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ASTARTE

Assessment,STrategyAndRiskReductionforTsunamisinEurope

GrantAgreementno: 603839Organisationnameofleadcontractor: IPMACoordinator: MariaAnaBaptista

Deliverable8.39Quantifyingandmanaginguncertaintyintsunamiriskassessment

methods:applicationtotheASTARTEtestsitesDuedateofdeliverable: M38

ActualsubmissiondatetoPC: M40

Startdateoftheproject: 01/11/2013

Duration: 42months

WorkPackage: WP8“FromHazardToRiskAssessment”

Leadbeneficiaryofthisdeliverable: INGV

Author(s): INGV: J. Selva, S. Lorito, S. Orefice, B. Brizuela, S.Iqbal,F.Romano,M.Volpe,R.Tonini,R.Basili,M.M.Tiberti;NGI:F.Løvholt,S.Glimsdal,C.Harbitz;GFZ:A.Hoechner, A. Babeyko; UNIBO: A. Armigliato, G.Pagnoni, S. Tinti; IPMA: R.Omira;METU: S. Acar, A.Yalciner,B.Aytore,N.Dogulu,O.Cabuk,U.Kanoglu,B. Yalciner;KOERI: O. Necmioglu, C.O. Sozdinler,MOzel;SRB-RAS:A.Zaytsev

Version: Final

Projectco-fundedbytheEuropeanCommissionwithintheSeventhFrameworkProgramme(2007-2013)DisseminationLevel

PUPublic xPPRestrictedtootherprogrammeparticipants(includingtheCommissionServices) RERestrictedtoagroupspecifiedbytheconsortium(includingtheCommissionServices) COConfidential,onlyformembersoftheconsortium(includingtheCommissionServices)

ASTARTE[603839]–DeliverableD8.39

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TABLEOFCONTENTS

EXECUTIVESUMMARY...........................................................................................................................4

ListofFigures.........................................................................................................................................6

ListofTables...........................................................................................................................................7

1.Introduction.......................................................................................................................................8

2.Treatmentofuncertaintyinhazardandrisk,inamulti-riskperspective........................................11

2.1Stateoftheartfornaturalhazards............................................................................................13

2.1.1Quantificationofuncertaintiesinhazardandriskassessments.........................................13

2.1.2Basicformulationofprobabilistichazardandriskanalyses................................................16

2.1.3Factorizationofriskfactors.................................................................................................19

2.1.4Commonsimplificationsofthegeneralformulation..........................................................20

2.2 Stateoftheartfortsunamis...............................................................................................22

2.2.1Comparisonbetweentsunamisandothernaturalhazards................................................22

2.2.2HazardandriskquantificationmethodsadoptedinASTARTE............................................26

2.3Comparingtheresultsofdifferentlevelsofsimplificationsintreatinguncertainty:examplesfromASTARTETestsites..........................................................................................32

2.3.1GullukBay:ProbabilisticVSDeterministictsunamihazard.................................................32

2.3.2Sines:ProbabilisticVSDeterministictsunamihazard.........................................................34

2.3.3Siracusa:ProbabilisticVSDeterministictsunamirisk..........................................................36

2.4Comparisonbetweenscenario-basedandprobabilistictsunamihazardandriskassessment:guidelinesforfuturetsunamihazardandriskassessments.................................41

3.Proposalforahomogenisedtreatmentofuncertaintyfortsunamihazardandrisk,withexamples..............................................................................................................................................................47

3.1RegionalSeismic-ProbabilisticTsunamiHazardAnalysis(SPTHA)intheNEAMRegion,underdevelopmentwithinTSUMAPS-NEAMProject..................................................................48

3.1.1TSUMAPS-NEAMMethodologyforRegional-scaleS-PTHA.................................................49

3.1.2TSUMAPS-NEAMMultiple-expertprocessforuncertaintyquantification..........................54

3.2Quantificationoftsunamirun-upuncertaintyusingapproximateamplificationfactormethods...........................................................................................................................................62

3.2.1Newsetofamplificationfactorsbasedonlocalbathymetrictransects.............................64

3.2.2Setupoflocalinundationsimulations................................................................................67

3.2.3Estimatingthemaximuminundationheightuncertainty...................................................69

3.2.4Results.................................................................................................................................70


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3.2.5Summaryanddiscussion.....................................................................................................79

4.Conclusionsandoutlook..................................................................................................................82

References............................................................................................................................................83


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EXECUTIVESUMMARY

ASTARTEprojecthasdealtwithuncertaintyintsunamihazardandriskassessmentinseveraldeliverables. Toprovide a homogeneousdescriptionof uncertainty treatment throughouttheproject,themainconceptsaresummarisedintoasinglefinaldocument.Thisdeliverableismeant to serve as initial set of guidelines for future assessments, to be likely updatedduring ongoing and future efforts (e.g. the Global Tsunami Model - GTM,www.globaltsunamimodel.org).

The earliest ASTARTE document about uncertainty treatment was the deliverable D4.13,wheresomeconceptsweredevelopedalready.Thoseconceptsarefurtherelaboratedandextended to a more general framework here. We also deepen into the practicalimplementationofuncertaintyquantificationintsunamihazardandriskassessment,whileattemptingtopreserveamulti-riskperspective.

Thegeneral frameworkofuncertainty treatmentdescribed inD4.13 is firstdiscussedandupdated. Then, best practices and state-of-the-art in treating and quantifying uncertaintyfornaturalhazards(withfocusonseismicandvolcanicapplications)andhighlightingsomepeculiaritiesfortsunamisisdiscussedalsofromamulti-hazardperspective.Severaldifferentmethodsadopted in thetsunamicommunity, their rationale,prosandcons,andmethodsfor comparingdifferent results fromdifferent approaches arediscussedalsobymeansofexamplesofuncertainty treatmentadopted insomeof thehazardand/or riskanalysesattheASTARTEtestsites,previouslyreportedinWP8deliverables(D8.8,D8.14,D8.33).

Finally,we introduce a novel general framework for tsunami hazard quantification at theregionalscale,enablingafullexplorationofuncertaintyfortsunamisofseismicorigin.Themethodalsoestablishesastandardizedprotocol tomanagesubjectivitywithinamultiple-expert environment. The method is being applied in the TSUMAPS-NEAM project(http://www.tsumaps-neam.eu/), which will provide the first community-based regionalSeismic Probabilistic Hazard Analysis for the NEAM region. TSUMAPS-NEAM was madepossiblebytheworkdonewithinASTARTEforthedefinitionofgoodpracticesforthesourcetreatment(D3.12,D3.40)andofmethodsfortheregional-scalehazardanalysis(e.g.D8.8).Amultiple-expert approach for the management of critical choices was instead mainlydeveloped within the STREST project (http://www.strest-eu.org/); its application inTSUMAPS-NEAM involves several ASTARTE partners. An example is drawn and presentedfromthisregional-scaleanalysisforhazardcalculatedatoffshorepoints.Finally,aproposedmethodology for treating theuncertainty in approximatedmethods for the calculationofmaximum inundation heights, where the uncertainty in inundation quantities is derivedfromnumericalsimulationsatASTARTEtestsites,ispresented.


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DOCUMENTINFORMATIONProjectNumber

FP7–603839 Acronym ASTARTE

FullTitle Assessment,STrategyAndRiskReductionforTsunamisinEuropeProjectURL http://www.astarte-project.eu/DocumentURL EUProjectOfficer DenisPeterDeliverable Number D8.39 Title Quantifyingandmanaging

uncertaintyintsunamiriskassessmentmethods:applicationtotheASTARTEtestsites

WorkPackage Number WP8 Title FromHazardtoRiskAssessment

DateofDelivery Contractual M38 Actual M40Status version finalXNature prototype□ reportX dissemination□Disseminationlevel publicX consortium□Authors(Partner) INGV

ResponsibleAuthorName JacopoSelva E-mail [email protected] INGV Phone

VersionLogIssueDate Rev.No. Author Change0.1.0 06/09/2016 INGV Table of contents0.2.0 01/03/2017 All First draft0.3.0 28/03/2017 All Final draft1.0.0 INGV Submitted


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ListofFiguresFigure1:FragilitycurvesforRC(above)andBrick(below)buildings,foralldamagestates(fromSuppasrietal.2013).............................................................................................................................38Figure2:Numberofbuildingsineachdamagestate,forallbuildings(top),Masonrybuildings(middle)andRCbuildings(bottom),adoptingtheprobabilisticmethodbasedonSuppasrietal.(2013)...................................................................................................................................................39Figure3:Numberofbuildingswithdamagestatesgreaterorequaltocollapse(D5andD6ofSuppasrietal.,2013)forallbuildings(top),Masonrybuildings(middle)andRCbuildings(bottom),adoptingtheprobabilisticmethodbasedonSuppasrietal.(2013)fragilitycurves(histogram)andthequalitativemethodsSCHEMAandPVHA-3....................................................................................40Figure4:ComparisonbetweenProbabilisticHazardAnalysis(hazardcurveinredandgrey),scenario-basedintensity(blue),andpastdata(green),modifiedfromSelvaetal.(2016)................................46Figure5:HazardmapsrelativetoanAverageReturnPeriodof475yr(above),975yr(center),and4975yr(below),correspendenttoprobabilitiesof0.10,0.05and0.01in50yrwithinaPoissonprocess.Themeanoftheepistemicuncertaintyisreported..............................................................53Figure6Comparisonofweightsassignedtoexpertsbasedonalternativeweightingschemes.........58Figure7:AHPresults............................................................................................................................61Figure8:Exampleofasetof40depthprofilesrepresentingahazardpoint......................................65Figure9:ExampleofasubsetofprofilesfortheMediterranean........................................................65Figure10:TheamplificationfactorsforthesevendepthprofilesrelatedtoagivenlocationintheMediterraneanversusthewaveperiod(seconds).Theredandbluecurvesarefactorsforleadingpeakandleadingtrough,respectively.Thethincurvesarethefactorsforthesevenlocalprofiles,whilethethicklinesarethemedianvaluesforleadingpeakandleadingtroughatthislocation......66Figure11:TheamplificationfactorsfortheMediterraneanandBlackSeaforthecasewithaleadingtroughandawaveperiodof600s.Thefactorsarefilteredalongtheshorelinewithamedianfilterasexplainedinthetext............................................................................................................................66Figure12:TheamplificationfactorsforBlackSeaasfunctionofthehazardpointslyingalongtheshoreline(IDnumbers).Thefigureshowstheeffectoffilteringthefactorsalongtheshoreline.Thelabels"neg"and"pos"relatetoleadingtroughandleadingpeak,respectively.Thetag"-sm"meansthefilteredvalues(medianfilter)........................................................................................................67Figure13:Exampleofextractingthewavecharacteristicsfromthehazardpointonthe30arcsecsimulations(blackline)atahazardpointwithID10746.Theverticalaxisisthesurfaceelevationinmeters,whilethehorizontalaxisisthetimeinminutes.Themaximumvalueismarkedwithamagentabullet,whilethewaveperiodismeasuredbetweenthetwocyanverticallines.................68Figure14:DistributionofMIHandfittedlognormaldistributionfortheHerakliontestsiteusingtheComMITmodel.Upperpanel,Mw7scenario;lowerpanel,Mw7.5scenario........................................71Figure15:DistributionofMIHandfittedlognormaldistributionfortheHerakliontestsiteusingtheComMITmodel.Upperpanel,Mw8scenario;midpanel,megathrustsubductionscenariofromtheHellenicArc(notcorrectedfortopographicchange),lowerpanel,megathrustsubductionscenariofromtheHellenicArc(correctedfortopographicchange)..................................................................72Figure16:DistributionofMIHandfittedlognormaldistributionfortheColoniaSantJorditestsiteusingtheComMITmodel.Upperpanel,Mw7scenario;midpanel,Mw7.5scenario;lowerpanel,Mw8.0scenario.....................................................................................................................................75


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Figure17:DistributionofMIHandfittedlognormaldistributionfortheColoniaSantJorditestsiteusingtheHySEAmodel.Upperpanel,Mw7scenario;midpanel,Mw7.5scenario;lowerpanel,Mw8.0scenario................................................................................................................................................77Figure18:DistributionofMIHandfittedlognormaldistributionfortheSinestestsiteusingtheComcotmodel.Upperpanel,Mw7scenario;lowerpanel,Mw7.5scenario.........................................77Figure19:DistributionofMIHandfittedlognormaldistributionfortheSinestestsiteusingtheComcotmodel.Upperpanel,Mw8.0scenario;midpanel,Mw8.5scenario(notcorrectedfortopographicchange),lowerpanel,Mw8.5scenario(correctedfortopographicchange)....................79Figure20:Histogramshowingthelognormalbiasforthedifferentsimulationsinvestigated.Themeanbiasisclosetozero.Here,thetopographychangeisnottakenintoaccount.Ifwetakeintoaccountthetopographychange,thebiaswillincreasefrom-0.03to+0.02.......................................80Figure21:Histogramshowingtheuncertaintydistributionforthedifferentsimulationsinvestigated...............................................................................................................................................................80

ListofTablesTable1:Fundamentalscaleofabsolutenumbers..............................................................................58Table2:ResultsfortheprioritizationofSTEPS...................................................................................59


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1.IntroductionAleatoryuncertainty isquantifiedby theexpected long-run frequenciesof randomeventswithinthemodelofthesystem.Suchfrequenciesareobjectiveprobabilitiesθ,andtheycanbe potentially measured through a well-defined experimental concept. The experimentalconceptdefinescollectionsofdata-observedandnotobservedyet–thatarejudgedtobeexchangeable. The long-run frequencies are determined by this data-generating process(Marzocchi&Jordan,2014).Thequantificationofthealeatoryuncertaintyisthemaingoalofanyprobabilisticmodelforhazardorrisk.Fortsunamis,wewillindicatetheseanalysesasProbabilisticTsunamiHazardAnalysis(PTHA)andProbabilisticTsunamiRiskAnalysis(PTRA);wewillalsorefertoPTHAfortsunamisofseismicoriginasseismic-PTHA(S-PTHA).

Epistemic uncertainties measure the lack of knowledge in the estimation of suchfrequencies. Models assessing θ are often based on expert opinions, thus epistemicuncertainty isdescribedby subjectiveprobabilities.Bayesianmethodsareappropriate forreducing epistemic uncertainties as new knowledge is gained through observations. Theepistemicuncertaintyarisingfromthisframeworkdescribes‘thecenter,thebody,andtherange of technical interpretations that the larger technical communitywould have if theyweretoconductthestudy’(SSHAC1997,2012;Marzocchietal.,2015).

Differentapproacheshavebeenusedinliteratureofnaturalhazardstodevelopalternativemodels of the aleatory uncertainty, andmerge them into a singlemodel simultaneouslyquantifying both aleatory and epistemic uncertainty. The most common approaches arebasedonexpertelicitations (e.g.,Cook,1991;BedfordandCooke,2001;Nerietal.,2008;Morgan, 2014), multiple-expert processes (SSHAC, 1997; Selva, et al. 2015), Bayesianmethods(e.g.,Gelman,etal.1995;SelvaandSandri,2013;Marzocchietal.,2010;Grezioetal., 2010), Logic Trees (from Kulkarni et al., 1984; Geist & Parsons, 2006), and ensemblemodelling approaches (e.g., Toth and Kalnay, 1993; Araujo and New 2007; Cloke andPappenberger,2009,Marzocchietal.,2015;Selvaetal.,2016).

Thequantificationofepistemicuncertaintyisoftenlimitedtohazardassessmentsonly,andmore seldom considered in subsequent risk assessments; it has been recognized thoughthatthevariabilityoftheresultsduetopossibledifferentandsubjectivechoicesrelatedtothevulnerabilitymaypotentiallyintroduceunforeseenconsequencesinloss/risk(e.g.,Pate-Cornell,,z1996,Selvaetal.,2013).

Ontologicalerrorisidentifiedbytherejectionofanullhypothesiswhichstatesthatthetrue(long-run) frequencies of the random events are samples from the (joint) probabilitydistributiondescribingtheepistemicuncertainties.Inotherwords,ifthisnullhypothesisisrejected, itmeans thatourmodeldescribing theuncertaintyon thedefinitionof the truefrequency is ‘ontologically’rejected,possibly indicatingthattheselectedframework isnotcapableofsatisfactorydescribinguncertainty(MarzocchiandJordan,2014).Thepossibility


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offormallytestingthefulluncertaintyquantificationagainstreal(andindependent)dataisoneofthemainadvantagesofthedescribedframework(Marzocchietal.,2015).

In the following sections, we discuss how the quantification of uncertainty is generallytreatedinthefieldofnaturalhazards(withfocustoearthquakesandvolcanoes,whicharealso sources of tsunamis), andwe compare themainmethods adoptedwithin ASTARTE,whichwellrepresentthemostusedmethodsadopted inthecommonpracticeoftsunamihazardandriskassessments.

Quiteadvancedtechniquesinuncertaintyquantificationhavebeenhistoricallydevelopedinthefieldofseismichazardandriskassessment(SSHAC,1997,2012;CornellandKrawinkle,2000;DerKiureghian,2005).Generallynonhomogeneous levelsofquantificationofthesetypes of uncertainty are instead adopted in the scientific literature when dealing withtsunamihazardandriskanalysis.

Someofthetechniquesusedindifferentfieldsmaybeextendedtotsunamis(e.g.,GeistandParsons,2006).However,many technical andpractical limitationsdoexist,mainlydue toseveralpeculiaritiesoftsunamis(e.g.,GeistandLynett,2014;Loritoetal.,2015;Selvaetal.,2016;Daviesetal.,2017).Tofacilitatethisdiscussion,someexamplesofapplicationstotheASTARTE test sites of Gulluk bay (Turkey), Sines (Portugal), and Siracusa (Italy) arepresented, together with the comparison and critical review of complementary and/oralternativescenario-basedandprobabilisticapproachestohazardandriskanalysis.

By limiting ourselves to seismic sources only, we finally discuss and present an examplewhich illustrates the methodology for uncertainty quantification in a regional S-PTHAproject.Clearly,allmethodsaswellasanyspecificassessmentmayinvolverathersubjectivechoicesatall levels,whichmaybeevenhiddeninthecomplexityoftheprocess.Thisverymuchcriticalaspectofhazardandriskanalysisisachallengeforscientistsandpractitionersresponsible for the analysis. Here, we then also discuss, in the frame of the above-mentioned regional assessment, a possible structured process for adopting workingsimplifications;forperformingcriticalchoicesbetweenpossiblealternativemodels;andfortheirrelativeweighting.

Overall,thisapproachrepresentsarefinementofthemethoddescribedindeliverableD8.8of ASTARTE and published in Lorito et al. (2015) and Selva et al. (2016); it neverthelessbenefittedofthehugeamountofworkmadewithinASTARTEbymanypartners;andalsobytheeffortsdevelopedintheSTRESTproject.TSUMAPS-NEAMisinasenseaspin-offoftheASTARTE project; however, it clearly marks the transition between hazard analyses andstudies with uncertainty treatment on one hand, towards an operational assessmentmotivatedby regulatoryconcernson theotherhand,andcommissionedby theDG-ECHOforCivilProtectionpurposes.


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Sincethecomputationalfeasibilityofsite-specific/high-resolutionprobabilisticinundationmaps is a challengeper-se, anexample is alsopresentedhere concerningapossible two-step approximate method for dealing with tsunami inundation quantities. Rather crudeapproximatemethodsbasedonlocalamplificationfactorsoftheoffshorewaveamplitudeprobabilitiesare firstused.Then,detailednumericalsimulationsat theASTARTEtestsitesare used for assessing a probability density function, which accounts for uncertaintypropagationduetothecrudeinundationapproximation(seealsoDaviesetal.,2017).TheapproachdevelopedhereisbeingaswellappliedintheTSUMAPS-NEAMassessment.

Ideally,thepresentdeliverablewillbeafirststepofalonger-termprocessinitiatedwithinASTARTE,asitisforeseeablethattheseguidelineswillbefurtherdevelopedandupdatedinthefuture,forinstancebytheGlobalTsunamiModel(GTM,www.globaltsunamimodel.org),a network of coordinated action for tsunami hazard and risk assessmentworldwide. ThisGTMhasbeenalreadyendorsedbyGFDRRandbyUN-ISDR,withtheauspiceofcontributingto the implementation of the 2015-2030 Sendai framework for disaster risk reduction(http://www.unisdr.org/we/coordinate/sendai-framework).


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2.Treatmentofuncertaintyinhazardandrisk,inamulti-riskperspective

Inanygivenplace,differentphenomenamayoccurthatcanrepresentahazardforanassetor a person located in that place. However, it is clear that the specific interest of anyindividualorstakeholderordecisionmaker istopreventthepotentialoddconsequencesindependently from the hazard originating the consequence. For instance, amunicipalitymay be interested to know inwhich direction and field themitigation efforts have to beimplemented (which hazard should we try to mitigate first?), considering that availableeconomicalandhumanresourcesarealwayslimited.

