSkGisthe skewnessofthedeposit.aisthegrainsizedistributionforPL40,bforPL10,cfor PL19,dforPL24andeforPL55. 16

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Figure2.4.GrainsizecharacteristicsoftheBF2layer.aPlotofthemediandiameter Md vs.distancefromthevent.bPlotofthestandarddeviation vs.distance fromthevent.cPlotof vs.Md .Reddotsarefordatafromaxis1ESE,bluedots arefordatafromaxis2SE,greendotsarefordatafromaxis3SW,andblackdotsare fortherestofthedataset.Solidlinesareregressionsthroughthedatafromthedierent axescolorschemesameasbefore.Thepyroclasticowandfalleldsaredenedafter Walker. 17

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Incomparison,particlesfrom-1 to1 clearlyshowdispersiontowardthewest.The2 grainsizeclassshowsamorecirculardispersalpattern.Therefore,whenthedepositis brokendownintoindividualgrainsizeclasses,thecircularpatternobservedintheisopach mapFigure2.7aisnotevident.Thecircularityobservedinthedepositthicknessisthe resultofthedierentialaccumulationpatternofthedierentgrainsizeclasses. Figure2.7bshowsthedistributionoftheMd aroundPululagua,andiso-Md lines tendtoberoughlycirculararoundthevent,althoughtheyshowadispersiontowardthe southwest,similartothepatterndisplayedbytheisopachmapFigure2.7a.The-2 and -1.5 contoursalsodisplayadistortiontowardthesouth-southeast.Theiso-Md lines aremoresensitivetowinddispersalthanisopachs.Thischaracteristicisanotherfactor leadingtotheinterpretationthatatleastpartoftheBFi.e.theBF2,BF3andWAlayers eruptionhappenedinstillatmosphericconditions,becauseifasignicantwindeldhad beenpresentatthetimeoftheeruption,theiso-Md lineswouldhavebeenmorestrongly distortedbythewindeld,asnotedbyRoseetal.forthe1974FuegoGuatemala sub-Pliniantephrafalldeposit. Inmanytephrafallstudiese.g.Pyle,1989;Sparksetal.,1992;PapaleandRosi,1993, Md iscorrelatedwithdistancefromtheventalongthedispersalaxis,butmightnotbeso wellcorrelatedwhenallthesamplelocationsareplottedwithdistancefromtheventRose etal.,2008.Weinvestigatesuchrelationshipsandfocusouralongthreeaxesaroundthe volcanoESEaxis,SEaxisandSWaxis,seeFigure2.1b.AsfortheBF2,Figures2.4aand 2.4bshowthatboththeMd and decreasewithdistancefromthevent,andfollowsa power-lawthinningtrend.However,therateatwhichMd and decreasewithdistance fromtheventisnotthesamealongthedierentaxesinvestigated.ThedecreaseinMd and isfasteralongtheESEaxisaxis1inredthanalongtheSEaxisaxis2in blueandtheSWaxisaxis3ingreen.ThescatteroftheMd vs.distancefromthe ventmightbetheresultofnon-uniformsedimentationduetoatmosphericdiusionorwind interaction.Thedierenceinthehorizontalpositionoftheplumecorneralongthedierent axesseediscussionbelowmightbeanotherexplanationforthescatteroftheMd vs. 18

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Figure2.5.Isomassmapsforeachindividualgrainsizeclassfrom-5 to-2 oftheBF2 layer.SeeFigure2.1bforabbreviations.Dashedlineswhereisomasscontoursareextrapolated. 19

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Figure2.6.Isomassmapsforeachindividualgrainsizeclassfrom-1 to2 oftheBF2layer. SeeFigure2.1bforabbreviations.Dashedlineswhereisomasscontoursareextrapolated. 20

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Figure2.7.aIsopachmapfortheBF2layerofthe2450BPPlinianeruptionofPululaguaVolcano.Individuallocationthicknessesandcontoursareshown.Valuesarein centimeters.Notethecircularshapeoftheisopachs.Dashedlineswhereisopachcontours areextrapolated.bMapshowingthedistributionoftheMd valuesoftheBF2layer. Notethatthecircularshapeislesspronouncedthanfortheisopachmap,andthatthe distributionofMd isslightlytowardthewest.Dashedlineswhereiso-Md contoursare extrapolated.SeeFigure2.1bforabbreviations. 21

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distancefromthevent.Md and donotcorrelateinmanyfalloutdepositsWalker, 1971;Houghtonetal.,2004;Costantinietal.,2009;Roseetal.,2008.Incontrast,the BF2layershowsarelativelygoodlinearcorrelationbetweenthesetwoparametersR 2 = 0.79 )]TJ/F15 10.9091 Tf 8.485 0 Td [(0.83Figure2.4c.Theabsenceofwindmaybeafactorinimprovingthecorrelation, asthewindeldtendstoimprovethesortingofthedepositregardlessoftheparticlesize. 2.4.1.2Totalgrainsizedistribution Acrucialeruptiveparameterforthemodelingoftephrafalldepositsisgivenbythe totalgrainsizedistributionTGSD.TheTGSDisanimportantparameterusedto i constraintephrasedimentationmodelsBursiketal.,1992b;BonadonnaandPhillips, 2003, ii inferfragmentationanderuptionprocessesKaminskiandJaupart,1998, iii assesstephrahazardsforpopulationvulnerabilityConnoretal.,2001;Bonadonnaetal., 2005a,criticalfacilitiesvulnerabilityVolentiketal.,2009andaviationsafetyRose andDurant,2009;Mastinetal.,2009,and iv evaluatehumanhealthhazardsdueto thesettlingofneparticlesinpopulatedareasHorwellandBaxter,2006.Severalways toestimatetheTGSDhavebeenproposedWalker,1981;CareyandSigurdsson,1982; BonadonnaandHoughton,2005;Roseetal.,2008;Durantetal.,2009.Themostrecent one,theVoronoitessellationaspatialanalysismethoddevelopedbyBonadonnaand Houghton,canbedenedasthepartitioningoftheplanee.g.thetephrablanket suchthat,foranysetofdistinctdatapoints,thecellassociatedwithaparticulardatapoint containsallspatiallocationsclosertothatpointthantoanyother.Inthisstudy,wehave usedthefollowingapproaches: i simpleunweightedaverageofgrainsizeanalysisfromall theavailablelocationsTechniqueAWalker,1981, ii mass-weightedaverageofgrain sizeanalysisfromalltheavailablelocationsTechniqueBWalker,1981, iii isopach weightedTechniqueCRoseetal.,2008and iv theVoronoitessellationTechnique DBonadonnaandHoughton,2005.Weappliedthesefourapproachestotwosetsof samples:thecurrentsetofsamplesset1availablefromoureldstudyandanother set,inwhichwehaveaddedvirtualsamplelocationsset2inareaswherethedeposit 22

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Table2.1.CompilationofgrainsizecharacteristicsforthedierenttechniqueofTGSD calculations.Dataonthe1980eruptionofMountSt.HelensMSHarefromDurant etal.. TechniqueDataSetMd SkGashwt. % neashwt. % TechniqueAset1-0.552.43-0.2057.351.92 set202.50-0.2464.563.33 TechniqueBset1-1.852.78-0.0540.050.99 set2-2.152.95-0.0336.810.94 TechniqueCset1-1.12.68-0.1649.331.68 TechniqueD,35kmset1-0.842.46-0.1452.531.22 set2-0.722.75-0.1853.711.96 TechniqueD,40kmset1-0.712.41-0.1554.641.27 set2-0.602.79-0.1855.242.31 TechniqueD,50kmset1-0.512.32-0.1657.961.37 set2-0.362.82-0.2157.892.92 TechniqueD,100kmset1-0.012.09-0.1966.481.68 set20.842.78-0.3669.785.66 TechniqueD,200kmset10.251.92-0.1871.931.98 set21.751.92-0.3784.579.06 InversiononGSalldata0.822.31-0.41n/an/a without-7 0.951.93-0.34n/an/a 1980MSHn/a4.82.5-0.21 95 57 isnowlacking,basedontheassumptionofcircularityofthedepositandonthecurrent samplescollectedintheeld.TheVoronoitessellationapproachrequiresthedenition ofazeroaccumulationlimit,whichisnotavailableforpasteruptions.Nevertheless,we usedacircularzeroaccumulationlinewithvariableradius,40,50,100and200km,see Figure2.8andTable2.1toinvestigatethesensitivityofthetechniquetothepositionof thezeroaccumulationline. TheresultsofthedierenttechniquesusedtocalculatetheTGSDoftheBF2layeron thetwodatasetsarepresentedinFigure2.8andTable2.1.TheVoronoitechniqueclearly showsagreaterconsistencyintheMd valuesfromthetwodierentsetsofdatapoints usedtocalculatetheTGSDcomparedtoTechniquesAandB.Figures2.8gand2.8hand 23

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Figure2.8.ResultsoftotalgrainsizedistributionsTGSDcalculationsusingdierent techniques.aTechniqueAwiththetwosetsofdatapoints;bTechniqueBwiththe twosetsofdatapoints;cTechniqueC;dTechniqueDwiththerstsetofdatapoints; eTechniqueDwiththesecondsetofdatapoints;fFromtheinversionongrainsize, includingandexcludingthe-7 sizefraction;gTechniqueDwithazeroaccumulation lineat100kmforthetwodatasets;hTechniqueDwithazeroaccumulationlineat100 and200kmwiththerstdataset. 24

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Table2.1showthattheVoronoitechniqueismoresensitivetothedistributionofsample locationsthantotheactualpositionofthe"zeroaccumulationline".TechniqueA,C andDseemtoshowroughlythesamepatternofTGSDFigure2.8,whileTechniqueB displaysacoarser,widebell-shapedTGSDcomparedtotheothertechniques.Therefore, theVoronoitechniqueislesssensitivetothenumberofdatapointsavailablecomparedto othertechniquesusedtocalculatetheTGSDofatephradeposit.TechniqueA,andtoa lesserextentTechniqueB,areverysensitivetothedistributionofthesamplelocations, asshownbythelargedierenceintheMd -0.55 fordataset1and0 fordataset2 inTechniqueA.AnotherimportantobservationisthattheVoronoitechniqueisnotthat sensitivetothepositionofthe"zeroaccumulationline",neededtoconstrainandcalculate theTGSDapplyingtheVoronoitessellationBonadonnaandHoughton,2005,asshown bytheonlyslightvariationsinthegrainsizeparametersfromtheVoronoitechniqueusing acircular"zeroaccumulationline"at35,40,50,100and200kmfromtheinferredventfor theBF2eruption.Themaindierencebetweenthethreedierentzeroaccumulationline resultsliesintheamountofneashpresentinthedeposit,anamountincreasingwithan increasingdistancefromtheventofthezeroaccumulationline,thereforegivingahigher weighttotheneportionofthedeposit. 2.4.2Eruptedvolume Statisticalmodelsarewidelyusedtoestimateeruptionvolumesfromcomparatively sparsedata.Thevolumeoftephraemittedduringanexplosivevolcaniceruptioncanbe inferredusingcurve-ttingmethodsonasemi-logarithmicplotofthicknessvs.thesquare rootoftheareaenclosedbytheisopachofagiventhickness.Followingthemodelof Pyle,anexponentialtrendlineistthroughmeasurementsoftheBF2deposit thicknessesplottedagainstthesquare-rootoftheareaFigure2.9.Volumeiscalculated usingtwodierentexponentialcurves.TherstFigure2.9adoesnottakeintoaccountthe 1and2cmisopachareas,becausetheseareasarenotwell-constrainedbyeldobservations Figure2.7a.Thetotalvolumeisabout0.3km 3 R 2 =0.99.Thesecondexponentialcurve 25

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Figure2.9.Semi-logarithmicplotsoflogofthicknesscmagainstthesquarerootofthe areaenclosedbyanisopachmapcontourfortheBF2tephradeposit.aFielddataare ttedaccordingtotheexponentialdecayproposedbyPyle,excludingthe1and 2cmisopachs.bFielddataarettedaccordingtotheexponentialdecayproposedby Pyle,includingthe1and2cmisopachs.cFielddataarettedusingthepowerlawtechniqueproposedbyBonadonnaandHoughton,excludingthe1and2cm isopachs.dFielddataarettedusingthepower-lawtechniqueproposedbyBonadonna andHoughton,includingthe1and2cmisopachs. Figure2.9btakesintoaccountthewholesuiteofeldobservationsandthusincludesthe 1and2cmisopachareas.Inthiscase,thecorrelationcoecientislowerR 2 =0.95,but thevolumeisalsoabout0.3km 3 .Inbothcases,theseresultsindicatetheBF2layerwas aVEI4eruptionNewhallandSelf,1982. WehavealsoappliedthemodelofBonadonnaandHoughtonthatconsistsof ttingelddatausingapower-lawcurveonasemi-logplotofthicknessvs.squarerootof theisopachareas.Asfortheexponentialmodel,wehaveappliedthepower-lawmethodto boththedatasets,withandwithoutthe1and2cmisopachareasFigures2.9cand2.9d, respectively.Animportantstepintheapplicationofthepower-lawmethodisthechoice 26

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oftheouterlimitofintegration,i.e.themaximumdistancefromtheventreachedbythe depositi.e.thickness=0,whichisparticularlycriticalforwidelydisperseddepositsi.e. power-lawexponent < 2.Asmalltephralayerfromthe2450BPeruptionofPululaguahas beenidentiedalongthePaciccoastofEcuadorP.Monthes,personalcommunication some200 )]TJ/F15 10.9091 Tf 8.485 0 Td [(250kmawayfromPululagua.Using200kmor250kmasoneoftheintegration limits,thetotalvolume,excludingthe1and2cmisopachareas,is 0.8 )]TJ/F15 10.9091 Tf 8.485 0 Td [(1.0km 3 ,whileit isreducedto 0.4 )]TJ/F15 10.9091 Tf 8.485 0 Td [(0.5km 3 whenthe1and2cmisopachareasareincluded.Thesevolumes estimatesalsoindicateaVEI4eruption.BonadonnaandCosta2009haveshownthat volumecalculationsfordepositscharacterizedbyapower-lawexponent < 2i.e.widely spreaddepositsaresensitivetothechoiceoftheouterintegrationlimit.Forexample,the volumeoftheBF2layervariesbetween0.5km 3 and1.8km 3 foranouterintegrationlimit between100and500km,respectivelyandapower-lawexponentof1.2elddatawithout the1and2cmisopachareas.ThevolumeoftheBF2layervariesbetween0.3km 3 and0.6 km 3 foranouterintegrationlimitbetween100and500km,respectivelyandapower-law exponentof1.7elddatawiththe1and2cmisopachareas. Thelowervolumeestimateyieldedbytheexponentialcurve-ttingmethodPyle,1989 comparedtothatfromthepower-lawttingtechniqueBonadonnaandHoughton,2005 isprobablyduetotheabsenceofboththeveryproximalandthedistalpartoftheBF2 depositinthegeologicalrecord.Infact,theexponentialmodelunderestimatesthetotal eruptedvolumeunlessfoursegmentscanbeidentiedinthesemi-logplotsvs.distance fromtheventplotsBonadonnaandHoughton,2005. Inconclusion,weconsideratotalvolumeoftephraejectedduringtheclimacticphase oftheeruptionlayerBF2ofPululaguaofabout0.5 0.15km 3 fromtheapplication ofthepower-lawmethodtothecompleteelddatasetandconsideringtheouterlimitof integrationbetween100and500kmfromthevent.Thebulkdensityofthedeposithas beenmeasuredintheeldandwascloseto1000kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 ,yieldingatotalmassofabout 5 1 : 5 10 11 kg. 27

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2.5Analyticaldeterminationoferuptiveparameters WeusetheTEPHRA2semi-analyticalmodelBonadonnaetal.,2005a;Connoretal., 2008toinvestigatethedispersionandsedimentationoftheBF2layer.Thenumericalsimulationoftephraaccumulationisbasedonananalyticalsolutiontotheadvection-diusion equationandcalculatesthetotalmassperunitarea M kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(2 oftephraaccumulated atagivenlocationonthegroundwiththecoordinates x;y ,whichisoneofthequantity ofgreatestinterestintephrasedimentationmodelsandintephrahazardassessments.The modelallowsforgrainsize-dependentdiusionandparticledensity,astratiedatmosphere, particlediusiontimewithintherisingplume,andsettlingvelocitiesthatincludeReynolds Numbervariationsalongtheparticlefall.Modeledparticlesareassumedtobespherical, verticalatmosphericdiusionnegligible,andhorizontalatmosphericdiusionuniformand isotropic. Forpastandunwitnessederuptions,thethicknessand/oraccumulationoftephraper squaremeterthequantity M mentionedaboveismeasuredintheeldandcanbeusedto infereruptionparameterssuchascolumnheight,totalmassoftephraerupted,TGSDand winddirectionandspeedCareyandSparks,1986;Pyle,1989;FiersteinandNathenson, 1992;BonadonnaandHoughton,2005.Thosemodelsarebasedoneithercurve-tting techniquesofeldobservationsoronempiricalmodelsofvolcaniceruptions,butnoton aphysicalmodelthatdescribestephradispersalandsedimentation.Therefore,theuse ofphysicalmodels,suchasTEPHRA2,toinfereruptiondynamicsiscriticaltobetter constraineruptiondynamics.However,byusingonlyforwardmodelingoftephradispersal, thehighlydimensionalspaceofpossibleeruptioninputparameterscannotpossiblybe fullyinvestigatedduetothegreatnumberofinitialinputparameters.Thereforeitis unlikelythatthebestsetoferuptionparameterscanbefoundusingaforwardmodeling approach.Byusinganinversiontechnique,itispossibletondasetoferuptionparameters especiallycolumnheight,totalmassoftephraerupted,totalgrainsizedistributionand windconditionthatbestreproducetheobservedtephraaccumulationonthegroundat eachsamplelocation. 28

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ConnorandConnorproposedatechniquetobetterunderstanderuptiondynamicsbyinvertingtephrafallout.Thisinversiontechniquesearchesfortheoptimalsetof eruptiveparametersthatbestexplainvariationintheelddataFigure2.10andTable2.2 usingthedownhillsimplexalgorithm.Thegoalistodiscoverasetoferuptiveparameters thatminimizestheerrorbetweenthemeasuredandcalculatedtephraaccumulationateach eldpoint.TheRootMeanSquareError RMSE representsacriterionofgoodness-of-t betweenthecalculatedandobservedtephradeposit,following: RMSE = v u u t N X a =1 Mc a )]TJ/F21 10.9091 Tf 10.909 0 Td [(Mo a 2 Mo a .1 where N isthenumberofeldobservations, Mo a istheobservedmassperunitarea atlocation a and Mc a isthecalculatedmassperunitareaatlocation a Astephradepositscontainmoreinformationthandepositthicknessalone,namelythe grainsizedistributionofthedeposit,wedecidedtoruntheinversiontechniquebasedon grainsizedataateachlocation.Basically,wedividedthetotaltephraaccumulationfor agivenlocationintoanaccumulationofparticlesforeachgrainsizeclassat1 interval accordingtothegrainsizedistributionobtainedbysievingthetephradepositateach location.Wetheninvertedthosedatatondthebest-teruptionparametersthatwould reproducebesttheobservedaccumulationbygrainsizeontheground. 2.5.1Eruptedmass Mass,andhencevolumeoftheeruption,canbeestimatedfromtheinversionand comparedwithvolumeestimatedbasedonthecurve-ttingmethodsdescribedearlier.All non-linearinversionmethodscanbesensitivetolocalminima.Toavoidthisissue,weplot atwo-dimensionalspacerepresentedbythecolumnheightvs.totalmassFigure2.11. WeinvertthemeasuredBF2tephradepositbyusingdierentrangesofinputparameters Table2.2.Thetotalmasswasincrementedby0.2logofthemassfrom10.6to12.4log 29

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Figure2.10.Comparisonbetweentheobservedtephraaccumulationonthegroundand thecalculatedtephraaccumulationfromoneofthebest-tinversionresultsontheBF2 thicknessateachlocality.Thediagonalblacklinerepresentstheoptimalcase,whenthe modelequalstheactualaccumulation. 30

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Table2.2.Exampleofinputparameterrangesfortheinversionandoutputexamplefrom theinversion. ModeledParametersInputmin.Inputmax.OutputUnits MaximumColumnHeight260002800027101m TotalEjectedMass1 : 58 10 11 2 : 51 10 11 2 : 50 10 11 kg LogTotalEjectedMass11.211.411.398MeanParticleSizeMd -2.02.0-0.2 Std.DeviationofParticleSize 1.03.02.0 DiusionCoecient0.110000092066.1m 2 s )]TJ/F7 6.9738 Tf 6.226 0 Td [(1 ofthemass,andthecolumnheightwasincrementedby2km,from8to40km.Theresult oftheinversioninvestigationofthecolumnheight-massspaceispresentedinFigure2.11. Ourinvestigationofthistwo-dimensionalspaceshowsthatthereisanon-uniquesolutionintermsofcolumnheightandtotalmasseruptedfortheBF2layerfromtheinversion oftotaltephraaccumulationonthegroundateachlocation.Indeed,thecolumnheight vs.logmassspaceshowsanareaofpossibleeruptionparametersthatdescribetheBF2 tephradepositequallywell.However,ourmodelshowsthatthetotalmassoftheeruption isrelativelywell-constrainedbetween2 : 5 10 11 kgand4 10 11 kg,correspondingtoabout 0.25 )]TJ/F15 10.9091 Tf 8.485 0 Td [(0.4km 3 ,assumingabulkdensityofthedepositof1000kgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(3 ingoodagreement witheld-measuredbulkdensities[920 80kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 ].Conversely,thecolumnheightshows awiderangeofpossiblesolutions,fromaheightaslowas8kmanduptoabout40km. Theseresultsprimarilyarisefromthesampledistribution,whichislimitedbytheoutcrop distributionageneralprobleminstudyingprehistoriceruptions. Byaddingtogetherallofthesimulationsbygrainsize,itisthenpossibletoreconstruct thetotalmassoftephraeruptedthatdepositedtheBF2layer.Thetotalmasscalculated bytheinversionongrainsizefortheBF2layeris5 10 11 kg,whichcorrespondstoavolume of0.5km 3 assumingabulkdensityfortheBF2depositof1000kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 ,whichagreeswell withthetotalvolumepredictedbytheinversiononthetotaltephraaccumulationateach location.25 )]TJ/F15 10.9091 Tf 8.485 0 Td [(0.4km 3 andnarrowstherangeoftotalvolumeestimatedwithcurve-tting techniques.3 )]TJ/F15 10.9091 Tf 8.485 0 Td [(1.0km 3 31

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Figure2.11.2-DspaceofinputparametersfortheinversionontheBF2thickness.Plot showingthecolumnheightvs.logmass.Theblackdotrepresentssolutionswitha RMSE> 100. 32

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2.5.2Columnheight Invertingtephraaccumulationdidnotuniquelyconstrainthecolumnheight,ascolumn heightsrangingfrom8kmto40kmgivesolutionsthatequallyreproducetheobserved depositFigure2.11.Incontrast,theinversiononindividualgrainsizeclassesproves especiallyusefulforconstrainingthecolumnheight.Byinvertingongrainsize,thatis themassperunitareaofindividualsizeclasses,ambiguityisremovedthatstemsfrom uncertaintyingrainsize,andhenceparticlefallvelocity. ArstsetofresultsfromtheinversionongrainsizeisshowninFigure2.12,wherewe comparedthecalculatedaccumulationversustheobservedaccumulationforthreedierent grainsizes-3 ,0 and2 .Figure2.12suggeststhatourinversionmodelbasedongrain sizedatadoesareasonablygoodjobinreproducingtheobserveddeposit.Infactallthe pointslierelativelyclosetotheidealmodelrepresentedbythethicklinewithaslopeof 1.0.Notethat,althoughwedonotpresentalltheresultshere,theresultsforothergrain sizeclassesfrom-7 downto < 4 showthesamegoodtbetweenmodeledandobserved data. Thecolumnheightsobtainedfromtheinversiononthedierentgrainsizeclassesare presentedinTable2.3,alongwiththediusioncoecientsfoundfromtheinversionson grainsizetomodelthesedimentationofeachphiclasswithTEPHRA2.Excludingthe-7 4 and > 4 sizeclasses,werecordednosignicantvariationincolumnheightskm to30km,Table2.3asafunctionofgrainsize,indicatingnodierenceintherelease heightsforthedierentparticlesizes.Thisobservationmightleadtotheconclusionthat theeruptivecolumniswell-mixed,contradictingthe"envelopeapproach"ofmodelingthe eruptioncolumnofCareyandSparks,althoughitmightalsorepresentanartifact ortheresolutionlimitofthemodel.Infact,theinversioncannotresolvethedierent heightsofparticlerelease,whileanotherapproachBursiketal.,1992bdescribedlater inthetextwillallowthisdistinction.Thecolumnheightobtainedforthe-7 classis 20kma.s.l.,andthereforecouldrepresentalowerreleaseheightforbiggerparticles.But themodelforthe-7 andtoasmallerextent,forthe-6 aswellisnotwellconstrained, 33

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Figure2.12.Comparisonbetweentheobservedtephraaccumulationonthegroundandthe calculatedtephraaccumulationfromtheimproved-inversionresultsontheBF2grainsize ateachlocality.Resultsshownareforthreedierentgrainsizesateachlocation:athe -3 grainsize;bthe0 grainsizeandcthe2 sizefraction. 34

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Table2.3.Outputfromtheinversionongrainsize,andtheuncertaintyanalysis.GS:grain size,H t :columnheight,DC:DiusionCoecient,FTT:FallTimeThreshold. GS H t m Mass kg DC m 2 s )]TJ/F7 6.9738 Tf 6.226 0 Td [(1 FTT s Uncertainty H t m Uncertainty Mass kg -7194982 : 57 10 10 4002.6311.824630 47502 : 78 1 : 91 10 10 -6279763 : 23 10 9 27260.15262.828500 18504 : 36 0 : 03 10 9 -5268781 : 05 10 10 75193.0333.727700 25509 : 89 1 : 64 10 9 -4257821 : 14 10 10 53585.09514.229250 14001 : 75 0 : 10 10 10 -3277921 : 73 10 10 46045.21687.729410 13802 : 38 0 : 07 10 10 -2298942 : 15 10 10 27992.52185.829870 2302 : 65 0 : 04 10 10 -1298723 : 34 10 10 36003.23532.129710 4524 : 19 0 : 40 10 10 0297474 : 92 10 10 16204.99921.429770 2905 : 00 0 : 20 10 10 1281139 : 12 10 10 33354.02200.028180 9309 : 11 0 : 60 10 10 2240001 : 36 10 11 95984.02026.121336 901 : 08 0 : 01 10 11 3257329 : 37 10 10 29661.31039.120850 7605 : 07 0 : 60 10 10 4101853 : 74 10 9 7291.33592.8n/an/a > 4100089 : 60 10 10 23517.9659.1n/an/a becausethelownumberoflocationswhere-7 particlessedimentedonlytwolocations inthemostproximalareas.Furthermore,theseclastsmighthavefallenoearlyfrom themarginofthevolcanicplumes.Incontrasttocoarserparticlemodels,thecolumn heightsforthe4 and > 4 particlesizesshowalowcolumnheightabout10kma.s.l.. Wesuspectthisdierenceisattributabletotheoverallproximityofallourlocationsall closerthan35kmfromthevent.Thereforewearemissingmuchofthenefractionofthe deposit,whichislikelytohavebeensedimentedfurtherawayfromPululaguavolcanicash fromthe2450BPeruptionofPululaguahasbeenidentiedonthecoast,PattyMothes, personalcommunication. Usingthemodelsbygrainsize,itispossibletoreconstructthegrainsizedistribution ateachsamplesiteandtocomparethesewiththeobservedgrainsizedistributionsFigure2.13.ThemodeledgrainsizedistributionatthedierentlocalitiesshowninFigure2.13 mimicstheobservedgrainsizecharacteristicoftheactualBF2layer.However,the-5 andespeciallythe-6 and-7 forthetwomoreproximallocalitiesarenotwellmodeled byourinversionapproachongrainsizedata.Thismaybeaconsequenceofthesparseness ofbigparticlesinthedepositespeciallyforthe-7 fractionorthesedimentationfrom theplumemargins,whichisnotwelldescribedintheTEPHRA2model. 35

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Figure2.13.Reconstructionofthemodeledgrainsizedistributionaccumulationinkg m )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 inredandcomparisonwiththeactualgrainsizedistributionfromelddata,in black,forlocalitiesfromproximaltomedial,alongaxis1. 36

