The evaluation of forest crop damages due to climate change. An application of Dempster-Shafer method

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JournalofForestEconomics17 (2011) 285–297

ContentslistsavailableatScienceDirect

Journal

of

Forest

Economics

j o u r n a l h o m e p a g e :w w w . e l s e v i e r . d e / j f e

The

evaluation

of

forest

crop

damages

due

to

climate

change.

An

application

of

Dempster–Shafer

method

Iacopo

Bernetti, Christian

Ciampi,

Claudio

Fagarazzi,

Sandro

Sacchelli

∗

Dept.ofAgriculturalandForestEconomics,Engineering,SciencesandTechnology,18,PiazzaledelleCascine,I-50144Florence,Italy

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received19January2010

Accepted28April2011

Keywords:

Dempster–Shafertheoryofevidence

Climatechange Forestry Fuzzysets Spatialanalysis Uncertainty JELclassiﬁcation: Q19 Q54

a

b

s

t

r

a

c

t

Inordertoassessdamageriskcausedbyclimatechangein for-estareas,Dempster–Shafertheoryofevidenceandfuzzymeasures wereappliedtodevelopaframeworkfortheestimationof eco-nomicforestdamage.Accordingtothedefinitionofrisksupported bytheIntergovernmentalPanelonClimateChange,afunctionof hazardandresiliencelinesofevidencewasdefined.Theresults ofthehazardandresilienceassessmentwereusedtodevelopan economicframeworkbasedonFaustmannstudies.Theevaluation model,implementedthroughaspatialanalysisprocedure,was car-riedoutlinkingFaustmann formulawithhazardandresilience rastermaps.Themodelpermittedtoestimateinmonetaryterms twopossiblecoststobesupported:thefirstoneisexpressedas theexpecteddamagetotheforestcroponthebasisofthecurrent obtainablewoodyassortmentsandthesecondonereferredtothe potentialexpensestopayinordertomitigatetherisk.Finally,the frameworkwastestedonanareaofcentralItaly(Tuscanyregion).

Introduction

ResearchonthepossibleimpactofclimatechangeonforestsinEuropeandthedevelopment

ofadaptationandmitigationstrategiesstartedintheearly1990s;sincethen,assessmentonclimate

change,itsimpactandconsequencesonnaturalresourcesmanagementhavebeenthefocusof

contin-uousresearchefforts(EFIetal.,2008).Amongtheknowneffectsofclimatechangetherearealteration

∗ Correspondingauthor.

E-mailaddress:sandro.sacchelli@uniﬁ.it(S.Sacchelli).

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intreesgrowthandproductivity(KauppiandPosch,1988;Loustauetal.,2005),variationsin

for-estareaandcompetitionbetweenspecies(Solomon,1986;Lexeretal.,2002)anddamagevariation

causedbynaturaldisturbances(Flanniganetal.,2000).

Severalmethodologieswereimplementedtoassesshazardandresilienceinforestsector.One

promisingevaluation ofthesetwovariables hasbeenprovided byNitschkeand Innes(2008).In

theirresearchameta-modellinganalysiswasdevelopedtoincorporatethestrengthofmanysmaller

modelsintoaframeworkthatconsidersnaturaldisturbances,ﬂoralandfaunalspeciesandspecies

habitats.

Awidereviewonmodellingforestecosystemdisturbancesandonnaturalhazardassessingwere

developedinrecentworksofSeidletal.(2011)andHanewinkeletal.(2010a),respectively.Fromthese

studiesitispossibletodepictseveralexamplesofmethodologiesthatcanbeappliedtodescribeharm

andadaption.Seidletal.(2011)classifythemodelsaccordingtodisturbancestypology(event-based

orregime-based)in:(i)statistical,(ii)staticordynamicprocess-based,(iii)vegetationorlandscape

dynamicsand(iv)plantphysiologymodels.Hanewinkeletal.(2010a)dividemethodstomodelrisk

inexperimental(e.g.mechanisticmodel)andempirical(bothanalyticalandoutputorientedmodels).