Evenifthistypeofquestionsisoffundamentalandevidentinterestforthesociety,itisnotasimpletasksofartoanswerquantitativelyandexhaustively.Thequantificationofrisksisindeed usually done through the independent analysis of single hazardous phenomena,developedindifferentfieldsofscience.Additionally,thisimpliestheinappropriateinmanycases assumption of independence among the different hazards. Therefore, thequantificationoftheriskscausedbydifferenthazardousphenomenaisbasedondifferentdefinitions and/or approaches and/or assumptions, making them substantially notcomparable(e.g.,Marzocchietal.,2009).

Differentstudieshaveshownthe importanceofmakingcompatibleassessments,allowingforaquantitativecomparisonofthedifferentrisks(e.g.,FEMA,1997;Grünthaletal.,2006;Douglas,2007), aswell as, for the treatmentof the important interaction thatmayoccuralongtheriskchainsduetodifferenthazardinitiators(e.g.,Bovoloetal.,2009;Marzocchietal.,2009,2012;Selva,2013;Mignanetal.,2014,2016).

The development of parallel and homogeneous and coordinated management of risks(multi-hazard risk approach) requires also a correct treatment of uncertainties related toeach individual riskassessmentand in the“aggregated” results. Indeed,a commonsetofboundaryconditionsfortheriskquantification(suchastheexposuretimewindowand/orthedefinitionoftheconsideredtypeofdamage)areonlyapre-requisiteforaneffectiveriskcomparison.Verydifferentlevelsofknowledgeexistforthedifferenthazards.Forexample,while seismic hazard and risk analyses have nowadays rather well defined standardsadoptedworldwide(e.g.,SSHAC,1997;USNRC,2012;Woessneretal.,2015),atleastasfaras the management of the critical choices and the communication of uncertainties areconcerned, risks due to other hazards do not have accepted standardizations of theassessmentprocess itself (e.g., theones linked tovolcanic sources, see IAEA-PVHA,2016;Loughlinetal.,2015;orfortsunamis,hencetheGTM,www.globaltsunamimodel.org).


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Very different levels of knowledge exist even for the different factors of the same riskquantification. For example, the different choices on vulnerability modelling in riskassessmentshavebeenseentoresult insignificantdiscrepanciesbetweentheseismicriskassessments made by different authorities for the same location, structure type andseismicity (e.g.,RossettoandElnashai,2005;Selvaetal.,2013).Also, for somestructuresmanydifferentalternativevulnerabilitymodelsmaybeavailable(e.g.,RCbuildings),whileforotherstructuresonlyfewmodels(ifany)maybeavailable(PitilakisandCrowley,2015),leading tocompletelydifferent levelsofconfidenceon the resulting riskmodels. Ifall thesourcesofuncertaintyarenotcorrectlypropagatedintotheriskassessment,thedifferencesbetweendetailedmultiple-expertanalysesandsimplifiedsingle-expertquantificationsmaycompletelydisappearorbeoverlooked,leadingtopotentiallymisleadingcomparisons(seediscussionsinSelvaetal.,2013).

In the next subsections, we first briefly discuss the state of the art for risk assessmentswithinamulti-hazardenvironmentinSection2.1.InSection2.2,webrieflyrecapthemaintsunamihazardandriskassessmentmethods,discussingthemainspecificitiesthattsunamihazard/risk quantifications have with respect to other hazards. Then, in Section 2.3, wecompare the different methods, providing examples from the ASTARTE case studies anddelineating some guidelines for the comparison of the results obtained when differentmethodsareadopted.


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2.1Stateoftheartfornaturalhazards

Asdiscussed inSection1, thegeneral framework for thequantificationofuncertainties inrisk analyses has been anticipated inASTARTE in deliverableD4.13, in order to provide ageneral homogenized reference framework for the assessments at an early stage of theproject.Here, this framework is firstdiscussed inmoregeneral terms,withoutspecificallyreferringtotsunamis.

The quantification of risk induced by natural phenomena is commonly based on thecombinationof threemainrisk factors: theprobability thatacertaineventwilloccur, thevalueoftheassetsthatmaybeaffectedbytheeventandtheextentofdamagesthattheeventmayinduceintheseassets.Thus,itisoftenquantifiedby

R=H×L×V (2.1)

where H is the hazard, V the vulnerability, and L the value at risk (e.g., EN 1050, 1997;Marzocchietal.,2012a).Equation2.1isobviouslyasimplificationsincehazard,vulnerabilityand value cannot be satisfactory described by single values. This equation is rather aconceptualnonquantitativedescriptionoftheproblem.Itshouldbealsoclearthatriskisanon-normalizedprobability,withazerolowerlimit(noappreciablepossibilityofanadverseevent or the event cannot cause damages), but not necessarily an upper limit (unlessEquation 2.1 is provided as percentages of the area’s total value, i.e., normalized risk,Marzocchietal.,2012a).

Inthenextsubsections,wefirstdiscussthebasicprinciplesallowingforthequantificationofuncertainties (Section2.1.1) inhazardand riskassessments. Then,wediscuss thegeneralformulation(Section2.1.2)thatisrequiredtoquantifysuchuncertainty,discussingindetailsthemostcommonfactorizations(Section2.1.3)ofhazardandvulnerabilityassessment.Thisquantificationframeworkleadstoarathercomplexcomputationalframeworkthat,inmanycases,requiresspecificsimplificationstrategiestobeadoptedinrealcasestudy.InSection2.1.4,webrieflydiscussthemostcommonsimplificationstrategiesadopted.

2.1.1Quantificationofuncertaintiesinhazardandriskassessments

Anaturalevent(e.g.,anearthquake)maygenerateaphenomenon(e.g.,seismicwaves)thatreaches a place andmay cause damages.Different eventsmay cause similar phenomena(e.g., different earthquakesmay cause similar ground shaking at a given place). Also, thesamephenomenonmay cause different damages (e.g., similar ground shakingmay causedifferentlevelandtypeofdamagetooneasset).Thisisduetothenaturalvariabilityofthephenomenonthatisusuallyreferredtoasaleatoryuncertainty.

Hence,sinceunpredictableinthestrictsense,onewoulddesiretoknowtheprobabilitythata certain type of damage will occur in the future, considering this natural variability. To


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answertothisapparentlysimplequestion,aprobabilisticformulationofhazardandriskisrequired.

The basic principle of the probabilistic formulation is that – ideally – all the potentialsourcesandthepotentialconsequencesshouldbetakenintoaccount,inordertoquantifytheprobabilitythattheoddconsequence(e.g.,thecollapseofonebuilding)happenswithina timewindow (exposure time). To do this, the total hazard or risk can be computed byapplying the theorem of total probability, which expresses the total probability of anoutcome in terms of the conditional probabilities of the events through which it can berealized. This means that the potential consequences that all the possible sources maycause should be quantified and combined, by weighting them by their probability ofoccurrence. Inpractice, thismeans thatanyhazardor riskquantification should take intoaccount all the potential sources that may cause the phenomenon (e.g., variability inearthquakegeneration),theuncertaintiesrelatedtothepropagationfromsourcetotargetofthehazardousphenomenon(e.g.,forseismicwavespropagation),andofthegenerationofdamages(e.g.,variabilityintheresponseoftheasset).

Inprobabilistichazardandriskassessments,allaleatoryuncertaintiesareformallyincluded,asitwillbediscussedinSection2.1.2.However,alternativeformulationsoftheprobabilisticframework, also concerning the very physics andmodelling of the problem at hand, areusually possible. Due to our limitations in the knowledge of the studied system and thepaucityofpastdata,weoftencannotquantitativelyselectamongscientificallyacceptable(not falsifiable) alternative models. This uncertainty is usually referred to as epistemicuncertainty. Note that the definition of aleatory and epistemicmay be source of debateamong practitioners. In the followings,we refer to the definitions and discussion alreadyaddressedinSection1ofthisdeliverableandinthepreviousD4.13,whileadoptingaquitepragmaticapproachinthepresentdiscussion.

The quantification of epistemic uncertainty derives from alternative applications of theprobabilistic formulation,adoptingdifferentmodellingchoices foroneormoreof theriskterms. The application of these alternatives, along with the quantification of therepresentativenessofsuchalternativeswithinthetechnicalcommunity,isusedtoquantifytheso-calledcommunity (orensemble)distribution(e.g.,Bommer,2012;Marzocchietal.,2015)describingtheepistemicuncertainty(e.g.,SSHAC,1997).

Alternative formulations can be separated into two main broad groups, exploring thevariability of the values of parameters within statistical models or, on the other side,exploring theone related toalternativemodelsandparameterizations (e.g.,BommerandScherbaum, 2008; Rougier et al., 2013). Many methods have been proposed to treatparameter uncertainty (e.g., Kijko and Sellevoll, 1992; Straub and Der Kiureghian, 2008;Koutsourelakis,2010;FranchinandCavalieri,2013;Keller,2014).MostofthemarebasedonhierarchicalBayesianprocedures,inwhichstatisticaldistributionsontheparametersvaluesare adopted to model their potential variability. Conversely, few methods have been


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proposed in geosciences to treat both sources simultaneously. In the scientific literaturedealingwithnaturalhazards,differenttechniqueshavebeenadoptedindifferentcontexts,suchaslogictrees(fromKulkarnietal,1984),ensemblemodelling(TothandKalnay,1993;AraujoandNew2007;ClokeandPappenberger, 2009;Marzocchi et al., 2015; Selvaet al.2016)andBayesianmodelling(Gelmanetal.,1995;StraubandDerKiureghian,2008;SelvaandSandri,2013;Selvaetal.,2013).Othermethodsaremorestrictlyrelatedtoextracttherelevantinformationdirectlyfromexperts,likestructuredexpertelicitationmethodsbasedonmathematical aggregation (e.g., Cook, 1991; Bedford & Cook, 2001; Neri et al., 2008;Morgan, 2014), or on behavioral aggregation based on complex group interactionprocedures(e.g.,DelphimethodsasinLinstoneandTuroff,1975;multiple-expertintegrationasinSSHAC1997,Budnitzetal.,1998,USNRC2012).

Thedevelopmentofalternativesisoftenproducedinamultiple-expertcontext(SSHAC1997and following specifications), in order to standardize all the procedural aspects of expertinteraction,andproducemorerobustresults.ThisspecifictopicisdiscussedinmoredetailsinSection3.


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2.1.2Basicformulationofprobabilistichazardandriskanalyses

AmorecomprehensiveformulationofriskthanthatinthegenericdefinitionofEquation2.1isbasedonthequantificationofaleatoryuncertaintybymeansof riskcurves.Riskcurvesrepresenttheprobabilityofexceedingdifferentlosslevelsduetothepotentialoccurrenceofaclassofevents(e.g.,earthquakes,volcaniceruptions,tsunamis,floods,etc).

Morespecifically,theriskcurveduetoagenericeventEforagivenareainagivenexposuretimeDTrepresentstheprobabilitythatagivenlossvaluelisovercomeinatargetareaandin theexposure timeDT. IndeliverableD4.13,wediscusseda formulation representingasimplification of the Pacific Earthquake Engineering Research (PEER) formula (Cornell andKrawinkle,2000;DerKiureghian,2005),thathasbeenproposedasgeneralformulationforany kind of natural risks in several papers (Marzocchi et al., 2012a; Selva et al., 2013,Mignanetal.,2014)andEuropeanprojects(Marzocchietal.,2009;MATRIX:Liuetal.,2015;STREST:Espositoetal.,2017).Thisformulationreads:

𝝀 𝑳 ≥ 𝒍; 𝚫𝑻 = 𝑮 𝒍 𝒅 ⋅ 𝒅𝑮 𝒅 𝒉 ⋅ 𝒅𝝀(𝒉)𝒉𝒅 (2.2)

where

• lrepresentsalossmeasureinaspecificmetric(e.g.,economicloss,casualties,dead);drepresentsagivendamagelevel(rangingfromnodamagestocompleteloss);hagivenhazard intensitymeasure (typically,butnotnecessarilya scalar). Indifferentcontexts, theyaregivendifferentnames. Forexample, in seismicengineering,h isoften referred to as IntensityMeasure (IM),d as DamageMeasure (DM) and l asdecisionvariable(DV)(e.g.,YeoandCornell,2005).

• l(x)representsthemeanannualrateofexceedanceofagenericvariablex.

• G(y|x) represents a conditional survivor function, that is, G(y|x) represents theprobabilityofexceedanceofy,conditionedtothevaluex.

Thehazardintensitymeasureh isusually(butnotnecessarily)selectedasascalarvariablethatwellcorrelatewithdamages(e.g.,Pinto,2007).Incommonpractice,allthevariablesh,dand lareevaluatedatadiscretenumberoflevels,eachofthemeffectivelyrepresentinganentire intervalofpossiblevalues (e.g.,NIBS,2004).A rougherdiscretization is typicallyadoptedforthedamagemeasure,whichisoftendefinedoverarelativelysmallnumberofpre-definedlimitstates(e.g.,Minor,Moderate,ExtensiveandCompletedamages).

The curve l(h) represents themean annual rate of exceedance of a given value for thehazard intensity h, and it is typically referred to ashazard curve (e.g., SSHAC, 1997). Thehazard curves are usually quantified adopting a computational approach, that is, bymodelling the occurrence of all possible sources and the propagation of the hazardous


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phenomenon from the source to the target, and then aggregating the results into thehazard curves as absolute or exceedance probabilities or rates of a set of pre-definedintensitythresholds.

Analternativeapproach is theempiricalone, inwhichdataat the targetareused to fitaprobabilistic model. Usually the computational approach is preferred over the empiricalone, since (especially for rare events like earthquakes, tsunamis, volcanic eruptions, etc.)thepastdatararelymaycompletelycoverthefullvariabilityofpossiblehazardintensities.

ThedistributionG(d|h)representsthefragilityfunctionofagiventargetasset,thatis,theprobabilitythatthedamageleveldisovercomeduetoahazardintensityh(e.g.,ALA,2001;NIBS, 2004). In their original form, fragility curves have been introduced in seismic riskanalysisand theyquantify theprobabilityofa structurebeingdamagedbeyondaspecificdamagestateforvariouslevelsofgroundshaking(e.g.,ALA,2001;NIBS,2004).Sincethen,fragility curveshavebeenwidelyadopted in seismic lossand riskassessments (e.g.,NIBS,2004;CornellandKrawinkler,2000;Pitilakisetal.,2006). Indeed, theynotonlyprovideaquantitative base for risk quantification accounting for uncertainties, they also providecontributes in the retrofitting decisions, emergency response planning and estimation ofdirect and indirect losses of built environments aswell as lifeline systems (Pitilakis et al.,2006;Kapposetal.,2008;Azevedoetal.,2010).Morerecently, fragilitycurveshavebeenadoptedforotherhazards(e.g.,Spenceetal.,2005;Suppasrietal.,2013),andhavebeenproposedas thegeneral framework for vulnerability assessment for all natural risks (e.g.,Douglas,2007;Schmidtetal.,2011).Manymethodsareusedtoquantify fragilitymodels,suchastheempiricalmethodbasedonfittingastatisticalmodeltopastrecordeddamages(e.g.,Basözetal.,1999;Maruyamaetal.,2010;RossettoandElnashai,2003;Suppasrietal.,2013), analytical modeling of the structures (e.g., Akkar et al., 2005; Moschonas et al.,2009), expert judgment (e.g., ATC-13, 1985; ATC-25, 1991) or on a combination of suchmethods(hybridmethods,e.g.,Kapposetal.,2006;forbuildings).

The distribution G(l|d) is the probability that a given loss level l is overcome, given thedamage leveld. Inpractice, theexpectedcosttorepairagenericasset isoftenwrittenasfractionofthetotalreplacementcostandacostdamagefactorthatdefinesthefractionofreplacementcostnecessarytorepairafivedamagestated(StergiouandKiremidjian,2006).

The results of the convolution of Equation (2.1.2) is l(l) that represents the cumulativemeanannualrateofexceedanceofagivenvalueoflossl.Thecurvel(l)istypicallyreferredto as risk curve. Inorder to allowa simpler comparisonamong the same risk indifferentareas, aswell as, different risks in the same area, a single-risk index is often considered,insteadofusingthewholeriskcurve(e.g.,Marzocchietal.2009).Asriskindex,theaverage(mean)oflossesinthetargetareaintheexposuretimeisoftenconsidered.Inthecaseofearthquakes,bynormalizingtheaverageper1year,thisriskindexisreferredtoasAverageAnnualEarthquakeLosses(AELinNIBS,2004;FEMA,2008).


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AllthetermsofthisformulationareassumedvalidandstationarywithintheexposuretimeDT. Starting from l(l), it usually quantifies the probability of observing at least oneexceedance episode within the exposure timeDT. To do that, it is required to define agenerationprocess,whichisusuallyassumedtobePoisson(startingfromCornell,1968).Inthiscase,theprobabilityofobservingatleastoneexceedanceepisodeinDTiscomputedas1minustheprobabilityofobservingexactly0exceedances,thatis:

𝐏𝐫 𝑿 ≥ 𝒙;𝜟𝑻 = 𝟏 − 𝐞𝐱𝐩(−𝝀 𝒙 ⋅ 𝚫𝑻) (2.3)

In several cases, the Poisson process hypothesis does not really hold. For example,earthquakesaretypicallyclusteredinspaceandtimeand,toadoptthePoissonassumption,the analysis is referred to the so-called mainshocks (main events in each cluster),individuated through a declustering procedure of the original catalogue of events (e.g.Gardner and Knopoff, 1974; Reasenberg, 1985). Analogous reasoning can be made fortsunamis(e.g.,GeistandParsons,2008).

Epistemicuncertaintyarisingfromtheadoptionofalternativemodellingprocedurescanbequantified by modelling the different probability values obtained, for example, fromEquation(2.3).Thisvariabilitycanbeinterpretedintheframeworkofensemblemodelling,asintroducedbyMarzocchietal.(2015)and,specificallyfortsunamisofseismicorigin,bySelva et al. (2016). In this framework, as previously discussed, aleatory uncertainty isquantified by objective probability θ that represent the expected long-run frequencies ofrandomeventswithinthemodelofthesystem.Epistemicuncertaintiesmeasurethelackofknowledge in the estimation of θ. This uncertainty is quantified through a probabilitydistribution,describedbysubjectiveprobabilities,thatdescribes‘thecenter,thebody,andthe range of technical interpretations that the larger technical community would have iftheyweretoconductthestudy’(SSHAC,1997;USNRC,2012;Bommer,2012;Marzocchietal.,2015;Selvaetal.,2016).

Toquantifysuchcommunitydistribution,afinitesetofdifferentmodels{θi,ωi}(i=1,...,N)canbedeveloped,whereθiandωi aretheoutcomeandtheweightofthe i-thmodel.TheNdifferentmodelsdescribethevariableofinterestθ,thatis,inthiscase,thehazardorrisk curve of Equation (2.3). Each alternative model is considered as a sample of theunknown parent distribution f(θ), the community distribution. In order to produce aconsistent ensemblemodel, the set of samples andweights {θi ,ωi} should represent anunbiasedsampleoftheepistemicuncertainty(seediscussioninMarzocchietal.,2015),thatis, they should consistently represent the variability of models and opinions within thereference community. The development of alternatives and the quantification ofweightsshouldthereforeemergefromamultiple-expertprocess(e.g.,SSHAC,1997),asdiscussedinSection3.


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2.1.3Factorizationofriskfactors

Further factorizations are typically introduced in each of the factors inEquations 2.2, forboththehazardandthefragilityfactors.

AsdiscussedinthedeliverableD4.13forPTHA,whileempiricalapproachestargettoassessdirectlythehazardcurvesfrompastdata,incomputationallybasedhazardassessmentsthehazardfactorisoftenfactorizedbysourceandpropagationcontributions:

𝜆 ℎ = 𝐺 ℎ 𝜎 𝑑𝜆(𝜎)? (2.4)

where,again,hrepresentsthehazardintensityatthetarget,andlandGrepresentmeanannualratesandaprobabilisticsurvivorfunction,respectively,whiles representsasinglepossiblesourceinthesetSthatincludesallthepossiblesourcesthatmaycauseanintensityxatthetarget.Thisfactorizationallowstoseparatetheanalysisofsourcesσ,theiraleatoryvariabilityΣandtheirmeanannualfrequenciesλ(σ),foranyσ∈Σ,fromtheanalysisofthepropagationofthetsunamifromanysourceσtothesiteofinterest.

Thesourcefactorl(x)isusuallyfurtherfactorizedinatleasttwoparts(fromCornell,1968),expressing the size of the event (e.g., magnitude for an earthquake, volcano explosivityindex or intensity for volcanic hazard, volume for landslides) and a spatial factor (e.g.,hypocentres,ventpositionandlandslideposition,forearthquakes,eruptionsandlandslides,respectively).Furtherfactorsdodependonthespecifichazardunderconsideration.Thesesubfactors are usually quantified using an empirical approach, that is, a statisticalmodelfitted to the empirical data (e.g., smoothed seismicity fitted to a seismic catalog, e.g.,Hiemeretal.,2014).