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2.5.3Totalgrainsizedistribution TheinversionofgrainsizedataalsoyieldsanestimateofTGSDoftheBF2layer Figure2.8f,anditcanbecomparedtotheeld-basedTGSDsFigure2.8a-eandg-h discussedpreviously.AlthoughtheTGSDobtainedfromtheinversionofgrainsizeseemsto underestimatetheamountofcoarseparticlescomparedtothevariousaveragingtechniques consideredfromsimpleunweightedaveragetotheVoronoitessellation;Table2.1,the resultsareinreasonableagreement.ThecoarserMd predictedbythevariousaveraging techniquesisprobablyduetothelackofdistallocationsinourgrainsizedataset,which createsabiasoftheTGSDtowardcoarserparticles.Theinversionofgrainsizedoes notshowsuchabiasbecauseitisbasedonaphysicalmodeloftephradispersionand sedimentation. 2.5.4Uncertaintyanalysis Uncertaintiesexistinthedeterminationoferuptiveparameterssuchasthetotalmass oftephraeruptedorthecolumnheight,andareusuallynotaddressedintheliterature. Theuncertaintyontheseparameterscanbedueto i theoriginaldataseti.e.sample distribution,eldobservations,erosionofthedepositand ii themodelusedtoinfer eruptiveparameters.Inordertoexploreandassesstheseuncertainties,weusedamodiedversionofasmoothedbootstrapapproachdevelopedbyPressetal.,which inturnedwasbasedonthebootstrapmethodsproposedbyEfronandTibshirani. Weassumedthattheoriginaldatasetcontainsarepresentativedistributionofsample locationsandtheaccumulationmeasurementsateachsitearetruevalues.Furthermore, wealsoassumedthattheTEPHRA2modelisabletoaccuratelyreproducetheobserved accumulationontheground.Then,werandomlyselectedalocationwithinasquarekilometeraroundeachoriginalsamplelocationthepseudosetofpointsandcalculatedthe predictedaccumulationforeachnewlocationusingtheforwardsolutionoftheTEPHRA2 modelusingeruptiveparametersdrawnfromtheinversiononsinglegrainclasses.We appliedtheinversiontechniqueusingthisnewsetofdatapointstocalculateanewset 37

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oferuptiveparametersthatreproducethepseudosetofpoints.Ourapproachfollowsthe bootstraptheoryaswearere-samplingtheoriginalsetofsamplelocationstoderiveanew oneanditissmoothedbecausethenewaccumulationvalueateachpointiscalculated fromtheforwardsolutionoftheTEPHRA2modelratherthansampledfromasubsetof theoriginalsamplelocations.Thisapproachhasbeenrepeated50timesonthetotalaccumulationandforeachgrainsizeclassfrom-7 to3 followingaMonteCarloapproach. Wedidnotperformtheanalysisforthe4 and > 4 grainsizesbecauseofthelackof controlintheoriginalinversionongrainsizeseeabove.Ouranalysisyieldsamean totaleruptedmassof4 : 5 0 : 3 10 11 kgandameancolumnheightof30 3kmwith arangebetween20kmand33km.Resultsforindividualgrainsizeclassesarepresented inTable2.3uncertaintiesgivenatonestandarddeviationfromthemean.Resultsfrom theuncertaintyanalysiscomparewellwiththeresultsfromtheinversiononoriginaleld data,exceptforthe2 and3 fractions,forwhichthemeancolumnheightcalculatedby thesmoothedbootstrapmethodyieldslowerestimatesinthecolumnheights. 2.6Massdischargerateanderuptionduration PapaleandRosiproposedamagmadischargerateof2 10 8 kgs )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 ,usingthe modelofSparks,fortheBFlayerbasedonthemaximumgrainsizedatacollected onthecoarsestpartoftheBFdeposit,whichwedenedinthispaperasbeingtheBF2 layer.Byusingthismagmadischargerateandthetotalmasscalculatedfromtheempirical methodsdiscussedabove,weobtainedaneruptiondurationofabout37 13minutesfor theBF2layer,arelativelyshort-livederuption. Weusedthreedierentmodelstocalculatethemagmadischargerate MDR ofthe BF2layerSparks,1986;WilsonandWalker,1987;Sparksetal.,1997.Fromthe MDR wethencalculatedtheeruptiondurationbasedonthemassresultingfromtheinversion analysis : 5 )]TJ/F15 10.9091 Tf 12.106 0 Td [(5 : 0 10 11 kg.ThemodelofSparksforatropicalatmosphere yieldsa MDR of6 : 2 3 : 8 10 7 kgs )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 ,resultinginaneruptiondurationof194 153 minutes,assumingamagmaeruptiontemperatureof1000 Candamagmadensityof 38

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2400kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 .CalculationsmadeusingthemodelofWilsonandWalkeryielda MDR of1 : 8 0 : 8 10 8 kgs )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 andaneruptiondurationof50 34minutes.Finally, valuesof MDR anderuptiondurationresultingfromtheapplicationofthemodelofSparks etal.are1 : 2 0 : 5 10 8 kgs )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 and72 47minutes,assumingamagmadensityof 2400kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 .Thevaluesof MDR anderuptiondurationcalculatedherearesmallerand largerrespectivelycomparedtothevaluescalculatedbyPapaleandRosi,because thecolumnheightusedtoderivethe MDR ishigherkmcomparedtoour24 )]TJ/F15 10.9091 Tf 8.485 0 Td [(30km range,resultinginhigher MDR andshortereruptiondurations. 2.7Particlepath Theinversionofgrainsizeyieldedanotherinterestingoutput:thebest-twindprole tomodeleachgrainsize,representedinFigure2.14asacompilationofrosediagrams showingthewinddirectionandspeedateachatmosphericlevelforeachgrainsize.Each atmosphericlevelhasathicknessof270m.Weusedthewindproleforeachgrainsize tocalculatetheparticlepathsduringtheirfallfromtheheightofreleaseobtainedfrom theinversionongrainsizetotheirdepositionontheground.Ourcalculationsusedthe dierentsettlingvelocityequationscorrespondingtothedierentfallregimes,asdescribed byBonadonnaandPhillipsaswellasaheight-dependentatmosphericdensityprole followinganexponentialdecayrelationshipwithheight: g =1 : 25 )]TJ/F21 10.9091 Tf 8.485 0 Td [(z 8 : 2 .2 with g kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 beingtheairdensityand z kmtheelevationabovesealevel. TheresultsofourparticlepathmodelingareshowninFigure2.15.Clastsofthe-7 -6 ,-5 and-4 fractionseemtohavefollowedasouthwardtrajectory,whilethe-3 fractionfollowedasouthwestwardpath,inbetweenthepreviousandfollowinggroupof particles.Particlesrangingfrom-2 to4 withtheexceptionofthe3 fractionshow 39

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Figure2.14.Windrosediagramfromtheinversiononindividualgrainsizeclassesfrom the-7 ato4 lsizeclasses,indicatingthedirectiontowhichthewindisblowingat eachatmosphericlevel.Unitbarsrepresentthewindvelocityms )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 40

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Table2.4.InputparametersforaforwardsolutionfortheBF2layerusingtheTEPHRA2 model.SeeFigurerefg2-1bforabbreviations. InputParameterValueUnits MaximumColumnHeight27000m TotalEjectedMass2 : 50 10 11 kg MeanParticleSizeMd -0.2 Std.DeviationofParticleSize 2.0 DiusionCoecient92066m 2 s )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 adispersiontowardthewestwest-northwest.Inconclusion,thisapproachoflookingat themodeledparticletrajectoryfromtheinversiononindividualgrainsizeconrmedthe observationsdrawnfromtheisomassmapsonsinglegrainsizeclassesFigures2.5and 2.6,theisopachmapFigure2.7aandtheiso-Md mapFigure2.7bthattheoverall dispersionoftheBF2layeristowardthewest. 2.8Forwardmodeling BycompilingalloftheeruptionsourceparametersfromthisstudyseeTable2.4,we couldultimatelyrunaforwardsolutionfortheBF2layerusingTEPHRA2.Theresult isshowninFigure2.16,andtheslightdispersiontowardthesouthwestisalsoclearly visible.Thisforwardsolutioncomparesfavorablywiththeisopachmappresentedinthis studyFigure2.7aandshowsaslightdistortionofthecontourlinestowardthesouthwest, conrmingpreviousobservations. 2.9Plumedynamics 2.9.1Cornerposition WeusegrainsizedataalongthethreeaxesFigure2.1bmentionedpreviouslyto investigatethevariationofaccumulationofindividualgrainsizeclasseswithdistancefrom thevent.Insteadofusingtheaccumulationperunitarea,wefollowedtheexampleof Bursiketal.bandcalculatedtheaccumulationperunitdistancekgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 atany 41

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Figure2.15.Particlepathsfromtheheightofreleaseabovetheventredtriangledown tosedimentationontheground,calculatedfromwindadvectionusingtheresultsfromthe inversionongrainsize.Particlepathsfromthea-7 to-5 ,b-4 to0 andc1 to4 sizeclasses.Wepresenttwodierentparticlepathsforthe4 fraction,withtwo dierentreleaseheights:10and20km 42

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Figure2.16.IsomassmapfortheBF2layerfromaforwardmodelingusingtheTEPHRA2 modelandinputparametersresultingfromtheanalysispresentedinthisstudyseeTable2.4.Notetheslightdispersaltowardthesouth-west. 43

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givenlocalitybymultiplyingthemassaccumulatedbyunitareabytheperimeterlength ofthecircularisopachcontourthatpassesthroughthislocalityFigures2.17,2.18,2.19. Afth-orderpolynomialhasbeenttedtoelddatatocalculatethehorizontaldistance ofthemaximuminaccumulationonthegroundofeachindividualgrainsizeclasses. FromFigures2.17,2.18and2.19,wecanobservethattheaccumulationofparticlesfrom 64mmto32mmdecreasesawayfromthevent,forthethreeaxesofinterestinthisstudy. Thispatternreectsparticlesfallingoutoftheplumemargins.Thetransitionfroma sedimentationfromtheplumemarginstoasedimentationfromtheumbrellacloudoccurs forparticlesbetween32mmand16mm,fortheSWandESEaxes,andforthe16mm particlesfortheSE.Clastsrangingbetween8mmand2mmgrainsizeclassesdisplayrst anincreaseinaccumulationperunitdistance,reachamaximumandthendecreaseaway fromthevent.Themaximumisassociatedwiththeplumecornerandcanbedetermined usinga5 th orderpolynomialfunctionttedthroughelddata:7kmfortheESEaxisand 10kmfortheSEandSWaxes.ThisisinthesamerangeofdistancesfoundfortheFogoA eruption.8 )]TJ/F15 10.9091 Tf 8.485 0 Td [(8.0kmcharacterizedbyacolumnheightof21 )]TJ/F15 10.9091 Tf 8.485 0 Td [(27kmBursiketal.,1992b. Forparticlessmallerthan2mm,asecondarymaximuminaccumulationcanbeidentied downtothe125 mand63 mfraction,especiallyfortheESEandSEaxes,whileitis notclearlydenedalongtheSWaxis.Thissecondarymaximumislocatedabout17km fromtheventforbothaxes.Bursiketal.balsoshowedasecondarymaximum forparticlessizesof1mmand0.5mm,alsolocatedaround17kmfromthevent.Asfor theSWaxis,thereisnoclearlydenedsecondarymaximum,probablybecauseitmaybe locatedbeyondourareaofobservation.Thisresultcombinedwiththedierentpositions oftheplumecorneralongthedierentaxesleadustothinkthatawestwarddispersion ofthedeposithasoccurred,shiftingthepositionoftheplumecorneronthegroundfrom 7kmto10kmfromtheESEaxistotheSWaxisandshiftingthepositionofthesecondary maximumoutsidetherangeofobservationfortheSWaxis.Inaddition,acornerof7km resultsinamaximumcolumnheightof29kmBonadonnaandPhillips,2003,whereasa cornerof10kmwouldresultinamaximumplumeheightof42km,whichisnotrealistic, 44

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Figure2.17.Massaccumulationperunitdistancekgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 ofparticlesingrainsizeclasses from64mmto63 m-6 to4 ,respectivelyforaxis1ESEaxisdenedinFigure2.1b. 45

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Figure2.18.Massaccumulationperunitdistancekgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 ofparticlesingrainsizeclasses from64mmto63 m-6 to4 ,respectivelyforaxis2SEaxisdenedinFigure2.1b. 46

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Figure2.19.Massaccumulationperunitdistancekgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 ofparticlesingrainsizeclasses from64mmto63 m-6 to4 ,respectivelyforaxis3SWaxisdenedinFigure2.1b. 47

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andthereforeindicatesashiftduetothewind.Theshiftofthecornerfrom7kmto10km couldbeduebothtoawindeectandtoanasymmetricalsedimentationfromtheplume marginse.g.Houghtonetal.,2004,assuggestedbyFigures2.5and2.6wheremainlythe coarsefractionshowsamaindispersaltotheSE. 2.9.2Strongplumemodel Weappliedthe1DtephradispersalmodeldevelopedbyBonadonnaandPhillips forstrongvolcanicplumes.WeusedtheVoronoiTGSDresultingfromtherstdataset onlytheactualelddataandforazeroaccumulationlineat200kmawayfromthevent Figure2.8h.Thestrongplumemodelwasusedto: i investigatethethinningtrend ofthetephradeposit,whichcangiveimportantinsightsintotheempiricalmodelsused forthedeterminationoferuptedvolumeand ii investigatethesedimentationdynamics ofvolcanicparticles.Figure2.20showsagoodtofthenormalizedisopachthicknesses withthethinningtrendfromthestrongplumemodelforaplumeheightof20kma.s.l. InFigure2.20,wealsoreproducedtheexponentialdecayandpower-lawmodelsforthe wholedatasetincludingthe1and2cmisopachdata.Thislatterapproachshowsa goodcomparisonbetweenthepower-lawthinningtrend,includingthe1and2cmisopach data,andthethinningtrendfromthemodel.Thereforeourvolumeestimatesfromthe power-lawmethod,includingthe1and2cmisopachs,ofabout0.4km 3 seemsreasonable. Acolumnheightof20kmisconstrainedhereinordertoreproducethethinningtrend observedintheeld. Furthermore,thestrongplumemodelalsopredictsthefractionofparticlesfromthe dierentfallregimesturbulent,intermediateandlaminartosettleonthegroundFigure2.20.TheturbulentregimeincludesparticleshavingaReynoldsNumber Re 500, theintermediateregimeincludesparticleswith6 Re< 500,whilethelaminarregime isdenedbyparticleshavinga Re< 6BonadonnaandPhillips,2003.Thevariationof thedierentfalloutregimescanbeusedtodeterminethepositionofthebreak-in-slopein thethinningtrendBonadonnaetal.,1998.Thepositionoftherstbreak-in-slopeinthe 48

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Figure2.20.Resultsofthestrongplumemodelforaplumeheightof20km.Triangles areelddata.Thethicksolidlineisthethinningtrendpredictedbythemodelusingthe TGSDfromtheVoronoimethodwithazeroaccumulationlineat200km;thesolidlineis theexponentialdecaymodel;thedashedlineisthepower-lawmodel;thethinsolid,dotted anddashedlinesrepresenttheproportionofparticlesfallingfromtheumbrellacloudin theturbulent,intermediateandlaminarregime,respectively. thinningassociatedwiththesedimentationfromtheumbrellacloudbetweenSegments1 and2isdenedbythedistanceatwhichtheproportionofturbulentparticlesfallstonear zeroandthepositionofthesecondbreak-in-slopebetweenSegments2and3isdened bythelocationwhere > 60%oftheparticlesfallsinthelaminarregime.FromFigure2.20, therstbreak-in-slopeshouldbelocatedatadistanceof 28km p area / p fromthe ventandthesecondoneat 60km.Theabsenceofaclearlydenedbreak-in-slopeinour elddataFigure2.7aand2.20at 28kmcorrespondingto 50km p area isdueto thelimitofobservationoftheBF2layer. Finally,wealsousedthestrongplumemodeltocomparetheobservedandpredicted accumulationoftephraonthegroundfortheBF2layeralongthethreedierentaxes Figure2.21.Thediscrepancybetweentheobservedaccumulationblacktrianglesand themodeledaccumulationwhitetriangles,greytrianglesandgreycirclesisprobablydue tothepredictedterminalvelocityoftheassociatedparticles.Infact,thesetofterminal velocitiesusedcouldoverestimatetherealterminalvelocitiesmainlyfortworeasons: i becausetheterminalvelocitiesarecalculatedontheassumptionofsphericalparticlesand 49

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ii becausethetotalgrainsizedistributionusedisnedepleted.Inordertoinvestigate thesecondoptionwehavealsoplottedtheresultsforasimulationcarriedoutusingthe totalgrainsizedistributionofthe1980eruptionofMountStHelensCareyandSigurdsson, 1982Md =4.7 and =2.3 .Suchasimulationshowsabetteragreementwitheld datagreysquares,conrmingthatthestrongplumemodelofBonadonnaandPhillips isverysensitivetothechoiceofthetotalgrainsizedistributionandthattheeldderivedtotalgrainsizedistributionoftheBF2layerisprobablynedepletedduetothe lackofdistalsamples. 2.10Discussion 2.10.1Statisticalvs.numericaldeterminationoferuptiveparameters ThetotaleruptedmassobtainedusingtheexponentialttingmodelofPyle i.e.3 10 11 kgandthepower-lawttingmodelofBonadonnaandHoughtoni.e. 5 1 : 5 10 11 kgcomparewellwiththetotaleruptedmassobtainedfromouranalytical analysesusingtheTEPHRA2modeli.e.4 : 5 0 : 3 10 11 kg.Thisvalueissmallerthan theoneproposedbyPapaleandRosiof1.1km 3 equivalentto1 : 1 10 12 kgwith adepositbulkdensityof1000kgm 3 ,andtheoneproposedbyPalliniof0.5km 3 equivalentto5 10 11 kgwithadepositbulkdensityof1000kgm 3 .Thesediscrepancies areduetothefactthatPapaleandRosistudiedtheBFdepositasawholeincluding theBF1layersthatshowaNEdispersion,BF3andWA,andPalliniincludedthe BF2andtheBF3layersinhiscalculation,whilewefocusedonlyontheclimacticphaseof theeruptionBF2layer.Itisalsoworthmentioningthattheisopachmapproposedby PallinifortheBF2andBF3layerstogethershowsaslightdispersiontowardthe west.Volumecalculationsusingthepower-lawmethodincludingalltheisopachdata alsomatchwellwiththethinningtrendfromthestrongplumemodelofBonadonnaand PhillipsFigure2.20.Furthermore,thethinningtrendfromthestrongplume modelcanbeusedtochoosetheouterintegrationlimitforthepower-lawmethod,instead ofusinganarbitraryvalue.Assumingwewanttoknowthevolumeoftephraejected 50

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Figure2.21.Comparisonbetweentheobservedaccumulationonthegroundblacktrianglesandthepredictedaccumulationonthegroundfromthestrongplumemodel,using i theTGSDfromtheVoronoianalysisandazeroaccumulationlineat50kmwhitetriangles, ii theTGSDfromtheVoronoianalysisandazeroaccumulationlineat200km greytrianglesand iii theTGSDfromtheinversionongrainsizedatalightgreycircles.Forfurthercomparison,weusedtheTGSDfromthe1980eruptionofMountSt. Helensgreysquares.ThethreeplotsrepresentatheESEaxis,btheSEaxisandc theSWaxisofFigure2.1b. 51

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withinthe1mmisopach,fromFigure2.20tephraaccumulation=1kgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 ,corresponding to1mmoftephrathicknesswefoundthatthesquarerootoftheareaenclosedwithin the1mmisopachis 180km.Thisvalueagreeswellwiththe100 )]TJ/F15 10.9091 Tf 8.485 0 Td [(200kmusedinthe TGSDcalculationswiththeVoronoitechniqueandwiththeouterintegrationlimitsusedin volumecalculationsbasedonthepower-lawtechniqueandyieldingatotaleruptedvolume of0.3 )]TJ/F15 10.9091 Tf 8.484 0 Td [(0.5km 3 ,dependingonwhichpower-lawmodelisusedincludingorexcludingthe 1cmand2cmisopach,respectively. Asnotedfromthetotalgrainsizedistributionanalysis,theBF2layerislackingthene partofthegrainsizedistribution.Themissingneparticlesmighthavesettledwiththe successivelayersBF3and/orWAor,moreprobably,mighthavebeenblowndownwind bytheslightwindconditionsatthetimeoftheeruptionoftheBF2layer.Sincethene particlesaremissing,thetotaleruptedmasscalculatedrepresentsaminimumestimateof thetotalmassoftheBF2layer. ColumnheightdeterminationbyPapaleandRosiandPalliniyielded heightsrangingfrom21kmforthe-6 fractionupto36kmusingtheCSmethodand28 kmusingthemodelofPyle,withanaverageacceptedvaluebythelaterauthors of32km.Invertingonthetotalaccumulationateachsamplelocationdidnotimprove thesolutioninthecolumnheightdetermination,ascolumnheightsrangingfrom8kmto 40kmwouldreproducetheobservedaccumulationonthegroundFigure2.11.However, invertingonindividualgrainsizeclassesnarrowstherangeofsolutionsforthecolumn heightto27 3km,whichcomparesrelativelywellwiththeresultsfromempiricalmethods usedbyPapaleandRosiandPallini.ThestrongplumemodelofBonadonna andPhillipsreproducesrelativelywellthethinningtrendandparticlefractionsof eachsedimentationregimeforacolumnheightof20km.Thisheightisslightlylowerthan alloftheotherestimates,exceptingtheinversiononthe-7 fractionandCSmethodonthe -6 fraction.However,thecolumnheightobtainedfromthestrongplumemodelislower comparedtotheoneobtainedfromCSandtheinversionmethodbecauseitrepresents anaveragecolumnheight,whilethecolumnheightcalculatedusingCSandresulting 52

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fromtheinversiononthegrainsize,representsamaximum.Bursiketal.bfound adiscrepancybetweentheheightcalculatedfromgrainsizedataandtheheightfromCS kmand27km,respectively,adiscrepancyverysimilartotheonebetweentheresults fromthestrongplumemodel,andtheCSandinversiontechniqueongrainsize.Itisalso worthnotingthattheCSapproachonthe-6 fractionyieldsacolumnheightof21km,close totheoneresultingfromtheinversiononthe-7 fractionkm,seeTable2.3.Column heightscalculatedfromthemodelofCSwiththe-6 clastsyieldanunderestimateofthe columnheightbecausetheseclastsfallfromtheplumemargins,andthisistruetoofor thecoarserclastsaswell,suchasthe-7 modeledwiththeinversionongrainsizedata. ThestrongplumemodelofBonadonnaandPhillipsisverysensitivetothe choiceoftheTGSDFigure2.21.AlthoughtheTGSDofthe1980eruptionofMount St.HelensMSHseemstobetterreproducetheobservedaccumulationonthe ground,itcannotbeusedinthisstudybecauseofthestrongnesinputfromco-ignimbrite activity.Nevertheless,thiscomparisonpointsoutthattheTGSDcalculatedfromeldderivedtechniquesisne-depletedandfromTable2.1,wecancalculatefromTechnique D,Voronoi-200kmand1980MSHthattheamountofashandneashrequiredtobetter reproducetheobservedaccumulationsonthegroundis 20%and 50%,respectively. ThelackingneparticleswithintheBF2layermightbepresentintheBF3andespecially intheWAorjustatagreaterdistancefromthevent,beyondoursamplingarea. Theresultsdrawnfromtheuncertaintyanalysisusingasmoothedbootstrapmethod showsthattheuncertaintyinthedeterminationofthetotaleruptedmass : 5 0 : 3 10 11 kgandcolumnheight 3kmisintherangefoundfromtheinversionontotal accumulation : 5 )]TJ/F15 10.9091 Tf 13.048 0 Td [(4 10 11 kgandindividualgrainsizeclasses 3km.However, theresultsforthe2 and3 fractionsshowalowerestimateofthecolumnheightresulting fromtheuncertaintymodelcomparedtotheresultsfromtheinversiononthesegrainsize classes.Thismightbeduetothelackofmoredistaldepositwhichwouldhaveimprovedthe spatialresolutionofourdataset,resultinginamorerobustcorrelationwiththeinversion ongrainsize.Furthermorethisapproachshowsthatinvertingtephradepositsongrainsize 53

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ratherthanontotalaccumulationgivesrelativelygoodanswerswithcomparativelylower uncertaintyintermsofbothtotaleruptedmassanderuptioncolumnheight,becausethe settlingvelocityofparticlesisbetterconstrained. 2.10.2Plumedynamics Againstwhatweexpected,theinversionongrainsizedoesnotshowanydierencein particlereleaseheightsexceptmaybeforthe-7 ,withreservationsaboutthevalidityofthe inversiononthisdataforthedierentclassesofgrainsizeTable2.3.Thisobservation, combinedwiththerelativelyshortdurationoftheeruption,couldleadtotheconclusion thattheeruptivecolumnwaswell-mixed,contradictingthe"envelopemodel"ofCS,and thattheexplosiveeruptionwasmoreatransientratherthanasustainedevent.However, thevariationinaccumulationperunitdistanceofeachindividualgrainsizewithdistance fromtheventforthethreeaxesstudiedinthispaperFigures2.17,2.18and2.19resolves thisproblem.Infact,theseguresclearlyshowthatparticlesfromthe64mmand32mm -6 and-5 ,respectivelyfractionsarefallingfromtheplumemarginsandthereforedo notreachthetopoftheeruptivecolumnandtheumbrellacloud.Thetransitionfroma sedimentationfromtheplumemarginstoasedimentationfromtheumbrellacloudoccurs inbetweenthe32mmand16mmfraction-5 and-4 ,respectivelyandclastsofthe8mm -3 fractionandsmallerareclearlysedimentingfromtheumbrellacloud.Therefore,the lackofconsistentvariationsincolumnheightforindividualgrainsizefromtheinversion cannotbelinkedtoplumecharacteristics,probablybecausethevariationsobservedare outsidetheresolutionlimitsofthemodel. Thesecondarymaximumlocatedat 17kmfromtheventFigures2.17,2.18and2.19 observedintheaccumulationperunitdistanceforparticlessmallerthan2mm was alreadyobservedbutnotdiscussedbyBursiketal.bandcouldbeattributedto i convectiveinstabilities, ii aggregationalthoughnotobservedinthedeposit, iii preferentialfalloutofcrystalsalsoconsideringthatBFiscrystalrichasobservedby PapaleandRosi,1993or iv hydrometeorformationinthecloudDurantetal.,2009. 54

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However,convectiveinstabilities,aggregationandhydrometerformationshouldalsoresult inpolymodalgrainsizedistributionwhichisnotobservedatthisdistancefromthevent Figure2.3d,althoughaslightsecondarypopulationofneashupto4wt.%at17km fromtheventwithamodearound6 seemstoappear.Thesecondarymaximumcould alsobeexplainedbyachangeinthesedimentationregime,fromparticlesmostlyfalling intheturbulentregimetoparticlesfallingmostlyintheintermediateregime.Infact, accordingtothepredictionofthemodelofBonadonnaandPhillipsthereisalready astrongpredominanceofparticlesfallingintheintermediateregimeat 17km.9vs.0.1, fractionforparticlesfallingintheintermediateandturbulentregimerespectively,even thoughaclearbreak-in-slopebetweenturbulentandintermediateregimeintheglobal thinningtrendisshownonlywhenthenumberofhigh-Reynolds-numberparticlesfallsto nearzeroBonadonnaetal.,1998,atadistanceof 28kmfortheBF2layerFigure2.20. 2.10.3Diusioncoecient Diusioncoecientsusedintephradispersalmodelsarenottrueatmosphericdiusion coecients,whichareusuallyonorderof3m 2 s )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 ,butrepresentapparentvalues.Complex plumeandatmosphericprocessesarecollapsedintothissingleparametertosimplifytephra dispersionmodels,butmayignoreprocessesthatcanaecttephradispersion. Animportantresultfromtheinversiononeachgrainsizeidentieslargevaluesfor diusioncoecientvalues > 15,000m 2 s )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 ,seeTable2.3,whicharehigherthanvalues typicallyusedinadvection-diusionmodelsi.e.1 )]TJ/F15 10.9091 Tf 8.484 0 Td [(6000m 2 s )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 ,Bonadonnaetal.a fortheTEPHRA2modelandHurstandTurnerfortheASHFALLmodel.Smaller valuesofthediusioncoecientwillnotmodeltheaccumulationofcoarserparticlesaway fromtheventasobservedontheeldFigure2.13.Wesuggestthatlargevaluesof thediusioncoecientarenecessarytodescribethegravitationalspreadinginano-wind condition. Table2.3showsthefalltimethresholdsFTTfoundinourinversionofgrainsize.In theTEPHRA2model,ifthetotalparticlefalltimeissmallerthantheFTT,diusionis 55