Despitetheintensiveresearcheffortsintheabovetopics,inclimatechangescenariotheprecise

evaluationofeconomiclosseswithhighterritorialdetailisadifﬁculttask.Speciﬁcally,themainaspects

tobetakenintoaccountare:(1)theimpactassessmentvarieswidelydependingonthesimulation

modelapplied,theclimatescenarioinvestigatedandthegeographicandecologicalcharacteristicsof

thecrop;(2)thereisconsiderableuncertaintyconcerningtheinteractionsbetweenvulnerabilityand

adaptationabilityofforestecosystems.

Themainobjectiveofthisstudyistogiveapreliminaryassessmentoninnovativekindofeconomic

analysisinclimatechangeforestsector,inparticular: (i)toevaluatetheriskofvulnerabilityand

theprobabilityofresilienceoftheforeststhroughprobabilisticandsubjectiveestimationand(ii)to

estimatetheﬁnancialconsequencesofclimatechangebywayofthecalculationofboththehazard

damageandthevalueofriskmitigationinforeststands.Theappliedprocedureimplementedland

expectationvalue(LEV)calculatedbyFaustmannapproachandDempster–Shafertheoryofevidence

(DS).

Asamatteroffactseveralauthors(e.g.Buongiorno,2001)demonstratedthattheFaustmann

for-mulaisabletoincorporatebiologicalandeconomicrisks.Themethodologychosentocarriedoutthe

research(DStheoryofevidence)permitstoovercomethelimitsofBayesianapproachinanuncertain

frameworkasfortheclimatechangeone.

DStheorywasalreadyusedinenvironmentalsectorindifferenttopics.Severalstudiesdeﬁneland

coverestimationandlandcovermonitoringtechniquescarriedoutthroughtheuseofDStheory(see

e.g.Cayuelaetal.,2006;Comberetal.,2004).Thistheorywasalsointroducedinclimatechange

uncertaintyevaluation(RajeandMujumdar,2010;LouandCaselton,1997).Indifferentresearches

DStechniquewasappliedinforestsector;someexamplesconcern:(i)waystomeasuresustainability

offorestmanagementandtooperationaliseitintermsofutilitymaximisationinlandusestrategies

(Varmaetal.,2000);(ii)deﬁnitionofuncertaintyinforestmanagementandsilviculturaldecision (Ducey,2001)and(iii)provisionofpracticaltoolinordertoestimatestandregenerationmaps(Mora

etal.,2010).Actually,accordingtoauthorsknowledge,DStheoryofevidencehasneverbeenusedfor

economicevaluationofforestunderclimatechangeconditions.

Methodologicalframework

TheadoptedmethodologicalframeworkissummarizedinFig.1.Accordingtointernational

litera-tureriskhazardtoclimatechangeandresilienceofforestcropswasdeﬁned.Then,basedonexperts’

knowledge,thefactors(criteria)deﬁninghazardandresiliencewereanalysed,evaluatedthrougha

fuzzymethodologyandlinkedtoaGeographicInformationSystem(GIS).TheuseofDempster–Shafer

(DS)approachpermittedtoaggregateallcriteriainthreeindicatorsofsubjectiveprobabilitiesdeﬁned,

accordingtoDStheory,as:beliefofhazard,beliefofresilienceanduncertainty.

Finallyexpectedlosscausedbyclimatechangewasestimatedbylinkingsubjectiveprobabilityand

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I.Bernettietal./JournalofForestEconomics17 (2011) 285–297 287

Fig.1.Flowchartonmethodologicalframework.