The propagation factorG(h|σ) quantifies the probability that a given hazard intensity isovercomeatthetarget,giventheoccurrenceofthesourceσ,thatis,G(h|σ)=Pr(H≥h|σ).Depending on the specific problem, this probability distribution may include differentprocesses, like boundary conditions for the propagation like wind for tephra fallout ofvolcanic hazard (e.g., Costa et al., 2009), or intra-event variability of ground motionprediction equations (e.g. Cotton et al., 2008). It can also include some variability notincludedinthesourcemodelling,liketheintra-eventvariabilityofgroundmotionpredictionequations,orearthquakeslipdistributionfortsunamihazard(e.g.,Daviesetal.,2017).Forsomehazards(e.g.,seismichazardorregionaltsunamihazard),thisprobabilityisfactorizedin propagation and site amplification (e.g., Field et al., 2000; Løvholt et al, 2012). Thequantification of this propagation factors may be based on empirical data (e.g., groundmotion prediction equations of seismic hazard), or on explicit (time-domain) numericalmodelling(e.g.,tsunamiorvolcanichazard).


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Alsothefragilityfactormaybefurtherfactorized,dependingontheanalysis.Forexample,in seismic risk analysis (e.g., Yeo and Cornell, 2005) the fragility factor is sometimesfactorized by considering the engineering demand parameters (EDPs) as an intermediatefactorbetweenhazardintensityhanddamaged,thatis

G 𝑑|ℎ = ∫ 𝐺 𝑑 𝑒𝑑𝑝 ⋅ 𝑑𝐺(𝑒𝑑𝑝|ℎ) (2.5)

In practice, this means that the hazard intensity is first translated in what the structureshould do to resist to the hazard sollicitation (demand), and the probability that a givenstructure can sustain thisdemand.Thequantificationof these factors isusuallybasedondirect modelling of the structures, adopting a variety of empirical hazard inputs (e.g.,groundmotiontimehistorycausedbyagivenearthquake).

2.1.4Commonsimplificationsofthegeneralformulation

AsdiscussedinSection2.1.2andSections2.1.3,theassessmentofthefactorsofEquation2.1andthequantificationoftheepistemicuncertaintythroughthecommunitydistributionare rather demanding, in terms of scientific and computational effort. There is indeed aclear trade-off between the computational feasibility and the exploration of uncertainty(e.g., for tsunamis, and relatively to the computational cost of high-resolution inundationsimulations,Loritoetal.,2015).Forthisreason,severalsimplificationapproachesareoftenadopted.

The level of simplification should in theory depend on the regulatory concern of theassessment (e.g., nuclear power plant vs small infrastructures) and/or the type (and thecost)ofdecisionsthatwillbebasedontheassessment(e.g.,SSHAC,1997;MarzocchiandWoo, 2009; Esposito et al., 2017). For example, if there is no regulatory concern or thedecision tobe takendoesnot imply significant societal and/oreconomical consequences,large simplificationsmay be acceptable.Other important examples of the dependency ofthelevelofthesimplificationonthegoaloftheassessmentincludethescaleoftheproblem(if the analysis is required at a regional scale, many site-specific details and modellingsophistications can be avoided), the sensitivity of the results on model sophistications(specificrequirementsareonlysometimesrequired;forexample,spatialcorrelationscanbeinmanycaseneglected,sincetheyareoftenrequiredonlyifthereareinter-dependenciesamongspatiallydistributedcomponents,e.g.,Argyroudisetal.,2015),or theamountandthe quality of the available data (there is no need of sophistications if the epistemicuncertaintywillhidetheirimpactand/orthedatacannotsupportthesophistications).

Manydifferentsimplificationsstrategieshavebeenselected in literature,basedmainlyonreducing i) the quantification of the epistemic uncertainty, ii) the quantification of thealeatoryuncertainty,and/oriii)thetotalcomputationalcost.


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The simplification in the quantification of the epistemic uncertainty is typically based onreducing the number of alternatives to be implemented, even to the limit of onemodelimplementation (no epistemic uncertainty). In other cases, only the mean or the modalmodelsareconsidered.Anotherpotentialsimplificationarisesinhowalternativemodelsareselectedandweighted(e.g.,seedefinitionsoflevelsinSSHAC,1997).

Thesimplification in thequantificationof thealeatoryuncertainty isusuallybasedon thereductionofthesourcevariability.This isreducingthenumberofdiscretescenariostobeaccountedfor,byadoptingcoarserandcoarsergridsorsimplificationstrategies likeEventTrees(fortsunamisofseismicorigin:Loritoetal.,2015;Selvaetal.,2016).Thisreductionisoften pushed toward the adoption of very few scenarios, like for example the use ofreference scenarios. In these cases, themost critical pointbecomes the selectionof suchreferencescenarios.

Thereductionofthetotalcomputationalcostisusuallyobtainedbyreducingtheresolutionandthenumberoftimesthepropagationmodelsaretobeused.Propagationmodelsareindeed typically highly sophisticated and computationally challenging. Depending on thecases,onepossibleandoftenadoptedstrategytoreducethecomputationalcostofhazardand risk assessments by replacing the direct propagationmodellingwith analytic or verysimplifiedmodels(e.g.,IAEA-Volcanoes,2012),aswellas,fullyempirical(statistical)laws(asforearthquakeGroundMotionPredictionEquations,e.g.,Cottonetal.,2008).

Anotherdrastic simplificationof thecomputational cost is tobuild theanalysisonlyuponpastobservations,asfortheempiricalprobabilistichazardassessments(e.g.,fortsunamis:Geist&Parsons2006).However,computationallybasedanalysesareusuallypreferred,duetothescarcityofpastobservations. Indeed,suchdatacannotfullyrepresenttheeffectivevariability of potential phenomena at source and at target (e.g., for tsunamis: Geist &Lynett,2014),especiallyinthetailsofdistributionswhereeventsareveryrare(e.g.,Geist&Parsons,2014).


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2.2 Stateoftheartfortsunamis

This section focusses on comparing the quantification frameworks and simplificationsusually adopted for tsunami hazard and risk assessments with the general assessmentframework discussed in Paragraph 2.1. Some examples concerning the modelling of thetsunamisourcesandthesimplificationsthatcanbemadeinviewoftsunamihazardanalysishavebeenalreadydiscussedinD3.40,whichistheninthisrespectcomplementarytothisdeliverable.

Here,inparticular,inSection2.2.1wehighlightthemainpeculiaritiesthattsunamishaveincomparisonwithothernaturalhazards. InSection2.2.2,we recap fromdeliverablesD8.8,D8.14 and D8.33, andwe describe themainmethodologies adopted in ASTARTE, also incomparisonwiththesepeculiarities.

2.2.1Comparisonbetweentsunamisandothernaturalhazards

With respect toothernaturalhazards, tsunamishave severalpeculiarities that influencedthedevelopmentofmethodsforthequantificationofuncertainty. It ispossiblethatthesepeculiaritiesled,intime,tomanysimplificationsthatarereflectedinthemethodsadoptedfortsunamiriskandhazardquantificationmethods.

The attention to quantitative uncertainty assessment was only lately taken intoprogressivelymoreseriousconsideration,mainlyafterthe2004IndianOceantsunami.Onereason for this is that both the 2004 Indian Ocean and the 2011 Tohoku tsunamis werecaused by earthquakes of a magnitude which was unanticipated at that locations. Somefeatures of those earthquake ruptures had probably never testified before, such as therupture length on one hand for the Sumatra-Andaman earthquake, and the amount andcharacteristics of the slip distribution (e.g. the huge slip close to the trench); taken as awhole, these two events document the possibility of a large variability around themeanvaluesofempiricalearthquakescalinglaws.Severalotherearthquakesandtsunamisinthelast decadeor sohave shown somehow surprising features aswell (see e.g. Lorito et al.,2016).ItismoreoverwellknownthattheTohokuearthquakealsoraisedseriousquestionsonhowtoimprovetsunamiwarningsystemsaswellastoincreasetheresilienceofcoastalcommunities.

Indeed, fully probabilisticmethods that quantify (epistemic) uncertainties havebeenonlyrecently developed for tsunami hazard but mainly focussing in the treatment of seismicsources (e.g. Selva et al., 2016; Davies et al., 2017); and sometimes only for somecomponentsofthetsunamiriskassessment(forexampleonlythePTHA:Chocketal.,2016).


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Somepeculiarfeaturesoftsunamis(notnecessarilyexclusive)whichinfluencetheprocessofhazardandriskassessmentarebrieflydiscussed inthenextpages.This ishowevernotmeanttobeanexhaustivediscussion,butastartingpointforfuturediscussions(e.g.withinthe GTM); the purpose is only to highlight with some examples the need for properuncertaintyquantification.

Tsunamisarelowfrequencyhighimpactnaturaldisasters.Adirectimplicationofthisisthatthepasttsunamiobservationsarerelativelyscarce,andthatcomputationally-basedhazardassessments are complex and characterised by an inherent high uncertainty; but thechallenge is worth the effort given the potentially disastrous consequences of tsunamis.Appropriatemethodsneedtobeusedfortakingintoaccounttheuncertaintyassociatedtorareevents(e.g.GeistandParsons,2014;Daviesetal.,2017),forexampleinthetailsoftheearthquakemagnitude frequencydistributions,whicharerelativelyunconstrainedbydata(tooshortcatalogues),andcausethe largest tsunamis,as tsunami impactdoesn’t tendtosaturateforhighmagnitudesasearthquakeimpactmaydo.Therarityoftheeventsinturnalsomeansthatinmanyareasoftheworldthereisnecessarilyarelativelypoorawarenessof tsunamis, even in areas where well-documented and very large historical tsunamishappenedinrelativelyrecenttimes(e.g.,LisboninPortugal,MessinainItaly).

Tsunamis are multi-source hazardous phenomena. They can be generated by differentsources (e.g., Geist and Lynett, 2014), including earthquakes, landslides, volcanoes, andevenmeteorologicalandastronomicalevents.Thesesourcesareusuallystudiedbydifferentand non-overlapping communities, in which different methods have been developedthrough time. In addition, in the different fields, very different levels of knowledge anddifferent standards exist, also due to the differences in source complexity and tsunamigenerationmechanism,ortothevariableextenttowhichispossibletoconstrainthesourcerecurrence.SeeD3.40 foradiscussionofsomeof these issues,particularlyas regards thecomplexityof tsunami sourcemodeling. Fromanhazardand riskassessmentperspective,instead, we note that, in the seismological community, the probabilistic treatment ofsources is pretty well established (since Cornell, 1968); this treatment has been ofteninherited in PTHA studies from PSHA, as discussed also below. In other fields, like involcanology, tsunamis arewell known tohappen,but theyare rarely included in volcanichazarddocuments (Pariset al. 2014). In these fields, tsunamishavebeen studiedonlybyanalysing specific case studies (e.g., Tinti et al., 1999). In many cases, these difficultiesprobably led either to focus mainly on the propagation and shoaling of the tsunamis,limitingthesourcevariabilitytoacollectionoffewscenarios(Toninietal.,2011),ortofocusmainly on a homogenous treatment of sources, limiting the quality of propagationmodelling (e.g., Grezio et al., 2012). Still, these are quite remarkable attempts of multi-sourcetsunamihazardmodelling.

Thecomplexityof the tsunamipropagationand impact ishigh.Systematicanalysesof thesource uncertainty and its consequences in tsunami hazard and risk quantification have


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beendevelopedbylimitingthesourcevariability,thatis,bymodellingonlyoneoftypesthepotentialsourcesfortsunamis.Forexample,inseismology,thetreatmentofsourcesiswellestablished.Thistreatmentcanbenaturallyextendedtotsunamis(e.g.,GeistandParsons2006). Inthesecases,tsunamisareseenaspurelysecondaryeventsofearthquakes,tobepropagated from source to target as seismic waves. However, in the seismologicalcommunity, it iswellestablishedtheuseofempirical lawstomodel thispropagation, theso-calledGroundMotion Prediction Equations (e.g., Cotton et al, 2008).On the contrary,tsunamis force to propagate explicitly waves from source to target (e.g., Sørensen et al.2012; see also Geist, 2009, for a review). This introduced a trade-off between theexplorationofthevariabilityofsourcesandtheaccuracyinmodellingpropagation(Loritoetal.,2015).Thistrade-offleadtoadichotomybetweenregionalstudies(withpropagationondeepwateronlyandsimplifiedamplification,likeSørensenetal.,2012;Daviesetal.,2016)and local studies (with propagation modelled in nested grids, but conversely simplifiedsourcevariabilitymodel,likeGonzálezetal.,2009).Onlyrecently,specifictechniqueshavebeendevelopedtotryandsolvethisdichotomy,basedontheselectionof“representativescenarios” that statistically approximate the full source variability (Burbidge et al., 2008;Thioetal.,2010;Mitsoudisetal.,2012;Loritoetal.,2015).

Tsunamisaresensitivetosourcefeatures.Somesourcecharacteristics(seealsoD3.40)mayhave limited or less important effects on “primary” hazards like earthquakes themselves.For example, Ground Motion Prediction Equations (GMPE) usually depend only on fewspecific characteristic of sources (usually, magnitude, distance and, sometimes, tectonicregime, e.g., Bazzurro and Cornell, 1999; Cotton et al., 2008); even if near-source effectsmay be important also in this context and there is recent research devoted to that (e.g.,STRESTProject).Othersourceparametersareincludedintothestatisticaltreatmentoftheempirical models. For example, fault geometry and dimensions are included into thecomputation of the source-target distance for GMPEs. Such approaches are notsatisfactorilyyenoughinPHTA,wheredefiningindividualscenariosisessentialfortsunamimodelling (e.g., Sørensen et al., 2012), such as the dip and the slip distribution whichdetermine the features of the initial sea level elevation, tsunami energy focussing in thebroad-sideofthesourcedirection,andthefollowingcomplexinteractionwithbathymetry(seee.g.Geist,2002;Geist,2009;Geist,2012).Moreingeneral,tsunamismaybesensibletospecificcharacteristicsofthesourcesthatmaynotberelevant intheoriginalhazard(e.g.,theseismichazard),andthatinsteadrequireaspecialtreatmentofuncertainty(Selvaetal.,2016).

The strategies to tsunami risk mitigation are diverse. Another important peculiarity oftsunamisisthatthewavepropagationisslowcompared,forexample,toseismicwaves.Thismakes the early warning strategy very effective, especially in large seas like oceans fordistant tsunamis, while near-field tsunami warning presents some issues and must becomplemented by a very good preparedness to respond to natural signs of a strongearthquake and tsunami possibly coming (intense and/or very long ground shaking, sea


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withdrawal,roars,etc.).Inadditiontothis,tsunamihazardmaybemitigatedbythedesignofspecificcoastalstructures,suchascoastalwallsandverticalevacuationstructures;andbyawiseland-useplanning.Boththesepossibilitiesarepartlyoressentiallydependentofthedevelopment of good propagation models, as well as, in efficient near-real-time sourceinversion, like for example implementedbyUSNOAAPMEL,or for theGiTEWS,orunderdevelopment forotherregions in theworld.Nevertheless,astrongattention isneeded inthiscontexttootoprogressivelyimprovetheeffectivenessofrisk-reductionmeasures.

Tsunamis have multiple paths to damages. Tsunamis pose both a direct and an indirectthreat to people, that is,may kill both directlywhen a tsunami hit people and indirectlywhenatsunamihitsabuildingthatcollapses,potentiallykillingpeople inside. Inaddition,tsunamisareusuallygeneratedbyanotherdangerousevent(e.g.,anearthquake)thatmayhavealreadypre-damaged(e.g.,Iervolinoetal.,2016)onestructure,orsimplyalteredthedistributionofpeople(e.g.,Selva,2013).Also,cascadenon-naturalphenomena like inthecase of the Fukushima nuclear disaster may be triggered which determine an hugeworsening of the tsunami consequences. The study of this type of paths to risk hasincreased the difficulty of risk assessments and often lead to the development of eithersimplified risk models or the selection of few scenarios, neglecting uncertainties. Morerecently,severaltechnicalsolutionstodealwiththisproblemhavebeendevelopedintheframeofsingleandmultiple-hazardriskassessments(e.g.,Selva,2013;Mignanetal.,2014;Liuetal.,2015;Chocketal.,2016).


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2.2.2HazardandriskquantificationmethodsadoptedinASTARTE

FollowingthegeneraldefinitionofriskexpressedbyEquation2.1,theASTARTEConsortiumhastackledseparatelythehazard,vulnerabilityandriskassessmentproblems,drawingupthreedistinctdocuments(D8.8,D8.14andD8.33).Eachofthemcontainsamethodologicalintroductory part, followed by a more extensive description of the application of themethodologiestotheASTARTEtestsites.Weprovidehereashortrecapofmethodologicalapproachesforthehazardandvulnerabilityquantification,detailedrespectivelyinD8.8andD8.14.Wewill referneither toanyspecific resultnor toanyspecificpartner,keeping thediscussionatamethodologicallevel.

TsunamiHazard

Regardingtsunamihazardassessment,twomaingeneralapproacheswerefollowed:

- ProbabilisticTsunamiHazardAnalysis(PTHA)

- (credibleworst-case)Scenario-Basedapproach(SBTHA)

In line with what was already recalled in the previous sections for probabilistic hazardanalyses, themaingoalofPTHA is todetermine theprobabilityofexceedanceof a giventsunamimetric (flowdepth, run-up, current speed,etc.)overagivenexposure time foraselectedcoastalarea/site,quantifyingbothaleatoryandepistemicuncertainty.Toreachthegoal, two different philosophies were adopted in D8.8. One was computationally-basedPTHAthattargettoafulltreatmentofuncertaintyasdescribedinSection2.1.InASTARTE,the PTHA analyses have been limited to seismic sources only, and thus they are hereinreferredtoasSeismicPTHA(S-PTHA;fromLoritoetal.,2015).S-PTHAisacomputationally-based method that takes into account all potential (tectonic) tsunamigenic sources,irrespective ofwhether it is known that they generated or not tsunamis in the past. Thepotentialtectonicsourcesarefullycharacterised intermsofmagnituderanges,geometry,focal parameters and activity rates. For each of the resulting configurations, tsunamigeneration, propagation and inundation at the selected coastal area/site are simulatednumerically.

The other general approachwas referred to as Empirical PTHA: it takes as reference theeffectsoftsunamisrecordedinthepast,typicallymaximumrun-upsforeventsoccurredinthe pre-instrumental era (the largest part in the NEAM region) and tide-gauge and deepocean sensor records for more recent events. These are treated statistically to retrievetsunamiactivityratesandheight-frequencyrelationships.


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TypicalproductsofthePTHAarehazardcurves,providingtheexpectedmaximumvalueofagiven tsunamimetric (e.g. tsunamiheight) as a functionof returnperiod, and inundationmaps,ormapsofmaximumwaterheightalongapre-selectedoffshoreisobath,fordifferentreturnperiods.Theresultsareusuallyprovidedasaggregateproducts,butde-aggregationisalwayspossiblewhentheeffectofaspecificsourcehastobeanalysed.

Similarlytocomputationally-basedPTHA,SBTHAheavilyreliesuponacorrectchoiceofthesourceareasofinterestfortheselectedtargetcoastalarea/site:thisiscarriedoutbymeansof a thorough analysis of catalogues (when available) of historical occurrences of a giventsunamigenicsourcetype,ofavailabledatabases/studiesofpotential/knowntsunamigenicsources,ofthegeomorphologyandgeodynamicsoftherelevantgeographicaldomain.Thisinitial step (choice of the source areas) can be long and challenging: in addition toearthquakes, in SBTHA also landslides and volcanoes can be taken into account, even ifvolcanoes have not been tackled in ASTARTE. This enlarges the spectrum of publishedstudies and data to be analysed. Once the source areas have been identified, SBTHAforesees that for each type of tsunamigenic source identified in each area (earthquake,landslide,volcaniceruption)the“credibleworstcase”isselected.ThisisthemostdelicateandcriticalpointoftheentireSBTHAapproach.Inthecaseofseismogenicfaults,definingthe “credible worst case”means choosing themaximum value for themagnitude of theearthquakesthatagivenseismogenicfaultmightproduce.Thechoicecanbebasedonpastearthquakes,onthegeometryoftheseismogenicarea,onitsbackgroundseismicityand/orstrain accumulation rates.Whatever the criterionor combinationof criteria adopted, themaximumchosenmagnitudeallowstoestablishthegeometryofthefaultandtheslipbasedonscalinglaws.Inthe“credibleworstcase”perspective,thefocalmechanism(faultstrike,dip and rake) is chosen as a trade-off between the constraints posed by localtectonics/geomorphology, and the need tomaximize the tsunamigenic potential and thetsunami energy focussing towards the target area. In the case of landslides, thetsunamigenic potential results from a combination of the sliding mass volume, of thepositionfromwhichthelandslidedetaches(thedepthinthecaseofsubmarinelandslides),oftheexpectedslidedynamics(translationalorrotational),partlyontherun-outdistance.Geomorphologicalandgeotechnicalanalysesareoffundamentalimportanceindefiningatleast some of the above factors, especially the maximum volume of mass that can bemobilisedalongaselectedslope.Unfortunately,itisnotrarethatthistypeofinformationisinsufficientorevenmissing,sothatpurespeculationmustbeused.Foreachoftheselectedsources and related credible-worst-case scenarios, tsunami generation, propagation andinundation at the selected coastal area/site are simulated numerically, usually on nestedgrid configurations allowing fine resolutions (down to few tens of meters of even fewmeters)inspecifictargetareas.