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linearFickianlaw,forcoarseparticleandstronglydependsonthediusioncoecient. Otherwise,diusionfollowsapower-lawrelationshipanddoesnotdependonthediusion coecientforsmallparticles.Ourresultsshowthatlargerparticles < -1 haverelativelyhighFTT,andthereforewilldiusemainlyfollowingFick'slaw,sincethetotalfall timeofparticlesislikelytobesmallerorsimilartotheFTT.Thediusionoftheseparticlesisstronglydependentonthevalueofthediusioncoecient.Forsmallerparticles, theFTTislikelytobesmallerthantheirtotalfalltime,andthereforewillexperiencea shiftindiusionlawduringfallfromlineartopower-law.Therefore,thevalueofthe diusioncoecientforsmallerparticlesisnotasimportantinparticledispersionasfor largerparticles. Anotherimportantobservationmadeduringtheinversionprocesswasthatitwas possibletomodeltheBF2depositwithasmallerdiusioncoecientbutahighertotal eruptedmass.Therefore,usingasmallvalueforthediusioncoecientwheninversionon tephra-thicknessdataisappliedonlyonproximalandmediallocationsmightoverestimate thetotalmassofthedeposit.Incontrast,modelingonindividualgrainsizeclasseswill helpavoidthispossibleissue. 2.10.4Windornowind? ThecircularityofthedepositalongwiththeoccurrenceoftheWhiteAshlayerstrongly suggestsnearlystillatmosphericconditionsatthetimeoftheeruption.Nevertheless,the isopachmap,theMd contourmap,theisomassmapsforindividualgrainsizesandthe inversionongrainsizeshowageneraldispersiontowardthesouthwest,indicatingthata lightwindprolewaspresentatthetimeoftheeruptionoftheBF2layer.Thevariations ofMd and withdistancefromtheventforthedierentaxesinvestigatedinthisstudy seeFigure2.4showthattheMd and decreasefastertowardtheESEthantowardthe SW.Therefore,clastsofagivensizearetransportedfurtherawayfromtheventalongthe SWaxisthanalongtheESEaxis,probablyasaconsequenceofaslightwindtransport. Thisobservationisemphasizedbytheshiftinthepositionoftheplumecornerfrom7kmto 56

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10kmfortheESEandSWaxesrespectivelyseeFigures2.17,2.18and2.19.Acornerof 7kmresultsinamaximumcolumnheightof29km,whereasacornerof10kmwouldresult inamaximumplumeheightof42km,whichisnotrealistic,andthereforeindicatesashift probablyduetothewind.Connoretal.bhavedemonstratedthatthecircularityof tephradepositscanbereproducedinwindyconditionswithactualwinddata,implying windshearforCotopaxivolcanoEcuador.However,wethinkthatthe2450BPeruption ofPululaguaoccurredinverycalmatmosphericconditions,becauseofthepresenceofthe WA,thepositionoftheplumecornerandthemodelingofthegrainsizedataproposed inthisstudy.Resultsfromtheinversionsofbothtotalaccumulationandindividualgrain sizeclassseeFigure2.14showwinddirectionsmainlytowardthesouthorthewestwith speed 10ms )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 Theoverallcircularityofthedepositmaybetheresultofdierentialdispersionof individualgrainsizeclassesindierentdirections,asshownbyFigures2.5,2.6and2.15. Then,thewindmighthavediedoutafterthedepositoftheBF2andpossiblyBF3to allowtheslowsettlingoftheneparticlecomposingtheWhiteAshlayer.However,the moreirregularisomasscontoursshownbythecoarsestparticles-6 and-5 ;Figure2.5 couldindicateanasymmetricalsedimentationfromtheplumemarginstowardsthesouth inagreementwithapossiblemodelforproximalsedimentationdescribedbyHoughton etal..Theseirregularisomasscontourscouldreectamixingofvolcanicclasts fallingfromdierentreleaseheights,thereforesedimentingsimultaneouslyfromdierent transportregimestheplumemarginsandtheumbrellacloud.Suchanasymmetrical sedimentationisalsoconrmedbytheshiftofplumecornershownbygrainsizedata Figures2.17,2.18and2.19. 2.11Conclusions OurstudyoftheclimacticphaseBF2ofthe2450BPPlinianeruptionofPululagua volcanobasedonelddataboththicknessandgrainsizedata,empiricaltechniques,and analyticalmodelingshowsthat: 57

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1.Statisticalandnumericalapproachesagreewellinthedeterminationofthetotal massoferuptedtephraandyieldastatisticaltotaleruptedmassof5 1 : 5 10 11 kgand anumericaltotaleruptedmass4 : 5 0 : 3 10 11 kgoffortheBF2layer. 2.Invertingtephrafalloutdepositonthetotalaccumulationorthicknessgivesa goodconstraintonthetotalmasseruptedbutnotonthecolumnheight.Byinvertingon individualgrainsizeclasses,thepossiblerangeincolumnheightsthatcanreproducethe depositisbetterconstrained. 3.Theplumehadaheightof36km,28km,27 3kmand20kmwhendetermined usingthemodelofCareyandSparks,Pyle,fromtheinversiononindividual grainsizedata,andusingthemodelofBonadonnaandPhillipsrespectively.The empiricalmodelsandtheinversionongrainsizeyieldamaximumcolumnheight,while thestrongplumeapproachyieldsanaveragecolumnheight,resultinginlowerelevations. 4.TotalgrainsizecalculationsTGSDfortheBF2layerarestronglydependanton thenumberanddistributionofsamplelocationsasalreadyobservedbyBonadonnaand Houghton,2005and,toalesserextent,alsotothepositionofthezeroaccumulation line.TheTGSDresultingfromtheVoronoitechniquewithazeroaccumulationlineat 100kmand200kmandtheinversiononindividualgrainsizedataareingoodagreement. ThestrongplumemodelisverysensitivetotheTGSDofthedeposit.TheTGSDof theBF2layerisne-depletedandlacks 50%ofneashinordertomodeltheobserved accumulationontheground. 5.Basedontheinversiononsinglegrainsizeclasses,largevaluesofthediusion coecientarenecessarytomodeltheBF2layer.Althoughsmallervaluesofthediusion coecientcanmodelthedepositrelativelywellbyinvertingonthicknessoraccumulation only,theresultingtotalmasseruptedwillbeanoverestimateofthetruemassofthedeposit. Thisconclusionhastobeacknowledgedinthemodelingofrelativelyproximaldepositsby usingadvection-diusionmodels.Webelievethatsuchhighvaluesarenecessarytodescribe thegravitationalspreadingoftheplumeinano-windcondition. 58

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6.Theinversiononindividualgrainsizeclassescannotresolvethedierenceinparticle releaseheights,whiletheapproachproposedbyBursiketal.bshowsthatthetransitionfromplume-marginandumbrella-cloudsedimentationoccursforparticlesbetween 32mmand16mm,whereasparticles 8mmmostlyfellfromtheumbrellacloud. 7.Ouruncertaintyanalysisconrmedthatinversiononindividualgrainsizeclasses ratherthantotalaccumulationgivesbetterestimatesofthecolumnheight,withrelatively lowuncertaintyonthecalculatedvalues.Therefore,integratinggrainsizedatatothetotal tephraaccumulationinmodelingtephradepositsshouldbeconsideredinfuturestudies. 8.Theclimacticphaseofthe2450BPPlinianeruptionofPululaguaoccurredinrelativelycalmatmosphericconditions,asdemonstratedbytheoccurrenceandubiquityofthe WAlayer.However,theisomassmapsonindividualgrainsize,theisopachandiso-Md maps,theinversionongrainsizeandtheresultsfromthestrongplumemodelsuggestthat theBF2dispersionwasinuencedbyaslightnorth-easterlywindtransportwindspeeds leq 10ms )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 atthetimeoftheclimacticphaseofthePlinianeruption.Theatmospheric conditionsmightthenhavecalmeddownevenmoretoaccommodatetheslowsettlingof thenevolcanicparticles < 1mmthatformtheWAlayer. 59

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CHAPTER3 INFLUENCEOFPARTICLESHAPEONTEPHRADISPERSAL 3.1Introduction Explosivevolcaniceruptionsejectamixtureofhotgasesandvolcanicparticlesfrom theconduit,includingjuvenilepumice,crystalsandincidentalfragmentslithics.This mixtureintrudestheatmosphereandcangenerateabuoyantvolcanicplumereaching stratosphericlevelsforthemoreenergeticeruptions,iftheconditionsforbuoyancyare achievedi.e.densityofthevolcanicmixture < densityofthesurroundingatmosphere. Volcanicplumescanbedenedaseitherweakorstrongplumesifthewindvelocityis greaterorsmallerrespectively,thantheverticalvelocityoftheeruptivecolumnSparks etal.,1997;BonadonnaandPhillips,2003;Bonadonnaetal.,2005b.Oncethelevelof neutralbuoyancyisreached,thevolcanicplumerisesfurtherduetomomentumforces beforespreadinghorizontallyasagravitycurrentaroundthelevelofneutralbuoyancy, formingtheumbrellacloudofvolcanicplumesSparks,1986;Bursiketal.,1992a;Sparks etal.,1997;BonadonnaandPhillips,2003. Volcanicparticlessettleouteitherfromtheplumemarginsorfromtheumbrellacloud. Sedimentationprocessesaremainlygovernedbytheterminalsettlingvelocityandwind advectionofvolcanicparticles,wheretheterminalsettlingvelocity V t ofvolcanicparticles isdenedasthevelocityatwhichthedragforcebalancesthegravityforce,following: V t = s 4 gd s )]TJ/F21 10.9091 Tf 10.909 0 Td [( f 3 C d f .1 60

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where g isthegravityaccelerationms )]TJ/F19 7.9701 Tf 6.587 0 Td [(2 d istheparticlediameterm, s isthe particledensitykgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 f istheuiddensitykgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(3 and C d isthedragcoecient dimensionless. C d isdependentonboththeparticleshapeandparticleReynoldsnumber R e ,whichisinturnafunctionoftheterminalvelocity V t ,givenbytherelation R e = f dV t / ,with beingtheairviscosityPas.Itiswellknownthatirregularparticle shapewillgreatlyincreasedrag,thereforeloweringsubstantiallytheterminalvelocityof thevolcanicparticle. SincetheearlystudiesofterminalvelocitiesofvolcanicparticlesbyWalker, WilsonandHuangandSuzuki,showingtheimportanceofparticleshapeon clastterminalvelocitiesandproposinganempiricalrelationshipbetweenaparticle'sshape anditsterminalvelocity,noquantitativestudieshavebeenmadeonparticleshapeandits inuenceonterminalvelocityofvolcanicparticlesuntiltherecentstudiesofRileyetal. ,Dellinoetal.andColtellietal.. Rileyetal.showedthattheaspectratio,feretdiameteri.e.theperpendicular distancebetweenparalleltangentstouchingoppositesidesoftheparticleandtheperimeter measurementsofavolcanicparticlewerethemostusefulincharacterizingtheinuence ofparticleshapeonitsterminalvelocity.Theyalsoobservedthatthediametersofash particleswere10 )]TJ/F15 10.9091 Tf 8.485 0 Td [(120%largerthantheequivalentperfectspheresfallingatthesame terminalsettlingvelocity. FollowingtheirexperimentalanalysisofvolcanicparticlesfromVesuviusandCampi FlegreiItaly,Dellinoetal.proposedannewempiricalequationtocalculatethe terminalvelocityofvolcanicparticlesbasedonthedensity,diameterandshapefactorof theparticles,completelyindependentofthedragcoecient C d andtheReynoldsnumber R e .Thereforetheterminalvelocitycanbecalculatedwithoutimplementinganiterative procedure.Dellinoetal.proposedtoimplementnumericalsimulationsoftephra dispersionandtephrafallouthazardsscenariosbasedontheirapproach. TheworkofColtellietal.oncharacterizingtheshapeofvolcanicparticlesranginginsizebetween0.026and1.122mmfromtheDecember2002eruptionofMt.Etna 61

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Italyshowedthatparticleshapeparametersareonlyweaklydependentonparticlesize. Furthermore,theyalsoobservedthatterminalvelocitiesassumingtephraparticlesasperfectsphereswere1.28timesgreaterthanthoseforwhichtheshapeistakenintoaccount, andthatapproximatingvolcanicparticlesasspheresincalculatingtheirterminalvelocities isreasonableforthesmallestparticlesizetheymeasuredi.e.4 fraction. Finally,Scolloetal.werethersttoactuallydocumentdirectmeasurements ofterminalvelocitiesofvolcanicparticles,usingadopplerradar,duringtheDecember 2002explosiveeruptionatMt.EtnaItaly.Theirresultsshowedthatmeasuredterminal velocitieswereingoodagreementwiththeoreticali.e.KuniiandLevenspiel,1969and experimentali.e.WilsonandHuang,1979approachestopredictterminalvelocitiesof volcanicparticles. AccordingtoChhabraetal.,thebestmethodtoestimatethedragcoecient C d ofnon-sphericalparticlesistheoneproposedbyGanserbasedontheequal volumespherediameterandthesphericityoftheparticles.ThemethodofGanser isvalidforparticlewitha R e rangingfrom10 )]TJ/F19 7.9701 Tf 6.586 0 Td [(4 to5 10 5 ,thereforeforthethreedierent fallregimesturbulent,intermediateandlaminardescribedbyBonadonnaandPhillips .Unfortunately,themodelproposedbyGanserisbasedonmorphological parametersofparticlesthatarenoteasytomeasure.Infact,thePVSdevicedoesnot providesuchparameters,impedingmetousethemodelofGanser. Intephradispersalmodels,regardlessofwhethervolcanicparticlesaremodeledas perfectspheresBonadonnaandPhillips,2003;Connoretal.,2008ornotSuzuki,1983; Pfeieretal.,2005;Costaetal.,2006,itisassumedthatparticleshapedoesnotvary withdistancefromthevent.However,intuitively,sphericalvolcanicparticlesfromagiven sizefractionshouldfallclosertotheventcomparedtonon-sphericalclasts.Avariationin shapeparameterswithdistancefromtheventshouldbeexpected,withtheformerfalling outoftheeruptioncolumnearlierandsedimentingclosertotheventthanthelatter. Consequently,thegoalsofthisstudyaretoinvestigatethevariationinparticleshape withgrainsizeandwithdistancefromthevent,touseparticleshapeparameterstoquantify 62

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thechangesintheterminalsettlingvelocity,tocomparethemeasureddiameterofvolcanic particleswiththeequivalentdiameterofspheresfallingatthesameterminalvelocityand toinvestigatetheinuenceofparticleshapeintephraaccumulation. 3.2Methodology Samplesanalyzedinthisstudyaretephrafalldepositsfromtheclimacticphaseofthe 2450BPdaciticPlinianeruptionofPululaguavolcano,Ecuador.Thiseruptionhasbeen describedandstudiedbyPapaleandRosiandalsoextensivelyinChapter2.The eruptionisthoughttohaveoccurredinrelativelycalmatmosphericconditions,resulting innearlycircularisopachandisoplethmaps,thereforehasnoclearlydeneddispersal axis.ThetotaleruptedmassforthemainphaseoftheeruptiontheBF2layerhasbeen estimatedat5 1 : 5 10 11 kginChapter2,andthecolumnheightat20kmwiththe modelofBonadonnaandPhillips,27 3kmthroughtheinversionofgrainsize data,30 3kmusingastatisticalapproachand32 )]TJ/F15 10.9091 Tf 8.485 0 Td [(36kmfollowingthemodelofCarey andSparks. Inthisstudy,IanalyzedthetephradepositoftheBF2layerwiththePharmaVision 830PVSdevicetoextractshapeparametersonsingleparticlesfrom0 mmdownto 10 msizefractions.SamplesoftheBF2layerweredry-sieveddownto4 ,following normalsievingproceduresCasandWright,1987,andeachfractionwasthenanalyzed withthePVStoobtainshapeparametersforeachsingleparticle.Thefraction < 4 was analyzedasabulkwiththePVSandshapemeasurementswerethenmadeforeachphi sizesfrom5 to10 ThePVSisamicroscopethatscansthesamplepreviouslydispersedonaglassslide, takespicturesofeachsingleparticleandextractsmorphologicalparametersfromthese picturesFigure3.1.Particlesareassumedtohavedepositedontheglassslidewiththeir largersurfacefacingtheglassslideandthereforethemicroscopeofthePVS.Morphological parametersinclude:meandiameter,diameterequivalentdiameterofacirclehavingthe sameareathanthemeasuredparticle,maximumdistance,width,length,area,volume 63

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Figure3.1.Representationofahypotheticalvolcanicparticleandsomeofthemorphological parametersmeasuredbythePVS.Meandiameter:theradius r fromthecenterofthe masstotheparticleperimeterismeasuredateverypixelontheperimeter.Themean diameteristhencalculatedfromthemeanvalueofthosemeasurements.Diameter:the diameterisdeterminedbythediameterofacirclewiththesameareaastheparticle. derivedfromarea[ A ]andmeandiameter[ d ]following: v =2 ad= 3,roundnessandconvexityofagivenparticle.Roundnessisameasurementofthelength )]TJ/F15 10.9091 Tf 8.485 0 Td [(widthrelationship, withavalueintherange[0to1].Aperfectcirclehasaroundnessof1.0,whileavery narrow,elongatedobjecthasaroundnesscloseto0.Convexityisdenedastheparticle areadividedbytheareaenclosedbytheconvexhullanidealrubberbandwrappingthe particle.Aconvexshapehasaconvexity1.0,whileaconcaveshapehasalowervalue, closerto0.Theconvexityisameasureofparticleroughness.Thisapproachislimitedtoa two-dimensionalanalysisofparticleshapebuthastheadvantageofanalyzingalargenumberofparticlesinashortperiodoftime,thereforeallowingforstatisticallyrepresentative populationstobeanalyzed. Ianalyzedatotalof53samplescollectedfromtheBF2layerseeChapter2andI presentheretheresultsofthisanalysisforeverysampleandinturnforeachgrainsize classandalongthethreeaxesdescribedinFigure2.1b.Theparticleshapedescriptors usedinthepresentanalysisare: i theparticleaspectratio AR denedbyRileyetal., 2003asthelength/widthofagivenparticle, ii theshapefactor F denedbyWilson 64

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andHuang,1979as F = b + c = 2 a ,where a b and c arethethreeorthogonalaxes ofagivenparticlewith a>b>c butasthePVSmethodisa2-Dapproach,thenthe relationshipis a>b = c iii theroundness R ,and iv theconvexity C givenbythe PVS. 3.3Particleshape 3.3.1Bulkresultsforeach class Resultsforindividualgrainsizeclassincludingallthesamplesanalyzedarepresented inFigures3.2and3.3,andinTable3.1.Figures3.2and3.3showthefrequencydistribution ofeachshapedescriptordenedearlier AR C and R forgrainsizeclassesfrom0 to 10 .Theseresultsregroupdataforallthesamplesanalyzedforeachgrainsize.Data fortheaspectratio AR shapedescriptorarebestdescribedbyatruncatedlognormal distributionsolidlineintheleftcolumnofFigures3.2and3.3,whiletheroundness R andtheconvexity C arebetterdescribedbyatruncatednormaldistributionsolidlines themiddleandrightcolumnrespectivelyinFigures3.2and3.3.Theshapefactor F is notrepresentedintheseguressinceitwillfollowtheinversetrendof AR .Iobservedthat shapefactor F isalsobestdescribedbyatruncatednormaldistributionasfor R and C Thetruncatednormaldistributionisgivenby: t x = f x cdf n )]TJ/F21 10.9091 Tf 10.909 0 Td [(cdf m .2 where f x istheprobabilitydensityfunctionforanormaldistribution,and cdf m and cdf n arethevaluesofthecumulativedistributionfunctionat m and n ,respectivelythe loweranduppervaluesofthetruncationwith m
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T x = F x R n m F x dx .3 where F x istheprobabilitydensityfunctionforalognormaldistributionand m and n aretheloweranduppervaluesofthetruncationrespectivelywith m
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Figure3.2.Frequencydistributionsoftheaspectratio AR ,convexity C androundness R fordierentgrainsizeclassesfrom0 to5 .Atruncatedlognormaldistributionhas beenttedtotheaspectratio AR dataandatruncatednormaldistributionhasbeen ttedthroughtheconvexity C androundness R dataforeachgrainsizeclasses. 67

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Figure3.3.Frequencydistributionsoftheaspectratio AR ,convexity C androundness R fordierentgrainsizeclassesfrom6 to10 .Atruncatedlognormaldistributionhas beenttedtotheaspectratio AR dataandatruncatednormaldistributionhasbeen ttedthroughtheconvexity C androundness R dataforeachgrainsizeclasses. 68

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Table3.1.Mean ,1 standarddeviationStdandnumber N ofparticlesanalyzedfor dierentshapeparameters:aspectratio AR ,convexity C ,roundness R anddiameter oftheequivalentsphere ED .GSstandsforgrainsize. GS AR AR C C R R ED ED N 01.3180.2260.9580.0250.7260.1411577.7319.813964 11.3440.2460.9640.0240.7120.149804.8164.430670 21.3490.2630.9660.0250.7100.153406.761.542073 31.3960.3100.9530.0280.6830.164216.531.627482 41.3900.3120.9460.0320.6810.165105.420.649113 51.3500.2470.9220.0510.6820.16140.57.68642 61.4540.3160.9200.0540.6370.17623.35.351051 71.5220.3640.9210.0500.6410.17211.62.763444 81.5600.4050.9570.0400.6380.1766.191.45352987 91.6080.4530.9840.0270.6560.1783.320.77489826 101.6130.6010.9940.0240.7370.1691.520.51708652 constantwithdistancefromtheventwithinagivengrainsizeclass,oratleastvariations arewithinthestandarddeviationonthemeanvalueoftheshapedescriptorseeTable3.1. However,particleshapevaluesvarysignicantlybetweenthedierentgrainsizeclasses, incontrastwiththeobservationsofColtellietal.forthe2002eruptionofEtna volcanoItaly. ThevariationsinshapedescriptorssimilartothoseobservedinFigures3.2and3.3 withdistancefromtheventforveryneashparticles 9 mightbeduetothelower resolutionlimitofthePVStechnique,andthereforemaynotbearealpattern,butrather abiasfromtheoriginaldataacquisition. AnotherimportantobservationdrawnfromFigures3.4,3.5and3.6leftcolumnis thatthetrendforthethreedierentshapedescriptorswithdecreasinggrainsizesisfairly constantforthedierentsamplelocationsnoteforexamplethetroughin AR and C or thebulgein R at5 ,withagainasmallbutsignicantdeparturefromthetrendfor particlesof9 and10 ,andpossiblyforthe8 fraction.Thispatternisagainattributed tothelowerresolutionlimitofthistechnique. 69

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Figure3.4.Variationsofshapeparameters AR C and R asafunctionofgrainsize leftcolumnanddistancefromtheventrightcolumnfortheESEaxisaxis1,see Figure2.1b. 70

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Figure3.5.Variationsofshapeparameters AR C and R asafunctionofgrainsizeleft columnanddistancefromtheventrightcolumnfortheSEaxisaxis2,seeFigure2.1b. 71

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Figure3.6.Variationsofshapeparameters AR C and R asafunctionofgrainsizeleft columnanddistancefromtheventrightcolumnfortheSWaxisaxis3,seeFigure2.1b. 72

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3.4Terminalvelocity 3.4.1Comparisonbetweendierentmodels Basedontheresultsobtainedfromtheshapeanalysiscarriedoutintheprevious section,Iinvestigatedtheinuenceofparticleshapeontheterminalvelocityofvolcanic ashparticles.Theterminalvelocityanalysisandeveryfurtheranalysisinthisstudywill focusonparticlesizesfrom0 downto5 ,asforparticles > 5 ,thecalculatedterminal velocitiesbecametoosmallforsignicantcomparisonsbetweenthedierentmodels.To achievethisgoal,Iusedseveralmodelstocalculatetheterminalvelocityofashparticles. First,IappliedtheequationsproposedbyKuniiandLevenspieltopredictthe terminalvelocitythereafterreferredas V KL ofvolcanicparticles,assumingashparticles tobeperfectspheres.ThisapproachhasalsobeenusedbyBonadonnaetal.and BonadonnaandPhillipstocalculatethesettlingvelocityofvolcanicparticlesin theirmodeloftephradispersal.KuniiandLevenspielproposedthreedierent equationstocalculatetheterminalvelocityofparticlesbasedontheowregimearound thefallingclastslaminarregime[ l ]for R e < 6,intermediateregime[ i ]for6 R e < 500 andturbulentregime[ t ]for R e 500: V KL;l = gd 2 s )]TJ/F21 10.9091 Tf 10.909 0 Td [( f 18 .4 V KL;i = d 4 g 2 s )]TJ/F21 10.9091 Tf 10.909 0 Td [( f 225 f 1 3 .5 V KL;t = 3 : 1 gd s )]TJ/F21 10.9091 Tf 10.909 0 Td [( f f 1 2 .6 73

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where g isthegravitationalaccelerationms )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 d istheequivalentdiameterofasphere m, s isthedensityoftheparticlems )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 f isthedensityoftheuidmediumms )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 and istheuidviscosityPas. Walkeretal.andWilsonandHuangconductedaseriesofexperiments todeterminetheterminalvelocitiesofvolcanicparticles.Theyconcludedthatsettling velocitiesmeasuredonnaturalsamplesarealwayslowerthanthosecomputedassuming particlesasspheres.Inparticular,basedontheirexperimentaldata,WilsonandHuang proposedthefollowingrelationshipbetween C d ,particleshapefactor F andparticleReynoldsnumber R e : C d = 24 R e F )]TJ/F19 7.9701 Tf 6.586 0 Td [(0 : 828 +2 p 1 : 07 )]TJ/F21 10.9091 Tf 10.909 0 Td [(F .7 Bycombining3.1and3.7,theterminalvelocityofWilsonandHuangthereafter referredas V WH canbewrittenas: V WH = s gd 2 9 F )]TJ/F19 7.9701 Tf 6.587 0 Td [(0 : 828 + q 81 2 F )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 : 656 + 3 2 s f d 3 p 1 : 07 )]TJ/F21 10.9091 Tf 10.909 0 Td [(F .8 However,Suzukiproposedaslightlymodiedversionoftheterminalvelocity equationofWilsonandHuang,basedonabetterttosmallerparticles < 100 mu m, asfollows: V WH;suzuki = s gd 2 9 F )]TJ/F19 7.9701 Tf 6.586 0 Td [(0 : 32 + q 81 2 F )]TJ/F19 7.9701 Tf 6.587 0 Td [(0 : 64 + 3 2 s f d 3 p 1 : 07 )]TJ/F21 10.9091 Tf 10.909 0 Td [(F .9 Inthepresentstudy,IwillusethelatterformulaEq.3.9asitagreesbetterwith nerparticles,whicharethefocusofthisanalysis.Iwillneverthelessrefertotheterminal 74

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velocityofWilsonandHuang V WH astheyrstproposedthisexpression,later modiedbySuzuki. IdidnotusetheempiricalmethoddescribedbyDellinoetal.todeterminethe terminalvelocityofvolcanicparticles,because i Icouldnotcalculatetheshapefactor Psi proposedbyDellinoetal.withthemorphologicalmeasurementsobtainedfrom thePVS,and ii becausetheirrangeofobservationofparticlesizesisdierentthanthe oneofthisstudy. Figure3.7showstheresultsoftheterminalvelocitycalculationsusingthetwodierent modelsdescribedpreviouslyKuniiandLevenspiel,1969;WilsonandHuang,1979.In Figure3.7,Idenedtheeldof V WH vs. V KL inblue.Thebluetrianglerepresentsthe meanterminalvelocityfor V WH ,calculatedfromallofthedatapointsforeach size.For volcanicclastsof0 and1 sizes,themodelofWilsonandHuangisconsiderably lowerabout35%lowerforthe0 fractionandabout20%lowerforthe1 fractionthanthe modelofKuniiandLevenspielassumingparticlesasperfectspheres.Forvolcanic particles 2 ,themodelofWilsonandHuangpredictsterminalvelocitiessimilar to,butmostlylowerthan,thosefollowingKuniiandLevenspielseeFigure3.7for the2 ,3 ,4 ,5 sizefractions. Basedontheresultspresentedabove,Icalculatedthecumulativefrequencydistributionforeachparticlesizefractionandforeachterminalvelocitymodele.g.Kuniiand Levenspiel,1969;WilsonandHuang,1979inordertodeneandcomparethedistribution ofterminalvelocitiesforeachmodelateachgrainsizefraction.Resultsarepresentedin Figure3.8,wherethecumulativefrequencydistributionfortheterminalvelocitiescalculatedwiththemodelsofKuniiandLevenspielandWilsonandHuangare showninredandbluerespectively.TheterminalvelocitiescalculatedusingtheWilsonand HuangmethodinbluearealwayssmallerthantheonescalculatedwiththeKunii andLevenspielmethodinred.Thedierenceinterminalvelocitiesresultingfrom thesetwotechniquesdecreaseswithdecreasingparticlesizefraction,indicatingthatthe smallertheparticlethesmallertheinuenceofparticleshapeonitsterminalvelocity,and 75