Climatechange,vulnerabilityandadaptationcapability

Resilienceisdeﬁnedastheabilityofaforesttoreacttoexternalenvironmentalchanges,

maintain-ingacertaindegreeofecologicalstability,bothintermofspeciescompositionandmaintenanceofthe

structure.Hazardrepresentsthedegreeofriskofdestructionand/ordamageofanarea.Inthisresearch

thepresentvalueofvariablesthatpotentiallyhaveagreaterinﬂuenceonthehazarddegreewasrelated

withthepossibilityofaclimatechange,accordingto:(i)averagespeedofwind,(ii)yearly

cumula-tiveprecipitationsand(iii)yearlyaveragetemperatures.Futurevalueoftheseclimaticvariablesare

basedonA2scenariooftheHadleyCentreMetOfﬁceClimateModelling3(Hadcm3)developedby

IntergovernmentalPanelonClimateChangeandre-elaboratedforTuscanyregion(Moriondoetal.,

2010).

Accordingtothenationalandinternationalliterature(Carraroetal.,2007;EFIetal.,2008)the

followingindicatorsarechosenfortheevaluation:

• Resilience

◦Managementinterventionsontheforestcrops(expressedasapercentageofforestsurfacewith

managementinterventions);

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◦ Presenceofprotectedareas;

◦Ecologicaldiversity;

◦Landscapediversity.

• Hazard

◦ Wind,asnumberofyearlyextremeevents;

◦ Aridity(basedonDeMartonneindex);

◦ Slope; ◦ Aspect;

◦ Changeinphytoclimaticzone(basedonPavariclassiﬁcation).

Theoryofevidence

Researchfornewmethodologiesdealingwithsubjectiveprobabilitiesandwiththeresulting

uncer-tainty(mainlyasanalternativeorarevisiontoBayesianapproach)wasintensiﬁedoverthelast50

years.Inforesteconomicandpolicysector,a varietyofnewapproachesforthis topichave been

proposed(e.g.HildebrandtandKnoke,2011;GadaudandRambonilaza,2010).Animportantissue

intheclimatechangeassessmentcanberepresentedbythedifﬁcultyuncertaintyevaluation;ina

decisionproblem-solvingframework,uncertaintycouldbeaccessibleandusefultodecision-makers.

AsexpressedbyPattandDessai(2005)“theliteratureinbehavioureconomicsprovidesmanyexamples

ofhowpeoplemakedecisionsunderconditionsofuncertaintyrelyingoninappropriateheuristics,

lead-ingtoinconsistentandcounterproductivechoices”.Thereforeanin-depthanalysisabletorelaterisk

managementevaluationanduncertaintyisanecessarypolicytool.

Themethodologicalframeworkappliedinthispaperfortheclimatechangeconsequences

esti-mationderivesfromthesefollowingmethodologies:(i)fuzzysettheory,inwhichtheuncertaintyis

associatedwithvague(typicallylinguistic)variables(appliedtoclimaticresearchinScherm,2000);

(ii)Dempster–Shafertheoryofevidence(DS),thataimsatgoingbeyondthelimitsofaprobabilistic

formulation(Bayesianapproach)(LouandCaselton,1997).

TheBayesianformulationrepresentsthestartingpointoftheplausibilitynotiontreatmentinDS

theory:thetwoapproachessharetheideathattheplausiblereasoningisatypeofuncertainreasoning

becauseitiscarriedoutbyusingsourcesthatgiveinformationcharacterizedbyadegreeofreliability

butnotofcertainty.UnliketheBayesianprobabilities,DStheorydoesnotneedcompleteinformation

inthespaceoftheevents;thus,thistheoryallowstheuseoftwodifferentvaluesinordertoexpress

thecredenceinaspeciﬁcproposition,orthecredenceinitsnegation.

Inthisstudytwopropositions(calledlinesofevidence)weredeﬁned:hypothesish=vulnerabilityof

thegeographiclocalizationandhypothesiss=resilienceofthelocalization.The“non-singular”

hypoth-esis[h,s]representsthevalueoflocalizationsthatareatthesametimevulnerableandresilient.The

conceptofDSprobabilitypdiffersfromtheconceptofBayesianprobabilitybecausefortwo

hypothe-sesA1 andA2 intheDStheorywewillhavep(h)+p(s)+p(h,s)=1and thusp(h)+p(s)<1,whilein