TypicalproductsoftheSBTHAareaggregatedfieldsofmaximumwaterheight(offshoreandinland), flow depth onshore, particle velocities (offshore and onshore), maximummomentumflux(onshore).


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The previous short excursus on the two main approaches for the hazard quantificationadoptedinASTARTE(asemergedfromD8.8)highlightssomeimportantpointsofinterestinlightofthescopeofthepresentdeliverable.

OneofthemostevidentdifferencesemergingfromtheASTARTEapplicationsisthatSBTHAmoreeasilydealswithdifferenttsunamigenicsources:forexamplebyanalysingjointlyandcomparing the effects of several tsunami scenarios generated by both earthquakes andlandslides.EmpiricalPTHAintrinsicallydealswithallsources,sincelocaldataarenotfilteredbasedonthesource.Conversely,computationally-basedPTHAhasbeenappliedhereonlytoearthquakesources,and thusnamedS-PTHA.This limits fornowtheapplicabilityofS-PTHAtothosetestareaswherethemainthreat intermsoftsunami isrelatedtotectonicsources.However,somefirstcasesofapplicationsofcomputationally-basedPTHAtonon-seismicsourcesarebeingdeveloped(seee.g.discussioninGeistandLynett,2014),despiteof somechallenges, including thedifficulty inconstraining thesource recurrence (seee.g.discussioninD3.40).

Limitingtoseismicsourcesonly,itisevidentthatthecomputationaleffortinvolvedbythetwoapproaches iscompletelydifferent. InS-PTHA,allpotential seismogenicsourcesmustbeincludedandweightedaccordingtotheirrelativeprobabilityofoccurrence.Inprinciple,foreachsourceamulti-dimensionalspaceofparametersshouldbeexplored,resultingfromthecombinationofthediscretevaluesthateachrelevantgeometricalandfocalpropertyofthe fault can assume. The often prohibitive number of simulations to be run makes itfeasibleonlytorunlinearsimulationsovercoarseormedium-resolutiongrids, limitingthecomputationoftherelevanttsunamimetricsalongaselectedoffshoreisobath.Ifinundationmappingonfine-resolutiongrids isneeded,thenafilteringproceduremustbeadoptedatthesourcelevel,anexampleofwhichisdescribedinD8.8.Eveninthiscase,however,thenumber of simulations to be computed is verymuch larger than that involved in SBTHA,whereatmost10-15high-resolutionmodelsareproduced.

Another difference regards the “return period” concept, which is a key feature of PTHAmethodologyand results,while it isnotapparent in theSBTHAapproach.This concept isintrinsicallyrelatedtothepossibilityofquantifyingtheuncertaintyofhazardquantificationand,asdiscussedinsection2.4,representsthebasicconcepttomakehazardquantificationcomparable and scientifically testable. Here, we stress that in the “credible-worst-case”perspective the return period is not absent, and even if in some cases it is not explicitlyaddressed, itcanbethoughttobeontheorderoftheknownorhypothesisedrecurrencetimeofthelargest-magnitudeearthquakesthatcanbegeneratedbyagivenfault,henceitisdependentonthespecificcaseanditwouldberecommendabletodiscussitcasebycasewhenperformingSBTHA.


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Finally,asexplainedmoreindetailinthenextsections,whilethesourcesofuncertaintyarevery similar in PTHA and SBTHA, theway they are treated is totally different in the twoapproaches. Limiting to the results developed in ASTARTE, uncertainties were taken intoaccountonlyinPTHA.

TsunamiVulnerability&Risk

ThefirstpartofDeliverableD8.14providesacompletereviewofthemaintopicsrelatedtotsunamivulnerabilitydefinitionandassessment.WebrieflysummariseherewhatwethinkarethekeyconceptsusedinASTARTE.

First of all, it is recognized within the tsunami community that a clear definition ofvulnerability related to tsunamis need to be established: in ASTARTE, we define tsunamivulnerabilityeverythingthatregardsthecharacteristicsandcircumstancesofacommunity,system or asset that make it susceptible to the damaging effects of tsunami hazard.Exposure isanotherconcept that is tightly linkedto thatofvulnerability,consisting in thepresenceofpeople,property,systemsorotherelementsintsunamihazardzonesandhencesubjecttopotentiallosses.Finally,wedefinetsunamidamagethelossorharmcausedbyadestructivetsunami.

Like formanyothergeo-hazards,vulnerability relatedtotsunamiscanbetreatedthroughqualitative,semi-quantitativeandquantitativeapproaches.Givenasetofelementswhosevulnerability is to be assessed (e.g. buildings or people), a qualitative approach assignsattributes to the elements, scores to each element attribute on the basis of some (oftensubjective) criteria and groups them in classes of vulnerability, based on suitablecombination of the scores. In a quantitative approach, as discussed in Section 2.1.2, thevulnerability isdefinedthroughcurvesthatrelatephysical indicators(likefragility/damageforbuildings)orsocial indicators (likemortality inthecaseofpeople) torelevanttsunamimetrics,suchastheflowdepthand/ortheflowvelocity.Itisworthnotingthatuncertaintiesarequantifiedonlyinthecaseofquantitativevulnerabilityquantifications.

The approaches used in ASTARTE D8.14 focussed almost exclusively on buildings andinvolved both a qualitative (PTVA-3) and a semi-quantitative (SCHEMA) approach. Forcomparativereasons,inthepresentdocument(inSection2.3.3),aquantitativemethodwillalso be introduced based on fragility curves, i.e., probabilistic vulnerability models thatdescribetheconditionalprobabilitythatadamagestatewillbereachedorexceededforagivenhazardlevel(seeSection2.1.2formoredetails).

Full details on the PTVA-3 and the SCHEMA approaches can be found in D8.14, togetherwiththeadaptationsmadeforthedifferenttestsites.Herewesummarizeonlytherelevantcharacteristics.

ThebuildingclassificationschemeproposedbytheSCHEMA(SCenariosfortsunamiHazard-inducedEmergenciesManagement)projectwassetupaccordingto intrinsicpropertiesof


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thebuildings, constructionmaterial and structure, including foundation. ItwasbuiltupontheanalysisofthedamagetoconstructionscausedinBandaAceh,northernSumatra,bythe2004IndianOceantsunami(Leoneetal.,2010),withmodificationstoadaptittoEuropeanbuildingstandards(Valenciaetal.,2011).Thetsunamihazardmetric(inSection2.1,calledhazardintensitymeasure)chosenastheoneinfluencingmostthedamageistheflowdepth.Basedonthevulnerabilityclassificationandtheexperimentaldataontsunamiflowdepth,foreachbuildingclassadamagefunctionwasbuilt,providingthemaximumlevelofdamagethatabuildingbelonging to that classmay incur corresponding toagivenmaximumflowdepth. The resulting damage discretization in classes leads to a discretization also of thedamage functions: the result is a damage matrix, with rows and columns coincidingrespectively with the damage and vulnerability classes and with the elements being thediscreteintervalsoftheflowdepth.Thedamagematrixcanbeadaptedtoacertainextenttocopewiththespecificcharacteristicatanygiventest-site.

PTVA isacronymstanding for “PapathomaTsunamiVulnerabilityAssessment”: itwas firstdevisedbytheGreekresearcherPapathomawhoappliedittotheCretantownofHeraklion(Papathoma et al. 2003). PTVA-3 is “version 3” of PTVA and has been introduced byDall’Ossoetal.(2009).InPTVA-3themainvulnerabilityindexisthe“RelativeVulnerabilityIndex” (RVI), which is defined as follows. The first step consists in defining the index ofvulnerabilityofabuilding(Bv):thisisanintegerrangingfrom1to5.Inordertocomputeit,PTVA-3introducesfirstanintermediateindex,Bv’,thatiscomputedbytakingintoaccountsevenstructuralparameters(attributes),eachofwhichisgradedbyascoreselectedbytheevaluatoramongalistofpossibilities.TheindexBv’istheweightedaverageofthesescoreswithweightsthatarenumericalconstantscalibratedinthefield(alldetailsinDall’Ossoetal.2009). By construction, the index Bv’ can take values within the interval [-1, +1] and islinearlymapped and discretized in the integer index Bvwith five levels from 1 to 5. Thesecondsteprequiresthecalculationofthreemorevariablesrelatedtothewatercolumn(ExandWV)andtothelevelofprotection(Prot).TheparameterExdependsdirectlyfromthewatercolumn;WVistheratiobetweenthenumberoffloodedstoriesandthetotalnumberofstories;Protexpressesthelevelofprotectionagainstthetsunamiaccordingtothetypeofobstaclesthatcanmitigatetheeffectsofthetsunamiitself(houses,stonewalls,seawalls,treesorothernaturalprotections).“Natively”,thedifferentparametersmayattainvaluesindifferent intervals: anyway, in the PTVA-3 procedure they are all rescaled to a [+1, +5]interval.Finally,RVIiscomputedas:

RVI=2/3⋅SV+1/3⋅WV (2.6)

where

SV=(BV)x(Ex)x(Prot) (2.7)

SVcanvarybydefinitionbetween1and125,butisthenrescaledtotheinterval[+1,+5]:itisthisscaledvaluethatentersthedefinitionofRVI.ThesameappliestoWV.Asaresult,RVI


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rangesfrom1to5butdoesnotnecessarilyattainanintegervalue.Asaconsequence,thisintervalhasbeenfurtherdividedinto5equalsub-intervalsof0.8extension,correspondingtotherelativeleveloftheexpecteddamageofthebuilding:minor,moderate,average,highandveryhigh.

It is worth stressing that there are still several problems that make the generalizedapplication of such approaches difficult. The most important issue is that the twoapproaches are not computational. In particular, the SCHEMA approach is empirical: theoriginalfragilityanddamagecurvesproposedbythemethodsarebasedonempiricaldatafrom Banda Aceh after the 2004 IndianOcean tsunami, and not analytical and based ondirectmodellingofthetargetstructures(asbrieflydiscussedinSection2.1.2).Thisimpliesthatthestructuresusedtobuildthecurvesaretypicallydissimilartothosefoundinotherplaces,liketheASTARTEtestsites,requiringanadaptationtailoredtoeachsite.Thisisoneproblemthatwouldexistalsointhedevelopmentofquantitativetsunamivulnerabilityandriskbasedonfragility(quantitativemethod),sincefortsunamisonlyveryfewexamplesofanalytical models exist. This may potentially introduce substantial epistemic uncertaintythatcanbequantifiedbyadoptingalternativemodels(seediscussioninSection2.3.3).

Ontheotherhand,PTVA-3isaqualitativeapproachprovidingavulnerabilityclassificationand damage assessment in absence of fragility curves. It is a quite flexible approach inwhich, anyway, the Relative Vulnerability Index defines only a comparative ranking ofdamageamongbuildingsbutcannotdefineanabsolutestateofdamage.


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2.3Comparingtheresultsofdifferentlevelsofsimplificationsintreatinguncertainty:examplesfromASTARTETestsites

Inthissection,wepresentsomeexamplesfromthehazardandriskquantificationsinsomeof the test sites of ASTARTE, with focus in the comparison between different levels ofsimplificationsusedintheseassessments.

2.3.1GüllükBay:ProbabilisticVSDeterministictsunamihazard

DeterministicandprobabilistictsunamihazardanalysesareperformedforGüllükbay.

Accuratebathymetry/topographydata and ruptureparametersof tsunami sourceare therequired inputs for convenient numerical modelling in order to perform tsunami hazardanalysis.Bathymetry/topographydataareobtainedfromGEBCO©with900mresolutioninthesea,andfromASTERsatellitedatawith30mresolutionatland.Inordertoimprovethequalityof thedata in the shallowzoneanddataof shorelineadditionaldigitizations fromnavigational charts are performed. Gridded data sets are developed from the availablebathymetry/topography data and also digitized data for both nested and single domainsimulationswithdifferentgridsizes.

Inthedeterministicapproach,probableworstcaseseismictsunamisources(s18-z22)withtheir estimated rupture parameters and non-seismic tsunami sources (calderamotion ofSantorini andColumbus volcanos)with theirdimensionalparameters aredeterminedandsimulated.

In the probabilistic approach, the data based on seismicmonitoring between 1950-2014years is used and the earthquake magnitudes which may occur in 100, 500, 1000 yearsreturnperiodsarecomputedstatisticallybyextremevalueanalysis.Theruptureparametersaredeterminedwiththehelpofmeasuredruptureparametersfrompastearthquakesintheregion(Kalafat,2009).

The tsunami numerical tool NAMIDANCE is used as the computational tool in numericalmodelling. Simulations are performed for each selected tsunami scenario according to240min simulation duration (for seismic cases) and 300min simulation duration (for non-seismiccases).Simulationdurationsaredeterminedaccordingtodistancebetweentsunamisourceandthestudyregiontoproperlycomputeandvisualizegeneration,propagationandcoastalamplificationoftsunami.Inthedeterministicapproach,nesteddomaingriddeddataareused(DomainBwith270mgridsize,DomainCwith90mgridsize,DomainDwith30mgrid size). Single domain gridded data are used (Domain B with 30m grid size) in theprobabilisticapproach.Nestedandsingledomainsimulationresultsareveryclosetoeachother,hencetheresultscanbecomparedtoeachotherconfidently.


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Someof themain critical regions under tsunami attack in theGüllük bay are selected asnumericalgaugepoints.Amongthose"DidimTekağaç"isselectedasoneofthenumericalgauge location because of the findings of the traces of historical tsunamis (Santorinieruptionapproximatelyin1600BC)fromtheexcavations(Papadopoulosetal.,2012)intheregion.Othervulnerablelocationsintheregionare"FishFarms".Thoseareselectedduetotheir vulnerability not only against stormwaves but also long waves. Another numericalgaugepoint isselectedatGullukvillagecalled"Güllük"wheretheMilasBodrumAirport islocated on the low land area at the end ofGulluk Bay. The commercial port nearGüllükvillage is another critical structure in Gulluk Bay. "Yalıkavak" is selected as anothernumerical gauge point to monitor the probable coastal amplifications around Yalıkavakmarina,nearby touristic coastalutilities and residential areas. The timehistoriesofwaterlevelfluctuationsandcomputednearshoretsunamiparametersforthosenumericalgaugepointsareobtainedtoprovidedataforthetsunamihazardanalysisforGüllükbay.

Among the scenarios in probabilistic analysis, the tsunami due to the 1000 years meanreturnperiodseismicsource(s18-z22)isfoundtocausehighertsunamiparametervaluesinGüllükbayincomparisontoothersources(Acar,2015).Inadditiontothissource,probableeffects of seismic source (s18-z22)with 500 years return period should be considered asimportant tsunami sources for probabilistic tsunami hazard analysis. Maximum waveamplitudesarecomputedas3.7mfor“DidimTekağaç”,3.57mfor“FishFarms”,4.51mfor“Güllük”and3.57mfor“Yalıkavak”.Inaddition,maximumcurrentvelocitiesarecomputedas2.18m/secfor“DidimTekağaç”,1.55m/secfor“FishFarms”,0.47m/secfor“Güllük”and0.33m/sec for “Yalıkavak”. Current velocitynear fish farms is greater than1m/sec (1.17m/secaccordingto500yearsreturnperiodsimulation,1.55m/secaccordingto1000yearsreturnperiodsimulation).

Probabilisticanalysisgivesimportantandreliableresultscomparingtodeterministicseismicsource(s18-z22)results.Extremevalueanalysisgivesearthquakemagnitudesonthesameorderof that selected for thedeterministicapproach.Ruptureparameters (dimensionsofthe fault, surfacedisplacement)areestimatedbythehelpofavailableandvalidempiricalequations.Inthelightofprobabilisticanalysisresults,deterministicseismicsource(s18-z22)hastheprobabilitytooccurwithlessthana500yearsreturnperiod.

It does not seem that devastating tsunami effects and resulting damages may not beforeseeableinthenearfutureinGüllükbayaccordingtotheresolutionofthedatausedforhazardanalysishere.However,marinas, commercialport, aquacultureplants (fish farms),airport,nearbytouristiccoastalutilitiesandresidentialareaslocatedinGüllükbayarestillcriticallocationsevenifasmallsizetsunamientersGüllükbay.Thesecriticalregionswouldbemoreextendedunderthetsunamiwith500and1000yearsreturnperiods. InundationzonesareformedalongGüllükcoastsespeciallyinlowelevatedcoastalareas.


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2.3.2Sines:ProbabilisticVSDeterministictsunamihazard

TsunamihazardassessmentisconductedforSinestest-siteusingbothdeterministic(DTHA)and probabilistic (PTHA) approaches.Only tsunamis of tectonic originwere considered inboth analyses. The tsunami hazard was assessed through deriving high-resolutioninundation maps. Inundation maps depict the spatial distribution of the maximum flowdepths for DTHA, while for PTHA, they show probabilities of exceedance consideringdifferentexposuretimes.

Bathymetric/topographicdatasetwasbuilttoserveaccurateassessmentoftsunamihazardin both deterministic and probabilistic approaches. Another common tool that wasemployed in both analyses is the non-linear shallow water equations code that allowedsimulating the tsunami from the source up to the coast, including inundation. Thetsunamigenic source models, on the other hand, were defined in different ways. In theDTHA,particularsourcescenarios(maximumcredible)wereconsidered.InthePTHA,wherethecontributionofsmallandlargeevents is included,abroadrangeofnear-andfar-fieldpotentialsourceswasused.

A set of bathymetric/topographic data grids is generated to cover the areas from thetsunami source area to the studied test-site. The grids are nested for consecutivecalculations of tsunami generation, propagation and inland inundation. For the near-fieldsourcezone(SWIberiaMargin),fournestedgridlayersofincreasingspatialresolutions(640m,160m,40m,and10m)havebeenemployed.Thefar-fieldtsunamisimulations(Gloriaand Caribbean source zones) were conducted using a system of five nested grids(resolutions from 2560 m to 10 m). Bathymetric Chart of the Oceans 30 arc-sec data(GEBCO),togetherwiththeSWIberianmarginbathymetrycompilation(Zitellinietal.,2009)wereused tobuild thecoarsegrids.Togenerate thedigitalelevationmodel for theSinestest-site,differenttypesofdatasetswereused:LIDARdata(2mresolution),completedbybothbathymetricmodelof theHydrographical Institute (100mresolution)anddata fromthenauticalchartsofthezone.ThecompileddigitalelevationmodelofSineswasvalidatedthroughfieldsurveyGPS-RTKdata.

InbothDTHAandPTHA,thenumericalcodeNSWING(NonlinearShallowwaterWIthNestedGrids)wasusedtosimulatethetsunamipropagationandinundation.Tsunamisimulationswereconductedtoquantifythetsunamimetrics(waveheight,flowdepth,velocityetc)thatwereusedtoassessthetsunamihazard.

Tsunamigenic sources were defined in different ways for DTHA and PTHA. In thedeterministicapproach,asetofmaximumcredibleearthquakescenarioswereconsidered.These include a limited number of events: four source models in the SWIM zone ofmagnitudesrangingfrom8.25to8.75andone8.3magnitudescenarioinGloriafault.Unlikethescenario-basedapproach,theprobabilisticanalysisforSinestest-siteinvolvedtheuseofa broad range of near- and far-field potential sources (Mw7.5 up to Mw9.0) with their


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annual recurrence rates. Threemain source zones were distinguished (SWIM, Gloria andCaribbean)andforeachoneofthemthemaximumpossibleearthquakemagnitudeswereassigned considering instrumental andhistorical catalogues in addition to apply a seismicprobability model allowing to derive the recurrence rates of individual earthquakescenarios. Also, aleatory uncertainty into the source location was treated by letting theearthquake fault, representing the tsunami event, float with a regular interval along thefaulttraceallowingtocoverpossiblerupturezones.