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Figure3.7.Comparisonsbetweenparticleterminalvelocitiescalculatedfromdierentmodels: V KL ,approximatingvolcanicparticleassphereKuniiandLevenspiel,1969; V WH blueeldandbluetrianglecalculatedfromWilsonandHuang.Thediameterof theparticleistheequivalentdiameterofasphere. 76

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thecloseraparticlefallsasaperfectsphere.Thejumpinterminalvelocityaround5.5 ms )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 forthe0 fractionisduetothechangeinowregimeofthefallingvolcanicparticles fromturbulenttointermediateasalreadyobservedbyBonadonnaetal.,1998. Recently,Rileyetal.andColtellietal.showedthatthemeasureddiametersofvolcanicparticleswithdimensionsbetween10and150 mweremuchgreater between10%and120%accordingtoRileyetal.,2003andbetween7%and66%according toColtellietal.,2008thantheonescalculatedforsphericalparticleswiththesameterminalvelocity.Similarly,Icalculatedthediameteroftheequivalentspherethatwouldfall atthesameterminalvelocity V WH byinvertingtheequationsofKuniiandLevenspiel i.e.equations3.4,3.5and3.6.Figure3.9showsthecomparisonbetweenthemeasureddiameterofeachashparticleandthecalculateddiameteroftheequivalentsphere forvolcanicparticlesfrom0 to6 .Onaverage,themeasureddiametersofthevolcanic particlesarelargerthanthediametersoftheirequivalentspheres%forthe0 fraction, 33%for1 ,8%for2 ,10%for3 ,10%for4 ,5%for5 and6%for6 3.4.2 V WH / V KL vs AR Rileyetal.observedthatthebestshapedescriptorforvolcanicparticlesis theaspectratio AR ,calculatedthesamewayasinthepresentstudy.Coltellietal. showedalinearrelationshipbetweentheratioof V WH to V KL andtheiraspectratio parameterthereafterreferredas AR Coltelli forallofthe2065particlestheyanalyzedfrom the2002eruptionofEtnavolcanoItalywhenallparticlesaregroupedinbinsof0.1of AR Coltelli .Coltellietal.calculatedtheaspectratio AR Coltelli ofvolcanicparticle asbeingthebreadth/width.Therefore, AR Coltelli =1/ AR .Coltellietal.proposed aneasysolutiontocalculate V WH from AR Coltelli ,andfoundthefollowingexpression linking V WH / V KL and AR Coltelli : V WH V KL = : 6 AR Coltelli +0 : 4.10 77

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Figure3.8.Cumulativefrequencydistributionofterminalvelocitiescalculatedwiththe dierentmodelsexplainedinthetext V KL inred, V WH inbluewith F calculatedassuming c = b and V WH indashed-bluewith F calculatedassuming c =0.Notethejumpin V KL valuesforterminalvelocitiesofabout5.5ms )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 inthe0 fraction. 78

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Figure3.9.Comparisonbetweenmeasureddiametersofvolcanicparticlesanddiameters ofspheresfallingatthesameterminalvelocity.Resultsforthe0 inblack,1 inred,2 inblue,3 inyellow,4 ingreen,5 inorangeand6 inpurple. 79

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Coltellietal.stressedthatthisrelationship,thoughappealingtoquicklycalculate V WH fromthe AR Coltelli oftheparticles,mightnotberepresentativeofallvolcanic particles,butonlyofthetypeoferuptionanalyzedi.e.the2002eruptionofEtnavolcano andtherangeinparticlesizetheyobservedbetween0.026and1.122mm.Totestthis statement,Iusedtheresultsobtainedpreviouslytoinvestigatesucharelationship,foreach fraction,fortheBF2layerofPululaguavolcano.Inordertoapplythisapproach,Ihad toinvertthevaluesof AR calculatedpreviouslyanddene AR =1/ AR ResultsarepresentedinFigure3.10showingthemeanratioof V WH / V KL andthe corresponding1standarddeviationforeach0.1 AR bin.Alinearregressionistted throughthedatapoints.Forparticlesrangingfrom2 to8 ,thereisanexcellentlinear relationshipbetween V WH / V KL and AR R 2 0.96,withafairlyconstantrelationship throughthedierentgrainsizesseeequationsonFigure3.10.However,thisrelationship isworseforthe0 fractionandnotwell-constrainedforthe1 fractionR 2 =0.81and 0.69respectively,Figure3.10.Therefore,itseemsthatthisrelationshipholdsforsmall particles,butmightnotbeapplicableforlargerparticles 1 ,wherethereisasignicantdeparturefromalinearrelationshipbetweentheterminalvelocityratioandthe shapeparameter AR andthelinearrelationshipisquitedierentaswellseeequations inFigure3.10. 3.5Sedimentation Afteranalyzingtheinuenceofparticleshapeontheterminalvelocityofvolcanic particles,Iwasinterestedinexploringtheimpactthatvariationsinparticleshapehave onthesedimentationoftephradeposits,astheterminalvelocityisarstorderparameter controllingthesedimentationoftephradepositsBonadonnaetal.,1998;Pfeieretal., 2005.AsIgatheredextensiveinformationonparticleshapeparametersforindividual grainsizeclasses,Idecidedtoinvestigatetheinuenceofparticleshapeonsedimentation forparticlesizesfrom0 to5 ,asbelow5 ,theterminalvelocityofvolcanicparticles becomesverysmall. 80

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Figure3.10.Relationshipbetweenthemeanvaluesof V WH / V KL and AR forparticle groupedin0.1 AR binsandforeachgrainsizefractionfrom0 to8 .The1standard deviationisshownastheverticalerrorbar.Equationsandcorrelationcoecientforeach linearrelationshiparealsoshown. 81

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IusedtheequationdescribedbyBonadonnaandPhillipstopredicttheaccumulation m ,inkgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 ofvolcanicparticlesofagivenphisize atthebaseofthe spreadingcurrenti.e.,theumbrellycloud H cb ,inm.Thisapproachiscorrectsince theaccumulationatthebaseofthespreadingcurrentwillleadtoverticalfalloutinthe caseofaneruptionwithoutasignicantwindeld,whichwasthecaseoftheBF2layer ofthe2450BPeruptionofPululaguaseeChapter2.Therefore,thetephraaccumulation onthegroundwillreecttheaccumulationatthebaseofthespreadingcurrent.The accumulation m isgivenby: m = 4 M 0 V t Q p exp )]TJ/F21 10.9091 Tf 9.681 7.38 Td [(V t Q x 2 )]TJ/F21 10.9091 Tf 10.909 0 Td [(x 2 0 .11 where M 0 isthetotalmassoftephraforeachgrainsizefractionkg, x isthedistance fromtheventwheretheaccumulationiscalculatedm, x 0 isthehorizontalpositionof theplumecornerm, Q isthevolumetricowratem 3 s )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 intothespreadingcurrent attheneutralbuoyancyleveland V t istheterminalvelocityms )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 oftheparticlesofa givensize attheheightofthespreadingcurrent H cb .Thedierentterminalvelocity models V KL V WH and V D describedpreviouslywillbeusedinthismodelingapproach. BonadonnaandPhillipsdenedtheheightofthebaseofthespreadingcurrent H cb as: H cb = H max 0 : 6.12 where H max misthemaximumcolumnheight.Thehorizontalpositionoftheplume corner x 0 isdenedbyBonadonnaandPhillipsas: x 0 = H max 0 : 24.13 82

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Finally,thevolumetricowrateattheheightofneutralbuoyancyisgivenbyBursik etal.bas: Q = H max 0 : 287 5 : 263 .14 Asmodelinputparameters,Iassumedthemaximumcolumnheight H max tobe 20kmsamevaluefoundinChapter2bymodelingtheBF2layerwiththestrongplume modelofBonadonnaandPhillips,2003andIusedthemassforeachgrainsizefraction M 0 resultingfromthetotalgrainsizedistributioncalculatedwithazeroaccumulation lineat200kmseeFigure2.8h.TheparticlediameterandshapedescriptorRandF werereportedforeachparticlesizefractionfromthisanalysis.Ialsousedtheprobability densityfunctionsi.e.equations3.2and3.3thatbestttedtheshapedescriptordatafor eachparticlesizefractionseeFigures3.2and3.3toinvestigatetheinuenceofparticle shapedistributionontephrasedimentation. ResultsarepresentedinFigure3.11,wheretheredlinesaretheaccumulationsusing V t = V KL andbluelinesusing V t = V WH .Asexpected,thedierencesshownpreviouslyinthe terminalvelocitiesfromthedierentmodelshaveaprimaryinuenceontheaccumulation oftephraawayfromthevent.Forthe0 fraction,thevariationsinaccumulationwith distancefromtheventareminimalandagreereasonablywellamongthetwomodelsof terminalvelocityadoptedinthisstudy.Thetephraaccumulationmodelwith V WH leadsto smallertephraaccumulationsinproximaltomedialregions < 20kmandslightlyhigher accumulationsinmoredistalareas > 20kmcomparedtotheterminalvelocitymodelfrom KuniiandLevenspiel.Thecalculatedaccumulationswithdistance,usingthemodel ofWilsonandHuangarealwayslowerthanthosecalculatedassumingparticlesas beingperfectspheresKuniiandLevenspiel,1969,althoughtheinuenceofparticleshape ontephraaccumulationdecreaseswithdecreasingparticlesize,asdenotedbythealmost perfectagreementofredandbluelineswithdecreasing sizes. 83

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ThedashedblacklineinFigure3.11representsthetephraaccumulationusingtheparticleshapeprobabilitydensityfunctiontruncatednormaldistributiondescribedpreviously forthe F shapedescriptorasaninputinthe V WH terminalvelocitymodel.Regardless oftheparticlesize,thetephraaccumulationonthegroundmodeledwithaparticleshape distributionoftheRshapedescriptorarealmostsimilartothecalculatedaccumulation usingthemeanvalueoftheRshapefactor,thereforeIdidnotshowtheseresultshere. 3.6Discussion IncalculatingtheterminalvelocityusingthemodelofWilsonandHuang,Ihad toassumethatthesmalleraxisoftheparticles c isequaltotheintermediateaxis b indeterminingtheshapefactor F .Thisisaconsequenceofthe2Dapproachinparticle measurementswiththePVS.Theconversionfrom2Danalysisto3Disnottrivialand hasbeenaddressedusingstereologyforcrystalandbubblesizedistributionbyCashman andMarsh,Manganetal.,CashmanandManganandSahagianand Proussevitchamongothers. Ifollowedtwoapproachestotestmyassumptionthat c = b isreasonableinmy2D analysis.Intherstapproach,Imeasuredthethreeperpendicularaxesof117large pumices < -5 .ThenIcalculatedtheshapefactor F usingthevaluesofthethreeaxes andusingtheassumptionthat c = b .Ifoundthatformorethan80%oftheobservations, thevaluesof F calculatedwiththe2Dapproachareatmost20%largerthanthetrue valueof F .Thisresultshowsthatmy2Dassumptionisreasonable.Theassumptionthat c = b leadstoamaximuminthevalueoftheshapefactor F .Therefore,inthesecond approach,IalsocalculatedtheterminalvelocityfollowingthemodelofWilsonandHuang V WH ,assuming c =0inthedeterminationof F ,whichgivesaminimuminthe valueof F andthereforealsoaminimumin V WH .Figure3.8showstheresultsofthese calculations.Thesolidbluelineisthevaluesof V WH calculatedwiththeassumptionof c = b andthedashedbluelineshowsthevaluesof V WH computedwiththeassumptionof c =0.Thedierencebetweenthesetheterminalvelocityislarge,butsinceIhaveshown 84

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Figure3.11.Inuenceofthedierentmodelofterminalvelocitycalculationsonthesedimentationoftephradepositfordierentgrainsizeclassesfrom0 to4 .Inred,sedimentationcalculatedusing V KL andinblue V WH .Thedashedblacklinesaresedimentation calculatedwithatruncatednormaldistributionfor F .ThesimulationsarefortheBF2 layerofPululaguavolcanoseeChapter2,withacolumnheightof20kmandatotalmass varyingforeachgrainsizeaccordingtothetotalgrainsizedistributioncalculatedfora "zeroaccumulationline"at200kmfromtheventseeFigure2.7andTable2.1. 85

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thatforlargerparticles,formostoftheparticlestheshapefactor F isoverestimatedby nomorethan20%,Ifoundmy2Dapproachtobeacceptable. Thedierentshapeparametersusedinthisstudyshowawiderangeofpossiblevalues foreachgrainsizeclass,adistinctfrequencydistributionandcanbeapproximatedasa truncatedlognormaldistribution AR oratruncatednormaldistribution C F and R TheresultspresentedinFigures3.7,3.8and3.9clearlyindicatethatthemodelof WilsonandHuangpredictthatlargerparticlesfallataslowersettlingvelocity thantheirequivalentsphere.Thisobservationimpliesthatparticleshapeshouldsortwith distancefromthevent,withsphericalparticlesfallingclosertothevent,andirregularlyshapedparticlesfallingfurtherawayfromthevent.However,Figures3.4,3.5and3.6show fairlyconstantvaluesinparticleshapedescriptorforagivenparticlesizewithdistance fromthevent,whileparticleshapedescriptorsdosortwithgrainsize.Thisobservation showsthattheassumptionthat,intephradispersalmodels,particleshapedoesnotvary withdistanceiscorrect,unlessachangeinshapeforparticlesofagivenfractionhappens beyondtheobservationandsamplingareaoftheBF2.ThisisunlikelysinceIincluded themostdistalpointPL55amongtheSWaxisaxis3datapointsintheanalysis, althoughitdoesnotreallybelongtothatparticularaxis,andnovariationsinparticle shapewereobservedFigure3.6.Theseresultshaveimportantimplicationsintephra dispersionmodelingandthereforeintephrafallouthazards.Infact,myresultsimply thattotalparticlesettlingtimeisnotstronglyinuencedbyparticleshape,butadditional factorsaremoreimportantinthetransportandsedimentationofvolcanicparticles,factors suchas i motionoftheatmosphereturbulence,thatcanincreasedragontheparticle, ii particleentrainmentsettlingofcohortsofparticlesthatwilllikelyreducedragon particlesand iii iceformationonvolcanicparticlesregardlessoftheirsizeandsurface areathusshapeDurantetal.,2008.Thepresentstudyistherstofthiskind,and maysuggestthatcurrenttephradispersionmodelsdonotneedtoimplementafunction toaccountforparticleshape,butshouldbetterconstrainthephysicalprocessesdescribed above. 86

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However,theshapeparametersvaryasafunctionofgrainsizesfortheBF2layerof Pululagua,incontrasttotheresultsofColtellietal.forthe2002eruptionofEtna, andimplyingthattephramodelersmayneedtobetterconstrainparticleshapeparameters asafunctionofparticlesizeandusethesevaluesasinputparametersintephradispersal modelstobetterreproduceobservedtephradeposits.Shapeparametersforagivensizeof volcanicparticlesaremostlikelytodierfromeruptiontoeruptionasafunctionofmagma compositionanderuptivestyle.Itisnotreasonabletoassumethatvaluesofparticleshape presentedinthisstudybeusedasproxiesinothertephrastudies. Anotherinterestingresultfromtheparticleshapeanalysisliesinthefairlyconstant trendinthedierentshapedescriptorsfordierentsamplelocationsasafunctionofgrain sizeFigurerefg3-2a,refg3-2bandrefg3-2c.Suchanobservationmightmeanthat thereisanunderlyingprocessleadingtothisparticulartrendinparticleshape.Fragmentationprocessesinferredfrompumicetextureswithintheconduitmightberesponsible fortheobservedtrend,butfurtherquantitativeinvestigationsinbubbleshape,bubble sizedistributionandcrystalsizedistributionarenecessarytolinkfragmentationprocesses withparticleshape.Furthermore,theobservedtrendsinparticleshapearemostlikelyto changewithmagmacompositionsasalreadyobservedbyRileyetal.,2003,forthemean aspectratiovaluesbetweenbasalticandrhyoliticcompositionsanderuptivestyles. Thecomparisonbetweenthedierentmodelsofterminalvelocityi.e.KuniiandLevenspiel,1969;WilsonandHuang,1979showsthatthetwomodelsagreewellwiththe theoryforparticlesizesof0 and1 ,forwhich V WH accountingforparticleshapeis similartoandbothsmallerthan V KL assumingparticlesasperfectspheres. V WH is alwayssmallerthan V KL ,asexpected,andthedierenceinterminalvelocitiesbetween thetwomodelsdecreaseswithdecreasingparticlesize,untilitisassumedthatparticles willfallatthesameterminalvelocityastheirequivalentsphereforparticlesizes 4 particlesfallinginthelaminarregime. Thecomparisonbetweenthemeasureddiameterofvolcanicparticlesandthecalculated diameteroftheequivalentspherefallingatthesameterminalvelocityshowsthatthe 87

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measureddiametersarelargerthanthediametersoftheequivalentspheres,andthebigger theparticle,thelargerthedierence.Theseresultssuggestthattheterminalvelocityof ashparticlesisgreatlyreducedforparticlesdepartingfromasphericalshapeandthat thelargertheparticle,thegreatertheinuenceofparticleshapeonitsterminalvelocity. However,forparticles 5 thedierencebetweenmeasureddiametersanddiametersof theequivalentspheresis < 10%,suggestingthatsuchsmallparticlesfallinginthelaminar regimecouldbemodeledasspheres.Therelativedierencesbetweenthemeasuredparticle diametersandthediameteroftheequivalentspheresfallingatthesameterminalvelocity foundinthisstudycannotbeusedasaproxyforotherkindsoftephradeposits,since volcanicparticlesarelikelytohavedierentshapeparametersasafunctionofmagma compositionanderuptivestyles. TherelationshipproposedbyColtellietal.betweentheratioof V WH to V KL as afunctionof AR mightbetrueforvolcanicparticles 2 ,butisprobablynotapplicable forlargervolcanicparticlesasshowninFigure3.10.Thiskindofrelationshipislikelyto varyfromvolcanotovolcanoandevenfromeruptiontoeruptionatagivenvolcanoasa functionofmagmacompositionanderuptivestyles. Finally,usingaparticleshapedistributionfunctiontruncatednormaldistributionfor theshapedescriptor F insteadofthemeanvalueoftheshapeparametertocalculatethe tephraaccumulationonthegrounddoesnotyieldstrongvariationsintephraaccumulation. ThesevariationscanbeobservedinthemodelofWilsonandHuangbutarealways < 5%. 3.7Conclusions ThestudyofparticleshapeparametersoftheBF2layerofthe2450BPPlinianeruption ofPululaguavolcanoandtheimplicationsfortheassociatedterminalvelocityandtephra sedimentationmainlyshowsthat: 1.Thetrendofshapeparametersasafunctionofgrainsizeisfairlyconstantforallthe samplesanalyzedinthepresentstudy.Thereforetheassumptionmadeintephradispersal 88

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modelsthatparticleshapeparametersdonotvaryawayfromtheventissupportedbythe dataontheBF2layerofPululaguavolcano. 2.Comparisonbetweenthemeasureddiameterofvolcanicparticlesandthecalculated diameteroftheequivalentspheresfallingatthesameterminalvelocityshowsthatthe measureddiametersarelargerthanthediametersoftheequivalentspheres,andthebigger theparticle,thelargerthedierence.Theseresultssuggestthattheterminalvelocityof ashparticlesisgreatlyreducedforparticlesdepartingfromasphericalshapeandthatthe largertheparticle,thegreatertheinuenceofparticleshapeonitsterminalvelocity. 3.Particleshapeparametersforagivenparticlesizedonotsortoutwithdistance fromthevent,whiletheydovaryasafunctionofgrainsize.Therefore,otherphysical processeshappeninginthevolcanicplumeatmosphericmotion,particleentrainmentor iceformationhaveastrongerinuenceonthetransportandsettlingofvolcanicparticles thantheshapeoftheseparticles.Abettercharacterizationofsuchphysicalprocessesmay improvetephradispersalmodelsandthereforetephrahazardforecasts. 4.Valuesofparticleshapeparametersandotherrelationshipsbetweenparticleshape andterminalvelocityandtephrasedimentationarerestrictedtothestudyoftheBF2 layerofthe2450BPPlinianeruptionofPululaguavolcanoandcannotbeusedasproxies inothertephrastudies.In-depthanalysisofparticleshapehastobecarriedoutforeach speciceruptionoratleastvolcanotobetterunderstandandforecasttephradispersion andsedimentation. 89

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CHAPTER4 ASPECTSOFVOLCANICHAZARDSASSESSMENTFORTHEBATAAN NUCLEARPOWERPLANT,PHILIPPINES 4.1Introduction HowwouldtheeruptionofavolcanoaectanearbynuclearpowerplantNPP? Specically,wouldtheproductsofavolcaniceruptionimpacttheoperationofaNPP locatednearaneruptingvolcano?Theanswertothisquestionbeginswithanassessment ofthegeologicalphenomenathatresultfromvolcaniceruptions.Thesephenomenaare diverse,andincludetephrafallout,pyroclasticowsandlahars,amongothersConnor etal.,2009.Theeectsofthesephenomenadependonahostoffactors,suchasthe proximityofthevolcanototheNPP,thesizeandcharacteroftheeruption,winddirection, andtopographyaroundthevolcano. Thecomplexityanduncertaintyassociatedwiththesephenomenasuggestthattheir potentialimpactsbeassessedprobabilistically.Oneimportantaspectofprobabilisticassessmentinvolvesforecastingthetimingoferuptions.Whenwillthenexteruptionoccur? Or,phrasedanotherway,howmuchtimemustelapsebeforeavolcanonolongerhasa crediblepotentialforfutureeruptions?Thisquestionisnoteasilyresolved,asvolcanoes maygothousandsofyears,oreventensofthousandsofyearswithouterupting.Asecondaspectofvolcanichazardassessmentisestimationoftheeectsofvolcaniceruptions, oncetheyoccur.Whichareasmightbeinundatedbylahars,orexperiencetephrafallout? Aseruptionmagnitudesandtheireectsvarywidely,thisquestionmustalsobeanswered probabilistically.Admittedly,assessmentofthetimingandconsequencesofpotentialeruptionsisadauntingtask,requiringsite-specicdata,arenedunderstandingofvolcanic processes,andcomputationaltoolstoactuallyestimateprobabilities. 90

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Inthefaceofthesecomplexities,asystematicapproachiswarranted.Hilletal., recommendguidelinesforvolcanichazardassessmentforsurfacenuclearfacilitiesthat provideasystematicapproach.Inthischaptertheserecommendedguidelinesareapplied toaspecicNPPsitelocatedinthePhilippines.Ourgoalistoillustratekeypointsof theapplicationoftherecommendedguidelinestovolcanichazardassessmentforsurface nuclearfacilities. WeillustrateaspectsofvolcanichazardassessmentusingtheBataannuclearpower plantBNPPsite,locatedonNapotPointonthewestcoastoftheBataanPeninsula, WesternLuzonPeninsula,Philippines,at14 38 0 N,120 19 0 E,or,inUTMZone51Ncoordinates,210500E,1619000NFigure4.1.ThisNPPwassitedandconstructedduring thelate1970sandearly1980s,usingthencurrentdesignsforapressurizedwaterreactor.Althoughsomenuclearfuelwasdelivered,thereactorneveroperated.Theproject wasquitecontroversialatthetimeofsitingandconstruction.IntheUnitedStates,for example,questionsaroseaboutwhetherhazardassessmentsatthesitewerepartlythe responsibilityoftheUSNuclearRegulatoryCommission,becauseUScompaniesexported technologyusedtoconstructtheBNPPD'AmatoandEngel,1988.TheUSNuclear RegulatoryCommissionultimatelydecidedthatithadnolegalroleinreviewingthehazardsassessmentsfortheBNPP.Nevertheless,concernsaboutthesitingassessmentforthe BNPPremained.TheUnionofConcernedScientistscitedtheproximityofthesiteto thepotentiallyactiveMt.NatibvolcanoasamajorsourceofconcernD'AmatoandEngel,1988.TheconclusionsofvolcanichazardassessmentsperformedbyaUSconsulting companyEBASCO,1977,1979onbehalfofthePhilippineAtomicEnergyCommission werequestionedbyUSscientistsNewhall,1979,expertsfromtheInternationalAtomic EnergyAgencyIAEA,1978andoversightpanelsinthePhilippines. Itisnotourintenttoreview,orrecreate,thiscontroversy.Rather,datagathered duringthesiteinvestigationandafterthesiteinvestigationareusedtoassesshazards, withintheguidelinesoutlinedbyHilletal.,asanillustrationoftheapplication oftheseguidelines.Thisassessment,some30aafterconstructionoftheNPP,utilizes 91

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Figure4.1.LocationmapshowingtheBataanPeninsula,formingthesouthernpartof theLuzonPeninsulawithinthePhilippinesarchipelago.Blacktrianglesindicateactive volcanoes.WhitetrianglesindicateactivevolcanoesclosesttotheBataanNuclearPower PlantBNPP.TheBataanPeninsulaismainlyformedfromtwolargevolcanoes,Mt.Natib tothenorthandMt.Marivelestothesouth.ThelocationoftheBNPPismarkedwitha blacksquare. 92

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modernmethodsfornumericalmodelingofvolcanicphenomena,particularlywithregard toassessmentoftephrafallouthazardsandsusceptibilityofthesitetopyroclasticowsand lahars.Asmentionedpreviously,thisassessmentstopsshortofacomprehensivevolcanic hazardassessment.Inthisregard,onecriticismoftheoriginalhazardassessmentwasthe lackofadequategeologicmappingofMt.NatibvolcanoIAEA,1978;Newhall,1979.To ourknowledge,suchcomprehensivemappinghasnotyetbeenundertakenforMt.Natib volcanoandhenceacomprehensivehazardassessment,fullymeetingtherecommendations describedbyHilletal.,isnotpossibleatthistime. 4.2Volcanicsetting TheBNPPsiteislocatedwithinaQuaternaryvolcanicprovinceknownastheBataan LineamentWolfeandSelf,1983,formedbytheeastwardsubductionoftheSouthChina SeaooralongtheManilaTrenchothewestcoastofLuzonPeninsula.TheBataanLineamentis320kmlongandcomprisesatleast27volcanoes,includingMt.NatibFigure4.1. ThesummitofMt.Natibvolcanoislocatedabout15kmNEoftheBNPP.Mt.Pinatubo andMt.Marivelesvolcanoes,whichmayberelevanttothehazardassessment,lieabout 57kmNand22kmSEofthesite,respectivelyFigure4.1. Mt.NatibandMt.MarivelesarebothQuaternarycompositevolcanoesandtogether formthedominanttopographicfeaturesoftheBataanPeninsula.Thesevolcanoeshave noteruptedhistorically.GeologicmappingandradiometricdatingofMt.Natibdeposits indicatethatthisvolcanohasproducedviolentexplosiveeruptionsduringthelastseveral hundredthousandyears.Theseeruptionsproducedtephrafallout,pyroclasticdensity currentspyroclasticowsandsecondarylaharsEBASCO,1977;Newhall,1979;Wolfe andSelf,1983;SiebertandSimkin,2007.TheNapotPointTu,asdescribedbyNewhall ,isapyroclasticowdepositthatresultedfromsucheruptions.TheNapotPoint TuandlahardepositsarelocatedwithintheBNPPsitearea.Detailsofpasteruptionsare diculttodecipher,however,becausebothMt.NatibandMt.Marivelesvolcanoeshave poorlydenedstratigraphies.GeologicmappingNewhall,1979;RuayaandPanem,1991 93