Bayesp(h)+p(s)=1.Theremainingp(h,s)representsthecontributiontouncertainty.Theevaluation

ofthehypothesisisbasedontheconceptofBasicProbabilityAssignment(BPA).TheBPArepresents

thecontributionthatacertainfactor(ai)givesasasupportforaspeciﬁchypothesis(forinstancethe

vulnerabilityofastand).TheassessmentofBPAisbasedonthecombinationoffuzzyfunctionson

environmentalandsocio-economicvariablesandlinguisticevaluatorswhichwereusedinthemodel

(expressedasadegreeofbelief).Theevaluatorsweregivenbyexpertsasoralterms(Bentabetetal.,

2000);modelformulationwasexplainedinthefollowingformula:

BPA(ai,x)=linguistic(ai)·ai(xai) (1)

withlinguistic(ai)assessmentthroughafuzzylinguisticevaluatorofthecontributeinforestcrops

damage–inclimatechangescenario–ofvariableaiandai(xai)assessmentthroughamembership

functionoftheenvironmentaleffectofthevariableaionthelocalizationx.

Theaggregationforthehypotheses“hazardtoclimatechange”and“resiliencetoclimatechange”,

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(orthogonalsum–Shafer,1976).FortwobasicprobabilityassessmentBPA(ai,x)andBPA(aj,x)(for

examplei=ecologicaldiversityandj=landscapediversity)theorthogonalsumis:

BPA(ai,aj)=

BPA(ai,x)·(1−BPA(aj,x))

1−BPA(ai,x)·BPA(aj,x)

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Allfactorsareprogressivelyaggregatedinpairstocalculatethemassprobabilityofhazardm(h)

andthemassprobabilityofresiliencem(s).Theaggregationofthetwohypothesisfallsinthecaseof

linesofevidencemarkedbyconﬂictandthusitiscarriedoutbynormalizingthesumofthejointly

probabilitiesnotinconﬂict:

Bel(h)= m(h)·(1−m(s))

1−m(h)·m(s)

Bel(s)= m(s)·(1−m(h))

1−m(h)·m(s)

U(h,s)=Bel(s)−(1−Bel(h))= (1−m(h))·(1−m(s))

1−m(h)·m(s)

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Bel(h)andBel(s)arebeliefofhazardandbeliefofresiliencemeasures;U(h,s)beliefintervalrepresents

theuncertaintydegreeoflocation,derivingbothfromoccurrenceofhighhazardandhighresilience

inthesamearea.

Evaluationoftheeconomicdamage

OnceDempster–Shafermethodologywasappliedtothetwolinesofevidenceandtheresultswere

aggregated,thequantiﬁcationoftheeconomicdamagethatclimatechangecancauseuptotheyear

2036wascalculated.

ThebasicelementforthatdeﬁnitionistheapplicationoftheFaustmannformula,whichinits

foundationisdeﬁnedasfollows:

F= Sf−R+

St·(1+r)f−t (1+r)f−1 −R+ a−e r (4)

withSfnetstumpagevalueofﬁnalcut,Rregenerationcost,Ststumpagevalueofthinninginterventions,

rdiscountrate,frotation,tageofthethinningoftheforestcrop,aannualrevenuesandeannual

expenses.TheFaustmannformulaisastand-leveleconomicmodelthatwasoriginallyconceivedfor

pureeven-agedstands.Forthecurrentcase,landexpectationvalue(LEV)isusedasaproxyforthe

assessmentoftheperceivedutilitybytheownerfortheuseoftheforestrycrops.Thisformulawas

implementedthroughaGISprocedureofspatialanalysis(Bernettietal.,2009a).

Theproposedmethodusestheconceptofsubjectiveexpectedutilityvariationinordertotryto

quantifyinmonetarytermstheexpecteddamageduetoclimatechange.Thetheoryofsubjective

expectedutility(Savage,1954)combinesanutilityfunctionandasubjectiveprobabilitydistribution.