AnothersourceofuncertaintythatwasconsideredinthePTHAatSinestest-siteregardsthetidalstage.ThisisimportantforSinestest-site,locatedintheNEAtlanticcoast,becausethetidevariationissignificantandthepeak-to-peaktidalamplitudecanbeashighas4–5minthis region. To incorporate the tide uncertainty in the PTHA the following steps wereadopted(furtherdetailscanbefoundinOmiraetal.2016):i)Runthenumericalcodeforanumberof ‘static’ tidestages(i.e.MLLW,MSL,andMHHW),andcomputeɳ(hazardcase:wave height/flow depth) at each point of the simulation grid; ii) Construct the curve ofevolutionofɳ(verticalaxis)infunctionofthetidalstage(horizontalaxis)foreachgridpointusingapiecewise linear interpolation; iii)Compute, fromlongtime-seriesrecordedbythetide gauge (or predicted if records arenot available) the tideprobability density function(PDF),whichexpressesthecumulativeprobability(verticalaxis)ofexceedanceoftidelevels(verticalaxis);iv)Selectingtheexceedancethresholdandthenahorizontalcutofthecurveofevolutionofɳinfunctionofthetidalstagegivesthetidalstage(Ts)thatleadstoexceedthethreshold;v)UsingthisTsvalue,averticalcutofthetidePDFcurvegivesthecumulativeprobabilityofexceedingtheTs.

Hazardcurves,asakey resultofanyPTHA,werecomputedateachpointof thegridandpresentedforsomePoIsoff-andon-shore.Averticalcutofthesehazardcurves,consideringa selectedexceedance threshold, led toderive theprobabilityexceedancemaps forSinestest-siteconsideringexposuretimesof100,500,and1000years.

Considering the contribution of large and small tsunami sources in PTHA led to deriveprobabilisticmapsthatprovideamorecompletepresentationoftsunamihazardthantheDTHA.Thefactthatthereisnosingleacceptedwayofdeterminingtheworst-casescenarioinDTHAconstitutesthemainlimitationofthescenario-basedapproachincomparisonwiththeprobabilisticanalysis.This isclearlyhighlighted intheobtainedtsunamihazardresultsfor the Sines test-site showing that the calculated inundation area using the probabilisticapproach(~4km2)ismuchlargerthanthosesimulatedforfouramongthefiveconsideredscenarios in the DTHA. Moreover, probabilistic tsunami hazard results for Sines test-siteshow that most coastal zones, including the critical installations, are prone to tsunamiinundationwithprobabilitiesreaching80%for500-yearexposuretime.Ontheotherhand,the same zoneswere assumed as “safe”when considering somemaximum tsunamigenicscenariosimpactingthestudiedtest-site.


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2.3.3Siracusa:ProbabilisticVSDeterministictsunamirisk

InpreviousWP8deliverables,andparticularlyinD8.8andD8.14,thename“Siracusa”wasused to describe awide geographic area ranging from the town of Augusta to the northdowntoSiracusaanditsinnergulftothesouth.HerethefocuswillbeonlyonthetownofSiracusa: the reader interested in its history, including the accounts andevidencesof theimpactofpasttsunamis,andintheresultsofthetsunamihazardassessmentisreferredtodeliverableD8.8.Herewe extract someof the results presented inD8.14 concerning thevulnerabilityclassificationanddamageassessmentperformedbyapplyingthePTVA-3andSCHEMA-projectmethodologies to selected zonesof Siracusa. These results, expressed interms of number of expected damaged buildings for a “bathtub scenario” of 5 m, arecompared to those computed for the same scenario by means of a purely probabilisticmethodbasedonfragilitycurves.Theoutcomesofthecomparisonarediscussed.

A set of 1:2000 scale numerical maps provided by the “Servizi Informatici Territoriali eCartografia, Nodo Regionale S.I.T.R.” of the “Regione Siciliana, Assessorato Territorio eAmbiente, Dipartimento Urbanistica, Area 2 Interdipartimentale” allowed to extract thebuildingsinterestedbyascenario“bathtub”inundationlevelof5m:theresultingnumberofextractedbuildingsis2446.

SCHEMAandPTVA-3approaches

AsdescribedinD8.14andinPagnoniandTinti(2016),theSCHEMAclassificationadaptedtoSiracusa involvesbuildingvulnerabilityclassesfromA(lightconstructions)toE(reinforcedconcretebuildings).Thedamagetobuildings isdiscretized in5 levelsgoing fromD1(lightdamage) to D5 (total collapse). The damage functions themselves are discretized in adifferentwaywith the respect to the original SCHEMA formulation, especially as regardsvulnerability classes A and B (Pagnoni and Tinti, 2016). In light of the comparison that ispresented in this document, we may further classify the building typologies in “Brick”buildings (covering SCHEMA classes A to C) and “Reinforced Concrete” (RC) buildings(covering SCHEMA classes D and E). The resulting vulnerability classification for the 2446buildings inSiracusacounts92%of“Brick”buildings(the largestpart inSCHEMAclassC–individualbuildings,villas)andonly8%in“RC”.Fortheconsidered5-minundationscenario,onlyabout10%ofthebuildingswouldsufferastructuraldamageleadingtopartialortotalcollapse(damageclassesD4andD5).Theselargerdamagesareexpectedincorrespondencewiththeharbourareas,thecommercial/industrialareasandtheshantytown(seeD8.14).

The applicationof PTVA-3 to Siracusa results in different aspects. Itwas evident that thedefinition of at least two of the attributes that enter the definition of BV (“foundationstrength”and“shapeandorientation”)areverydifficult todefineandrisk todepend toomuchonthesubjectivenessoftheevaluator.Thissaid,itresultedthatnobuildingsfallintoclass1,whichisthemostresistantclass.Moreover,91%ofthebuildingsfall intotheleast


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resistant classes (4 and 5), 75% being in class 4: these buildings are foundmainly in thecommercialandindustrialareaandintheshantytowninthenorth-westernpartofthebay.

Regarding the damage level, where about 21% of the damage is classified fromHIGH toVERYHIGH(classes4and5),andonly9%asVERYHIGH.

TheresultsobtainedthroughSCHEMAandPTVA-3forSiracusawerecomparedbothatthelevel of vulnerability classes andof SCHEMAdamage level vs PTVA-3RVI. The details aregiven in D8.14. We think it is worth to recall here that, notwithstanding the implicitassumption that the two damage scales are comparable (but they differ since RVI is arelativedamagescale,whiletheSCHEMAscaleisanabsoluteone),weobtainedthatin45%ofcasesthemethodPTVA-3resultsinadamagelevellargerthanSCHEMAandinonly3%itgivesasmallerdamage(66buildings).Inotherwords,SCHEMAtendstounderestimatethedamagelevelwithrespecttoPTVA-3.

ProbabilisticapproachbasedonFragilityfunctions

Fortheprobabilisticmethod,weconsiderthefragility functionsadoptedfromSuppasrietal. (2013). These fragility curveswere obtained by fitting the survey data from 2011 theGreat East Japan tsunami for differentbuilding typologies. Suppasri et al. (2013)define6damagestates:

1. Minordamage:there isnosignificantstructuralornon-structuraldamage,possiblyonlyminorflooding.Possibletobeusedimmediatelyafterminorfloorandwallcleanup.

2. Moderate damage: Slight damages to non-structural components. Possible to beusedaftermoderatereparation

3. Majordamage:Heavydamagestosomewallsbutnodamagesincolumns.Possibletobeuseaftermajorreparations

4. Completedamage:Heavydamages toseveralwallsandsomecolumns.Possible tobeusedafteracompletereparationandretrofitting

5. Collapsed:Destructivedamagetowalls(morethanhalfofwalldensity)andseveralcolumns(bentordestroyed).Lossoffunctionality(systemcollapse).Non-repairableorgreatcostforretrofitting

6. Washed away: Washed away, only foundation remained, total overturned. Non-repairable,requirestotalreconstruction.

Here, we consider 2 building typologies: Brick and RC buildings. For these typologies ofbuildings, the fragility curvesareassumed log-normal. The fragility curvesare reported inFigure1.Asexpected,masonrybuildingsaremore fragile thanRCbuildings.Forexample,for a flow depth of 10m, the probability of beingwashed away is around 0.80 for Brickbuildingsand0.20forRCbuildings.


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Figure1:FragilitycurvesforRC(above)andBrick(below)buildings,foralldamagestates(fromSuppasrietal.2013)

Topropagatethe(aleatory)uncertaintyquantifiedbythefragilitycurve,weadoptaMonteCarlomethod.Inparticular,wefirstsample1000timesthedamagestateforeachbuilding,by comparing one randomly generated number between 0 and 1 and the probability ofexceeding each damage state for the intensity at the place of the building given by theselectedscenario.Then,wecountthenumberofbuildingswiththesamedamagestateineachsampledconfigurationofdamages.WereporttheresultsinthehistogramsofFigure2,forallthebuildingsandforthetwoclassesofbuildingsseparately.Theeffectofpropagatingthealeatoryuncertainty is thatwehaveadistributionof thenumberofbuildings ineachdamage state, and not a single number. In this way, it is explicitly shown the range ofvariability that one should expect, given one pre-selected event. It isworth to note that,evenconsideringthisuncertainty,theresultsarequiteinformative.Forexample,themostrepresented damage state seems to be ‘collapse’, with a number of buildings rangingbetween300and350.Thelessrepresenteddamagestateisinstead‘washedaway’,withanumberofcollapses,withanumberofbuildingsrangingbetween225and275. Instead, ifwe look at RC buildings only, the number of collapsed and washed away buildings issignificantlylowerthanalltheotherdamagestates.


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Figure2:Numberofbuildingsineachdamagestate,forallbuildings(top),Masonrybuildings(middle)andRCbuildings(bottom),adoptingtheprobabilisticmethodbasedonSuppasrietal.(2013).

Comparison

TocomparetheresultsoftheprobabilisticmethodwiththeonesofSCHEMAandPTVA-3,weconsider the fragility curve corresponding to collapseand indicating theprobabilityofexceedingcollapse,thatis,collapseandwashedaway.ByadoptingthesameMCproceduredescribedabove,andsummingthenumberofbuildingswithdamagesequalorlargerthancollapse, we obtain a sample of 1000 total number of heavily damaged buildings. Theseresults are reported inFigure 3, and comparedwith the equivalent SCHEMAand PTVA-3results. These results clearly show that probabilisticmethods aremuchmore informativeandtheyallowformake judgementthatwouldhavebeen impossible inthecaseofmorequalitativemethods. Indeed, theplotsofFigure3clearly show that SCHEMAandPTVA-3resultsareincompatiblewiththeprobabilisticresultsbasedonSuppasrietal.(2013)results.This conclusion is possible only because the probabilistic methods quantify the fullprobabilisticdistribution.Inthiscase,inFigure3wecannotethatbothSCHEMAandPTVA-3resultsarewelloutsidetheuncertaintyboundsoftheprobabilisticmethod.Inparticular,theyforeseemuchlessheavilydamagedbuildings.Thismaybeasymptomofapotentiallysevereunderestimationofthe(epistemic)uncertaintyintheassessments.


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It is fair to argue that this is the result of two main factors that make the comparisonillustratedhereonlyindicative.Thefirstfactor,whichappliestotheSCHEMAresults,isthatSCHEMA is based on a vulnerability analysis (Valencia et al. 2011) relying on data andstatisticalprocessingthataresignificantlydifferent(andalternativeto)thoseofSuppasrietal. (2013). This is confirmedby theanalysispresented inTarbottonet al. (2015): theplottheyshowintheirFigure13brevealsthehugedifferenceinthefragilitycurvesbySuppasriet al. (2013) andValenciaet al. (2011), clearlyexplainingwhy theSCHEMA results are solargely underestimated even with respect to the lower bound of the probabilisticdistributionpresentedhere.Secondly,weproposedacomparisonbasedonaclassificationin“Brick”and“Reinforcedconcrete”buildingswhichisveryhardtocarryoutforthetownofSiracusa,especiallywhencomparedwiththeJapanesesituation.Finally,thecomparisonwas made by assuming that the damage levels in SCHEMA, the RVI of PTVA-3 and thedamageclassesofSuppasriaresomehowsuperimposable,anassumptionwhichdeservesatleastacarefulvalidation.

Figure3:Numberofbuildingswithdamagestatesgreaterorequaltocollapse(D5andD6ofSuppasrietal.,2013)forallbuildings(top),Masonrybuildings(middle)andRCbuildings(bottom),adoptingtheprobabilisticmethodbasedonSuppasrietal.(2013)fragilitycurves(histogram)andthequalitativemethodsSCHEMAandPVHA-3.


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2.4Comparisonbetweenscenario-basedandprobabilistictsunamihazardandriskassessment:guidelinesforfuturetsunamihazardandriskassessments

In general,we can state that probabilistic and scenario-based assessments differ in somerespects and share some common features, at least in the formulation presented inASTARTE (Section2.2.2andreference therein). In lightof thescopeof thisdocument,wearenotgoingtodiscusswhetheroneapproachisbetterthantheotheringeneral.Indeed,as discussed below, they may answer to different questions that may be of interest forstakeholders and local planners. Here,we focus on comparing probabilistic and scenario-based approaches in terms of their capability to account for and quantify uncertainty, tocomparetoeach-other,andtobetestedagainstrealdata.

As shown in Section 2.3, when available, probabilistic hazard, vulnerability, and riskquantificationsaremoreinformativethanscenario-basedand/orqualitativeassessments.Inparticular,theyallowforquantifyingtheuncertaintyand,inthisrespect,forunderstandingtheeffectivemeaningandstrengthofscenario-basedresults.Forexample,inSections2.3.1and 2.3.2, only the probabilistic tsunami hazard results allow quantifying therepresentativenessofthescenario-basedhazard,byquantifyingitsmeanreturnperiod.Itisalso shown that only the probabilistic results allow for the comparison among differentresults.Forexample,inSection2.3.3,itisshownthatthedifferentmodelsadoptedforriskquantification are incompatible to each other, meaning that a significant epistemicuncertaintyexistsovertheseriskresults.Thismeansthateitheronlyoneofthesemodelsisassumedtrueandtheotherfalse,orallmodelsmaybescientificallyacceptable.Inmostofcases, given that tsunamis are rare, the paucity of data prevents to falsify most of themodels (e.g., Marzocchi and Jordan, 2014), and robust results can be obtained only byquantifying the variability of among scientifically acceptable models in the form ofcommunitydistribution(e.g.,SSHAC,1997).

Consequently, hazard and risk quantifications that account for uncertainty (both aleatoryandepistemic)notonlyprovidemoresolid resultsonwhich tobasedecisionmaking,butalsoallow foradeeperunderstandingof theirmeaningand theirpotential limitations.Ofcourse, this derives from the fact that all the probabilistic methods are built by thecomputationofalargenumberofscenarios,weightedbytheirprobabilityofoccurrenceinthe exposure time, and combined by considering alternative and scientifically acceptablemodels. This complexity includes more information that, if well communicated, allowsincreasingawareness fordecisionmaking.However, thecommunication iscomplicatedbythecomplexityoftheresults,increasingtheneedofoutreachefforts.

The increasing complexity of hazard and risk quantifications that account for all thepotentialsourcesofuncertaintyisalsothemainlimitofprobabilisticanalyses.Indeed,theyare difficult to be implemented. Probably for this reason, inSection 2.3,we could reportonly3casestudies.Moreingeneral,lookingatallASTARTEcasestudies,wecannotethat


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probabilisticmethodsareessentiallylimitedonlytohazard(andnotextendedtorisk)andtoseismicsources.Inotherwords,mostofthehazardandriskcomputationsmadeinASTARTEtest sites arebasedon scenario-basedassessments. Themain reason for this is that fullyprobabilistichazardassessmentsaremorecomplicatedand recent in literature.However,wemustnotethatscenario-basedassessmentsmaybeselectedalsobecausei)thestateofknowledgeaboutsomeofthepossibletsunamisourcesisnotsufficientforfullprobabilisticassessments(e.g.,submarinelandslides),andii)thecomputationalpowerrequiredbyfullyprobabilisticmethodsisactuallydifficulttobereached.

Therelativesimplicityoftheanalysisofsinglescenariosallowsfocusingontheanalysisofsomedetailsthatshouldbeneglectedotherwise.Forexample,sincethereisnottheneedofsimplifyingthepropagation,itmayprovideveryimportantcluesfordesignpurposes,aswell as for investigating physical processes. Also, they provide a base for investigatingcascadeeffects,ormultiplehazardscausedbythesameevent.Allthesetypesofstudiescanbedescribedas“whatif”analyses.Theuseofscenariosforhazardandriskquantificationisinsteadmorecritical,sinceitenablesproducingresultsatmuchlowercosts,butitisentirelybasedonthe“selection”ofthescenario(s).Thisselectionandthegroundtomakeitisboththeoreticallyandpracticallycomplicated.

Someauthorsbasedtheselectionofthisscenarioonthesearchforthemaximumcredible(MC) event, often claiming the all people and structures shouldbeprotected against thismaximum,nomatterhowinfrequentitmaybe(e.g.,Wyssetal.,2012;PeresanandPanza,2012).However, thedefinitionof thismaximum is inpracticeverychallenging,and ithasbeen challenged in literature for its very physical ground. For example, Allen (1995; andmanyafterthispaper)describedMCEastheevent“whichisonlyashadesmallerthantheminimum incredible earthquake”. This tongue-in-cheek highlights the basic difficulty inrigorously defining the MCE concept, that is, define what it is actually possible andimpossible (even if absolutely rare). Events like the Boxing day earthquake in Indonesia,Tohoku in Japan, or even Christchurch in New Zealand, clearly demonstrated that thingsapparentlyincrediblemayindeedhappen,causingdestructiveevents.

Another possible interpretation of MC event may be based on the definition of a timewindow(Allen,1995).Inarow,thistimewindowmaybeassociatedtoa“returnperiod”ofclassical probabilistic hazard assessments (e.g., Hanks and Cornell, 1994). However,sometimes, this reference timewindow (ormean return period) is not defined explicitly.This isverydangerousand itposesseriousethical issues (e.g.Marzocchi,2013), since theselectionofthescenarioimplicitlyattributestheroleofdefiningtheacceptablerisktothescientists,whilethischoicehasnotascientificground(e.g.,Jordanetal.,2011;Marzocchietal., 2012; Geller et al., 2013). If instead this selection is made explicitly, it may indeedprovideaphysicalgroundfortheselectionofthescenarios(e.g.,Løvholtetal.,2012).Themaindifficultyisthefactthatitissometimesdifficulttodothiswithoutafullprobabilisticanalysis,sinceitmaybepossibletodefinesuchscenariosdependingontheirsources(e.g.,


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theirmagnitude),butitismorecomplicatedtodoitdependingontheirimpact(e.g.,run-upatsite).Indeed,thecomplexityofthetsunamienergypathfromthesourcetothesiteandthe strongly non linear character of the tsunami inundation process cause a strongheterogeneity of the tsunami impact. One possible solution is recurring to simplifyingassumptions for exploring the dependence of impact variability on the source variability,thatmaybethenchallengedexpost(e.g.,followingamethodsimilartoLoritoetal.,2015).Assuming that it is possible to define an objective ground tomake this selectionex ante(before producing a fully probabilistic assessment), this definition may help producingsimplifiedtsunamihazardandriskassessmentsthatmayresultusefulwheneverthecostofpotentialriskmitigationactions isso lowthatdonotrequirehighlydetailedanalyses(seediscussioninMarzocchietal.,2012).

Theselectionof thescenariosbasedonareferencemeanreturnperiodmayprovidealsotheground to compareprobabilistic and scenario-based results toeachother and to testthemagainsttheavailabledata.Oneexampleofthiscomparison ismade inFigure4.Theprobabilisticresultsarereportedintermsofafamilyofhazardcurvesreportingthemeanannual frequency of exceedance of different values of hazard intensity in one definedlocation (Figure 4A). Epistemic uncertainty is reported in grey as a confidence intervalaroundabestguessvalue.

A scenario-based hazard quantification consists of one point in the same graph for thelocation,reportinghazardintensityvalueandthereferencemeanreturnperiod(bluedotinFigure 4B1 and 4B2). The intercept between the hazard curves and the scenario hazardintensity defines an interval of annual frequency of exceedance for that intensity value(blackdashedboxinFigure4B1and4B2).Thisrangeshouldbecomparedtothereferencemean return period of the scenario-based analysis (blue dot) and, in particular, thisreference values should in theory bewithin the range, as in Figure 4B2. If the referencevalue is outside the range, as it is in the example of Figure 4B1, the two results areincompatible and should be rechecked. In this specific case, it seems that either theprobability of occurrence estimated for that scenario is too large in the probabilisticanalysis,orthescenarioselectedistoosmall(intermsofimpact)withrespecttothetargetreturnperiod.Sincetheseresultsmayhavebeenproducedindependentlybytwodifferentgroupswithoutanyinteractionandbypossiblydifferentmodelsoftheearthquake(scalinglaws, slip distribution, numerical modelling strategy), of the tsunami generation andpropagation(modellingassumptionssuchashydrostaticity,theadoptednumericalscheme),thismay be a symptom that epistemic uncertainty have not been fully addressed in theprobabilistic analysis, which then is not presently fully representing the communitydistribution, or just that “sanity-checks” of both models are necessary. This type ofproblems is not new at all. The main motivation for establishing SSHAC and the SSHACprocesswastheexistenceofincompatiblehazardestimatesprovidedbydifferentyethighlyrespectedgroups,whichhadputtheUSNuclearRegulatoryCommitteeinastallsituationinviewoftheirregulatoryconcerns.Inthenextsections,we’llbrieflytouchontheseissues,by


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presentingafeasibleschemeforthedecision-makingprocessapplicabletotsunamihazardandriskanalysis;thisprocesswasinitiallydiscussedandappliedwithintheSTRESTproject,andnowisbeingappliedfortheTSUMAPS-NEAMPTHA.