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ischallengingonthepeninsula,inpartduetopoorexposuresinthistropicalenvironment andinpartduetocomplexitiesofvolcanicstratigraphyinanarcterrain. ThevolcanichazardassessmentmadebyEBASCOprecededthedramaticvolcaniceruptionsofMt.Pinatuboin1991.Afterdormancyofabout540a,Mt.Pinatubo reawakenedinApril1991.ThevolcanicactivityculminatedinanexplosivePlinianeruptionon15June1991,thatproducedastrongverticalplumeandseveralpyroclasticdensity currentsNewhallandPunongbayan,1996.ThiseruptionisimportantforhazardassessmentattheBNPPintworespects.First,theeruptiondirectlyaectedthesite,depositing 6cmoftephrainthesitearea.Second,theMt.Pinatuboeruptionprovidesananalogfor potentialfutureeruptionsofMt.NatibandMt.Mariveles,atwhichnohistoricaleruptions haveoccurredandforwhichgeologicmappingisincomplete. The1991Mt.Pinatuboeruptioncolumnreachedamaximumheightof35 )]TJ/F15 10.9091 Tf 8.485 0 Td [(40kmKoyaguchiandTokuno,1993;Holaseketal.,1996;Koyaguchi,1996;Paladio-Melosantosetal., 1996;Rosietal.,2001.Tephrafalloutoccurredthroughouttheentireeruptionanddepositedseverallayersofpumiceouslapilliandash,withtwodistincttephralayersassociated withtheclimaticeruptionKoyaguchiandTokuno,1993;Paladio-Melosantosetal.,1996; Koyaguchi,1996;KoyaguchiandOhno,2001.Voluminouspyroclasticowsweregeneratedduringtheeruptionthattraveledasmuchas12 )]TJ/F15 10.9091 Tf 8.485 0 Td [(16kmradiallyfromtheventand wereabletoovercometopographicridgesashighas400minproximalareasScottetal., 1996.Thesepyroclasticdepositswereremobilizedbyheavyrainfalls,triggeringlargelaharsaroundMt.Pinatuboshortlyafterandmorethansixyearsfollowingtheeruption Rodolfoetal.,1996;WolfeandHoblitt,1996;Daag,2003;vanWestenandDaag,2005. AlthoughMt.NatibandMt.Marivelesseemtohaveeruptedvolcanicproductsthat areslightlymoremacthanMt.PinatuboDefantetal.,1991;Newhalletal.,1996, thesevolcanoesaresimilarinseveralrespects.Summitcalderastruncatethethreeedices. Mt.Natibcalderais6 7km,Mt.Marivelescalderais4kmindiameterandMt.Pinatubo calderaisthesmallest,only2.5kmindiameter.ThecalderaofMt.Pinatuboformedas aresultofonecollapseeventfollowingthe1991eruption.Itisunclearifthecalderason 94

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Mt.NatibandMt.Marivelesweresimilarlyformedfollowingonlyoneexplosiveeruption orbyincrementalcollapsesthroughtimeassociatedwithmultipleeruptions.Atleastfor Mt.Natib,pyroclasticowsseemtohavetraveledmorethan10kmfromthecaldera,toa pointwheretheyreachedthesea,andsecondarylaharsassociatedwiththesepyroclastic owsweregeneratedandtraveledinmaindrainages.Notephra-falldepositshavebeen reportedormappedforeruptionsfromMt.NatiborMt.MarivelesEBASCO,1977,1979; Newhall,1979.However,thisdoesnotimplythatextensivetephra-falldidnotaccompany pastvolcaniceruptionsfromthesevolcanoes.Forcomparison,thetephradepositfromthe 1991eruptionofMt.PinatubohasbeenalmostcompletelyerodedawayDaag,2003; Newhall,2007,personalcommunication. Today,volcanicactivityatMt.NatibismanifestedbythermalspringsthatarelocatedwithinthesummitcalderaRuayaandPanem,1991,suggestingthepresenceofa hydrothermalsystemwithinthevolcano.Mt.NatibandMt.Marivelesarenotcurrently monitored,sonothingmoreisknownaboutthecurrentstateofactivityatthesevolcanoes. MuchofwhatisknownaboutthehistoryoferuptionsatMt.Natibvolcanoisbased onradiometricagedeterminationsfromsamplescollectedbyEBASCO,Wolfeand Self,andthePhilippineInstituteofVolcanologyandSeismologyPHIVOLCS. Withoutadequatestratigraphicconstraints,theseagedeterminationscanonlyprovidea snapshotofvolcanicactivity,ratherthaninformationaboutthestratigraphicsequence orvariationsintherateofvolcanicactivity.EBASCOconcludedthatMt.Natib volcanowasactivebetween0.069 )]TJ/F15 10.9091 Tf 8.485 0 Td [(1.6Ma,basedonaseriesof27K/Ardatesonlavasand pyroclasticowsexposedontheanksofthevolcano.Atotalof31K/Ardatesreported byWolfeandSelf,1983suggestarangeofactivityfrom0.54 )]TJ/F15 10.9091 Tf 8.484 0 Td [(3.9Ma.Inaddition, ssiontrackagesonsevenpumicesamplesrangefrom20 )]TJ/F15 10.9091 Tf 8.485 0 Td [(59ka,butEBASCO, 1979suggestedthesemaybeunderestimatesoferuptionageduetopotential U migration inthesesamples.In1999,PHIVOLCSmadeanuncalibrated 14 Cagedeterminationof 27 0 : 63kaoncharcoalwithinayoungpyroclasticowdepositontheeasternankof Mt.Natibwrittencommunication,C.Newhall,1999.Morerecently,Cabatoetal. 95

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foundevidencetosupportanevenyoungerexplosiveeruptiononthewesternanksof Mt.Natib.Basedonahigh-resolutionseismicstudyoftheSubicBay,Cabatoetal. proposedanageof11.3 )]TJ/F15 10.9091 Tf 8.485 0 Td [(18kaforpotentialpyroclasticdepositinterlayeredwith sedimentsintheeasternSubicBay.Thispyroclasticdepositisthoughttooriginatefrom anexplosiveeruptioninthenorth-westernareaofthebreachedMt.Natibcaldera.These agedeterminationsaremuchyoungerthantheyoungestageof69kareportedbyEBASCO intheirhazardassessmentofMt.Natib,highlightingthatreconnaissancemapping anddatingmayhavemissedyoungerunits.NotethatanexplosiveeruptionatMt.Natib occurring11.3kawouldalmostsetMt.NatibasaHolocenevolcano,thereforeavolcano capableoffuturevolcaniceruptionse.g.Hilletal.,2009.Furthermore,theoccurrence ofyoungpyroclasticowsthathavetraveledthewesternanksofthevolcanoemphasizes thepotentialforvolcanichazardsaroundMt.Natibandnotonlyonitseasternanks,as mentionedbyEBASCOsreports,1979.Unfortunately,therearenoavailableages fortheNapotPointTu,whichcropsoutintheBNPPsitevicinity.Areconnaissance suiteofradiometricdateshavebeenreportedforMt.Marivelesvolcano.WolfeandSelf reportedarangeofactivityfrom0.19 )]TJ/F15 10.9091 Tf 8.485 0 Td [(4.1Ma,basedon20samples.However,the mostrecenteruptionatMt.Marivelesmaybeasyoungas2050BCuncalibrated 14 C date, SiebertandSimkin. 4.3Assessmentofvolcanocapability FortheclosestvolcanoestotheBNPPsite,thefrequencyandtimingofpastvolcanic eventsareincompletelyunderstoodandthushighlyuncertain.Theconceptofacapable volcanoHilletal.,2009isusedtoassessthepotentialforMt.NatibandMt.Mariveles volcanoestoproducehazardousphenomenathatmayreachtheBNPP.Followingits1991 eruption,Mt.Pinatuboisclearlyacapablevolcano,as 6cmoftephrafellontheBNPP duringthateruption.AsdescribedindetailbyHilletal.,acapablevolcanois oneforwhichboth i afutureeruptionorrelatedvolcaniceventiscredible;and ii such aneventhasthepotentialtoproducephenomenathatmayaectasite.IfMt.Natibor 96

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Mt.Marivelesvolcanoesarecapable,adetailed,site-specicvolcanichazardassessment iswarrantedthatconsidersthelikelihoodofoccurrenceandassociateduncertaintiesfor volcanicphenomenathatmayreachasite. Onestepindeterminingavolcano'scapabilityistoevaluateitspotentialforfuture eruptions.ActivitydocumentedduringtheHolocenei.e.withinthelast10kaisone criterionusedtodeterminethatavolcanoappearscapableoffuturevolcaniceruptions e.g.Hilletal.,2009.ThereisnodenitiveevidencethatMt.NatiborMt.Mariveles volcanoeshaveeruptedduringtheHolocene.Nevertheless,determiningHoloceneeruptive activityisdicult,especiallyinthetropicalenvironmentofthesevolcanoesandwhere mappingisincomplete.Insuchcasesevidenceofcurrentvolcanicactivityincludesongoing volcanicunrest,orthepresenceofanactivehydrothermalsystemandrelatedphenomena. AsMt.NatibandMt.Marivelesvolcanoesarenotmonitored,thereisnoinformation availableregardingcurrentunrest,suchastheoccurrenceofvolcano-tectonicearthquakes orgrounddeformation.However,thepresenceofthermalspringswithinMt.Natib's calderaRuayaandPanem,1991isindicativeofanactivehydrothermalsystem.Thus, futureeruptionsofMt.Natibarepossiblec.f.Hilletal.,2009.Therefore,ananalysis shouldbemadetoassessthepossibilityofvolcanicphenomenareachingthesiteofthe BNPP,givenapotentialeruptionofMt.Natibvolcano.Hydrothermalactivityhasnot beenreportedatMt.Marivelesvolcano,but,aspreviouslynoted,one 14 C datesuggests thatHoloceneactivityhasoccurred.ThusMt.Marivelesvolcanomayalsobeacapable volcano,basedonthetimingofpasteruptions. TheprobabilityoffutureeruptionsofMt.Natibishighlyuncertain,giventheincompleterecordofradiometricagedeterminationsandlackofdetailedstratigraphiccontrol onimportantgeologicunits.Basedonthisincompleterecord,EBASCO,1977estimated theprobabilityofafuturevolcaniceruptionofMt.Natibvolcanotobe 3 10 )]TJ/F19 7.9701 Tf 6.586 0 Td [(5 a )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 TheglobalrecordofreposeintervalsprecedinglargePlinianeruptionsi.e.VolcanoExplosivityIndexVEI6 )]TJ/F15 10.9091 Tf 8.485 0 Td [(7oflong-dormantvolcanoesSiebertandSimkin,2007provides onemeansofevaluatingthisprobability.Connoretal.afoundthatreposeintervals 97

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precedingVEI6 )]TJ/F15 10.9091 Tf 8.485 0 Td [(7eruptionsoflong-dormantvolcanoesfollowalog-logisticprobabilitydistribution.Applyingthisprobabilitymodelandusingareposeintervalof14.65ka,basedon theaverageddateoftheyoungestknownpyroclasticowonMt.Natib : 3 )]TJ/F15 10.9091 Tf 8.917 0 Td [(18ka,Cabato etal.,2005,theprobabilityofaVEI6 )]TJ/F15 10.9091 Tf 8.485 0 Td [(7eruptionofMt.Natibis 1 10 )]TJ/F19 7.9701 Tf 6.587 0 Td [(4 )]TJ/F15 10.9091 Tf 9.423 0 Td [(9 2 )]TJ/F19 7.9701 Tf 6.586 0 Td [(4 a )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 with95%condence,whichisalmostoneorderofmagnitudegreaterthantheEBASCO result.Suchprobabilitiesappearsucienttoconsiderfutureeruptionsascredible events,andindicatethatahazardanalysisfortheseeruptionsappearswarrantedHill etal.,2009.Followingthesameapproachbutusingareposeintervalof4.05ka,basedon theyoungestdateonvolcanicproductsfromMt.Mariveles,theprobabilityofaVEI6 )]TJ/F15 10.9091 Tf 8.485 0 Td [(7 eruptionofMt.Marivelesis 3 : 5 10 )]TJ/F19 7.9701 Tf 6.586 0 Td [(4 )]TJ/F15 10.9091 Tf 10.909 0 Td [(6 10 )]TJ/F19 7.9701 Tf 6.586 0 Td [(4 a )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 ,with95%condence. Hadweappliedthisprobabilisticmethodin1990,beforetheeruptionofMt.Pinatubo, theprobabilityofaVEI6-7eruptionofMt.Pinatubowouldhavebeen 0 : 6 10 )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 )]TJ/F15 10.9091 Tf -419.915 -21.922 Td [(1 10 )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 a )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 ,usingareposeintervalof0.54kabasedonitsmostrecentknownexplosive eruptionpriorto1991.Reposeintervalsbetweeneruptiveepisodesforthemostrecent eruptionsofMt.PinatuboNewhalletal.,1996,notincludingthe1991eruption,are chronologically:2.5ka,2.5ka,3.5ka,8.4kaand17.6kaNewhalletal.,1996;Siebertand Simkin,2007.AssumingthatthetimingoferuptionsisdescribedbyaPoissonprocess Connoretal.,2009,theintervalestimateofreposeforMt.Pinatubois3.4 )]TJ/F15 10.9091 Tf 8.485 0 Td [(21.2ka,with 95%condence.ThisintervalcorrespondstoaprobabilityofaneruptionofMt.Pinatubo tobe0 : 5 10 )]TJ/F19 7.9701 Tf 6.586 0 Td [(4 )]TJ/F15 10.9091 Tf 10.496 0 Td [(3 10 )]TJ/F19 7.9701 Tf 6.587 0 Td [(4 a )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 .AbootstrapwithreplacementprocedureEfronandTibshirani,1991yieldsanintervalestimateof3.8 )]TJ/F15 10.9091 Tf 8.485 0 Td [(9.9ka,with95%condence,corresponding toaprobabilityofaneruptionofMt.Pinatuboof1 10 )]TJ/F19 7.9701 Tf 6.587 0 Td [(4 )]TJ/F15 10.9091 Tf 11.234 0 Td [(2 : 6 10 )]TJ/F19 7.9701 Tf 6.587 0 Td [(4 a )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 .Notethat theperiodbetweeneruptionsofMt.Pinatubobecomesshorterwithtime.Thismayreectnonstationarityinreposeintervalsbetweeneruptions,ormaysimplyreectsampling bias,duetodicultyindistinguishingeruptiveunitsintheolderstratigraphicrecord. Regardless,itappearsthattheprobabilityoferuptionsofMt.Pinatubo,priortothe1991 eruptions,were 1 )]TJ/F15 10.9091 Tf 11.223 0 Td [(2ordersofmagnitudegreaterthanprobabilitiesoflargeexplosive eruptionscurrentlyestimatedforMt.Natib.Ourinterpretationofthiscomparisonisthat, 98

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althoughtheprobabilityofanexplosiveeruptionofMt.Natibappearstobemuchlower thantheprobabilityoferuptionsofMt.Pinatubo,explosiveeruptionsofMt.Natibare credible. ForMt.Natibvolcano,evidenceofanactivehydrothermalsystem,andprobability estimates,bothindicatethatthevolcanohasacrediblepotentialforfutureeruptions.The potentialforvolcanicphenomenatoimpacttheBNPPsiteshouldbeestimated.Thisstep isaccomplishedbyestimatingscreeningdistancevaluesforvolcanicphenomena,suchas tephrafallout,lahars,andpyroclasticows,thathavethehighestpotentialtoaectthe BNPPsiteadversely.Thesescreeningdistancevaluesconsiderthepotentialforvolcanic phenomenatoreachtheBNPPsite,usingconservativeassumptionsaboutthemagnitudes ofvolcaniceruptionsandsimpliednumericalmodelsofpotentialhazards.Theremainder ofthisstudydescribesnumericalandprobabilistictechniquestoestimatescreeningdistance valuesforthesephenomena.Thesevalues,inturn,areusedtodeterminethecapabilityof Mt.Natib,Mt.Mariveles,andMt.PinatubovolcanoestoaecttheBNPPsite. 4.4Estimatingscreeningdistancevalues GeologicalmapsoftheMt.Natibvolcanicdepositsindicatethatpyroclasticdensity currentsandsecondarylaharvolcanicmudowdepositsoccurintheBNPPsitearea EBASCO,1977;Newhall,1979.Thepresenceofthesedepositsisclearevidencethat theBNPPsiteislocatedwithinascreeningdistanceforthesephenomena.Ascreening distanceisdenedasthedistancefromavolcanothataspecicvolcanicphenomenon,such aspyroclasticows,mayplausiblyreachHilletal.,2009.Screeningdistancedepends onanumberoffactors,suchastopographyofthevolcano,possiblemagnitudesoffuture eruptionsandthetypesofvolcanicphenomenainvolved.Thereisuncertaintyinthe estimateofscreeningdistances,butitisoftenpracticaltodetermineifaspecicsiteis beyond,orwithin,ascreeningdistanceforspecicphenomenaoriginatingfromavolcano usingscopingcalculations.Suchscopingcalculationsareusedheretoassessvolcanic hazardsattheBataansite. 99

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Thesitemaybeexposedtobothproximalanddistaleectsofvolcaniceruptionsfrom Mt.NatibConnoretal.,2009.Inaddition,thesitemaybeexposedtofar-eldeects fromMt.PinatuboandMt.Marivelesvolcanoes,particularlyfromtephrafallout.We canreneourunderstandingofpotentialhazardsusingavarietyofnumericalmethodsto considerthemagnitudesofpotentialvolcaniceruptionsthatproducephenomenathatcould impactthesite.Analysisislimitedtoproductsofexplosiveeruptions,includingtephra fallout,pyroclasticows,andlahars.Otherphenomena,suchasnewventformationand lavaowsarenotconsideredinthischapter,andrequireadditionalanalysesinorderto assesstheirpotentialhazardstotheBNPPsite. 4.4.1Hazardsfromtephrafallout Tephrafalloutcreatesloadsonengineeredstructuresandmaydisruptventilation,electrical,andcoolingsystemsatnuclearpowerplants.Thicktephraaccumulationmight renderasitetemporarilyinoperable,andveryrapiderosionoftephradepositsmaygeneratepotentiallydamaginglahars.TheTEPHRA2computerprogramBonadonnaetal., 2005a;Bonadonna,2006;ConnorandConnor,2006;Connoretal.,2008isusedtoestimate potentialaccumulationsoftephrafalloutattheBNPPsiteandontheanksofMt.Natib volcanoabovetheBNPPsitewithaseriesofdeterministicandprobabilisticanalyses.The numericalsimulationoftephraaccumulationisbasedontheadvection-diusionequation Suzuki,1983;Armientietal.,1988;Connoretal.,2001,whichisexpressedbyasimplied mass-conservationequation: @C j @t + w x @C j @x + w y @C j @y )]TJ/F21 10.9091 Tf 10.909 0 Td [(v l;j @C j @z = K @ 2 C j @x 2 + K @ 2 C j @y 2 +.1 where, x y ,and z arespatialcoordinatesexpressedinmeters; C j isthemassconcentrationofparticleskgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 ofagivenparticlesizeclass, j ; w x and w y arethe x and y componentsofthewindvelocityms )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 ; K isahorizontaldiusioncoecientfortephra intheatmospherem 2 s )]TJ/F19 7.9701 Tf 6.586 0 Td [(1 ; v l;j istheterminalsettlingvelocityms )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 forparticlesofsize 100

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class, j ,astheseparticlesfallthroughalevelintheatmosphere, l ;andisthechangein particleconcentrationatthesourcewithtime, t kgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(3 s )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 .Thealgorithmimplemented inTEPHRA2assumesnegligibleverticalwindvelocityanddiusion,andassumesaconstantandisotropichorizontaldiusioncoecient K = K x = K y .Theterminalsettling velocity, v ,iscalculatedforeachparticlesize, j ,ateachatmosphericlevel, l ,asafunction oftheparticle'sReynoldsnumber,whichvarieswithatmosphericdensity.Windvelocityis allowedtovaryasafunctionofheightintheatmosphere,butitisassumedtobeconstant withinaspecicatmosphericlevel. Tephrafallouthazardstudiesaremostconcernedwithmassaccumulationatspecic locations.TEPHRA2calculatestephraaccumulation, M kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(2 ,ateachlocation, x;y : M x;y = H max X l =0 d max X j = d min m l;j x;y .2 where, m l;j x;y isthemassfractionoftheparticlesize, j ,releasedfromatmosphericlevel, l ,accumulatedatlocation, x;y H max isthemaximumheightoftheeruptingcolumn,and d min and d max are,respectively,theminimumandmaximumparticlediameters.Thus,the distributionoftephramassfollowinganeruptiondependsonboththedistributionofmass intheeruptioncolumnandthedistributionofmassbygrain-size.ThealgorithmimplementedinTEPHRA2assumesthatmassisuniformlydistributedintheeruptioncolumn, orcanbespeciedtobeuniformlydistributedinsomefractionoftheuppermostcolumn, tobeconsistentwithobservationsofstrongvolcanicplumes.Grain-sizedistributionis assumedtobelog-normal,andisdeducedfromcomparisonwithstudiesofwell-preserved deposits. 4.4.1.1Deterministicanalysis Hazardassessmentsrelyonprobabilisticmethodstoaccuratelyforecastthepotential occurrenceofdisruptivephenomena.Aspartofthismodelingprocess,deterministicassessmentscanbeusefulforestimatingpotentialtephraaccumulationresultingfromerup101

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tionsofaspecicsizeduringspecicmeteorologicalconditions.Forexample,onecan estimatetephrafalloutattheBNPPresultingfromalarge-volume,explosiveeruptionof Mt.Natib,whenthewindisblowingfromthevolcanotowardthesite.Theseanalysesare accomplishedbycompletelyspecifyingtheeruptionandmeteorologicalparameters,and calculatinganisomassmapbasedontheseparametersusingTEPHRA2.Suchboundingcalculationsareparticularlyusefulforestimatingscreeningdistancesandmayprovide usefulsupplementarymaterialfortheinterpretationofprobabilisticassessments. Fivedeterministicscenariosarepresentedbasedonthefollowingeruptionparameters: locationofthevent,columnheight,totaleruptedmassandgrain-sizedistribution.Meteorologicalparametersincludewinddirectionandspeed,asafunctionofelevationinthe atmosphere.EruptionsspanVEI3 )]TJ/F15 10.9091 Tf 8.485 0 Td [(7withassociatedmaximumcolumnheights H max of8,14,25,35and45km,respectivelyNewhallandSelf,1982.AsmallVEI3eruptionisrepresentedbyan8km-higheruptingcolumn.A14km-highcolumnrepresents theapproximateboundarybetweenVEI3andVEI4eruptions;thiscolumnheightisalso thelowerlimitofsub-PlinianeruptionsaccordingtoPyle,1989.AsEBASCO, 1979proposedananalysisoftephrahazardattheBNPPsitebasedonanalogywiththe 1912Katmaieruption,25kmwasselectedtomatchthemaximumcolumnheightofthat VEI5eruptionFiersteinetal.,1997.The35kmcolumnheightreectsthe1991eruptionVEI6ofMt.Pinatubo,and45kmrepresentsanupperlimitscenariobasedonthe historicaleruptionVEI7ofTamborain1815SigurdssonandCarey,1989. Eruptionduration, T ,andmaximumcolumnheight, H max ,areusedtocalculatethe totaleruptedmassforeachscenario,assumingsteady-stateconditions.Koyaguchiand Tokunoproposedaneruptiondurationof5hrforthe1991climacticeruptionof Mt.Pinatubo,basedontheexpansionoftheumbrellacloudinthestratosphere.Thisis, perhaps,anover-estimateoferuptionduration,astheumbrellacloudmayhavecontinuedtoexpandinthestratosphereaftercessationofappreciablemassdischargefromthe vent.Tahiraetal.proposedaneruptiondurationof3.5hr,basedoninfrasonicand acousticwavesgeneratedbytheexplosiveeruption.AccordingtoPaladio-Melosantosetal. 102

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,thepeakactivityoftheeruptionwassustainedforabout3hr,followedbywaning activityfor6hr.Forthesedeterministicscenarios,wechoseaneruptiondurationof3hr, whichmaximizesowrateforspeciccolumnheights. Forsteadyeruptions,themassdischargerateofaneruptionisempiricallyrelatedto thecolumnheightSparksetal.,1997: H max =1 : 67 Q 0 : 259 .3 where, Q isthemagmadischargeratem 3 s )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 .Fromthedensityofthedeposit dep and thedurationoftheeruption T ,themagmadischargerate Q is: Q = M o T dep .4 where, M o isthetotalmassofthedepositinkilograms.Thebulkdensityofthedeposit, dep kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 ,isassumedtobe1000kgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(3 ,correspondingwellwiththeaveragedensityof the1991phenocryst-richdaciticpumiceofMt.Pinatubokgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 proposedbyPallister etal..Thisvalueisalsoingoodagreementwiththerange500 )]TJ/F15 10.9091 Tf 8.485 0 Td [(1500kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(3 ,the bulkdensityofknownPliniandepositsSparksetal.,1997.Totalmassisrelatedto eruptioncolumnheightanderuptiondurationby: M o = T dep H max 1 : 67 4 .5 Thus,assumingmaximumeruptioncolumnheights,totaleruptionduration,anddeposit density,totaleruptionmassiscalculatedforeachscenario.Table4.1liststhethecolumn heightsandmassusedbyeachscenariotoestimatetephraaccumulationattheBNPP site.Forcomparison,theVEI6scenarioessentiallymatchessourceparametersthatare describedintheliteratureforthe1991climacticPlinianeruptionofMt.PinatuboKoyaguchiandTokuno,1993;Holaseketal.,1996;Koyaguchi,1996;Paladio-Melosantosetal., 1996;Rosietal.,2001. 103

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Table4.1.Eruptioncolumnheightandtotalmassinputsfordeterministictephramodels arebasedonanalogeruptionsandVolcanoExplosivityIndexVEI. ParameterVEI3VEI4VEI5VEI6VEI7 Columnheightkm812253545 TotalMasskg5 : 7 10 9 5 : 3 10 10 5 : 4 10 11 2 : 1 10 12 5 : 7 10 12 Tephradispersionalsodependsonthesizedistributionofparticlesgrain-sizedistributioneruptedfromthevolcano.Particleclastsizedistributionscanbecharacterizedin termsofseveralparametersInman,1952:minimumandmaximumvolcanicclastdiameter;medianclastdiameter Md ;graphicstandarddeviation,orsorting ;andthe graphicalskewness,ameasureoftheasymmetryofthegrain-sizedistribution.Complete andreliabletotalgrain-sizedistributiondataforexplosivevolcaniceruptionsaredicult toestablishfromelddataandarerarelyreportedBonadonnaandHoughton,2005. Problemsindeterminingthetotalgrain-sizedistributionforaneruptionstemfromdifcultyinsamplingallfaciesofthedeposit.Muchofthetephraofthe1991eruptionof Mt.PinatubofellintotheSouthChinaSeaWiesneretal.,1995,sodirectestimation ofthetotalgrain-sizedistributionisnotpractical.Nevertheless,basedonanumerical model,KoyaguchiandOhnoproposedagrain-sizedistributionofclassIIfragments pyroclaststhataccumulateatmedialdistancesfromtheventatthetopoftheeruption columnfortwodepositionallayersofthe1991PlinianeruptionofMt.Pinatubo.Although notoptimal,asproximalanddistalpyroclastsaremissinginKoyaguchiandOhno model,thegrain-sizedatafromthosetwotephralayerscanbecombinedFigure4.2to obtainatotalgrain-sizedistributionforthetephrafalloutofthe1991Plinianeruption. Themediandiameterofvolcanicclastsis1 : 35 = )]TJ/F15 10.9091 Tf 10.303 0 Td [(log 2 d d beingtheparticlediameterinmillimeters.Thesortingofthedepositis =1 : 16 ,representinggoodsorting fortephradepositsFisherandSchmincke,1984;CasandWright,1987.Thesevaluesare usedforallsimulationsinthedeterministicanalysisoftephrafallout,althoughtheactual totalgrain-sizedistributionofthe1991eruptionofMt.Pinatubomaybenerandless sorted.Thegraphicalskewnessofthetotalgrain-sizedistributionisassumedtobezero. 104

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Figure4.2.Thetotalgrain-sizedistributionusedinthetephramodelsisderivedfromthe analysisoftheclimacticPlinianeruptionofMt.PinatuboinJune1991ClassIIfragments. ModiedfromKoyaguchiandOhno. Tephraaccumulationatasiteisstronglydependentonwindspeedanddirectionduring thetimespanoferuption.Twodierentwindestimatesareusedforeachscenario.One estimateuseswindvelocitiesaveragedfortheyear2006basedonreanalysisdatafrom theNationalCenterforEnvironmentalPredictionReanalysisprojectKalnay,1996.The reanalysisdataconsistsofwindvelocityestimatesat17pressurelevelswhicharearelinearly interpolatedto30heightsfrom1 )]TJ/F15 10.9091 Tf 8.485 0 Td [(30kmabove30km,windconditionsareassumedtobe constantat1kmintervalsFigures4.3aandb.Thesecondestimaterepresentsanupper limit,wherebythewindisassumedtoblowtowardtheBNPPwithaspeed,ateachlevel, similartotheaveragewindspeedsfromthereanalysisdatafor2006.Windconditions,very similartothisupperlimitestimate,occurredin2006 3%ofthetimeforMt.Pinatubo, 9%ofthetimeforMt.Natiband 11%ofthetimeforMt.MarivelesFigure4.3c. ResultsofthedierentdeterministicscenariosaregiveninTable4.2.EstimatedpotentialaccumulationattheBNPPsitevariesfromtraceamountsto3.6mforaVEI7eruption atMt.Natibwithwindblowingtowardthesite.Thesethicknessescorrespondtoarange indrytephraloadofabout0.01kgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 to3600kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(2 .Rainfallsaturatestephradeposits andmaydoubletheseestimatedloadsBlong,1984. IsomassmapareshowninFigure4.4a )]TJ/F15 10.9091 Tf 8.485 0 Td [(c.NotethatthescenariopresentedinFigure4.5aforMt.Pinatuboshowsmanysimilaritieswiththeisopachmapsproposedforthe 1991eruptionintheliteratureKoyaguchi,1996;Paladio-Melosantosetal.,1996,although 105