BasedonthemapsofthehazardandofthevulnerabilitydegreeoftheTuscanyforestitispossible

toapplytheFaustmannformularesultsinordertoquantifyinmonetarytermstwopossibleexpected

utilityvariations:theﬁrstoneexpressedastheexpecteddamagetotheforestcrop(onthebasisofthe

currenttimberassortmentsobtained–Eq.(5))andthesecondonereferredtotheexpectedexpenses,

tobesupportedinordertotrytoprotectforestfromdamages(Eq.(6)).

EUV (damage)=F·Bel(h) (5)

EUV (adaptation)=

ea r +

Pt·(1+r)f−t (1+r)f−1

·(1−Bel(s)) (6)

withEUV(damage)expectedutilityvariationcausedbytheriskofcropdamage,Fcapitalizationvalue

offorestcropsfromFaustmannformula,EUV(adaptation)utilityvariationcausedbytheadaptation

cost,eacostfortheannualadaptationactions(viabilitymaintenance,ﬁresurveillance,monitoringof

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toavoidoverstockedstandssusceptibletoincreasedmortalityfromdrought,insects,diseaseand

wildﬁre)(AndersonandChmura,2009).

Therationalstrategyoftheforestowneristhemaximizationofhisutilityandthustheminimization

ofitsvariation(inourcasealwaysnegative).Thenthestrategicbehaviour(orstrategiccost)derives

fromtheminimizationofthetwopreviousexpectedutilityvariations:

strategic behaviour=min{EUV(damage), EUV (adaptation)} (7)

Studyareaanddata

Themodeldevelopedforthequantiﬁcationoftheeconomicdamageduetoclimatechangerefers

toforestcropsoftheTuscanyregion,localizedincentralItaly.Inthisregion,forestsurfacereaches

about1,150,000ha,withastrongvariabilitybothintermsofspeciescompositionand

geomorpho-logicalconditions.Themainimportantforestformationsaretheonescharacterizedbyprevalenceof

deciduousbroadleaved(79%),followedbyevergreenbroadleaved(13%)andconifers(8%).Themain

silviculturalsystemiscoppice(RegioneToscana,2008).

Theevaluationmodelwasimplementedthroughaspatialanalysisprocedureappliedtoraster

mapswitharesolutionof75m×75m.Thegeoreferreddatausedintheworkwerelinkedtothe

characteristicsoftheregionalforestsasforboththemanagerialaspectsdirectlyinﬂuencedbythe

humanactivityandthevariablesnotdependingondirectinterventions,suchasclimaticchangesand

morphologicalpeculiarities.

Theﬁrstpartofthestudyconsideredthenormalizationandtheweightsevaluationofthevariables

set(criteria)foreachlineofevidence.

ThesecriteriawerechosenthroughafuzzyDelphiprocedure(Cheng,1999),whichwascarried

outwiththecontributionofeightexpertsoftheforestsector,inordertodeﬁneseveralparameters

oftheanalysismodel,bymeansofaniterativequestionnaire.Thesurveyconsideredmanagersofthe

ConsortiumofMountainousAreas,oftheStateForestryCorpsandofforestacademicstaff.

Thequestionnairemadepossibletoobtainneededparametersforthecreationofthevaluesof

environmentaleffects(fuzzymaps)ai(ai)andoftheimportanceofvariableaiinclimatechange

sce-nario(degreeofcredence)_linguistic(xai);thesevalueswerenecessarytocalculatethebasicprobability

assignments(Eq.(1)).

Theexperts’opinionsweredescribedbyparametersandlinguistictermswhichcanbeexpressed

intrapezoidal(ortriangular)fuzzynumbers.Thepossibilityofcomparingdifferentindicatorsamong

eachother(suchasthepresenceofmanagedareasandthelandscapediversity)necessarilyrequires

anormalization(re-classiﬁcationofthefactorsinarangebetween0and1,thatisminimumand

maximumprobabilitythatthefactorcontributestotheevent,respectively).Table1showsthefuzzy

functionparametersusedinnormalizationofhazardandresilienceindicators.