Withasimilarlogic,theresultscanbetestedagainstrealdata.Bycountingthenumberofknowneventswhichexceedagiventhreshold, theobservational recordcanbetranslatedintoobserved frequencyofexceedance foranygivenhazard intensity threshold.Actually,providedtheobservationalwouldbecomplete,whichislikelyinherentlyimpossibleforlowprobability / high consequences events like tsunamis, thiswouldbe enough for assessingtsunami hazard; in many cases, frequencies estimated from tsunami data need to beconsideredas a lowerboundnot tobeexceededbyhazardestimates. InFigure4C1and4C2, we report for explanatory reasons two potential observation relative to the sameintensitydefinedforthescenario-basedhazardisrepresentedasahorizontalgreenpoint.Forwhat it concerns theprobabilistic hazard assessment, this observation represents thegroundforaquantitativetestagainstontologicalerrorsinprobabilistichazardassessments,asdiscussed inMarzocchi et al. (2015). Indicatively, this greenpoint shouldbe inside therangeofpossiblemeanannualfrequenciesdefinedintheblackdashedbox(Figure4C2).Ifinstead thepoint isoutside the range (Figure4C1), theprobabilistichazardmodel canbelikely rejected,eitherbecause it isnot test (asdiscussedabove)orbecause it includesanontological error (seediscussion in Section 1). A similar comparison (but only qualitative)canbemadealsowiththescenario-basedanalysis:iftheobservedfrequency(greendot)isdistantfromthetargetmeanreturnperiodadoptedforselectingthescenario(bluedot),anewselectionshouldbeconsidered.

This discussion had the simplifying assumption that the uncertainty associated to theobservationpoint is negligible, but it canbeeasily extended to account also formeasureuncertaintybymeansofstandardhypothesistestingtheory(MarzocchiandJordan,2014).Inparticular, themeasureuncertaintywouldresultwithbothhorizontalandverticalerrorbars inFigure4C1and4C2,expressingthemeasurementerrorandtheuncertainty inthefrequencyestimation.Notethatthismightbeusefulinthespecificcaseoftsunamis,giventhattheyarebegeneratedbydifferentsources,andareasonforinconsistencymightalsobe that the hazard assessment can be focused on only one (or few) source, while thetsunami cataloguesmaymix different sources. This indeed should be taken into account,anditcanbepossiblyquantifiedintermsofmeasureuncertainty.

Allthedescribedcomparisonscanbedonealsoforriskresults.Theonlydifferenceisthatintheabscissatherewillbealossmeasure,insteadofthehazardintensity.

Tosummarize:

• Probabilistic analyses allow for a deeper understanding of results, potentiallyincreasingtheawarenessofdecisionsbasedonhazardandriskresults;theanalysis


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ofresultsismorecomplicated,andacloserinteractionbetweenhazard/riskanalystsandend-users(decisionmakers)isrequired.

• The analysis of scenarios may provide important clues in all “what if” studies,allowing for some specificmodelling otherwise not feasible; for the considerationintohazard/riskanalysis, theselectionofscenariosshouldbe linkedtoareference“mean return period”. In this case, a scenario-based analysis can be seen as themaximum simplification of the hazard/risk analysis, that is, the definition of onepointintheintensity/probabilitygraph.

• Probabilistichazardandriskanalysisisacomplexandresource-demandingprocess.Sanitychecksofthedata,methodsandresultsarenecessary.Criticalchoicesduringeachoftheanalysisstepsmustbemadeinatransparentandreproducibleway,andby defining a structured process on purpose, for example by means of expertelicitations,participatoryandindependentreviews.

• WhilethePTHAforearthquake-generatedtsunamis isprobablymatureenoughforoperationalapplications, this isnotyet thecase forother tsunamisourcessuchaslandslidesandvolcanoes,whichatleastlocallymayseriouslycontributetotsunamihazard. For example because the source frequency is presently more difficult toconstrain.

• When available, probabilistic scenario-based analyses are comparable only ifscenariosaredefinedintermsofareferencemeanreturnperiod.Inthiscase,bothresultscanalsobecompared,inprinciple,andatleastqualitatively,withpastdata.However, for tsunamis, catalogues are likely to be under-representing the largestlow-frequencyevents,anditisdifficulttodiscriminatethecausativetsunamisource.


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Figure4:ComparisonbetweenProbabilisticHazardAnalysis(hazardcurveinredandgrey),scenario-basedintensity(blue),andpastdata(green),modifiedfromSelvaetal.(2016).


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3.Proposalforahomogenisedtreatmentofuncertaintyfortsunamihazardandrisk,withexamplesFor natural hazards and consequent risks, we deal with systems with many degrees offreedom,oftencharacterizedbynon-lineardependencies,andsometimesbyarelativelackofobservations.So,andparticularlywhenpotentialregulatoryconcernsarerelativelyhigh,the management of scientific and technical controversies within a multiple-expertenvironmentiscriticalforanyhazard/riskassessmentproject.

Asdiscussedalready in the Introductionand insomedetails inSection2, theremightbe,and indeed there are usually, different opinions within a group of scientists concerningsomeaspectsofthehazard/riskassessmentchain;it isthenmandatorynottooverlookorunderrate such controversies, as different opinions and approaches typically lead to verydifferentestimatesofhazardandrisk.

Alternative probabilistic formulationsmay produce and they have in fact produced in thepast highly variable and in some cases inconsistent hazard and risk estimates (e.g., Paté-Cornell,1996;Bernreuteretal.,1989;Selvaetal,2013;Marzocchietal.,2015).Since theresults of such analysesmay have consequences of public relevance, it is fundamental tomanagetheemerginguncertainty(e.g.,SSHAC,1997;USNRC,2012;IPCC,2013).

The integration of different expert opinions is then needed for managing subjectivedecisionsandinquantifyingtheepistemicuncertaintyintheformof“technicalcommunitydistributions”.Toproducerobustandstableresults,theexperts’diverserangeofviewsandopinions,theiractiveinvolvement,andtheirformalfeedbacksneedtobeorganizedintoastructuredprocess,ideallygrantingtransparency,accountabilityandindependency.

Inthefieldofnaturalhazards,andinparticularinseismichazardandriskquantification,themost applied and referencedprotocol is the onedevelopedby the Senior SeismicHazardAnalysis Commission (SSHAC) in 1997, and its subsequent specifications and integrations(e.g., Hanks et al., 2009; USNRC, 2012). One of the most relevant conclusions in SSHACguidelines about uncertaintymanagement and use of experts is that differences in PSHAassessment are often due to procedural rather than technical differences, and so a greatefforthasbeenputinestablishingappropriateprocedures.

However, when the regulatory concern is not the highest possible (e.g. for Nuclear CIs),and/orinsmall/mediumsizeprojects,applicabilityofthefullSHAACproceduremaynotbefeasible.Furthermore,thegroupinteractionandface-to-facemeetingsbetweentheexpertscan be challenging for the undesirable effects of personalities and reputations thatunavoidablymaybias the groupquantification (e.g., Bedford&Cooke, 2001;Aspinall andCooke,2013).Lastly,some“technicalneutrality”isdesired,sincewhatreallymattersisthestandardizationoftheprocess,notthespecifictool(e.g.alogictreeoranensemble)tobeused.


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A more flexible management of subjectivity in probabilistic single/multi-hazard/riskassessmentshasbeenaddressedwithinastructuredMultiple-ExpertManagementProtocolwithintheSTRESTproject(EU@STRESTinSelvaetal.,2015,STRESTD3.1).Adevelopmentofthis approach is being now applied specifically to seismic probabilistic tsunami hazardassessment(S-PTHA)withintheTSUMAPS-NEAMproject.

TheTSUMAPS-NEAMprojectbenefitsof somedataanalysesand -more importantlywithrespect to the topics discussed herein - of some several methodological advancementsaddressed within ASTARTE. They regard for example the seismic source definition andtreatment(seee.g.D3.12andD3.40),thegeneralapproachtouncertaintyquantification(asdiscussed within this deliverable and in D4.13), and several others, including verypreliminaryregionalhazardresultspresentedinD8.8.

AfurtherspecificadvancementachievedwithinASTARTE,andpresentedinthisdeliverable,concerns the development of the uncertainty treatment for approximated MaximumInundation Height (MIH) estimation through local amplification factors, applied to eachsinglescenariocontributingtoPTHAbeforeprobabilisticaggregation.

Thenextstepfollowingthesetechnicalachievements,aswellasseveraldiscussionswiththeASTARTEpartners,wastakeninTSUMAPS-NEAMasregardstheapplicationofamethodforthegeneralmanagementofuncertainty,includingthoseemergingfrompossiblealternativeformulationsofthesameproblem.

Inwhat follows,wethenbrieflydescribe theTSUMAPS-NEAMprojectasawholeandthePTHA methodology applied therein, with specific focus on the Multi-Expert UncertaintyManagement Protocol. We will then report on the methodology for the treatment ofuncertainty for MIH, developed within ASTARTE and which will be applied in TSUMAPS-NEAM.

3.1RegionalSeismic-ProbabilisticTsunamiHazardAnalysis(SPTHA)intheNEAMRegion,underdevelopmentwithinTSUMAPS-NEAMProjectAssaidintheIntroductionandearlierinthisSection,TSUMAPS-NEAMhasitsrootswithinthe ASTARTE Project. Also thanks to application, further development, and integration ofseveral studies performedwithin the ASTARTE project, TSUMAPS-NEAMwill develop thefirst homogeneous long-term PTHA for earthquake-induced tsunamis (S-PTHA), which ispresently unavailable for the coastlines of the NEAM region (NE Atlantic, theMediterranean,andconnectedseas).

The expected results are: 1) long-term PTHA (complete hazard curves), i.e. exceedanceprobabilityformaximumoffshoreamplitudeata50-mdepth,andforMaximumInundation


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Height(MIH),atpointsdistributedalongtheNEAMcoasts;2)regionalhazardmaps(hazardintensitywithgivenexceedanceprobability;3)probabilitymaps(probabilitycorrespondingtogivenintensities).

ThisregionalS-PTHAismeanttobethetermofcomparisonorabasisforexistingorfuturenationalandsite-specificS-PTHAandRiskassessmentefforts,forexampleasapreliminaryscreening for the prioritization of subregions or smaller areas for site-specific studies.Common risk assessment, long-term risk mitigation and planning, at the national andregional levels, and several specific applications (e.g. land-use and evacuation plans,identificationofCriticalInfrastructures(CIs)atrisk)canclearlybenefitfromhavingaregion-wideS-PTHAasinputandreference.

Therefore,thisS-PTHAwillrelyoncommonunderstandingofthebestviablepracticesandcomplieswithEUscientificandpolicystandardsforhazardandriskassessment(e.g.,seismichazard for building codes). Moreover, the development of standardized PTHA products(hazard and probability curves,maps, documentation, web-tools for their analysis) is thefirststepformulti-sourcetsunamihazardassessment,i.e.thecompletePTHA(e.g.includinglandslide and volcano sources), tsunami risk assessment, and also to include tsunamis inmulti-hazardriskassessments.

A quantitative definition of the tsunami hazard in the region is also crucial for betteraddressingfutureriskreductionpoliticalchoicesinthecontextoftheNEAMTWS(TsunamiWarningSystem),andacriticaltoolforathorougheffortforawarenessraisingintheregion.

3.1.1TSUMAPS-NEAMMethodologyforRegional-scaleS-PTHA

The workflow for S-PTHA adopted in TSUMAPS-NEAM is organized into the following 4STEPS:

• STEP1:PROBABILISTICEARTHQUAKEMODEL

• STEP2:TSUNAMIGENERATION&MODELINGINDEEPWATER

• STEP3:SHOALINGANDINUNDATION

• STEP4:HAZARDAGGREGATION&UNCERTAINTYQUANTIFICATION

EachofthesestepsisfurtherdividedintoseveralLevels,whichwillbeomittedinthisbriefoverview.TheseLevelsdescribethefinergrainoftheanalysisworkflowwithineachSTEP,andthedefinitionofthedatabasesonwhichtheanalysesrelyon.

Ingeneral,ateachoftheLevelswithineachSTEPseveralalternativemodels(asdiscussedintheintroductionofthissection)mightbeusedforthesameproblem:adifferentmagnitudefrequencydistribution(MFD)fortheearthquakes,twodifferentcornermagnitudesforthe


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sameMFD,ashallowwateroraBoussinesqapproachtotsunamimodeling, twodifferentbathymetric models, andmany others. Among all the alternatives considered technicallysound,onlyaselectionofthemisgenerallyworthtobeimplementedinarealassessment,sinceonlya sub-setof themusually control the largestpartof theepistemicuncertainty.The role of thepanel of experts (PoE) through a structuredprocess, as described furtherbelow (in Section 3.1.2), is to provide guidance on this selection (“trimming” of thealternatives);then,toprovideguidanceontherelativeweightsofthedifferentalternatives(usually within a logic tree; here within a more general “alternative” tree, within anensemblemodelingscheme;Selvaetal.,2016).

TheTSUMAPS-NEAMSTEPSasawholeareverysyntheticallydescribedinwhatfollows,thatiswithoutenteringintothedetailsoftheLevelswithineachSTEP.Then,thedifferentroleswithintheprojectaredescribed,inparticularthatofthePoEandtheirroleinthedecision-makingprocess.

STEP1-PROBABILISTICEARTHQUAKEMODEL

ThegoalsofSTEP1are thedefinitionof thesetof seismicsources, their frequency, theirparameterization,andtheprobabilitiesassociatedtodifferentconfigurationsofthesourceparameters.

Thisanalysis,i.e.thetreatmentofthealeatory(natural)variabilityoftheseismicsources,isconducted through the definition of an Event Tree (ET). An ET is a branching graphrepresentationofeventsinwhichindividualbranchesarepossiblealternativestepsfromageneral prior event, state, or condition, and which evolve into increasingly specificsubsequentevents.Examplesof theuseofanET forS-PTHAcanbe found inLoritoetal.(2015) and in Selva et al. (2016); see also ASTARTE D8.8. This type of approach helpsdecreasing the overall computational coast of S-PTHA, and it is an alternative to moreclassicalapproachesforthediscretizationofthetotalprobability inS-PTHA(e.g.GeistandParsons,2006).

STEP 1 defines the ET used in TSUMAPS-NEAM for the treatment of the seismic sourcesaleatoryvariability.AllLevelsinSTEP1exceptforLevel0coincidewiththenodesofthisET.AteachLevel(i.e.attheETnodes),discreteprobabilitiesareevaluatedfortheparametersunderinvestigation.TheLevelsareorganizedinalogicalsequence,andprobabilitiesateachLevelareconditionedtothebranches(“events”)atthepreviousLevel.

Without entering in any detail, we justmention that the Earthquakemodel at STEP 1 iscomposed by two types of seismic sources,which are: the “Predominant Seismicity (PS)”(already called “Interface Seismicity (IS)” in D8.8, and in Selva et al., 2016), and the“BackgroundSeismicity(BS)”.

PSisusedwhenwell-knownfaultstructures(e.g.geometricallywell-constrained)maybeofparticular relevance for tsunami generation (typically, subduction interfaces). With


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referencetoterminologyadoptedforthetypesofseismicsourcesdefinedintheproposedstandardizationbyASTARTED3.40,thesearethe“Earthquakefaultsources”.

BSseismicityisusedinsteadsincenoonecanexcludethatearthquakesmayoccuroutsidewell-known faults, and we cannot exclude that faults are not mapped well enougheverywhere(whichis likelyimpossible,particularlyoffshore).Hence,whendealingwithPSwe use complete faultmodels for the earthquakes,whilewe allow earthquakes to occureverywhereinagivenvolumewithagivenvariabilityofthefaultingmechanism.InD3.40,they were termed “Earthquake Grids”. The presence of known faults (not those alreadytreatedasPS),historicalseismicity(focalmechanisms)anddominantstressregimecanbeusedtoconstrainthefaultingmechanismprobability.

In each region defined by the regionalization (see D3.40), three different situationsmayoccur:1)aregion is treatedasamixofPSandBS(e.g.asubductionzoneandthecrustalearthquakesaboveit);2)aregionistreatedaspureBS(similarlytosomePSHAapproaches,in the present case were no really major structures that are mapped well enough arepresent);3)apurePSregion(e.g.subductionzones locatedveryfarawayfromthetargetcoast, for which modelling the largest earthquakes occurring on the known subductioninterface is enough, such as the Caribbean subduction with respect to the target NEAMcoastlines.

STEP2-TSUNAMIGENERATION&MODELINGINDEEPWATER

The goals of STEP 2 are the numerical simulation of the sea floor displacement, and thenumerical simulationof the tsunamigenerationandpropagation from the sourceup toagivenbathymetricdepthoffshoreofthetargetarea.Thetsunamipropagationissimulateduptoachosenisobathoffshoreofthetargetcoast,uptowhichthepropagationisassumedlinear.

This assumption allows the formulation of the problem as a linear combination of pre-calculated tsunamiGreen’s functionsproducedbyunit sources (‘unitary’Gaussian-shapedsea level elevation;Molinari et al., 2016; see also Selva et al., 2016;ASTARTED8.8). Thislimits thecomputationalburdenandmakes theanalysis computationally feasible. Furthercommonlyadoptedsimplifications(cf.ASTARTED3.40)arealsoemployedatalllevelsofthisSTEP(e.g.Okada-likefaultsinhomogeneoushalfspace).

However, the Levels inside STEP 2 (coseismic displacement, tsunami generation,propagation in deepwaters) are separated in away thatmakes the simulation ‘modular’allowing in principle to adopt more complex approaches for each Level (see e.g. D3.40,D4.19). The uncertainty introduced by these simplifications is treated jointly withpropagationinshallowwater,shoalingandinundation,atSTEP3.

STEP3-SHOALINGANDINUNDATION.


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ThegoalsofSTEP3arethesimulationofthe lastphasesofthetsunami impact, includingcombinationwithtides,andthequantificationoftheassociateduncertainty(usingalsothemethodologydevelopedwithinASTARTEandpresentedinSection3.2).

This STEP is kept separated from STEP 2 in TSUMAPS-NEAM as the linearity assumptiondoesn’tholdanymoreduring the later stagesof tsunamievolution invery shallowwatersandbeyond(shoaling,inundation).Moreover,thetypicaldiscretelength/time-scalesforthenumerical simulation of these stages need to be much finer than for modelling thepropagation in the deep ocean. As a consequence, the computational cost stronglyincreases, and full inundation calculations for each considered scenario are generally notfeasible for a regional hazard quantification (e.g., Davies et al., 2017). Hence, these lastphasesneedtobetreatedwithspecificandgenerallyquitecrudeapproximationsreplacingdirect numerical simulations (e.g. Løvholt et al., 2012); as a consequence, a specificuncertainty treatment (see Section 3.2 and also Davies et al., 2017) is needed and theapplicability of the results is nevertheless quite limited as far as site-specific studies areconcerned. Again, the modularity of Levels leaves the possibility open for differentapproaches for inundation calculations if enough computational resources and detailedenough topo-bathymetric models are available; or the re-use of the regional results forsubsequentlocalstudies(e.g.Loritoetal.,2015),disaggregationorsensitivityanalyses.

STEP4-HAZARDAGGREGATION&UNCERTAINTYQUANTIFICATION

ThegoalsofSTEP4 isthequantificationofthehazardcurvesatthetargetsites,that isofthe exceedance probability in a given time window for the chosen hazardmetric at thepointsofinterestincludingtreatmentofepistemicuncertainty.ItmergestheresultsofSTEP1,namelytheprobabilityassociatedtoeachconsideredscenario,withthetsunamiimpactduetoeachscenario (STEP2+STEP3) tocalculatethehazardcurvesatchosenpointsofinterest. At sites where this is possible because of data availability, this STEP includescomparison of the results of computationally based S-PTHA with observations (historicaltsunamis,paleotsunamis).