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Figure4.3.Hazardsassociatedwithtephrafalloutarestronglydependentonmeteorological conditions.Here,acompilationofreanalysisdatafortheBNPPsiteillustratestheaverage darklineandonestandarddeviationhorizontalbarsofwindconditionsin2006,fora thedirectiontowardwhichthewindisblowingandbwindspeedms )]TJ/F19 7.9701 Tf 6.587 0 Td [(1 ,asafunctionof heightabovesealevel.ThesedataareusedasinputparametersforTEPHRA2toestimate tephraaccumulationinthesiteregion.cTephradepositionattheBNPPsiteismaximum whenthewindblowsfromthevolcanotowardthesite.Thepercentageofthetimethe windblewtowardthesite 15 fromMt.Natibcircles,Mt.Pinatubodiamondsand Mt.Marivelestrianglesisgraphedasafunctionofheightabovesea-level. Table4.2.TephrafalloutthicknesscmattheBNPPsiteforeacheruptionscenariointhe deterministicanalysis. VolcanoWindeldVEI3VEI4VEI5VEI6VEI7 Natibwind2006 1 1.06.739100180 maxwind 2 1.61274190360 Mariveleswind20060.0010.010.030.10.7 maxwind0.45.33698200 Pinatubowind20060.0050.34.71330 maxwind0.010.58.02658 1 averagewindvelocityin2006 2 averagewindspeedin2006,butwindblowstowardsite 106

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thelatteraremorecircularanddispersedtowardtheWSWKoyaguchiandTokuno,1993; Wiesneretal.,1995;Koyaguchi,1996;Paladio-Melosantosetal.,1996.Thisdiscrepancy isduetowinddirection.Averagewinddirectionsatstratosphericaltitudesfor2006were mainlytowardtheSW.Stratosphericwindsweremoretowardthewestduringtheactual eruption.Themodelpredictsatephrafalloutthicknessatthesiteof 13cm,roughly doubletheobservedaccumulationduringtheeruptionofMt.Pinatubo,owingtothedierenceinwinddirection.Furthermore,althoughtheeectofthepassageoftyphoonYunya duringtheeruptionhadlittleeectonthesettlingofhigh-Reynolds-numberparticlesRosi etal.,2001,typhoonYunyamayhavebeenresponsibleformoresphericaldispersionof low-tointermediate-Reynolds-numberclasts,resultinginthemoresphericalisopachmaps proposedintheliteratureKoyaguchi,1996;Paladio-Melosantosetal.,1996.Comparisonoftheeruptionandthesimulationssuggestthathadthewindblowntowardthesite onJune15 th ,1991,theBNPPmighthaveexperiencedtephrafalloutasthickas25cm Table4.2. Althoughaveragewindconditionsfor2006closelymimictheshapeofthetephradepositofthe1991eruptionofMt.PinatuboFigure4.4a,theseconditionspoorlyestimate extremeevents.Asanexample,aVEI6fromMt.Mariveleswilldepositonly1mmof tephrawiththeaveragewindconditions,whilewiththewindblowingtowardthesite,the tephrathicknesscouldreach1mTable4.2.Figure4.3cshowsthatthisscenariowind blowingtowardthesiteoccurs 11%ofthetimeforMt.Mariveles.Theaveragewind conditionshappentodeposittephraawayfromtheBNPP,butalargefractionofindividual windeldsactuallyblowsclosertotheBNPParea. Theseisomassmapsalsopointtothepossibilitythatsecondaryphenomenaresulting fromtephrafalloutcouldpotentiallyaectthesitearea.Althoughtephraaccumulations attheBNPPsitearenotsignicante.g.notexceeding10cmformanyscenariose.g. < VEI6,lowerexplosivityeruptionsonMt.Natibmayresultinsignicanttephraaccumulationsup-slopefromthesite.Suchdepositsmaybesucienttoremobilizeandform laharsthatcouldpossiblyaectthesitearea. 107

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Figure4.4.ExplosiveeruptionsofaMt.Pinatubo,bMt.Natib,andcMt.Mariveles volcanoesmayresultinsubstantialaccumulationoftephraattheBNPPsite.These examples,basedonoutputfromTEPHRA2,showisomassmapsforeruptionsofvarious magnitudesandwindconditions.InaaVEI6eruptionofMt.Pinatuboduringaverage windconditionsfor2006resultsinanisomassmapthatisverysimilartotheactual tephradistributionfollowingthe1991eruptionofMt.Pinatubo.Inthisexample,tephra accumulationatthesiteis 100kgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 ,amassloadsucienttocausedamagetosome structures,andtoadverselyaectelectricalandwaterltrationsystems.Incontrast, amuchsmallermagnitudeeruption,VEI4,fromMt.Natibwouldpotentiallyresultin muchlargertephraaccumulationatthesite, > 1000kgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 b.Inthissimulationwindis assumedtoblowfromMt.Natibtowardthesiteataveragespeedasafunctionofelevation fortheregion.Similarly,themodelsuggeststhataVEI5eruptionofMt.Mariveleswould resultin > 1000kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(2 tephraaccumulationatthesite,ifwindsblewfromthevolcano towardthesite.Contoursareinmassoftephraaccumulationperunitareakgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(2 ,dry, wherekgm )]TJ/F19 7.9701 Tf 6.586 0 Td [(2 isroughlyequivalentto10cmtephrathickness. 108

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4.4.1.2Probabilisticanalysis Probabilisticmethodsmorethoroughlyassesstheeectsofrandomvariationineruptionparametersandmeteorologicalconditionsonestimatesoftephraaccumulation.Our probabilisticanalysisusesTEPHRA2tocalculatethedistributionoftephraaccumulation attheBNPPsiteforpotentiallyexplosiveeruptionsofMt.Natib,Mt.Mariveles,and Mt.Pinatubovolcanoes.Foreachofthethreesourcevolcanoes,aMonteCarloanalysis iscompleted,eachconsistingof1000simulations.Eruptioncolumnheightisrandomly sampledfromalog-uniformdistributionofrange14 )]TJ/F15 10.9091 Tf 8.485 0 Td [(40km.Alog-uniformdistributionis usedbecausethistruncatespossiblevaluesatthelowerlimitofcrediblecolumnheights forsmallexplosiveeruptions.Asnotedpreviously,thisminimumcolumnheightkm representstheapproximateboundarybetweenVEI3 )]TJ/F15 10.9091 Tf 8.485 0 Td [(4.Theupperboundoftherange alsohaspracticalsignicance.Althoughhighercolumnsmaybepossible,thepropertiesof theatmosphereatthesealtitudesaresuchthathighercolumnswouldhavelittleadditional impactonthedispersionoftephraparticles.Theuseofalogarithmicfunctionreectsthe higherfrequencyoflower-altitudevolcanicplumesSimkinandSiebert,1994. Thetotaleruptedmassoftephraiscalculatedusingequation.5fromeruption durationandcolumnheight.Durationisrandomlysampledfromauniformdistribution ofrange1 )]TJ/F15 10.9091 Tf 8.485 0 Td [(9hr.ThisrangeisconsistentwitheruptiondurationsreportedforVEI4 )]TJ/F15 10.9091 Tf 8.485 0 Td [(6 eruptions,andisconsistentwiththeeruptiondurationforthe1991Plinianeruptionof Mt.PinatuboKoyaguchiandTokuno,1993;Tahiraetal.,1996;Paladio-Melosantosetal., 1996.Nocorrelationisassumedbetweeneruptioncolumnheightanderuptiondurationfor thepurposeofestimatingtotaleruptionmass.Theresultingdistributionoftotaleruption massislog-normallydistributedFigure4.5,emphasizingthehigherprobabilityofsmaller eruptionsSimkinandSiebert,1994. Largevariationingrain-sizedistributionappearpossiblefordierenttypesofPlinian eruptionsfromsimilarvolcanoes.The1991PlinianeruptionofMt.Pinatubohasestimates of Md =1 : 35,and =1 : 16,forclassIIfragmentsatthetopofthevolcaniceruption columnKoyaguchiandOhno,2001.Typically, Md estimatesforentiretephra-fallout 109

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Figure4.5.Log-normallydistributedvaluesfortotalamountoftephraeruptedkg.The probabilisticassessmentoftephrafalloutrandomlychoosestotaleruptionmassvalues fromthislog-normaldistribution.Therangeofpossiblevaluesisinitiallycalculatedfrom arangeofprobableeruptioncolumnheightsanderuptiondurations. depositsmightrangefrom )]TJ/F15 10.9091 Tf 8.485 0 Td [(1 : 0 )]TJ/F15 10.9091 Tf 9.638 0 Td [(4 : 0 ,orevensmalleri.e. Md =4 : 4 )]TJ/F15 10.9091 Tf 9.638 0 Td [(4 : 8forthe1980 eruptionofMountSt.Helens;CareyandSigurdsson;Durantetal..The variationinthesortingofatephrafalldeposit maybesmaller,2 )]TJ/F15 10.9091 Tf 11.06 0 Td [(3 forPlinian eruptions.Giventhisuncertainty, Md and aresampledfromuniformdistributions withrangesof )]TJ/F15 10.9091 Tf 8.485 0 Td [(1 to5 ,and2 to3 ,respectively.Nocorrelationisassumedbetween thesegrain-sizedistributionparametersandcolumnheightoreruptionmass. Reanalysisdataare,again,usedtodescribethevariationinwindvelocitywithheight;a setof1460windprolesacquired4timesdailyduring2006,Kalnayarerandomly sampled.Althoughtheeruptiondurationmaybelongerthan6hr,onlyonerandomly selectedprolepersimulationisused. ResultsofthisprobabilisticanalysisindicatethattephraaccumulationattheBNPP sitefrompossibleeruptionsofMt.NatibandMt.Mariveleswouldlikelyexceedtephra accumulationfrompossibleeruptionsofMt.Pinatubo,byapproximatelyoneorderof magnitudeFigure4.6a.Forcomparison,theEBASCOhazardcurveFigure4.6b indicatesthattheprobabilityofexceeding1mtephraaccumulationatthesite,given anexplosiveeruptionofMt.Natib,is P f accumulation > 1m j explosiveeruption g = 55%.However,usingTEPHRA2,allcalculatedhazardcurves,givenanexplosiveeruption 110

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Figure4.6.Hazardcurvesshowtheconditionalprobabilityofexceedingdierentthicknesses oftephraatthelocationoftheBNPP,givenavolcaniceruption.Graphacompares tephrathicknessesmodeledforNatib,Mariveles,andPinatubo.Thecurveswere generatedfromTEPHRA2output,basedon1000simulationsusingwindvaluesrandomly selectedfromreanalysisdatafor2006anderuptionparametersrandomlyselectedfroma rangeofexplosiveeruptionconditions.Thisgraphindicatesthatgivenaneruption,tephra accumulationattheBNPPfromeruptionsofMt.NatibandMt.Marivelesaresimilar, andwouldlikelyexceedtephraaccumulationsassociatedwithaMt.Pinatuboeruption byoneorderofmagnitude.GraphbcomparestheEBASCOhazardcurve,basedon the1912eruptionofMt.KatmaiinAlaska,withtwohazardcurvesgeneratedby1000 simulationsusingTEPHRA2:curve2isidenticaltocurve1ingrapha,curve3isbased oneruptionparameterssimilartothe1991eruptionofMt.Pinatuboandarandomwind eld,alsobasedon2006reanalysisdata.Thisgraphindicatesthatusingthe1912Katmai eruptionasananalogfortephraaccumulationoverestimatesthehazardatthesiteby approximatelyoneorderofmagnitude. ofMt.Natib,yieldlowerprobabilitiesforexceeding1moftephraaccumulationatthe BNPPsite.ItappearsthattheEBASCOassessmentusingMt.Katmaianalog eruptiondata,mayoverestimatethetephra-fallhazardatthesitecomparedtotheresults ofnumericalsimulation. Theresultsofprobabilisticanalysescanalsoberepresentedasprobabilitymaps.These mapsshowtheprobabilityofexceedingagiventhresholdoftephraaccumulationoveran areaofinterest.Thresholdsoftephraaccumulationcanbechosentoreectpotential damagetobuildingsi.e.tephraloadleadingtopartialorcompleteroofcollapseinthe area,potentialaccumulationthatmightleadtolaharformation,orreectdesignfactors forNPPstructures.Avalueof10cmreectstheonsetofroofcollapse,20cmreects 111

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Figure4.7.Mapcontourstheprobabilityoftephraaccumulationexceeding10cm 100kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(2 ,givenanexplosiveeruptionofMt.Natib.Notethatthesesimulations indicatethattephraaccumulationismostlikelyontheWandSWanksofMt.Natib, suggestingtheseareasarepotentialsourcesforlaharsfollowingexplosivevolcanicactivity. widespreadroofcollapse,especiallyifthetephralayerissaturatedwithwaterSpenceetal., 1996.Theprobabilityoftephraaccumulationexceeding100kgm )]TJ/F19 7.9701 Tf 6.587 0 Td [(2 dryaccumulation, 10cminthicknessintheregionaroundtheBNPPisshowninFigure4.7andis 55% neartheBNPPsite.Ofcourse,roofsofnuclearfacilitiesmaybedesignedtowithstand higherloadsthantypicalbuildingsandhouses.Nevertheless,theprobabilitymapindicates thatwidespreaddamagetocommunityinfrastructureintheregionoftheNPPislikely intheeventofaneruptionofsignicantintensitye.g. VEI4.Suchconditionsare importanttoconsiderinsitesuitabilityassessmentanddesignHilletal.,2009. TheprobabilitymapalsoindicatesthatthecentralpartofMt.Natib,andtheWand SWanksofthevolcanoarethemostlikelyareastobesubjectedtotephrafallout.This indicatesthatintheeventofanexplosiveeruption,laharswouldlikelyoccur,potentially overwidespreadareas,onthisankofthevolcano.Theselaharswouldimpactcommunity infrastructureandpossiblydirectlyimpacttheBNPPsitearea. Insummary,itappearsthattheBNPPsiteislocatedwithinthescreeningdistance fortephrafalloutfrombothMt.NatibandMt.Mariveles.Ascreeningthresholdofapproximately10cmtephraaccumulationisused,basedonadamagethresholdcommonly 112

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observedforresidentialandcommercialbuildings.Adierentscreeningthresholdmaybe desirablefornuclearfacilities,whichmayhavegreaterresiliencyforroofloads,butmaybe moresensitivetoparticulatesinwaterandelectricalsystems.Inacomprehensivehazard analysis,thedesignofthefacilityshouldbeevaluatedfortherangeoftephraloadssuch asthosedescribedinouranalysiscf.Hilletal.,2009. 4.4.2Laharsourceregions Severaltypesofvolcanicphenomena,suchaspyroclasticowsandlahars,canbe stronglyinuencedbytopography.Estimationofscreeningdistancevaluesforthesevolcanicphenomenashouldaccountformajortopographicfeaturesofthevolcanoandofthe site.OnMt.Natibvolcano,forinstance,asteepcalderawallonthewestsideofthevolcanomaypreventmanytypesofowsthatoriginateinthecalderafromreachingthesite. Instead,suchowsmightdrainfromthecalderathroughabreakinitsNWrimEBASCO, 1977.Itisthereforesomewhatcounter-intuitivethatpyroclasticowdepositsandlahars aremappedattheBNPPsite.Eithertheseunitsweredepositedwhenthevolcanohada muchdierentform,priortotheformationofthesummitcaldera,orthesephenomenacan reachthesiteareadespitethetopographicbarrierprovidedbythewesterncalderarim. Thepurposeofscreeningdistancevaluecalculationsistodeterminewhethersuchows couldreasonablydevelopinthefuture,consideringcurrentorlikelyfutureconditions. OnMt.Pinatubovolcano,laharsweregeneratedasaresultoftheaccumulationofpyroclasticmateriale.g.tephraandpyroclasticowdepositsonsteepslopesandasaresult oftropicalrainfallsthatworkedtoerodethesedepositsrapidlyDaag,2003.Forpotential laharsfromMt.Natib,experienceonMt.PinatubovolcanoNewhallandPunongbayan, 1996suggeststhatcomplexscenariosaccompanyexplosivevolcaniceruptions,andthese scenariosmightcauselaharsourceregionstodevelopoutsidethecaldera,includinghigh onthewestankofthevolcano.Theexceedanceprobabilitymapfortephraaccumulation inthesiteregionmakesitclearthatifexplosiveactivityweretooccuronMt.Natibora nearbyvolcano,conditionsforlaharformationmaydevelopFigure4.7.Thesteepslopes 113

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onthewestandsouthanksofMt.Natibcouldserveassourceregionsforlaharsthat woulddescendrivervalleysloweronanksofthevolcano. Severaldierentmodelscanbeusedtoassessthepotentialhazardposedbylahars totheBNPPsite.Forexample,astatisticalmodel,suchasLAHARZIversonetal., 1998mightbeusedtoassesspotentialow-paths.Daagproposedawaterruno modelforlaharsfollowingthe1991eruptionofMt.Pinatubotopredictlaharrunoutand magnitude,utilizingacell-baseddistributedmodelcoupledwithahighresolutiondigital elevationmodelDEM.Daag2003modeliscatchment-scaleandusesphysicallawsof owdynamicstodescribelaharsonMt.Pinatubo.Althoughthesemodelshelpdelineate potentialareasoflaharinundation,theyrequirehighresolutioni.e.ideally < 10mgrid digitalelevationdatathatarecurrentlynotavailablefortheMt.Natibregion.Here,we focusonthecouplednatureoftephrafalloutandlahargenerationbyconsideringtwoempiricalmodels.Therstmodelisbasedonthepotentialforgravitationallyinducedfailure ofthetephradepositonthevolcanoslopesIverson,2000,thustriggeringlahars.The secondmodelisbasedontheincreaseinwaterandsedimentrunoastephraaccumulates Daag,2003;Yamakoshietal.,2005. Iverson'smodelassumesthatslopefailureisdescribedbyaCoulombfailure criterionexpressedasayieldcondition: j j = c + n tan .6 where isshearstress, c istephracohesion, n isnormalstressperpendiculartothe slopeand istheangleofinternalfriction.ThisCoulombfailuremodelcanbeexpressed asaratioofresistiveanddrivingforces,knownastheFactorofSafety FS : FS = ResistingForce DrivingForce = c + n tan j j .7 where = )]TJ/F21 10.9091 Tf 8.485 0 Td [(Zy t sin n = Zy t cos Z isthelayerthicknessherederivedfromestimates ofpotentialtephraaccumulation, y t isthetotalunitweightofthedepositperunitarea 114

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Figure4.8.aPotentiallaharsourceregionsdarkshadedareasresultingfromahypotheticalVEI5eruptionfromMt.Natibwindblowingtowardthesite,identiedasthose areaswheretheFactorofSafety, FS 1.ArrowshighlightmaindrainagesontheSSW partofMt.NatibwherelaharshavethepotentialtooccurandaecttheNPPsiteregion. Blackstarindicatesthelocationforthehazardcurveshowninb.bExceedanceprobability,basedontheVEI5eruptionusedina,andsurfaceruno% waterand sedimentrunodividedbytheamountofrainfallplottedasafunctionoftephrathickness.Thisplotindicatesthatlaharpotentialincreaseswithhighertephraaccumulation andhigherruno.Surfacerunovs.tephrathicknessvaluessolidtrianglesarefornegrainedtephraonMiyakejimavolcanoJapan,modiedafterYamakoshietal.. Runoisdiminishedforcoarse-graineddepositsopentriangleonMiakejimavolcano.For example,givenanexplosiveeruptionVEI5ofMt.Natib,theTEPHRA2modelindicates thattheprobabilityoftephraexceeding17cmis50%.EmpiricalobservationsonMiyakejimavolcanosuggestthatforthisthicknessoftephra, 25%ofrainfallandsedimentby volumewillrunointodrainages,forminghyper-concentratedows. and istheslopeoftheslipsurfacepre-tephradepositiontopography.Itfollowsthat: FS = c Zy t sin + 1 )]TJ/F21 10.9091 Tf 12.105 7.38 Td [(y w y t tan tan .8 where y w istheunitweightofwateraddedtothedepositbyrainfall.Slopefailureoccurs when FS< 1.Laharswillbegeneratedprimarilyonsteepslopesafterdepositionoftephra unitsthatbecomesaturatedbywaterinltration,greatlyreducingtheshearstrengthof thesetephralayersDaag,2003.Thisslopefailuremodelforlahargenerationisthus coupledtoatephrafalloutmodel,and,assumingdepositsaturationbyinltratingwater, areasoflikelyslopefailure FS< 1canbeinferredFigure4.8a. 115

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Theactualslopefailureprocessdependsonthenatureoftheslopegeologyi.e.inltration,strengthcharacteristicsunderlyingthepotentialtephradepositandthecoverof vegetation,grain-sizepropertiesofthetephrafalloutandinltrationratesbothintothe tephradepositandintotheunderlyingunits.Thesefactorsarecomplex,spatiallyvariable andnotexplicitlyaddressedbytheIversonmodel,butshouldbeconsideredininterpretingmodelresults.Giventhesecaveats,aFactorofSafetymapFigure4.8aindicates zonesofpotentiallahargeneration,fromwherethoseowsmayfollowmaindrainagesand inundateareaslowerontheanksofthevolcano,anideacompletelyconsistentwiththe screeningdistancecalculation. ThepotentiallaharsourceregionFigure4.8acoversanareaofabout12km 2 .The correspondingtotalvolumeoftephradepositoccurringonthesesteepslopes FS< 1 is1 : 7 10 7 m 3 .Iversonetal.developedanempiricalrelationshipbetweenlahar volumeandtheplanimetricareainundatedbylahars,basedontheiranalysisofnumerous lahardeposits: B =200 V 2 = 3 ,where B m 2 istheareainundatedbyalaharofvolume V m 3 .Usingthisrelationship,theplanimetricareainundatedbyoneormorelahars resultingfromslopefailureisabout13km 2 ,amoderatelaharevent,comparabletothe onethatoccurredatNevadodelRuizvolcanoin1985seeConnoretal.,2009.Therefore, thismodelsuggeststhatareasonthesouthwestankofthevolcanowouldpotentiallybe impactedbylaharsfollowingexplosivevolcanicactivity. Alternatively,laharscanbetriggeredwheneventhin,ne-grainedtephralayersaccumulate,becausetheselayersmayimpedeinltrationandincreasesurfacerunoYamakoshi etal.,2005.InastudyoflahargenerationfollowingrecenteruptionsofMiyakejima volcano,Yamakoshietal.foundapositive,nonlinearcorrelationbetweentephra thicknessanddecreasedinltration,resultinginincreasedsurfacerunothatmaytrigger laharswithverylowsedimentloadbyvolume.Suchowsarecalledhyperconcentrated ows.Essentially,asthetephradepositgetsthicker,waterislesslikelytoinltratethe wholetephradeposit,thusincreasingpotentialsurfaceruno.Daagobserved,from rainfallsimulationsontephradepositsfromMt.Pinatubo,thattephrafalloutdeposits 116

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havelowinltrationcapacitiesduetotheabundanceofneparticles,thusincreasingwaterruno.Inapplyingthisalternativemodel,ahazardcurvefortephraaccumulationina specicareaup-slopeofthesitecanbeevaluatedintermsoflaharstriggeredbyincreased run-oofsurfacewaterandtephraFigure4.8b. Thehazardsduetohyperconcentratedowsaredierentthatthoseassociatedwith slopefailure.Ratherthanasinglevoluminousdebrisow,theincreasedsurfaceruno resultsinpersistenthyperconcentratedowsandoods,whichmaycontinuetoaect theareaatthebaseofthevolcanoforyearsfollowingtheeruption.Individualevents, however,areofmuchsmallervolume.Forexample,inresponseto9mmrainfallandusing theempiricalrelationshipshowninFigure4.8b,thetephradepositwouldcauseanincrease inrunoofapproximately4 10 5 m 3 .Aswithlargervolumedebrisows,thesepersistent hyperconcentratedowswouldadverselyaecttheregiononthesouthwestankofthe volcano. Itappearsthattephradispersalcanpotentiallyresultinow-pathsforlaharstoward thesitevicinity,followingthemajordrainagesonMt.NatibsouthernanksFigure4.8a, despitenear-venttopographicbarrierspresentedbythecalderawall.Becausetephradepositionwouldlikelybewidespreadonthesouthwestankofthevolcanofollowingan explosiveeruption,thenatureofsedimentationonthisankofthevolcanowouldchange, resultinginlahars,hyperconcentratedowsand/orwateroods.Thiscouplednature ofvolcanicphenomenaisquiteimportanttoconsiderinestimationofscreeningdistance values. Cumulatively,theseanalysesindicatethattheBNPPsiteiswithinscreeningdistance forlahars,giventheirpotentialvolumeandtheareaspotentiallyinundatedbythem.Of course,thegeographicpositionoftheBNPPsiteonNapotPointmayprotectthesitefrom inundationbylahars.Comprehensiveanalysisoflaharow-pathswithahigh-resolution DEMmayverifythispossibility.Regardless,laharswouldsignicantlydisruptroadsand communitiesinthesiteregion,afactorimportanttodeterminationinsitesuitability. 117

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4.4.3Hazardsfrompyroclasticdensitycurrents Topographicbarriersalsomaypreventfuturepyroclasticdensitycurrentsfromreaching theBNPPsite.Weconsiderabasicbutwidelyusedmodeli.e.theenergyconemodel; Sheridanforthepotentialrunoutofpyroclasticdensitycurrentsforthepurposes ofevaluatingthispotentialhazard,andtodetermineifthesitelieswithinorbeyonda screeningdistancevaluethatisrepresentativeforsuchhighlymobileows.Theenergy conemodelwasrstproposedbySheridanalsoseeConnoretal.,2009.Essentially thismodelusestheheight, H ,fromwhichpyroclasticdensitycurrentsoriginate,directly relatedtothepotentialenergyoftheows,toestimatetheirrunout, L ,thehorizontal distancetheowsarelikelytotravelfromtheirsource.Theratio, H=L dependsonthe mobilityofthepyroclasticdensitycurrent.Examplesintheliteraturecommonlyrange from H=L =0 : 2forsmallows,to H=L< 0 : 01forlarge-volume,highlymobilepyroclastic densitycurrents. Forpyroclasticdensitycurrentsoriginatingfromdome-buildingeruptionse.g.the ongoingeruptionofSoufriereHillsvolcano,Montserratandfromlow-volumeexplosive eruptions < VEI5,ouranalysisshowsthatthecalderawallwilllikelyactasatopographicbarrierforpyroclasticowstravelingtowardthesitefromacentralventeruptionofMt.Natib.Suchowswouldhaveinsucientpotentialenergytoovercomethe 300 )]TJ/F15 10.9091 Tf 8.485 0 Td [(500m-hightopographicbarrierofthecalderawallandlikelywouldbechannelized towardthenorthwest,possiblyexitingthecalderathroughagapinthecalderawallFigure4.9a.Therefore,assuminglow-energyexplosiveeruptionsoccurwithintheexisting caldera,thesiteseemstobeoutsidethescreeningdistanceforpyroclasticdensitycurrents releasedfromcomparativelylow-lyingsourceswithinthecaldera. Inthecaseofanexplosiveeruptionof VEI5orgreater,oraneruptionoccurringfrom anewventlocatedonthesouthernanksofthevolcano,theenergyconemodelsuggests thatpyroclasticdensitycurrentsmayreachthesite.Flowsassociatedwithsucheruptions oftengeneratepyroclasticdensitycurrentsasaresultofcollapseoftheeruptioncolumnor byboiling-overofaparticularlydenseeruptioncolumn.Insuchcircumstances,thepoten118