Thefuzzylinguisticoperatorsarestrictlyrelatedtothefuzzylogicfunctions(ChenandHwang,

1992).Theserepresentamethodologywhichallowstogettoanumericquantiﬁcationofqualitative

opinionsgivenbytheexpertsofthesectorforparticulardecisionalprocesses,throughanevaluation

doneonspeciﬁcfunctionalshapes.Thus,withafuzzylinguisticoperatorwecanturntheverbal

evaluation(i.e.highinﬂuenceofavariableonthelineofevidence“hazard”)intoanumber,maintaining

theintrinsicuncertaintyoftheexpertestimation.ChenandHwangidentiﬁed8scalesoflinguistic

terms.Theconversionscaleadoptedforeachevaluation(Fig.2)waschosenbyexpertsintheprocess.

Theevaluationoftheothervariableswasthenimplementedthroughalinguistictermsetsderived

fromScale2oftheChenandHwangasitisshowedinTables2and3.Thelinguistictermswere

convertedintocrispvalues(high:0.808;medium:0.5;low:0.192)usingafuzzyrankingmethod.

TheBasicProbabilityAssignment(BPA)mapswereobtainedthroughtheproductofeachfuzzy

mapandtherelativedegreeofcredence.Thislastdegreederivesfromthenumericquantiﬁcation

ascribedtoeachvariablethroughafuzzylinguisticevaluatorfollowingthescale4ofChenandHwang

(linguisticvalues:low:0.115,medium-low:0.3,medium:0.5,medium-high:0.7,high:0.885).The

degreeofcredenceofeachvariablewasdeﬁnedinTable4.

Tomaketheconsensusoftheexpertsconsistent,itwasutilizedfuzzyDelphimethodtoadjust

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I. Bernetti et al. / Journal of Forest Economics 17 (2011) 285– 297 291 Table1

Deﬁnitionofthemembershipfunctionsoffuzzymaps.

Lineofevidence Criteria Mapdata Fuzzymembership Controlpoint

a b c d

Resilience

Management PercentageofMunicipalityforest surfacewithmanagement interventions

Linearincreasing 30 70

Accessibility Accessibilitytotheforestareasforthe managingintervention,expressedin termsof“cumulative”differencein heightsfromtheforestviability(m)

Lineardecreasing 0 100

Ecologicaldiversity Varietydensityindex Linearincreasing 0 Maximumvalueinarea

Landscapediversity Edgedensityindex Linearincreasing 0 Maximumvalueinarea

Hazard

Wind No.ofyearlyextremeevents Linearincreasing 0 Maximumvalueinarea

Aridity DeMartonneindex Lineardecreasing 15 30

Slope % Linearincreasing 0 100

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Fig.2.Scale2and4ofChenandHwang.

Table2

Evaluationofthevariable“forestsinnaturalprotectedareas”.

Typologyofprotectedareaincludingforestcrops Deﬁnitionoflinguisticevaluator

NationalPark High

RegionalPark,NationalReserve Medium

ProvincialPark,RegionalorProvincialReserve Low

experts’opinions,weconsideredthemeanoffuzzyratingsai(ai)andthemodalvalueofdegreeof

credencelinguistic(xai)(ChenandLin,1995;ChengandLin,2002).Theadoptedprocedurediffersfor

trapezoidalfuzzynumbers(ChengandLin,2002)andlinguisticsoperator,inparticularthisphasewas

carriedoutasfollows:

(a)Aggregationoffuzzynumbers.Step1:expertsprovideaparametersforeachfuzzymembership

function.Step2:foreachexpert,ﬁrsttheaverageofresultsofstep1andthen,thedifferences,

arefoundandsentbacktotheexpertsforre-examination.Step3:eachexpertpresentsarevised

Table3

Evaluationofthevariable“changeofphytoclimaticzone”.

CorineLandCover–CLCIV◦_level_code_and_description

(forestswithprevalenceof...)