Forquantifyingtheuncertaintyonhazardcurves,theworkflowofSTEPS1-3isrepeatedforeachalternativemodel(orasampleofit,seeSelvaetal.,2016)thatisadoptedatanyLevelwithin these STEPS. The process of alternative selection and weighting through expertelicitations is discussed in the next subsection 3.1.2. Note that the elicitation processinfluencesthealternativesconsideredatall levels intheprevioussteps,aswellas,at thisSTEP,forexampleby‘trimming’alternativemodelsthatarejudgedunnecessary.

The treatment of the epistemic uncertainty, expressed by alternative hazard curves, isfinally treated by ensemble modeling (see previous discussions in this deliverable; D8.8;Selvaetal.,2016).


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In Figure 5, we report some preliminary results of the actual implementation of thecomputational chain described so far, restricted to the Mediterranean see. For sake ofexamples, we report the hazard maps (intensity corresponding to a given Mean ReturnPeriod-MRP)forthemeanoftheensemblemodels(epistemicuncertainty),anddifferentMRP.

Figure5:PreliminaryRegionalHazardMaps(coveringthewholeMediterranean)relativetoan Average Return Period of 475 yr (above), 975 yr (center), and 4975 yr (below),corresponding to probabilities of 0.10, 0.05 and 0.01 in 50 yr within a Poisson process,respectively.Themeanoftheepistemicuncertaintyisreported.


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3.1.2TSUMAPS-NEAMMultiple-expertprocessforuncertaintyquantification

TheproceduralforthemanagementofsubjectivechoicesanduncertaintyquantificationofTSUMAPS-NEAMisrootedinacleardefinitionofrolesandinteractionamongthedifferentexperts,structuredelicitationsbasedonmathematicalaggregationofapoolofexperts,andin a participatory independent review. This is achieved with coordination of a technicalintegratorandaprojectmanager,withinaformalisedprocess.Severalgroupsaredefinedinthe framework of this process. The roles of the participants to each groupwill be brieflydescribedbelow.

Amongthedifferentpartsof theprocessandthedifferentgroups, themulti-step/multi-expert processwith the panel of experts (PoE), for addressing subjective choices,will bedescribed in slightly greater detail, since it is the core process for addressing subjectivechoices.

NotethatTSUMAPS-NEAMincludedseveralexpertsthatarealsoASTARTEpartners inthisprocess.

Inanutshell,thepurposeoftheprotocolis:

1. To establish roles and responsibility, in order to guarantee transparency,independencyofroles,accountabilityandachievementofproceduralconsensus;

2. To homogenize the management of decision making for subjective choices,guaranteeingdocumentedandtrackabledecisionmaking;

3. To establish homogeneous principles for the management of alternatives, that is,alternative and scientifically acceptable implementations for quantifying thecommunitydistribution.

RolesintheTSUMAPS-NEAMprocesshavebeendefinedasfollows:

• theProjectManager(PM);

• theTechnicalIntegrator(TI);

• theEvaluationTeam(ET);

• thePoolofExperts(PoE);

• theInternalReviewers(IR).


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ThePMcoordinatesthedevelopmentof thewholeproject,andhe is typically theProjectCoordinatorappointedbythemainstakeholder/representativeofthefundingagency.ThePMhas the responsibility fordecisions tobe rational and fair to stakeholders, authoritiesand to the public whenever this is the case. The PM don’t usually have a formal role instructured expert elicitations. In TSUMAPS-NEAM, the PM role is played by the ProjectCoordinator,withthesupportofoneortwoSteeringCommitteemembers.

The TI is project scientific manager; his main responsibility is to try and capture, and tointegrate, the views of the “informed technical community” to be implemented in thehazardandriskcalculations.Thefinalresultsaretobeexpressedintheformof“communitydistributions” (SSHAC, 1997), and the opinions expressed along the process should betrackable. The TI has a role that merge the one of the standard elicitator of structuredelicitations (e.g., Aspinall and Cooke 2013) and the one of technical integration SSHAC(1997;andfollowings).Itisdesirabletohaveasmallteamratherthanasinglepersonactingas TI; in TSUMAPS-NEAM this is performed by several Task Leaders and some projectpartners.

TheETisthegroupwhoactuallyperformthehazardassessment;thisgroupisledbytheTI.ThisteamisselectedjointlybytheTIandthePMand,inTSUMAPS-NEAM,itisconstitutedbytheprojectconsortium.

ThePoEismeanttoberepresentativeofthebroadertechnicalcommunity.ItsupportstheETforcriticalsubjectivechoicestroughthestructuredelicitationexperiments.ThePoEmaypartiallyoverlapwiththeET,anditactuallydoesinTSUMAPS-NEAM,butitshouldcontainasubstantial presence of external experts too, with no overlapwith other groups. Expertsshouldhaveeithersite-specificknowledge(e.g.,hazardsinthearea)and/orexpertiseonaparticular methodology and/or procedure useful to the TI and the ET in developing thecommunity distribution regarding hazard assessments. The experts of the pool actindependentlyandPoEmeetingsaremoderatedbytheTI.Typicalsizesofpanelsareintheorderof7-15components(e.g.,AspinallandCooke,2013),evenifsometimeslargerpanelsmaybeappropriate insomecircumstances(Hoffmannetal.,2007).ThePoEofTSUMAPS-NEAM ismade of 15 experts, selected among experts of earthquakes, tsunamis, both ingeneralandwithspecificknowledgeoftheNEAMregion,andofprobabilisticanalyses.Itiscomposed by 8 experts selected among the partners, and by 7 invited external expertsbelonging to the international scientific community. In particular, 3 of them are fromEuropeanInstitutions,4fromInstitutionsoutsideEurope.

The IR a group of experts who are meant to provide a peer-review of the process, themethods,andoftheresults.Commentsandrecommendationscanbeprovidedduringtheimplementation of the project (not only at the end); this participatory review processhappensatpre-defineddiscretestages.Inparticular,IRreviewstheprojectbothintermsoftechnical(scientificmodels,testingprocedures,etc.)andprocedural(actor’sindependency,transparency,consistencywiththeprojectplan,etc.)aspects (SSHAC,1997).The IRgroup


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size may on the complexity of the project. Note that through the participatory reviewscheme,theIRplaysanactiveroleduringtheprojectandthusitispartoftheprojectitself.Ifregulatorsorotherexternalauthoritiesforeseeanexternalreviewoftheprojectresults,this further review is performed independently and after the end of the project. InTSUMAPS-NEAM, the IR is composed by 5 experts, including end users belonging to CivilProtectionauthorities.

Wewon’t enterhere into thedetails of themanyactivities and the complex interactionsamong all these groupswhichoccurredduring severalmeetings, remote interactions anddaybydaywork.Wewill limitourselves todescribe, schematically, themainstepsof thetasksperformedortobeperformedwiththe involvementof thePoE; thesetasksarethecoreof a soliddecision-makingprocess concerning the subjective choicesamongpossiblealternative implementations and models, alternative weighting, and uncertaintyquantification.

The starting point for decisions is constituted by two formal feedbacks requested to thePoE,occurringduringtwodistinctTSUMAPS-NEAMprojectphases.

The first one is the pre-assessment,when a prioritization of the STEPS and LevelswithinwhichtheanalysisofthealternativesshouldbedeeperthanforotherSTEPSandLevels,astheyareexpectedtoinfluencetheepistemicuncertainty;hence,duringthispre-assessmentphase,thefullsetofmodelstobeactuallyimplementedisdefined,andconsequentlyotherpossiblemodels are excluded (“trimming” of the alternatives).When doing this, the PoEshould be provided with the necessary supporting material, including the description ofmethods,alternativemodelsand/orpotentialsensitivitytests.

Thisissueiscritical,sincetheexclusionofsomemodelscandrasticallymodifythebodyandtherangeofthecommunitydistribution;inotherworks,itcansignificantlyaltertheresultsof the assessment. Conversely, including all the available models is virtually impossible,probablyuseless,andsometimesdangerous(BommerandScherbaum,2008).

Thesecondphase istheassessment;theassessment includestheselectionoftheweightsforthealternativesincludedintheensemblemodelofS-PTHAuncertainty.

Both selection andweighting of alternativemodelsmay be based again on prioritizationtechniques, like the PC (Pairwise Comparison, e.g.,Maida et al., 2012), theAHP (AnalyticHierarchyProcess,fromSaaty,1980),andBBN(BayesianBeliefNetworks,e.g.,Bayraktaretal.,2009).

ThisprocessisconductedinTSUMAPS-NEAMasfollows.

Thepre-assessmentphasestartswithassessingtheorganizationalpartoftheprojectwithinthegivenconstraints (e.g. timing&totalbudget); theselectionofall themainactors, thepre-selectionof the structureof the assessment (STEPSand Levels presentedabove), the


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pre-selection of a vast range of possible alternative implementation. These activities endwiththeorganizationofaProjectkick-offmeeting,whichresultsinfulldocumentationofalltheseaspects.

Then a second meeting, the PoE kick-off meeting, is organized, where the experts arepresented with all the necessary elements and documentation. During this PoE kick-offmeeting,theassessmentworkflowandthepossiblealternativesarediscussedingreatdetailandinitialfeedbackisalsorequestedaboutpotentialgapsthePoEmayidentify.Moreover,the experts are presentedwith theworkflow of the foreseen decision-making process inwhichtheywillbeinvolved.Thisenabledaneffectivediscussionwithexpertstoclarifythescopeofthetasksofexpertelicitationsandtheirspecificrole.

TheformalfeedbacksofthePoEarebasedontheuseofstructuredexpertelicitationsofthePoE(forareviewofdecisionmakingbasedonexpertelicitations,seeMorgan2014),thatisthroughatrackableprocess.Notethattheuseofexpert judgements iswellestablishedinmany fields, such economics, politics, medicines, climate studies, volcanology andseismology,and ingeneral indecisionmakingunderuncertainty(e.g.,AspinallandCooke,2013;Morgan,2014).

The experts themselves are assigned weights for quantifying the “credibility” of theirfeedbacks.Weightingofexpertscanbedoneindifferentwaysanditisafundamentalpartoftheelicitationprocess,eventhoughoftenequal-weightedproceduresarestillconsidered(e.g., Cooke, 1991;Budnitz et al., 1998;Aspinall andCooke, 2013). In any case,weightedandnotweighted(i.e.equal-weighted)resultsarealwayscross-checkedforconsistency.

To achieve this, during the PoE kick-off meeting, the 15 experts of TSUMAPS-NEAMansweredtoaseedquestionnaire,preparedbytheTI,whichconsistedoftwoparts.

ThefirstpartofthequestionnaireconcernedtopicsrelatedtoS-PTHA,suchasearthquakeandtsunamisingeneral,probabilisticmethods,previousassessmentsintheNEAMregion.Theexpertswereaskedtoexpresstheirbestguessandconfidenceintervals(5th,50th,and95thpercentiles)toeachquestiontoquantifytheirownuncertaintyoneachsubject.Theirassessments were used to estimate weights using Excalibur, a software package forstructured expert judgement elicitation using the Classical Model (also called Cooke’sModel;Cooke,1991).

Duringthesecondpart,eachexpertwasaskedtoacknowledgetwootherexpertsofher/hischoicewithinthePoE.

Theseactivitiesarepropaedeutic to theapplicationofdifferentweightingschemes.ThreealternativeweightingschemesareindeedtakenintoaccountintheelicitationexperimentsofTSUMAPS-NEAM.ThealternativesschemesconsideredarePerformance-basedWeighting(PW;aimingtoquantifythe“credibility”ofexperts’answers intermsoftheircapability inconstrainingtheirsubjectiveuncertainty;Cooke,1991)andAcknowledge-basedWeighting


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(AW; aiming to quantify the “credibility” of experts’ answers in terms of theirrepresentativenesswithinthecommunity;Selvaetal.,2012).Weightsareassessedthroughthe questionnaire (Figure 6). EqualWeighting (EW) is also considered as a baseline. Theresults obtained in elicitation experiments under alternative weighting schemes will becompared, inorder tocheckconsistencyandsensitivityof theresults,andallwillprovidetheinputforfinaldecision-making.

OnceallissetduringthePoEkick-offmeeting,theformalinterviews(i.e.thetwoelicitationsteps, one for prioritization and trimming, and one for weighting) can be performedremotely,whichdecreasestheircost.

Figure6Comparisonofweightsassignedtoexpertsbasedonalternativeweightingschemes.

A firstelicitation round thenoccurs in theperiodof time following thePoEmeeting.Thiselicitationroundismeanttodesignthefinalschemefortheanalysisthatconcludesthepre-assessmentphase.

In this first elicitation the PoE is asked to make detailed pairwise comparison (PC, e.g.,Maidaetal.,2012)betweeneachpairofSTEPS,andthenbetweeneachpairofLevelswithineachSTEP,according toTable1. Theanalysisof the results is conductedwithanAnalyticHierarchyProcess(AHP,Saaty,1980).

Table1:Fundamentalscaleofabsolutenumbers

0

0,05

0,1

0,15

0,2

0,25

0,3

0,35

E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14 E15

Normalize

dweights

ExpertsinPoE

Comparisonofweights

AW

PW

EW


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As an example, we report only the result of the prioritization between the 4 STEPSpresentedbefore(Table2).AnalogousTablesexistfortheLevelswithineachSTEP.Wepointout once again that prioritization here means what STEP needs to be addressed byimplementing a larger number of alternative models since it is characterized by largerepistemicuncertainty;epistemicuncertaintyneeds, inturn,tobedescribedthroughthesealternatives.

Table2:ResultsfortheprioritizationofSTEPS

No. Modelcode Description1 STEP1 Definitionoftheseismicsourcevariabilityandquantificationofthelong-run

frequenciesofalltheseismicsources2 STEP2 Tsunamigenerationandoff-shorepropagation3 STEP3 Near-shoretsunamipropagationandinundation4 STEP4 ComputationoftheweightsofthealternativemodelsdevelopedinSTEPs1to

3tomeasuretheircredibility,andconstructionofthe“ensemble”model

Inparticular,theprioritizationsobtainedbythedifferentweightingschemesarecomparedbothintermsofcentralvaluesandofinter-expertdistributions.Basedonthiscomparison,thestepsandlevelsoftheSPTHAarerankedinthreegroups:

IntensityofImportance

Definition Explanation Weightsofmodels StandardAHPweights

1 Equalimportance

Twosteps/levels/sublevelscontributeequallytotheobjective

0.5-0.5 0.5-0.5(x1)

3 Moderatepreference

Experienceandjudgmentslightlyfavoronestep/level/subleveloveranother

0.6-0.4(x1.5) 0.75-0.25(x3)

5 Strongpreference

Experienceandjudgmentstronglyfavoronestep/level/subleveloveranother

0.75-0.25(x3) 0.83-0.17(x5)

7 Verystrongpreference

Astep/level/sublevelisfavoredverystronglyoveranother;itsdominancedemonstratedinpractice

0.95-0.05(x19) 0.86-0.14(x7)

9 Extremepreference

Overwhelmingevidencefavoringonestep/level/subleveloveranother

0.99-0.01(x99) 0.90-0.10(x9)


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- Highpriority(red):steps/levelswithclearhighpriorityinallweightingschemes.Forthese steps/levels, alternative implementations are strongly recommended by thePoE.Inthiscase,thealternativesshouldbecarefullyselectedtorepresentarangeofmodels that cover the full range of scientifically acceptablemodeling alternatives(following SSHAC 2012, “the center, body, and range of technically defensibleinterpretations”).

- Mediumpriority(orange):steps/levelswitheitherhighpriority inone(butnotall)theweightingschemes,orintermediatepriorityinallweightingschemes.Forthesesteps/levels, an evaluation of the potential consequence of alternativeimplementations is recommended by the PoE. In this case, some alternativeimplementations should be considered and/or some sensitivity test should beplanned.

- Low priority (green): steps/levels with low priority in all weighting schemes. Forthese steps/levels, the PoE suggests a relatively lowpotential impact of epistemicuncertainty,sothatonepreferredimplementationcanbeconsidered.

InFigure7,wealsoreportanexampleoftheAHPresults,obtainedfromtheanswersofthePoEduringthisfirstelicitation.Theplotscontain:

- The empirical CDF of the scores of the proposed alternatives, obtained byconsideringtheprioritizationofthedifferentexpertsasweightedsamples;

- The parametric variability of the scores of the proposed alternatives, consideringarithmeticandgeometricmeansandpercentiles16th,50th(median)and84th;

- TheConsistencyRatio(CR)(Saaty,1990)ofalltheexperts,comparedwiththresholdsof0.1and0.3;

- Theweightsoftheexperts,adoptingthedifferentweightingschemes.


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Figure7:AHPresultsfortheprioritizationofSTEPS,asdefinedinTable3.

After this elicitation the method could be drafted, with the selection of the alternativeimplementation. Basedon the above results, a larger number of alternativemodels havebeendevelopedtocarefullyexploreandquantifytheepistemicuncertaintyforSTEPS1and3thanforSTEPS2and4(andwithinthemfortheLevelsthatwerejudgedmoreimportant).Ofcourse,alternativemodelsareeitherimplemented,ifthisisfeasiblewithintheresourcesallocatedtotheproject;ortheneedfortheir implementationinafutureassessmentistobeclearlyreported.Thisdraftedmethodisthensenttoreviewers(IR).Afterthisreview,themethodcanbefinalizedandthefinalassessmentphasecouldbestarted.

Inansweringtothefirstelicitation,orduringtherevision, itmayemergetheexistenceofsubstantialgaps thatprevent thequantificationof the resultsunder specific conditions. Ifthesegapscannotbefilledwithintheproject,thesetypesofexclusionscanleadtoa“greyswan”(aneventwhichisforeseeable,butcannotbeconsideredintheanalysis;Paté-Cornell2012).Toquantifytheeffectsofthesegaps,missingmodelsandtheselectionofscenariosmight be, performed, for example through the so called “Classical model” or “Cooke’smethod”forstructuredexpertjudgment(e.g.,Cook,1991;Nerietal.,2008).InTSUMAPS-NEAM,onecriticalaspectthatemergedduringthePoEkick-offmeeting,wastheimmediateneedforalternativesatSTEP3andmoreingeneraltheuncertaintyquantificationrelatedtothisSTEP.Forthisreason,aspecificstudyhasbeendevelopedwithinASTARTE(describeinthenextSection3.2),todeviseanuncertaintyquantificationmethodtobethenappliedtotheTSUMAPS-NEAMS-PTHA.ThisispresentedinthenextSection.

AtthisstageofTSUMAPS-NEAM,afullpreliminaryS-PTHAhasbeenconducted,sofaronlyfor the Mediterranean (as already reported in Figure 5). Preliminary weights have beenassigned by now to the alternative models. The second elicitation will concern the


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assessmentthroughthePoEofthefinalweights,withsimilarmethodstothoseillustratedforthefirstelicitation.

Toquantifytheweightsofalternativemodels,thissubjectivecredibilitymaybealsomixedwithmoreobjective criteria (e.g., resultsof sanity checks; resultsofmodel’s correlations;likelihood score for independent data), based on the performance of the models onindependentdata(e.g.,Marzocchietal.,2012;Daviesetal.,2017)and/oronsanitychecksonrecentdata.

Once all methods are implemented and weighted, the different results should beaggregated to express the community distribution. This is done in TSUMAPS-NEAM bymeansofensemblemodelling(e.g.Selvaetal.,2015).

3.2Quantificationoftsunamirun-upuncertaintyusingapproximateamplificationfactormethodsThestandardwayofestimatingthetsunamirun-upandinundationmapsistoapplydepthaveraged nonlinear shallow water (NLSW) models that include drying-wetting schemes.However, these detailed numerical inundation simulations are too intensive computationwisewhen (i)weneed toestimate tsunami run-upheight formany (often thousandsandmillions) of scenarios (such as for PTHA) and (ii) we need to cover large stretches ofcoastlines with complex geometries, for instance covering scales over one or morecountries.

While intermediate methods limiting the number of scenarios in PTHA exists (e.g. thepioneering application of Gonzalez et al., 2009 and the formal procedures developed byLoritoetal.,2015),weneedsimplermethodsfordeterminingtsunamiinundationheightsinPTHA and over large regions. To this end, a faster procedure, with a higher degree ofapproximation, is to relate the near-shore surface elevations at the hazard points to themaximum shoreline water levels. The surface elevation at the shoreline then acts as anapproximation for themaximum inundation height or run-up height along the shoreline.ThemethodisdescribedbyLøvholtetal. (2012)andLøvholtetal. (2015).Combinedwithresultsfromoffshoretsunamisimulations, itcanbeusedtoestimatethemeanormediantsunamirun-upormaximuminundationheightatacoastallocation.