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Figure4.9.aThreepotentialpyroclasticowrunoutsfromthecalderaoorofMt.Natib, estimatedusingtheenergyconemodel.The3gray-shadedregionsrepresentpossibleareas inundatedbypyroclasticowsoriginatingfromthecollapseofa100m-highdome.The dierentshadedregionsrepresentareasinundatedbypyroclasticowsofincreasingpotentialenergy,representedbytheratioofdomeheighttorunoutlength: H=L =0 : 2darkest grayarea, H=L =0 : 15mediumgrayarea, H=L =0 : 1lightgrayarea.Uncertaintyin theappropriatevalueof H=L resultsinuncertaintyinthetotalrunoutoftheow.Inallof thesecases,thepyroclasticowsdonotovertopthecalderawall,andthusowawayfrom theBNPPsite.bIncontrast,higherreleaseheightse.g.,1000mabovethecalderaoor associatedwitheruptioncolumncollapseandhigherintensityeruptionsresultininundationoftheBNPPsite.Shadedareasshowinundationbypyroclasticdensitycurrentsfor H=L =0 : 15closesttothevent,darkestshading, H=L =0 : 1,and H=L =0 : 075farthest fromthevent,lightestshading. 119

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tialenergyoftheowmaybesucienttoovercometopographicbarriersapproximately 500m-high,suchasthecalderawall.Basedontheenergyconemodel,apotentialcolumn collapseassumedtoinitiateatthetopofthegas-thrustregionConnoretal.,2009,would needtooriginateatnomorethan1kmelevationabovethecalderaoor.Onceovercomingthesouthwestwallofthecaldera,thetopographicslopeissuchthattheowextends beyondthesiteareafor H=L< 0 : 15Figure4.9b.Basedonthissimpliedanalysis,it appearsthattheBNPPsiteislocatedwithinthescreeningdistancevalueofpyroclastic densitycurrentsforeruptionsVEI5orgreater.Asisthecasefortephrafallout,suchows couldalsogeneratevoluminouslahars,whichmayhavethepotentialtoaectthesite. Numericalmodelsofpyroclasticdensitycurrentse.g.Todescoetal.,2002might greatlyimprovethisassessmentandcouldbeconsideredaspartofacomprehensivehazardanalysisforpyroclasticdensitycurrents.Theenergyconecalculationstronglysuggests suchanassessmentwouldbeusefulforunderstandingarangeofpyroclasticdensitycurrenthazardsfortheBNPPsite.Inaddition,acompleteanalysisofhazardsalsoshould considerthepotentialfornewventformationontheanksofMt.Natib.Asobservedat othercompositevolcanoes,suchventsmightalsobeasourceofpyroclasticdensitycurrents thatmaycreateadditionalhazardsatthesite. 4.5Concludingremarks Thisanalysisisintendedtoillustrateseveralimportantstepsinavolcanichazardassessmentfornuclearfacilities.FortheBNPPsite,thismeansusingavailabledataandavailable numericalmethodstoassessthecapabilityofnearbyvolcanoestoeruptinthefutureand toproducepotentiallyhazardousphenomenaatthesite.DoMt.Natib,Mt.Mariveles andMt.Pinatubohaveacrediblepotentialforfutureeruptions?Futureeruptionsappear highlylikelyfromMt.Pinatubo,consideringitslastexplosiveeruptionin1991andmany othereruptionsintheHolocene.Severallinesofevidenceindicatethatfutureeruptions fromMt.NatibandMt.Marivelesarecredible,includingtheexistenceofanactivehydrothermalsystemwithinMt.Natibvolcano,thepresenceoflittle-erodedvolcanicfeatures 120

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e.g.calderadepressionstruncatingbothMt.NatibandMt.Mariveles,andprobabilistic assessmentbasedontheestimatedreposesincethelastdatederuptiveevent.Theprobabilityestimateishighlyuncertain,duetouncertaintiesinagesofpasteruptionsandpossibly underestimatesrecurrencerateduetopoorpreservationofsmallereruptionsinthegeologicrecord.Thisuncertaintysupportsaconservativeapproachtohazardsassessmentthat assumesfutureeruptionsarepossiblefromMt.Pinatubo,Mt.NatibandMt.Mariveles. Wehavemadesuchapreliminaryassessmentforasubsetofpotentialvolcanicphenomenautilizingascreeningdistancevalueapproach.Thisanalysis,madeusingrelatively simpleandwidelyavailablenumericaltechniques,indicatesthattheBNPPsitehasthe potentialtobeaectedbyphenomenasuchastephrafallout,lahars,andpyroclasticdensitycurrentsintheeventofafutureeruption.Cumulatively,theseanalysesindicatethat Mt.NatibandMt.Marivelesand,fortephra-fallhazards,Mt.Pinatubo,arecapablevolcanoes,followingthedenitionprovidedbyHilletal.. IdenticationofMt.NatibandMt.Marivelesascapablevolcanoesindicatesthata morecomprehensivevolcanichazardassessmentappearswarrantedfortheBNPPsite. Goalsofsuchacomprehensiveassessmentwouldincludeanalysisofthecurrentstateof volcanicunrestatbothMt.NatibandMt.Marivelesthroughimplementationofmonitoringtechniques,suchasaseismicnetworkonthevolcano,deformationmonitoring,and perhapsseismictomographytoascertaintheoriginandextentofthehydrothermalsystem withinthevolcano.Similarly,geochemicalanalysesmightbeextremelyusefultodelineate amagmaticcomponentinthermalspringslocatedinthecalderaofMt.Natib.Asecond goalofthecomprehensiveassessmentwouldbetomapthesetwovolcanoesinsucient detailtodevelopamorecompleteunderstandingofeachvolcano'sstratigraphy,andto placeradiometricdatesinstratigraphiccontext.Anintegratedprogramincludingnewradiometricdatesandpaleomagneticanalysisappearscriticaltodevelopingasuitablerecord ofpastvolcanicactivity.Suchageologicprogramwouldbenecessaryinordertomore fullyassesstheprobabilityoffuturevolcanism,thetimingofmostrecentvolcanism,and theimportantcharacteristicsofpasteruptions.Finally,moredetailedanalysisofvolcanic 121

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hazardscouldmakefulluseofavarietyofnumericalmodelsthatmightfurtherelucidate sitehazards,particularlyoflaharandpyroclasticowphenomena.Allofthesenumerical modelsofsurfaceowsrequireuseofahigh-resolutionpreferably < 10mresolutiondigitalelevationmodel,whichwasnotavailabletotheauthorsatthetimeofthisanalysis. Acquisitionofsuchamodelwouldbeanimportantstepinthevolcanichazardassessment. Regardlessofthedetailsinvolved,theanalysespresentedhereindemonstratethatseveral capablevolcanoesexistwithintheareaoftheBNPPsite.Basedonrecommendations in,forexample,Hilletal.,acomprehensiveanalysisappearsnecessarytosupport discussionsordecisionsregardingthesuitabilityoftheBNPPsite. Thiscasestudyalsoillustratessomegeneralfactorstoconsiderinvolcanichazard assessmentsofnuclearfacilities.ThetimingandrecurrencerateofvolcanismatMt.Natib andMt.Marivelesareamajorsourceofuncertaintyinestimatesofthelikelihoodof futureactivity.ItisunlikelythattheprobabilityoffutureeruptionsfromMt.Natib andMt.Marivelescouldbenarrowedmuchbelowoneorderofmagnitudebyadditional analyses,unlesstheglobalstratigraphicandchronologicalframeworkofthesevolcanoes wereimprovedorveryyoungvolcanicdepositswereidentied.Thisisacommonsituation wherenuclearfacilitiesareconsideredinvolcanicallyactiveregions.Screeningbasedon theprobabilityofoccurrenceofvolcaniceruptionsmayhavelargeuncertainties,givinga weakbasisfordecisionmaking. Screeningdistancesareaneectivemethodofassessingthepotentialforvariousphenomenatoimpactasite.Numericaltechniquescanhaveanimportantroletoplayin estimatingthesescreeningdistances.Forexample,EBASCOdidnothavemethods tosimulatetephrafalloutattheBNPPsitenumerically.Instead,alargeeruptionfroma presumablyanalogousvolcanowasused.Thisresultedinapossibleoverestimateofpotentialtephrafallouthazardsatthesite.Incontrast,probabilisticmodelsyieldhazard curvesfortheBNPPsitethatreasonablyreproducedobserveddepositsfromthe1991 Mt.Pinatubo.Thegreatadvantageofthesemodelsisthatvariousscenariosofactivity 122

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canbeevaluated,providingamorerobustperspectiveontheparametersthatcontribute tothepotentialhazardsatthesite. Similarly,atthetimeofsitingoftheBNPP,itwasarguedthatthetopographyofthe Mt.Natibsummitcalderaprotectsthesitefrompotentialpyroclasticows.Thiseect appearssupportableforrelativelysmalleruptions < VEI5,butouranalysissuggests pyroclasticowsfrom > VEI5eruptionsmayreachthesite.Furthermore,thecoupled natureofvolcanicphenomenae.g.,thepotentialoflaharsresultingfromtephrafallout warrantsfurtherconsideration.Fortunately,volcanologynowpossessesmanyofthetools requiredtomakesuchassessmentsatanappropriatelevelofdetail. 4.5.1Furtherreading Articlesinthevolume StatisticsinVolcanology Maderetal.,2006provideanoverview oftheliteratureonthetimingofvolcaniceruptionsandforecastingactivityatlong-dormant volcanoes.TheTEPHRA2codeisfreelyavailableontheWorldwideWebConnoretal., 2008.Modelingofvolcanicphenomenaisevolvingrapidly.Modelsofvolcaniceruptions anderuptionphenomenaarewidelydiscussedinthe BulletinofVolcanology and Journal ofVolcanologyandGeothermalResearch .See FireandMud NewhallandPunongbayan, 1996forcomprehensivediscussionoftheeruptionsofMt.Pinatubo. 123

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REFERENCES Andrade,D.andMolina,I..Pululahuacaldera:daciticdomesandexplosivevolcanism.FieldguidefortheCOV4meetinginQuito. Armienti,P.,Macedonio,G.,andPareschi,M.T..Anumerical-modelforsimulation oftephratransportanddeposition:applicationstoMay18,1980,Mount-St-Helens eruption. JournalofGeophysicalResearch ,93:6463{6476. Barberi,F.,Coltelli,M.,Frullani,A.,Rosi,M.,andAlmeida,E..Chronology anddispersalcharacteristicsofrecentlylast5000yearseruptedtephraofCotopaxi Ecuador:implicationsfrolong-termeruptiveforecasting. JournalofVolcanologyand GeothermalResearch ,69:217{239. Blong,R.J.. VolcanicHazards:ASourcebookontheEectsofEruptions .Academic Press,Sydney. Bonadonna,C..Probabilisticmodellingoftephradispersion.InMader,H.M.,Coles, S.G.,Connor,C.B.,andConnor,L.J.,editors, StatisticsinVolcanology ,number1, pages243{259.GeologicalSocietyofLondon. Bonadonna,C.,Connor,C.B.,Houghton,B.F.,Connor,L.,Byrne,M.,Laing,A.,and Hincks,T.K.a.Probabilisticmodelingoftephradispersal:Hazardassessment ofamultiphaserhyoliticeruptionatTarawera,NewZealand. JournalofGeophysical Research ,110:doi:10.1029/2003JB002896. Bonadonna,C.andCosta,A..Modelingoftephrasedimentationfromvolcanic plumes.pageinpress. Bonadonna,C.,Ernst,G.G.J.,andSparks,R.S.J..Thicknessvariationsand volumeestimatesoftephrafalldeposits:theimportanceofparticleReynoldsnumber. JournalofVolcanologyandGeothermalResearch ,81:173{187. Bonadonna,C.andHoughton,B.F..Totalgrain-sizedistributionandvolumeof tephra-falldeposits. BulletinofVolcanology ,67:441{456. Bonadonna,C.,Macedonio,G.,andSparks,R.S.J..Numericalmodellingoftephra falloutassociatedwithdomecollapsesandvulcanianexplosions:Applicationtohazard assessmentonMontserrat.InDruitt,T.H.andKokelaar,B.P.,editors, Theeruption ofSoufrireHillsvolcano,Montserrat,from1995to1999 ,number21,pages517{537. GeologicalSocietyofLondon. Bonadonna,C.andPhillips,J.C..Sedimentationfromstrongvolcanicplumes. JournalofGeophysicalResearch ,108:doi:10.1029/2002JB002034. 124

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Scollo,S.,Coltelli,M.,Prodi,F.,Folegani,M.,andNatali,S..Terminal settlingvelocitymeasurementsofvolcanicashduringthe2002-2003Etnaeruption byanX-bandmicrowaveraingaugedisdrometer. GeophysicalResearchLetters 32:doi:10.1029/2004GL022100. Scott,W.E.Hoblitt,R.P.,Torres,R.C.,Self,S.,Martinez,M.M.L.,andNillosJr., T..PyroclasticowsoftheJune15,1991,climacticeruptionofMountPinatubo. InNewhall,C.G.andPunongbayan,R.S.,editors, FireandMud ,pages545{570. UniversityofWashingtonPressandPHIVOLCS. Sheridan,M.F..Emplacementofpyroclasticows:Areview.InChapin,C.E. andElston,W.E.,editors, Ash-owTus ,pages125{136.GeologicalSocietyofAmerica SpecialPaper. Siebert,L.andSimkin,T.. Volcanoesoftheworld:anillustratedcatalogofholocene volcanoesandtheireruptions.SmithsonianInstitution,GlobalVolcanismProgramDigitalInformationSeries,GVP-3 .http://www.volcano.si.edu/world/. Sigurdsson,H.andCarey,S..Plinianandco-ignimbritetephrafallfromthe1815 eruptionofTamboravolcano. BulletinofVolcanology ,51:243{270. Sigurdsson,H.,Houghton,B.F.,McNutt,S.R.,Rymer,H.,andStix,J.2000. EncyclopediaofVolcanoes .AcademicPress. Simkin,T.andSiebert,L.. VolcanoesoftheWorld .GeosciencePresswiththe SmithsonianInstitutionGlobalVolcanismProgram. Sparks,R.S.J..Thedimensionsanddynamicsofvolcaniceruptioncolumns. BulletinofVolcanology ,48:3{15. Sparks,R.S.J.,Bursik,M.I.andAblay,G.J.,Thomas,R.M.E.,andCarey,S.N.. Sedimentationoftephrabyvolcanicplumes.Part2:controlsonthicknessandgrain-size variationsoftephrafalldeposits. BulletinofVolcanology ,54:685{695. Sparks,R.S.J.,Bursik,M.I.,Carey,S.N.,Gilbert,J.S.,Glaze,L.S.,Sigurdsson,H., andWoods,A.W.. VolcanicPlumes .JohnWiley&Sons. Spence,R.J.S.,Spence,R.J.S.,Pomonis,A.,Baxter,P.J.,Coburn,A.W.,White, M.,Dayritt,M.,andTeam,F.E.T.P..BuildingdamagecausedbytheMount PinatuboeruptionofJune15,1991.InNewhall,C.G.andPunongbayan,R.S.,editors, FireandMud ,pages1055{1061.UniversityofWashingtonPressandPHIVOLCS. Suzuki,T..Atheoreticalmodelfordispersionoftephra.InShimozuru,D.and Yokoyama,I.,editors, ArcVolcanism;PhysicsandTectonics ,pages95{113.TerraScienticPublishing. Tahira,M.,Nomura,M.,Sawada,Y.,andKamo,K..InfrasonicandacousticgravitywavesgeneratedbytheMountPinatuboEruptionofJune15,1991.InNewhall, C.G.andPunongbayan,R.S.,editors, FireandMud ,pages601{613.Universityof WashingtonPressandPHIVOLCS. 131

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AppendixAGrainsizedistributionandcharacteristicsoftheBF2layer 135

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AppendixAContinued 136

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AppendixBPerlcodetocalculatethehorizontaldisplacementofvolcanicparticlesduetowindadvection #PerlcodepreparedbyAlainVolentik,UniversityofSouthFlorida, #December2008 #################################################################### #ThisPerlcodeisusedtocalculatetheparticlepathduetowind #advectionfromtheheightofreleasepreviouslyobtainedfromthe #inversiontechniqueonindividualgrainsizetotheground.This #codeneedsthewindprofileoutputfromtheinversionasaninput #file,to#calculatetheamountofhorizontaldisplacementfor #particlesofdifferentsizeduetowindadvection.Thewindprofile #hastoshowthefollowingparameters:elevation,speed,direction. # #IMPORTANT: # #Thecodehastoberunseparatelyforeachgrainsize,andbesure #toupdate4differentvariablesandparametersbeforerunningthe #code:$columntheheightofrelease,$phitheparticlesizein #thephiscale,$zthedifferenceofelevationbetweenallthe #atmosphericlevelsfromthewindprofileoutputoftheinversion #andtheoutputfilenamehere"displacement-2phi.dat"asan #example. #Torunthecode,besuretotype: #perl./nameofthecode.plnameofthewindfile #Theoutputfilewillbeintheformofasuccessionofpostion #x,yfromthepointofreleasetheventlocationisassumedto #lieatthecenterofthecoordinatesystem,0downtothe 144

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AppendixBContinued #lastatmosphericlayermainlytheheightofthevent. #################################################################### #!/usr/bin/perl my$args=@ARGV; if$args<1{ printSTDERR"USAGE:particle-tracking.plnn"; exit; } openDATA,"<$ARGV[0]"||die"$!"; #needtodefinesomevariableforthecodetorun #$columnhastobedefined,inorderforthecodetostartto #calculatethehorizontaldisplacementofthegivenparticlesize #fromthiselevationandbelow.Andnotaboveit. $column=24000; #thereisaneedtodefinethesettlingvelocitylawthatwill #governtheparticlefall,accordingtoits#ReynoldsNumberRe, #forthedifferentclassofparticlesseeBonadonnaetal.,1998 #andBonadonnaandPhillips,2003.Basically,vttistheterminal #velocityintheturbulentregimeRe>500,vtiistheterminal 145

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AppendixBContinued #velocityintheintermediateregime
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AppendixBContinued $t=0; #otherimportantinputparametersthatcanbechosenbytheuser $phi=2;#$phiistheparticlediamterinphiunit,where #phi=-log2diameter $diam=0;#diameteroftheparticles,withd=2exp-phi $rho_part=1000;#densityoftheparticles $air_visc=1.8325e-5;#airviscosity $rho_air=0;#airdensity,calculatedasafunctionofheight $g=9.81;#gravityacceleration $delta_rho=0; $x_disp=0;#horizontaldisplacementalongthex-axis $y_disp=0;#horizontaldisplacementalongthey-axis $x_position=0;#positionoftheparticleateachatmospheric #levelalongthex-axis $y_position=0;#positionoftheparticleateachatmospheric #levelalongthex-axis openOUT,">displacement-2phi.dat"; while{ $elev,$speed,$direction=split"",$_; $rho_air=1.25*exp-$elev/1000/8.2; 147

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AppendixBContinued $delta_rho=$rho_part-$rho_air; if$elev<=$column{ $diam=**-$phi/1000; $vtl=$g*$diam**2*$delta_rho/*$air_visc; $vti=$diam**$g**2*$delta_rho**2/*$rho_air* $air_visc**/3; $vtt=.1*$g*$diam*$delta_rho/$rho_air**0.5; $Rel=$diam*$rho_air*$vtl/$air_visc; $Rei=$diam*$rho_air*$vti/$air_visc; $Ret=$diam*$rho_air*$vtt/$air_visc; if$Rel<6{ $vt=$vtl; $t=$z/$vt; $x=$speed*$t; } 148

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AppendixBContinued elsif$Ret>=500{ $vt=$vtt; $t=$z/$vt; $x=$speed*$t; } else{ $vt=$vti; $t=$z/$vt; $x=$speed*$t; } $direction_radian=$direction*3.1415927/180; $x_disp=$x*sin$direction_radian; $y_disp=$x*cos$direction_radian; $x_position=$x_position+$x_disp; $y_position=$y_position+$y_disp; printf"%.2f%.2f%.2f%.2f%.1f%.1fn",$vtt,$vti,$vtl, $vt,$x_position,$y_position; printfOUT"%.3f%.3fn",$x_position,$y_position; } } closeOUT; closeDATA; 149

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AppendixCPerlcodetoassesstheuncertaintyonthemassandcolumnheight usingtheTEPHRA2model #PerlcodepreparedbyAlainVolentik,UniversityofSouthFlorida, #February2009. ######################################################################## #ThisPerlcodeisusedtocalculatetheuncertaintyintheestimation #ofthetotaleruptedmassandthecolumnheightfromtheinversion #techniqueproposedbyConnorandConnor.ThePerlcodeusesthe #forwardtephradisperionmodelTEPHRA2Bonadonnaetal,2005,Connor #etal.andtheinversionmodelofConnorandConnor. #Theanalysisisbasedonasmoothedbootstrapmethod,modifiedfrom #Pressetal.,seetextinChapter2formoredetailsonthe #approachusedhere. # #IMPORTANT: # #Torunproperly,thecodeneedsseveralfiles:theoriginal #accumulationdataphi.in,awindprofile,aconfigurationfilefor #theforwardTEPHRA2modelandaconfigurationfilefortheinversion #model.FormoredetailsontheTEPHRA2modelanditsrequiredinput #files,pleasevisitthefollowinglink: #http://www.cas.usf.edu/~cconnor/vg@usf/tephra.html #Theoutputfileht-mass-0phi.datcontainsforeachsimulation: #ithesimulationnumber,iithetotalmass,iiithecolumn #heightandivthediffusioncoefficient.Theseparameterscanthen #beusedtocalculatetheuncertaintyfromthemodel. 150

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AppendixCContinued ######################################################################## #!/usr/bin/perl openDATA,">ht-mass-0phi.dat"||die"$!"; #####SPECIFYHOWMANYSIMULATIONSYOUWANTTORUNBYSETTINGTHE #####VARIABLE$ctBELOW.ASANEXAMPLEHERE,THENUMBEROFSIMULATIONS #####ISSETA50SEEBELOW. for$ct=0;$ct<50;$ct++{ openIN,"0phi.in"||die"cannotopenfile...losern"; openNEWIN,">new-0phi.in"||die"$!"; #####GENERATEANEWFILEWITHLOCATIONSRANDOMLYSELECTEDWITHIN1KM #####OFEACHOFTHEORIGINALLOCATIONSINA1KMSQUAREAROUNDEACH #####LOCATIONPOINT. while{ 151

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AppendixCContinued $x,$y,$elev,$accu=split"",$_; $new_x=$x-1000+*rand; $new_y=$y-1000+*rand; printfNEWIN"%.0f%.0f%.0fn",$new_x,$new_y,$elev; } closeIN; closeNEWIN; #####USETHEFORWARDMODELOFTEPHRA2TOCALCULATETHEISOMASSATEACH #####PSEUDOPOINTSGENERATEDBEFOREBESURETOSPECIFYTHECORRECT #####PATHTOTHETEPHRA2CODE!!! #####BELOW,THE"pululagua-0phi.conf"FILEISTHECONFIGURATIONFILE #####NEEDEDTORUNTHEFORWARDSOLUTIONOFTEPHRA2."new-0hpi.in"IS #####THENEWSETOFLOCATIONPOINTSGENERATEDRANDOMLY. #####"wind_levels_0phi.out"ISTHEWINDPROFILE,COMINGFROMTHE #####INVERSIONONINDIVIDUALGRAINSIZECLASSESANDFINALLY #####"tephra.out"ISTHEOUTPUTFROMTHEFORWARDSOLUTION. system"/home/ljc/src/tephra2/tephra2pululagua-0phi.confnew-0phi.in wind_levels_0phi.out>tephra.out"; 152

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AppendixCContinued #####NOWRUNTHEINVERSIONONTHENEWSOLUTIONFORTHENEWPSEUDO #####POINTS,GETTHEVALUESOFTHECOLUMNHEIGHTANDMASSOUTOFIT #####ANDSTORETHEMINOUTPUTFILESWITHDIFFERENTNAME.STOREALL #####THEVALUESOFCOLUMNHEIGHTSANDMASSIN1SEPARATEFILE. #####USETHEINVERSIONMODELOFTEPHRA2TOCALCULATETHEERUPTION #####PARAMETERS.BESURETOSPECIFYTHECORRECTPATHTOTHE #####INVERSIONCODE. #####"inversion-pulu-0phi.conf"ISTHECONFIGURATIONFILENEEDED #####TORUNTHEINVERSION."tephra.out"ISTHESOLUTIONOFTHE #####FORWARDMODELING,USEDHEREASININPUTFILEFORTHE #####INVERSIONINTHEBOOSTRAPANALYSIS. system"/home/ljc/src/tephra2_inversion/src/invert_phi_size inversion-pulu-0phi.conftephra.out"; openOUT,"model.out"||die"$!"; $i=1; while{ $x1,$x2,$x3,$x4=split"",$_; 153

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AppendixCContinued $array[$i]=$x4; $array_2[$i]=$x3; $i++; } printDATA"$ct$array[15]$array[17]$array_2[11]n"; closeOUT; } closeDATA; 154

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AppendixDShapeparameters:aspectration,shapefactorandroundnesswith their1-sigmastandarddeviation 155

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AppendixDContinued 156

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AppendixDContinued 157

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AppendixEPerlcodetocalculatetheterminalvelocityofvolcanicparticles followingthethreemodelsdescribedinChapter3 #PerlcodepreparedbyAlainVolentik,UniversityofSouthFlorida, #March2009 #################################################################### #PERLCODEUSEDTOCALCULATETHETERMINALVELOCITYFORTHEWILSON #HUANGMODEL,MODIFIEDBYSUZUKI;THEKUNIIAND #LEVENSPEILMODELBASEDONEQUIVALENTSPHERESANDTHE #DELLINOETAL.MODEL,BASEDONROUNDNESS. # #IMPORTANTTOREAD: # #NEEDSANINPUTFILEFOREACHGRAINSIZETOBECHANGEDMANUALLY #ANDALSOCHANGEMANUALLYTHEOUTPUTFILENAMEFOREACHGRAINSIZE #################################################################### #!/usr/bin/perl ################################### #####DEFININGSOMEVARIABLES##### ################################### $g=9.81;#####EARTHGRAVITYACCELERATIONINM/S2##### $ash=1000;#####PARTICLEDENSITYINKG/M3##### $air=1.229;#####AIRDENSITYINKG/M3##### $viscosity=1.73e-5;#####AIRVISCOSITYNS/M2##### 158

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AppendixEContinued $delta_rho=$ash-$air;#####DENSITYDIFFERENCE##### $vtt=0; $vti=0; $vtl=0; $Ret=0; $Rei=0; $Rel=0; #################################################################### #Theoutputfile"vt-0-phi.dat"willincludealltheinformations #ofeachparticleshapeparametersandthethreeterminal #velocities. #Theoutputfile"vt-0phi-dellino"containstheterminalvelocity #ofeachparticlecalculatedwiththemodelofKuniiandLevenspiel #andtheoneofDellinoetal.,whiletheoutputfile #"vt-0phi-wh"includestheterminalvelocitycalculatedwiththe #modelofKuniiandLevenspielandtheonofWilsonand #Huang,modifiedbySuzuki # #ATTENTION: # #Thenamesoftheinputfilehere"all-bf2-0phi.in"andoutput #filesmentionedpreviouslymustbechangesmanuallyaccordingto #thegrainsizefractionofinterest. #################################################################### 159

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AppendixEContinued openDATA,">vt-0phi.dat"||die"$!"; openDATA1,">vt-0phi-dellino.dat"||die"$!"; openDATA2,">vt-0phi-wh.dat"||die"$!"; openIN,"all-bf2-0phi.in"||die"cannotopenfile...losern"; while{ $mean,$equi_diam,$max,$width,$length,$area,$volume,$round, $convexity=split"",$_; if$width<=$length{ $ar=$length/$width; $f=*$width/*$length; $diam1=*$width+$length/3; $geo_diam=$length*$width*$width**/3; $d=$equi_diam/1e6; $vtl=$g*$d**2*$delta_rho/*$viscosity; $vti=$d**$g**2*$delta_rho**2/*$air*$viscosity **/3; $vtt=.1*$g*$d*$delta_rho/$air**0.5; $Rel=$d*$air*$vtl/$viscosity; 160

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AppendixEContinued $Rei=$d*$air*$vti/$viscosity; $Ret=$d*$air*$vtt/$viscosity; if$Rel<6{ $vt=$vtl; } elsif$Ret>=500{ $vt=$vtt; } else{ $vt=$vti; } $vt_kl=$vt; $num1=1.2065*$viscosity; $num2=$d**3*$g*$delta_rho*$air*$round**1.6 $viscosity**2**0.5206; $vt_d=$num1*$num2/$d*$air; $num=$ash*$g*$d**2; $denom1=*$viscosity*$f**-0.32; $denom2=*$viscosity**2*$f**-0.64; $denom3=.5*$ash*$air*$g*$d**3*sqrt.07-$f; 161