Deﬁnitionoflinguisticevaluator Fromcastanetum tolauretum Fromfagetum tocastanetum Frompicetum tofagetum 3111:evergreenoaksandotherevergreenbroadleaves Low Low Notpresent

3112:deciduousoaks Medium Low Notpresent

3113:autochthonousbroadleaves High High Notpresent

3114:chestnut High Medium Low

3115:Europeanbeech High High Medium

3116:hydrophilicspecies High High Notpresent

3117:exoticbroadleaves(locusttree) High Medium Notpresent

3121:Mediterraneanpinesandcypresses Low Low Notpresent

3122:mountainpines Medium Low Notpresent

3123:Norwayspruceand/orsilverﬁr High High Medium

3125:exoticconifers Medium Medium Notpresent

313:mixedforest Low Low Low

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Table4

Degreeofcredenceofhazardandresiliencecriteria.

Lineofevidence Variable Degreeofcredence

Resilience

Management Medium-low

Accessibility Medium

Protectedareas Medium-low

Ecologicaldiversity Medium

Landscapediversity Medium

Hazard

Wind Medium-high

Aridity Medium-high

Changeofphytoclimaticzone High

Slope Medium

Aspect Medium-low

trapezoidalfuzzynumber.Thisprocess,startingwithstep2,isrepeateduntilthesuccessivemean

becomesreasonablyclose.

(b)Aggregationoflinguisticsterms.Step1:sameasprevious.Instep2themethodpresentedinChen

(1998)isusedtodealwithfuzzyopinionaggregationforhomo/heterogeneousgroupsofexpert,

inparticular:(i)calculationofthedegreeofagreement(ordegreeofsimilarity)oftheopinions

betweeneachpairofexperts;amethodintroducedbyChenandLin(1995)isusedformeasuring

thedegreeofsimilaritybetweentrapezoidalfuzzynumbers.(ii)Constructionoftheagreement

matrix.(iii)Calculationoftheexpertaveragevalueofagreementbytheuseofagreementmatrix.

(iv)Calculationoftheconsensusdegreecoefﬁcient.(v)Allparametersaresentbacktoexpertfor

re-examination.Step3:eachexpertprovidesrevisedevaluationuntilconsensusdegreebecomes

acceptable.

Resultsanddiscussion

Fig.3showsthemapsandthebox-whiskerdiagramsforthebeliefofhazard,beliefofresilience

anduncertaintyinterval.Thebox-whiskerplotsinFig.3showthemean(blacklineinsidethe

box-whiskers),theﬁrstandthirdquartileandﬁnally,theupperandlowerlimitsreached.

Ingeneraltheriskofhazardisrelativelylimited,withanaverageprobabilityequaltoabout0.4.Half

oftheTuscanyforestspresentanhazardriskbetween0.35and0.49.Therearealsosomelocalizations

witharelativehigherrisk,withanupperwhiskerequalto0.71.Thevaluesregardingresilientforests

toclimatechangearehoweverrelativelylow,withameanvalueof0.38andﬁrstandthirdquartile

equalto0.29and0.44,respectively.Inthiscasealsotheupperlimitdoesnotseemhigh(0.66).The

uncertaintyintervalshowsanaveragevalueof0.21(ﬁrstandthirdquartileof0.18and0.24,upper

limit0.32),thusafewTuscanyforestsseemtohavebothhighhazardandhighresilienceevaluation

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Fig.4.Expecteddamage,adaptationcostandstrategiccost(D /ha).

inthesamearea.Onthegeographicpointofview,theforestlocalizationsshowingthehigherdegree

ofhazardandthelowerresiliencearesituatedinthemountainousareaoftheApennines

(northwest-southeastsideoftheregion),whiletheMediterraneanforestsseemtoshow,asawhole,alowerrisk.

TheseresultsmatchwiththeItalianandinternationalliteratureontheissue(EFIetal.,2008;Carraro

etal.,2007).

Fig.4highlightsthemapsthatrepresenttheexpecteddamage,themitigationcostandthestrategic

cost.