Anewversionoftheamplificationfactormethod,takesintoaccountthelocalbathymetry.The methodology has been developed for production of tsunami hazard maps for theTSUMAPSproject (http://www.tsumaps-neam.eu/). Thenewmethod, as briefly describedbelow,usesasetofdifferentlocaltransectsnormaltothecoastlineasabasisforestimatingtheamplificationfactortobeappliedtotheincomingtsunamiasmodeledatasinglepointofinterestinfrontofthestretchofcoastunderexamination.Thelocalamplificationfactormethod is expected to replicate the median tsunami inundation height more accurately


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than the previousmethod using idealized profiles (Løvholt et al., 2012). However, as themethodisintrinsicallydeterministic,weneedtocomparethemethodwithlocalinundationmodels toquantify itsassociatedbiasanduncertainty.Quantifying thisuncertainty isalsonecessaryforthegeneraluncertaintyquantificationoftsunamihazardsinTSUMAPS.

Previous attempts to measure the bias of the amplification factor method, as well asquantifyingtsunamiinundationheightuncertainty,islimitedtoasinglestudy(Daviesetal.,2017). This study estimated the amplification factor uncertainty and bias by comparingtsunamisimulationscombinedwithamplificationfactoranalysiswithobservedrun-upfromfield observations for four large tsunamis (Chile, 1960; Alaska, 1964; IndianOcean, 2004;Tohoku,2011).WealsonotethattheanalysisofDaviesetal.(2017)usedaversionoftheamplification factors that was based on idealized and much simplified bathymetrictransects.

Daviesetal.(2017)foundthattsunamisimulationscombinedwiththeamplificationfactorgave a relatively small bias compared to field observations (the amplification factoroverestimated the maximum inundation height), however, a large lognormal variance of(σ2≈1) was found. However, in these results the uncertainty was mixed with the sourceuncertainty.SinceDaviesetal.(2017)consideredrealcaseswherefielddataarecomparedto full simulations of tsunamis from the generation to the target site, this comparisonimplicitlycombinesthevariabilityduetoheterogeneousslip,othersimplificationsinsourceandtsunamigenerationandpropagationmodeling,inadditiontotheinherentvariabilityinthe run-up process itself. It is therefore desirable to conduct a dedicated study that onlyaddress the uncertainty of the run-up process, by directly comparing detailed high-resolutioninundationsimulationstothoseusingtheamplificationfactors,butstartingbyacommonsourceandopenoceanpropagationmodel.

In the present section, we carry out a set of local inundation simulations for differentearthquakesourcemagnitudes,andcompare thedistributionof themaximum inundationheights (MIH)withresults fromthe localamplification factors.Thework isacollaborativeeffortincludingpartnersfromNGI,INGV,GFZPotsdam,andIPMA.Inaddition,NOAandUBhavecontributedwithlocalbathymetricandtopographicdata.Thesimulationsarecarriedout at three ASTARTE test sites (Heraklion, Crete, Greece; Colonia Sant Jordi, Mallorca,Spain;andSines,Portugal).Foreachsimulation,weestimatethebiasof theamplificationfactormethod,bycomparingtheresultswithmedianlocalMIHvaluesderivedfromNLSWmodels. Furthermore,wederive the lognormalσof theMIH from theNLSWmodels.Wealsodiscuss theoverall uncertainty forall the simulations combined.Weuse thevariableMIHfromtheNLSWmodelstoincludeuncertaintytotheMIHamplificationfactormethod.Inaddition,weconductbasicstatisticsof theamplificationfactorbias.Thisstatistics isanadditionalsourceofepistemicuncertainty(inadditiontothelocalMIHvariability).


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3.2.1Newsetofamplificationfactorsbasedonlocalbathymetrictransects

Here,webrieflyexplainanimprovedmethodofamplificationfactors,basedontheoriginalwork of Løvholt et al. (2012).Where Løvholt et al. (2012) used a limited set of idealizedbilinearprofiles to represent thebathymetry,wehereuse localbathymetricprofiles. Thenewmethodisbasedonthefollowingsteps:

ü Theamplificationfactorsarecomputedforevenlyspacedhazardpoints locatedevery20kmalongtheshoreline.Thisispartlytoavoidtheimpressionthattheamplificationfactors canbeused for local analysis, as they are only to beused for rough regionalhazardestimation. In thisway,wealsoobtain thedesired slowly varying run-upas afunctionofthealongshorecoastalcoordinate.

ü Ateachhazardpoint,about40depthprofilesareextractedmoreorlessnormaltotheshoreline,eachwithadistanceof1kmapart(seeFigure8).Insomeareastheprofilesareextractedmanually,butmostoftheprofilesareproducedautomaticallyfromlinearinterpolationoverSRTMbathymetricmapsinArcGIS,seeFigure9.

ü Theamplification factorsarecomputedalong sevenarbitrarily selectedprofiles (fromthe40profiles)byusinga1HDlinearshallowwaterwavemodel(LSWmodel).Aninitialwaveof1mheightindeepwater,shapedasasingleperiodsinusoidalshapedwave(N-wave)isfedovertheboundaryofthemodel.

ü Foreachprofile,thefollowingparametersarevaried:§ Thepolarityoftheincidentwave,i.e.eitheraleadingtroughorleadingpeak.§ Thewaveperiodsare120,300,600,1000,1800,3600secondsrespectively.

ü Foreachsimulationthemaximalsurfaceelevationsat50mdepthandattheshoreline(0mdepth)areextracted.Theratiooftheheightbetweenthelatterandthefirstistheamplificationfactorforthepresentprofile.

ü Themedianvalueofthesevenamplificationfactorsareextractedforeachcombinationofwaveperiod,polarity,andhazardpoint,seeexampleinFigure10.Allcombinationsare stored in lookup-tables.As anexample, amplification factors for a leading troughpolarityandwaveperiodof600sfortheMediterraneanandBlackSeaaredepictedinFigure11.

ü Some hazard points that were accidentally left out without factors in the automaticselectionprocedure(forvariousreasons)aresetequaltoclosestneighbouringfactor.

ü Twoversionsofthefactorswereproduced,onesetusingtherawdatavalues,andoneset of factors smoothed along the shorelinewith amedian filter, to avoid artificiallyshort amplification fluctuations along the shoreline, see example for theBlack Sea inFigure12.


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Figure8:Exampleofasetof40depthprofilesrepresentingahazardpoint.

Figure9:ExampleofasubsetofprofilesfortheMediterranean.


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Figure10:TheamplificationfactorsforthesevendepthprofilesrelatedtoagivenlocationintheMediterraneanversusthewaveperiod(seconds).Theredandbluecurvesarefactorsforleadingpeakandleadingtrough,respectively.Thethincurvesarethefactorsforthesevenlocalprofiles,whilethethicklinesarethemedianvaluesforleadingpeakandleadingtroughatthislocation.

Figure11:TheamplificationfactorsfortheMediterraneanandBlackSeaforthecasewithaleadingtroughandawaveperiodof600s.Thefactorsarefilteredalongtheshorelinewithamedianfilterasexplainedinthetext.


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Figure12:TheamplificationfactorsforBlackSeaasfunctionofthehazardpointslyingalongthe shoreline (ID numbers). The figure shows the effect of filtering the factors along theshoreline. The labels "neg" and "pos" relate to leading trough and leading peak,respectively.Thetag"-sm"meansthefilteredvalues(medianfilter).

3.2.2Setupoflocalinundationsimulations

ThecomparisonsbetweentheamplificationfactorsandtheNLSWmodelsareundertakenatthe three ASTARTE test site locations Sines, Colonia Sant Jordi, and Heraklion. For eachlocation,weuse3-4earthquakesourceswithvaryingmagnitude.Wehaveemployedatotalof11differentsources,9withmagnitudesMw7.0,Mw7.5,andMw8.0(earthquakeswiththissourcemagnitude is employed for all locations). In additionwehaveapplied two sourceswith larger magnitudes, a Mw8.5 earthquake at Sines and a Mw9.0 at the Hellenic Arc(impactingHeraklion),respectively.

Different inundation models are employed for the different locations. The tsunamipropagation and local inundation simulations for Sines run-up are modelled with theNSWINGmodel (e.g.Wronnaetal.,2015).ForColoniaSant JordiweusebothHySEA(seee.g. de laAsunción, 2013) aswell as amodel combinationofGloBouss andComMIT (seePedersenandLøvholt,2008;TitovandGonzales,1997).ThecombinationofGloBoussandComMIT is also used for Heraklion. In both cases, GloBouss is used for the propagationstage and to produce the input to the inundationmodel ComMIT (propagation files), seeLøvholtetal.(2010).Alloffshoretsunamisimulationsareconductedonregulargridswitharesolution of 30 arcsec. The NLSW models used nested grids for simulating the localinundation.Inthepresentinvestigations,theresolutionofthefinestgridisabout10matalllocations.TheManning-friction(n)isinallsimulationssetton=0.03.

Foreachtestsiteandsourcescenario,weestimatethedeterministicMIHbyusingthenewamplification factor method as described above (Section 3.2.1). The wave characteristicsneeded to determine the amplification factors are extracted from the simulated offshoresurface elevations at thehazardpoint placedon the 50m contour outside each test sitelocation. Surface elevations arriving more than 2 hours after the first wave arrival were


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neglected.TheMIHisthenquantifiedbymultiplyingthemaximumsurfaceelevationatthehazardpointbytheamplificationfactorsfromthelookup-tables.WeinterpretthisvalueasthemediantsunamiMIH.

The characteristic wave period used to derive the amplification factor is extractedautomaticallybyalow-passfiltermethod.Thefilteringwasconductedtoremovespuriousshortoscillationsthatcouldleadtotoosmallwaveperiodestimates.Thedetailsofthelowpassfiltermethodarenotprovidedhere.Instead,weprovideanexampleofitsoutput.InFigure13,weshowanexampleofthesimulated(blackcurve)andafiltered(redcurve)timeseries of a tsunami offshore Colonia Sant Jordi emerging from aMw 8.0 earthquake. ThesimulatedtimeseriesisproducedbytheGloBoussmodel.Fromthefilteredtimeseries,thelocationofthehighestpeakwithinthetimeframeof2hoursaredetermined,seeverticalmagenta line. Themaximum surface elevation value is taken at the unfilteredmaximumlocation (marked with a magenta bullet). The wave period is the duration between thetroughsaheadandbehindthe leadingpeakmeasuredonthe filteredtimeseries,andthewave period interval is indicated by cyan coloured bars. We stress that the filteringalgorithm is only used to derive wave periods, and not the simulated offshore waveamplitudes.

Figure13:Exampleofextractingthewavecharacteristics fromthehazardpointonthe30arcsec simulations (black line) at a hazard point with ID 10746. The vertical axis is thesurfaceelevation inmeters,whilethehorizontalaxis isthetimeinminutes.Themaximum


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valueismarkedwithamagentabullet,whilethewaveperiodismeasuredbetweenthetwocyanverticallines.

3.2.3Estimatingthemaximuminundationheightuncertainty

For each scenario, we extract themaximum inundation height from the local inundationsimulationsforthefinestgrid.WethenmakeMIHdistributionsbyextractingmaximaeitherinNorth-SouthdirectionorEast-Westdirection lineby line. I.e., if the shoreline ismostlyEast-West, we search along lines oriented in the North-South direction, while if theshorelineispredominantlyorientedmoreNorth-SouthwesearchalonglinesorientedintheEast-Westdirection.Insomespecialcasestheheightoftheterrainlandsideoftheshorelineis too high and too steep to be inundated. In these situations, we include values ofmaximumsurfaceelevationforasmalldistanceseasidefromtheshoreline(atleastonecellaway).

Fromthis,weobtainaMIHprobabilitydensityforeachsimulation(i.e.foreachinundatedlocation).EachsuchMIHprobabilitydensityisthenfittedtoalognormalprobabilitydensityfunction(PDF)usingstandardPDFfittingproceduresinMatlab.WenotethatthelognormalPDF implies a normal distribution of the natural logarithm of the random variable withvarianceσ2,inthiscasetheMIH.ThelognormaldistributionoftheMIHreads:

𝑝 𝑀𝐼𝐻 =1

2𝜋 ∙ 𝑀𝐼𝐻 ∙ 𝜎𝑒L

(MN OPQ LR)STUS

WenotethattheMIHmedianandmeanvaluesforthelocalprobabilitydistributionsare𝑒Rand𝑒RVUS/T, respectively.BoththefittedmeanandmedianMIH'sarecomparedwiththeresults from the amplification factors, in order to quantify biases for the individualsimulations.Tothisend,twodifferentexpressionsforestimatingthebiasesareused;firstadirectcomparisonbetweenthelogarithmsoftheMIHfromtheamplificationfactorwiththenormalmeanfromthefitteddistribution

𝜖Y = ln 𝑀𝐼𝐻 − 𝜇

andsecondanormalizederrormeasure

𝜖T =𝑒R − 𝑀𝐼𝐻

𝑒R


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3.2.4Results

VariousexamplesoftheMIHdistributionsfromNLSWsimulationsareshowninFigure14-Figure19.Wenotethatinourpresentestimatesoftheoverallbias,wedonottakeincludetheeffectofthechangeinthetopographyduetheearthquakedisplacement.Theeffectofchangeintopographyaffectsthelargesttwoevents(Mw8.5SinesandMw9.0Heraklion).Forthesetwoevents,weshowresultsbothwithandwithoutthetopographiccorrection.

Withoutconductingaformaltest forquantifyingthesuitabilityofthe lognormal fit,visualinspectionofthedifferent individualsimulationsrevealsthatmorethan50%oftheNLSWsimulations exhibit lognormal characteristics. This is particularly the case for the highermagnitude simulations for Heraklion and Colonia Sant Jordi. The Mw7.0 events have atendencytobemoreirregular.Moreover,theMIH'sfortheSinestestsiteseemtoseparateintodifferentbins,beingmorecomplex thana simple lognormal.Thismaybedue to theparticularcharacteristicsofthistestsitecombinedwiththesource.

FortheHerakliontestsite,theamplificationfactormethodseemstooverestimatetherun-upinmostcases,andexceptfortheatypicalsubductionzoneevent,wefindalogarithmicbias of є1~0.2. The uncertainty σ seems to be largest for the smallestmagnitudes (0.36-0.47),beingclearlysmaller for the largestones (0.17).For thesubductionzoneevent,weseethatnottakingintoaccountthetopographychangesintroducesalargebias(Figure15).

For the Colonia Sant Jordi test site we find the largest biases compared to the ComMITmodel, whereas HySEA providesMIH's close to or slightly smaller than the amplificationfactormethod.Forthelargestmagnitudes,thebiasesarerelativelysmall,є1rangingfrom-0.09to0.23.Uncertaintiestypicallyrangefrom0.2to0.3.WealsoseethatHySeaprovidessmaller MIH's than ComMIT. We remark that both of these codes are thoroughlybenchmarkedtowardsstandardbenchmarktests(Liuetal.,2008).

TheSinestestsitediffersfromtheothersbyitsmorecomplicateddistributions,andthefactthattheamplificationfactorsseemtosystematicallyunderestimatetheMIH.Thenegativebias shows the biggest deviations for the smallest moment magnitude, which is againsupposedly due to the characteristics of the site. TheMIH uncertainty is otherwise quitecomparabletotheothertestsites.Forthelargest(Mw8.5)eventclosetoSines,weseethatnottakingintoaccountthetopographychangesintroducesalargebias(Figure15).


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Figure14:DistributionofMIHand fitted lognormaldistribution for theHeraklion test siteusingtheComMITmodel.Upperpanel,Mw7scenario;lowerpanel,Mw7.5scenario.


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Figure15:DistributionofMIHandfittedlognormaldistributionfortheHerakliontestsiteusingtheComMITmodel.Upperpanel,Mw8scenario;midpanel,megathrustsubduction


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scenariofromtheHellenicArc(notcorrectedfortopographicchange),lowerpanel,megathrustsubductionscenariofromtheHellenicArc(correctedfortopographicchange).


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Figure16:DistributionofMIHandfittedlognormaldistributionfortheColoniaSantJorditestsiteusingtheComMITmodel.Upperpanel,Mw7scenario;midpanel,Mw7.5scenario;lowerpanel,Mw8.0scenario.


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Figure17:DistributionofMIHandfittedlognormaldistributionfortheColoniaSantJorditestsiteusingtheHySEAmodel.Upperpanel,Mw7scenario;midpanel,Mw7.5scenario;lowerpanel,Mw8.0scenario.

Figure18:DistributionofMIHandfittedlognormaldistributionfortheSinestestsiteusingtheComcotmodel.Upperpanel,Mw7scenario;lowerpanel,Mw7.5scenario.


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Figure19:DistributionofMIHandfittedlognormaldistributionfortheSinestestsiteusingtheComcotmodel.Upperpanel,Mw8.0scenario;midpanel,Mw8.5scenario(notcorrectedfortopographicchange),lowerpanel,Mw8.5scenario(correctedfortopographicchange).

3.2.5Summaryanddiscussion

Bothpositiveandnegativeamplificationfactorbiasesarefoundforthevarioussimulations.Themeanbiasishoweverclosetozero(Figure20).Itisnotedthattheinvestigationisbasedon just a few locations, and ideally,manymore sites shouldbe investigated toprovide abroadersetofdataforamorereliabledistribution,particularlyforthebias.Ononehand,the present investigation does not hold evidence for the need for correcting theamplificationfactormethodtoalargeextent.Ontheotherhand,thereisaneedtakeintoaccountuncertaintyofthemedianvalueoftheMIHduetotheamplificationfactormethod(reflectedbythebias,σbias=0.3).Themeanlognormalσforallthesimulationsis0.26(Figure21).Altogether,thislocalvariability(lognormalσ)needstobeaddedtothevariabilityofthemean value for each simulation. If we assume that the two are independent, a simplestrategycanbe toadd theirvariances,givinga totaluncertaintyσtot~0.4.Thisuncertaintyshouldbeaddedtothesourceuncertaintyduetovariableslip,faultorientation,variabilityofsourcerigidity,etc.Forexample,Geist(2002)reportsofcoefficientsofvariationsintherange of 0.25-0.35 for variable slip uncertainty. A total uncertainty would need toincorporatethisinadditiontotheuncertaintiesfoundherefortheinundationalone.


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Figure20:Histogramshowingthelognormalbiasforthedifferentsimulationsinvestigated.Themeanbiasisclosetozero.Here,thetopographychangeisnottakenintoaccount.Ifwetakeintoaccountthetopographychange,thebiaswillincreasefrom-0.03to+0.02.

Figure21:Histogramshowingtheuncertaintydistributionforthedifferentsimulationsinvestigated.


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4.Conclusionsandoutlook

Uncertaintyquantificationisthekeyforcomparinghazardandriskanalyseswithpastdata,andtoscientificallytestandeventuallyfalsifythem(Section1).Thiscomparisonistheonlypossiblestrategytoidentifyontologicalerrors.Amongtheavailablemethods forhazardandriskquantification,onlyprobabilisticmodelsarefocusedtothequantificationofuncertainty(Section2).Scenario-basedapproachesdonotquantifyuncertainty,buttheymayprovideimportantcluestofeeddecisionmakingaswellasprobabilisticmodels.Thedefinitionof reference returnperiods for scenario-basedanalyses provides a tool to compare scenario-based and probabilistic hazard and riskquantifications. By means of this comparison, scenario-based and probabilistic methodsmayfeedtoeachother.Probabilisticapproachestargettoquantifyallsourcesofuncertainty(Section2).Ontheoneside, they should explore the effective variability of any potential tsunamis source,irrespective of the occurrence of tsunamis from that source in the (known) past. On theother side, they test the impact on the results of alternative and scientifically acceptablecomputationalmethodologies.Thisleadstoincreasethemethodologicalcomplexityandthecostsoftheeffortstowardthequantificationofhazardandrisk.Inparticular,itrequirestheestablishment of standards for the analysis of source variability and of protocols for themanagementofunavoidablesubjectivity.Within the tsunami community, fully probabilistic approaches are still in development. Inparticular, probabilistic tsunami hazard approaches are under development mainly forseismic sources (S-PTHA). Fewprobabilisticmodels are available for vulnerability and riskquantification,mainlybasedonempiricalapproaches.AnS-PTHAmodelisbeingproducedfor the NEAM region (http://www.tsumaps-neam.eu/). A global effort is ongoing forextendingtheavailablemethodologiesanddefiningcommonstandardsandgoodpractices,in the framework of the Global TsunamiModel (GTM, www.globaltsunamimodel.org). Inthis respect, thisdocument collectedandorganized several ongoingefforts toestablish afirst step in this direction (Section 3). This effort leads also toward a standardization oftsunami practices in line with the best practices adopted for other (natural) hazards, inmulti-hazardriskperspective.Hazardandriskassessmentsbasedonprobabilisticapproachesproducealargeamountofinformationthatcanincreasetheawarenessofdecisionmakingovertheseresults,forlocalplanners,stakeholdersandevenforthegeneralpublic.However,thecomplexityoftheseresultsmaybeanobstacle to thisprocess. Therefore, scientists shouldmakeaneffort toimprovethecommunicationofuncertainty,byorganizingappropriateoutreachactionsandby establishing tools andprocedures for assessing the results anddistilling the importantinformationincludedinthem.


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