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AppendixEContinued $vt_wh=$num/$denom1+sqrt$denom2+$denom3; printfDATA"%.3f%.3f%.3f%.3f%.3f%.3f%.4f%.4f%.4fn", $ar,$f,$round,$equi_diam,$diam1,$geo_diam,$vt_kl,$vt_wh, $vt_d; printfDATA1"%.4f%.4fn",$vt_kl,$vt_d; printfDATA2"%.4f%.4fn",$vt_kl,$vt_wh; } } closeDATA; closeDATA1; closeDATA2; closeIN; 162

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AppendixFPerlcodetocalculatethediameteroftheequivalentshperefalling atthesameterminalvelocitythanthemeasuredparticle #PerlcodepreparedbyAlainVolentik,UniversityofSouthFlorida, #March2009 #################################################################### #PERLCODEUSEDTOCALCULATETHEDIAMETEROFTHEEQUIVALENTSPHERE #FALLINGATTHESAMETERMINALVELOCITYTHANTHEMEASUREDVOLCANIC #PARTICLE.FIRST,THETERMINALVELOCITYOFTHEMEASUREDPARTICLE #HASTOBECALCULATED,USINGTHEMODIFIEDVERSIONOFWILSONAND #HUANG,ANDTHENTHEEQUATIONSOFKUNIIANDLEVENSPIELARE #REVERSEDTOCALCULATETHEEQUIVALENTDIAMETEROFTHESPHERE #FALLINGATTHESAMETERMINALVELOCITY. #THECODEWILLALSOCALCULATETHEMEANRATIOBETWEENTHEMEASURED #ANDTHECALCULATEDDIAMETER. # #IMPORTANTTOREAD: # #NEEDSANINPUTFILEFOREACHGRAINSIZETOBECHANGEDMANUALLY #ANDALSOCHANGEMANUALLYTHEOUTPUTFILENAMEFOREACHGRAINSIZE #################################################################### #!/usr/bin/perl ################################### #####DEFININGSOMEVARIABLES##### ################################### 163

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AppendixFContinued $g=9.81;#####EARTHGRAVITYACCELERATIONINM/S2##### $ash=1000;#####PARTICLEDENSITYINKG/M3##### $air=1.229;#####AIRDENSITYINKG/M3##### $viscosity=1.73e-5;#####AIRVISCOSITYNS/M2##### $delta_rho=$ash-$air;#####DENSITYDIFFERENCE##### $d_equi=0; $mean=0; $sum_ratio=0; $vtt=0; $vti=0; $vtl=0; $Ret=0; $Rei=0; $Rel=0; openDATA,">diam-equivalent-7phi.dat"||die"$!"; openIN,"all-bf2-7phi.in"||die"cannotopenfile...losern"; while{ $mean,$equi_diam,$max,$width,$length,$area,$volume,$round, $convexity=split"",$_; if$width<=$length{ 164

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AppendixFContinued $ar=$length/$width; $f=*$width/*$length; $diam1=*$width+$length/3; $geo_diam=$length*$width*$width**/3; $d=$equi_diam/1e6; $n++; #################################################################### #THEFIRSTSTEPISTOCALCULATETHETERMINALVELOCITYUSINGTHE #EQUATIONOFWILSONANDHUANG. #################################################################### $num=$ash*$g*$d**2; $denom1=*$viscosity*$f**-0.32; $denom2=*$viscosity**2*$f**-0.64; $denom3=.5*$ash*$air*$g*$d**3*sqrt.07-$f; $vt_wh=$num/$denom1+sqrt$denom2+$denom3; #################################################################### #NOWTHATTHETERMINALVELOCITYOFWILSONANDHUANGHASBEEN #CALCULATED,INEDDTOINVERTTHEFORMULAOFKUNIIANDLEVENSPIEL #TOFINDDIAMETEROFTHEEQUIVALENTSPHEREFALLINGATTHE #SAMETERMINALVELOCITY. #################################################################### $Re=$d*$air*$vt_wh/$viscosity; 165

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AppendixFContinued if$Re<6{ $d_equi=$vt_wh*18*$viscosity/$g*$delta_rho**0.5*1e6; } elsif$Re>=500{ $d_equi=$vt_wh**2*$air/.1*$g*$delta_rho*1e6; } else{ $d_equi=$vt_wh/*$g**2*$delta_rho**2 *$air*$viscosity**/3*1e6; } $ratio=$equi_diam/$d_equi; $sum_ratio=$sum_ratio+$ratio; printfDATA"%.2f%.2fn",$d_equi,$equi_diam; } $mean=$sum_ratio/$n; } closeDATA; 166

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AppendixFContinued closeIN; print"MeanRatio=$meann"; print"Number=$nn"; 167

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AppendixGPerlcodestocalculatethetephrasedimentationusingthemodel ofBonadonnaandPhilippsandthethreedierentapproachesdiscussed inthetextincomputingtheterminalvelocity #PerlcodepreparedbyAlainVolentik,UniversityofSouthFlorida, #March2009 #################################################################### #PERLCODEUSEDTOCALCULATETHETEPHRAACCUMUALTIONONTHEGROUND #BASEDONBONADONNAANDPHILLIPSSOLUTIONEQ.14. #IREGROUPHERETHETHREEDIFFERENTCODESIUSEDWITHTHETHREE #DIFFERENTMODELSOFTERMINALVELOCITYUSEDINMYANALYSIS #KUNIIANDLEVENSPIEL,1969;WILSONANDHUANG,1969;DELLINOET #AL.. #ONEUNIQUECODECOULDHAVEBEENWRITTEN,BUTASIWASMAKING #SOMEEXPERIMENTS,IKEPTTHEMSEPARATEDFOREACHTERMINAL #VELOCITYMODELUSEDINTHEPRESENTSTUDY.HOWEVERIPUTTHECODES #ONEBELOWEACHOTHER,SOTHEYCANBEUSEDINTHEFUTUREBY #ANYONEWHOISINTERESTED. # #ATTENTION: # #SHAPEPARAMETERVALUESHAVETOBECACULATEDSEPARETELYANDMUST #BEINCLUDEDINTHEVARIABLESDEFINESFORTERMINALVELOCITYCODE #PRESENTEDBELOW. #################################################################### #################################################################### #####CODEUSINGTHEMODELOFKUNIIANDLEVENSPEIL########## #################################################################### 168

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AppendixGContinued #!/usr/bin/perl #################################################################### #####DEFININGCONSTANTSTOBEUSEDINTHETEPHRAMODEL##### #################################################################### #####VENTLOCATION##### $x_vent=0; $y_vent=0; $g=9.81;#####EARTHGRAVITYACCELERATIONINM/S2##### $ash=1000;#####PARTICLEDENSITYINKG/M3##### $air=1.229;#####AIRDENSITYINKG/M3##### $u=0;#####WINDVELOCITYINM/S##### $phi=0;#####PARTICLESIZEPhi##### $viscosity=1.73e-5;#####AIRVISCOSITYNS/M2##### $z=20;#####HEIGHTATWHICHPARTICLESARERELEASEDKM##### $mass=7.42e10;#####TOTALMASSOFTEPHRAERUPTEDKG##### $d=1544.7/1e6;#####DIAMOFEQUIVALENTSPHERE##### #$std_d=; $shape=0.777;#####PARTICLESHAPEFACTORDIMENTIONLESS##### $std_shape=0.112;########## $C=0.4;#####EDDYDIFFUSIVITYINTHEATMOSPHEREM2/S##### 169

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AppendixGContinued $sum=0;#####INTEGRATIONOFMASSOVERAREATOCHECKMODEL##### $grid_spacing=250;#####GRIDSPACINGFORCALCULATION##### $tv=0;#####TERMINALVELOCITYOFPARTICLESM/S##### $t=0;#####PARTICLEFALL-TIMES##### $accumulation=0;#####MASSOFTEPHRAACCUMULATEDATX,YKG $f_phi=0.125;#####TOTALGRAINSIZEDISTRIBUTION##### $f_column=0.11111111111;#####TOTALGRAINSIZEDISTRIBUTION $Q=$z/0.287**5.263;#####fluxattheHCB##### $Hcb=$z*0.6;#####heightofthebaseofthecurrent##### $x_corner=$z*0.238*1000;#####positionoftheplumecorner $rho_Hcb=1.25*exp-$z/8.2; $vtt=0; $vti=0; $vtl=0; $Ret=0; $Rei=0; $Rel=0; $delta_rho=$ash-$rho_Hcb; openDATA,">accumulation-0phi-KL-bonadonna-03.dat"; 170

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AppendixGContinued for$i=0;$i<=200;$i++{ $x=$i*$grid_spacing; $x1=$x/1000; $y=0; $particle_size=$d; $vtl=$g*$particle_size**2*$delta_rho/*$viscosity; $vti=$particle_size**$g**2*$delta_rho**2/ *$rho_Hcb*$viscosity**/3; $vtt=.1*$g*$particle_size*$delta_rho/$rho_Hcb**0.5; $Rel=$particle_size*$rho_Hcb*$vtl/$viscosity; $Rei=$particle_size*$rho_Hcb*$vti/$viscosity; $Ret=$particle_size*$rho_Hcb*$vtt/$viscosity; if$Rel<6{ $vt=$vtl; } elsif$Ret>=500{ $vt=$vtt; } else{ 171

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AppendixGContinued $vt=$vti; } $tv=$vt; $term1=exp-$tv/$Q*$x**2-$x_corner**2; $term2=*$mass*$tv/$Q*.1416**0.5; $accumulation=$term1*$term2; sum_point=$sum_point+$accumulation; printfDATA"%.2f%.2fn",$x1,$accumulation,$tv; } closeDATA; #################################################################### #####CODEUSINGTHEMODIFIEDMODELOFWILSONANDHUANG##### #################################################################### #!/usr/bin/perl #################################################################### #DEFININGCONSTANTSTOBEUSEDINTHETEPHRAMODEL #################################################################### #####VENTLOCATION##### 172

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AppendixGContinued $x_vent=0; $y_vent=0; #####OTHERIMPORTANTCONSTANTSANDVARIABLES##### $g=9.81;#####EARTHGRAVITYACCELERATIONINM/S2##### $ash=1000;#####PARTICLEDENSITYINKG/M3##### $air=1.229;#####AIRDENSITYINKG/M3##### $u=0;#####WINDVELOCITYINM/S##### $phi=0;#####PARTICLESIZEPhi##### $viscosity=1.73e-5;#####AIRVISCOSITYNS/M2##### $z=20;#####HEIGHTATWHICHPARTICLESARERELEASEDKM##### $mass=7.42e10;#####TOTALMASSOFTEPHRAERUPTEDKG##### $d=1544.7/1e6;#####DIAMOFEQUIVALENTSPHERE##### #$std_d=; $shape=0.777;#####PARTICLESHAPEFACTORDIMENTIONLESS##### $std_shape=0.112;#####STDOFPARTICLESHAPEFACTOR##### $C=0.4;#####EDDYDIFFUSIVITYINTHEATMOSPHEREM2/S##### $a=1.88604123E-12;#####LOWERLIMITOFTHETRUNCATEDDISTRIBUTION $b=9.76712030E-01;#####UPPERLIMITOFTHETRUNCATEDDISTRIBUTION $sum=0;#####INTEGRATIONOFMASSOVERAREATOCHECKMODEL##### $grid_spacing=250;#####GRIDSPACINGFORCALCULATION##### $tv=0;#####TERMINALVELOCITYOFPARTICLESM/S##### 173

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AppendixGContinued $t=0;#####PARTICLEFALL-TIMES##### $accumulation=0;#####MASSOFTEPHRAACCUMULATEDATX,YKG/M2 $f_phi=0.125;#####TOTALGRAINSIZEDISTRIBUTION##### $f_column=0.11111111111;#####TOTALGRAINSIZEDISTRIBUTION#### $f_mass=0;#####MASSDISTRIBUTIONASAFUNCTIONOFSHAPE##### $step=0.05;#####STEPINTHESHAPEDISTRIBUTION##### $Q=$z/0.287**5.263;#####fluxattheHCB##### $Hcb=$z*0.6;#####heightofthebaseofthecurrent##### $x_corner=$z*0.238*1000;#####positionoftheplumecorner $rho_Hcb=1.25*exp-$z/8.2; $vtt=0; $vti=0; $vtl=0; $Ret=0; $Rei=0; $Rel=0; $delta_rho=$ash-$rho_Hcb; openDATA,">accumulation-0phi-truncated-suzuki-bonadonna-03.dat"; for$i=0;$i<=200;$i++{ $accumulation=0; 174

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AppendixGContinued $accu_shape=0; for$k=1;$k<=20;$k++{ $bin_shape=$k*$step; $dist_1=1/$std_shape**3.14159**0.5; $dist_2=exp-$bin_shape-$shape**2/ *$std_shape*$std_shape; $dist=$dist_1*$dist_2*$step/$b-$a; $f_mass=$mass*$dist; $x=$i*$grid_spacing; $x1=$x/1000; $y=0; $particle_size=$d; $num=$ash*$g*$particle_size**2; $denom1=*$viscosity*$bin_shape**-0.32; $denom2=*$viscosity**2*$bin_shape**-0.64; $denom3=.5*$ash*$rho_Hcb*$g*$particle_size**3*sqrt .07-$bin_shape; $tv=$num/$denom1+sqrt$denom2+$denom3; $term1=exp-$tv/$Q*$x**2-$x_corner**2; $term2=*$f_mass*$tv/$Q*.1416**0.5; 175

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AppendixGContinued $accumulation=$term1*$term2; $accu_shape=$accu_shape+$accumulation; $sum_point=$sum_point+$accu_shape; } printfDATA"%.2f%.2fn",$x1,$accu_shape; } closeDATA; #################################################################### #####CODEUSINGTHEMODELOFDELLINOETAL.################ #################################################################### #!/usr/bin/perl #################################################################### #####DEFININGCONSTANTSTOBEUSEDINTHETEPHRAMODEL##### #################################################################### #####VENTLOCATION##### $x_vent=0; $y_vent=0; 176

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AppendixGContinued $g=9.81;#####EARTHGRAVITYACCELERATIONINM/S2##### $ash=1000;#####PARTICLEDENSITYINKG/M3##### $air=1.229;#####AIRDENSITYINKG/M3##### $u=0;#####WINDVELOCITYINM/S##### $phi=0;#####PARTICLESIZEPhi##### $viscosity=1.73e-5;#####AIRVISCOSITYNS/M2##### $z=20;#####HEIGHTATWHICHPARTICLESARERELEASEDKM##### $mass=7.42e10;#####TOTALMASSOFTEPHRAERUPTEDKG##### $d=1544.7/1e6;#####DIAMOFEQUIVALENTSPHERE##### #$std_d=; $shape=1;#####PARTICLESHAPEFACTORDIMENTIONLESS##### $std_shape=0.112;########## $round=0.726;#####roundnessshapefactorfortheDellino's calculationofTV##### $std_round=0.141; $C=0.4;#####EDDYDIFFUSIVITYINTHEATMOSPHEREM2/S##### $a=1.29696E-07;#####LOWERLIMITOFTHETRUNCATEDDISTRIBUTION $b=0.973945349;#####UPPERLIMITOFTHETRUNCATEDDISTRIBUTION $sum=0;#####INTEGRATIONOFMASSOVERAREATOCHECKMODEL##### $grid_spacing=250;#####GRIDSPACINGFORCALCULATION##### $tv=0;#####TERMINALVELOCITYOFPARTICLESM/S##### $t=0;#####PARTICLEFALL-TIMES##### $accumulation=0;#####MASSOFTEPHRAACCUMULATEDATX,YKG 177

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AppendixGContinued $f_phi=0.125;#####TOTALGRAINSIZEDISTRIBUTION##### $f_column=0.11111111111;#####TOTALGRAINSIZEDISTRIBUTION $f_mass=0;#####MASSDISTRIBUTIONASAFUNCTIONOFSHAPE### $step=0.05;#####STEPINTHESHAPEDISTRIBUTION##### $Q=$z/0.287**5.263;#####fluxattheHCB##### $Hcb=$z*0.6;#####heightofthebaseofthecurrent##### $x_corner=$z*0.238*1000;#####positionoftheplumecorner $rho_Hcb=1.25*exp-$z/8.2; $vtt=0; $vti=0; $vtl=0; $Ret=0; $Rei=0; $Rel=0; $delta_rho=$ash-$rho_Hcb; openDATA,">accumulation-0phi-truncated-dellino-bonadonna-03.dat"; for$i=0;$i<=600;$i++{ $accumulation=0; $accu_shape=0; 178

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AppendixGContinued for$k=1;$k<=20;$k++{ $bin_shape=$k*$step; $dist_1=1/$std_round**3.14159**0.5; $dist_2=exp-$bin_shape-$round**2/ *$std_round*$std_round; $dist=$dist_1*$dist_2*$step/$b-$a; $f_mass=$mass*$dist; $x=$i*$grid_spacing; $x1=$x/1000; $y=0; $particle_size=$d; $num1=1.2065*$viscosity; $num2=$particle_size**3*$g*$delta_rho*$rho_Hcb* $bin_shape**1.6/$viscosity**2**0.5206; $tv=$num1*$num2/$particle_size*$rho_Hcb; $term1=exp-$tv/$Q*$x**2-$x_corner**2; $term2=*$f_mass*$tv/$Q*.1416**0.5; $accumulation=$term1*$term2; $accu_shape=$accu_shape+$accumulation; $sum_point=$sum_point+$accu_shape; 179

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AppendixGContinued } printfDATA"%.2f%.2fn",$x1,$accu_shape; } closeDATA; 180

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AppendixHBootstrapwithreplacementprocedureinPerltocalculatethe recurrenceintervalandthereforetheprobabilityofaneruptionofagiven volcano #PerlcodepreparedbyAlainVolentik,UniversityofSouthFlorida, #March2008 #################################################################### #Thiscodewillcalculatetherecurrenceintervalestimatewith #95%confidencebasedonthebootstrapwithreplacementmethod #proposedbyEfromandTibshibari. #IusedittocalculatetherecurrenceintervalforMt.Pinatubo #forwhichIhadseveralavailabledatesfromtheliterature. # #IMPORTANT: # #Thecodedoesnotusesdatesofvolcaniceruptions,butrepose #intervalsbetweeneruptions,whichhavetobecalculated #separetelyandinsertedmanuallyinthecodeatline111inthe #arraynamed"my@array".Thentheoutputwillbedisplayedonthe #terminalasthemeanrecurrenceintervalandtheminimumand #maximumreposeintervalwith95%confidence. #################################################################### #!/usr/bin/perl #sum my$n=0; my@a1=; 181

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AppendixHContinued my@array_mean=; my$j=0; #################################################################### ##scriptforthebootstrapstatisticalmethodforRIatPinatubo## #################################################################### for$j=0;$j<1000;$j++{ #################################################################### #####subroutinetoaddupelementsofarray####################### #################################################################### $s=0; subsum{ for$n=0;$n<@_;$n++{ #$sisthesumofthefirst$iarrayelements #$s==$_[$0]+..+$_[$n-1] $s=$s+$_[$n]; } return$s; } 182

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AppendixHContinued #################################################################### ####partofthescriptthatgenerate2differentrandomnumbers### #########fromalist############################################## #################################################################### usestrict; useinteger; my@Numbers=0..4; my$Limit=1; my@list=; formy$i=0;$i<=$Limit;$i++{ my$intRand=intrand@Numbers; if$i==0{ $list[$i]=$intRand; } else{ formy$j=0;$j<$i;$j++{ while$intRand==$list[$j]{ $intRand=intrand@Numbers; $j=-1; 183

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AppendixHContinued } $list[$i]=$intRand; } } } #formy$i=0;$i<=$Limit;$i++{ #print"$list[$i]"; #} #print"n"; #################################################################### #####coreofthescriptforthebootstrapstatisticalmethod###### #################################################################### ######################################## #####arrayofRIforMt.Pinatubo##### ######################################## #################################################################### #####ATTENTION:thearraybelowmy@arrayhastobedefined##### #####manuallybytheuserbyentreringtherecurrenceintervals### #####availableintheliterature.Thecodewillthencalculate#### 184

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AppendixHContinued #####therecurrenceintervalwith95%confidence################## #################################################################### my$sum=0; my$mean=0; my@array=,2500,3500,8350,17650; splice@array,$list[0],1,$array[$list[1]]; #printjoin'',@array,"n"; my$sum=sum@array; #print"Thesumofelementsinarrayis",$sum,"n"; $mean=$sum/$n; #print"Themeaninarrayis",$mean,"n"; #print"$n"; #print"n"; $array_mean[$j]=$mean; #print"nn"; } #print"@array_mean"; 185

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AppendixHContinued #print"n"; $s=0; my$sum_2=sum@array_mean; my$mean_mean=$sum_2/$n; @array_mean_sorted=sort{$a<=>$b}@array_mean; #print"Thesumofelementsinarrayis",$sum_2,"n"; print"ThemeaninRIis",$mean_mean,"n"; print"The0.025RIis",@array_mean_sorted[24],"n"; print"The0.975RIis",@array_mean_sorted[974],"n"; print"$n"; print"n"; 186

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AppendixIPerlandGMTcodesforlaharanaylsislaharsourceregion,total volumeandpotentialareaofinundationaroundMt.NatibvolcanoBataan Peninsula,Philippines #PerlandGMTcodespreparedbyAlainVolentik,UniversityofSouth #Florida,December2007 #################################################################### #ThisisNOTaonestepprocess,butastep-by-stepapproachto #identifythelaharsourceregion,thetotalvolumeandthe #potentialareaofinundationaroundavolcanofollowingan #explosiveeruptionofagivenVEI.Themodelisbasedonthelahars #beingfedbytheunstabletephrablanketseechapter4. #Thedifferentstepstofolloware: #################################################################### #AImportantinputparametersareneeded:DEMgridx,y,zand #amodeloftephradispersionandaccumulationinthiscasethe #Tephra2modelofBonadonnaetal.andConnoretal.. #ForeachpointoftheDEMgrid,theactualslopeiscalculatedand #alsothepredictedtephraaccumulationforagiveneruptioni.e. #aVEI4eruption. #################################################################### #BOnceafileiscreatedwithx,y,slopeandaccumulation,these #dataneedstobefilteredinordertoremovealllocationswith #aperfectlyhorizontalslope. #################################################################### #CThentheslopefailuremodelcanbeappliedandwillgenerate #anoutputintermofFactorofSafetyFS.IfFSis<1thenthe #tephraisnotstableandwillthenfailtoproducelahars. 187

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AppendixIContinued #################################################################### #DTocalculatethetotalvolumeofunstabletephraavailable #andthepotentialareaofinundationbythelahars #theoutputfromthefaluremodelneedstobefilteredinorderto #keeponlythedatapointswherethetephrablanketisunstable. #################################################################### #EAndnow,thetotalvolumeandpotentialareaofinundation #calculationscanbedone. #################################################################### #################################################################### ###HEREARETHEDIFFERENTCODESFOREACHSTEPS#################### #################################################################### ###STEPA-Tobedonebytheuser. #################################################################### ###STEPB-GMTcodetogettheslopeateachDEMlocation. ###ItneedsanDEMinputfileinUTMcoordinates,herenamed ###"srtm.natib.utm". ###Theoutputfileisnamedhere"slope_degrees.xyz"andhasthe ###followingformat:x,y,slopeindegrees. $in="srtm.natib.utm"; 188

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AppendixIContinued system"surface$in--D_FORMAT=%.4f-R198321/231032/1615570/1649160 -I90-Gtopo.grd-V"; system"grdmathtopo.grdDDX=ddx.grd"; system"grdmathtopo.grdDDY=ddy.grd"; system"grdmathddy.grdddx.grdR2SQRTATAN=slope.grd"; system"grdmathslope.grdR2D=slope_degrees.grd"; system"grdinfoslope_degrees.grd"; system"grd2xyzslope_degrees.grd-V>slope_degrees.xyz"; #################################################################### ###STEPC-ApplicationoftheslopefailurePerlcodeafter: ###Appendthepredictedtephraaccumulationforagiven ###explosiveeruptiondefinedbytheusertothepreviousfile ###Thefilenowhasthefollowingformat:x,y,slope,accumulation. my$args=@ARGV; if$args<1{ printSTDERR"USAGE:complex.failure-2.plnn"; exit; } openGRID,"<$ARGV[0]"||die"$!"; while{ $x,$y,$slope,$accumulation=split"",$_; 189

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AppendixIContinued $slope_radian=$slope*3.1415927/180; $tan_alpha=sin$slope_radian/cos$slope_radian; $cos_alpha=cos$slope_radian; $sin_alpha=sin$slope_radian; $cohesion=10000; $phi_rad=*3.1415927/180; $tan_phi=sin$phi_rad/cos$phi_rad; $y_water=9.81*1000; $y_deposit=9.81*1000; $y_total=$y_water+$y_deposit; $thickness_tephra=$accumulation/1000; $coeff1=$cohesion/$y_total*$sin_alpha*$thickness_tephra; $coeff2=1-$y_water/$y_total; $coeff3=$tan_phi/$tan_alpha; $FS=$coeff1+$coeff2*$coeff3; $status=1; if$FS<1{$status=0;} elsif$FS>1{$status=2;} print"$x$y$status$slopen"; } closeGRID; 190

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AppendixIContinued ###Thelaharsourceregioncanbeidentifiedbycontouring$status=1 ###intheoutputfile. #################################################################### ###STEPD-FilteroutallthedatapointthathaveaFS>1,thus ###retainingonlythelocationwherethetephrablanketisunstable. if@ARGV<1{ print"USAGE:ARGV=@ARGVperlvolume-calculation.pln"; exit; } openDATA,">location-where-tephra-unstable.dat"; while<>{ $x,$y,$fs,$slope=split"",$_; if$fs<=1.0{ printDATA"$x$y$fs$slopen"; } } closeDATA; #################################################################### 191

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AppendixIContinued ###STEPE-Calculatethetotalvolumeoftephraavailabletofeed ###laharsfromthelaharsourceregionsandthepotentialareof ###inundationofthelaharsfollowingtheprevioussteps. $n=0;#######numberofpointswheretephraisunstable####### $grid_spacing=90;#######gridspacingoftheDEMinMETERS##### $area=0;#######areaaffectedbypotentialtephrafailure inKM2####### $y_water=9.81*1000;#######specificweightofwater####### $y_deposit=9.81*1000;#######specificweightofthetephra deposit####### $cohesion=1000;#######cohesionofthetephradeposit####### $repose_angle=35;#######angleofreposeoftephra angleofinternalfriction####### $thickness=0;######thicknessoftephraforpointswhere FS<=1####### $volume=0;#######volumeoftephrathatwillfailfor1cell, basedon1pointofthegrid####### $volume_tot=0;#######totalvolumeoftephrathatwillgenerate lahars####### openDAT,"location-where-tephra-unstable.dat"||die"cannot openfile...losern"; 192

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AppendixIContinued while{ $x,$y,$fs,$slope=split"",$_; $n++; $slope_radian=$slope*3.1415927/180; $tan_alpha=sin$slope_radian/cos$slope_radian; $cos_alpha=cos$slope_radian; $sin_alpha=sin$slope_radian; $phi_rad=$repose_angle*3.1415927/180; $tan_phi=sin$phi_rad/cos$phi_rad; $y_water=9.81*1000; $y_deposit=9.81*1000; $y_total=$y_water+$y_deposit; $coeff2=1-$y_water/$y_total; $coeff3=$tan_phi/$tan_alpha; $thickness=$cohesion/$fs-$coeff2*$coeff3*$sin_alpha *$y_total; $volume=$thickness*$grid_spacing**2; $volume_tot=$volume_tot+$volume; #print"$thickness$volume_totn"; } $area=$n*$grid_spacing/1000**2; $area_inundated=*$volume_tot**/3/1000000; 193

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AppendixIContinued print"numberofpointswheretephraisunstable=$nn"; print"areaoflaharsourceregion=$areakm2n"; print"volumeoftephraavailableforlahars=$volume_totm3n"; print"areainundated=$area_inundatedkm2n"; closeDAT; 194

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ABOUTTHEAUTHOR AlainVolentikwasborninLocarno,Switzerland.Hegraduatedwithdistinctionin1996 fromtheLyceeMichelAnguierinEu.HeobtainedhisDiplomain2001andhisMaster's inGeologyin2002attheUniversityofLausanne,Switzerland.InJanuary2005,hejoined theDepartmentofGeologyattheUniversityofSouthFloridatoworkonhisPh.D.with Dr.CharlesConnorandDr.CostanzaBonadonnaonmodelingtephrasedimentation.He participatedtoseveraleldtripsandconferencesintheUSA,Ecuador,Japan,Iceland, ChileandArgentinatocollectelddataforhisthesisandtopresenthisresearchwiththe scienticcommunity.AlainwastherecipientoftheBestTeachingAssistantAward, theOutstandingServiceAwardandtheRichardA.DavisFellowshipfrom theDepartmentofGeologyandtheGraduateStudentAwardfromtheUSFGraduate ProfessionalSchoolCouncil.