Resultsanalysis,showsthatgenerallytheadaptationcostishigherthantheexpecteddamages.The

averagevalueoftheexpecteddamageisabout332D/ha,withtheﬁrstandthirdquartileequalto158

and524D/ha.Theadaptationcost,instead,showsameanof950D/ha(ﬁrstandthirdquartile719and

1,215D/ha,respectively).Forthisreason,thestrategiccostcomestobe,inthemajorityoftheforest

localizations,equaltotheexpecteddamage(mean326,ﬁrstandthirdquartile155and510D/ha).

Theseresultspointoutvaluesclosetotheonespresentedinanotherrecentstudycarriedoutby

Hanewinkeletal.(2010b)withasimilarmethodology(LEVreductioncalculatedwiththeFaustmann

formula)forsouthwestGermanyNorwayspruce;theauthorscalculateanaveragereductionsofLEV

equalto521D/hainA2IPCCscenario.

Thestrategiccostrepresentedinformula(7)andinFig.4,isexpressedasacapitalvalue.However,

consideringseveralofthebasicconditionsnecessaryfortheapplicationoftheFaustmannformula(i.e.

alongtimeconstitutedforestryfundandthuscharacterizedbyconstantrevenuesandcosts,aswell

asbyapermanenceinthedestinationandintheproductiveconditions),itispossibletohypothesize

thepresenceofregulatedanduneven-agedforestsinwhichthestrategiccostisreportedaspresent

valueofannuity.ThefrequencydistributionofthisvalueisrepresentedinFig.5.

Fortheentireregionalterritorythestrategiccostamountstoabout12,500,000D/year,

correspond-ingtothe33%ofthegrossproductofthesilviculturalsectorinTuscany(IRPET,2008).Thisreduction

canbecomparedwiththeonecalculatedforothersectorssensitivetoclimaticchanges.Inthe

agricul-turalsectorBernettietal.(2009b)evaluatedreductionsbetween1930and101,718_D/haforthewine

sectorand134D/haforthearablelands.Carraroetal.(2007)estimatedthat,innorthernItaly,

reduc-tionofthetouristincomecouldvaryfromaminimumof17.3%toamaximumof21.2%(asafunction

ofthescenarioandoftheconsideredregion).Internationalstudies(e.g.Stern,2007)evaluatedthat

thecostderivedfromtheclimaticchangeisvaryingbetween−4%ofGDP(thatis,netgains)to+15%

ofGDP;mostestimatesarestillcenteredaround1%ofGDP.Thus,theforestsector(togetherwiththe

agriculturalandthetouristones)seemstobemoresensitivewhencomparedtotheeconomicsystem

initscomplexity.

Theseresultsmayallownotonlytoestimatea monetaryquantiﬁcationbutalsotodeﬁnethe

localizationofthedamage.Thegeographiclocalizationandquantiﬁcationofhazard,resilienceand

uncertainty value, permitsto downscale resultsaccording to optimal administrativeand policy

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Fig.5.Annualstrategiccost.

Fig.6. Adaptationcost(leftbars)andexpecteddamage(rightbars)forTuscanyProvinces.

asamatteroffacttheoperativeactionsregardingtheItalianagriculturalpolicyaredelegatedtothe

Provinces(NUTS-3subdivision,accordingtoEurostatclassiﬁcation)andtheyarethemainlocal

stake-holders,abletoaddressfundsinparticularagro-forestrysectors.Quantiﬁcationofadaptationcostand

expecteddamageinTuscanyProvincesisexplainedinFig.6.

Conclusions

TheexaminedDempster–Shaferapproachappearstobeapromisingalternativeforconducting

economicanalysisinnear-ignoranceconditionsandinanenvironmentoflimiteddataandrelevant

uncertaintysuchastheclimatechangeinforestrysector.ThefuzzymeasureandDempster–Shafer

theoriesusedinthisstudyseemtobeefﬁcienttoolsfordataintegrationandenvironmentalimpact

assessment.

InparticulartheapplicationofDStheoryprovedtobeparticularlyusefulfromtheexpertsystems

viewpointasapowerfultoolforuncertaintyanalysis;inadditionitaggregatesallevidentialvariables

inanuniqueframeofdiscernmentthatisanefﬁcientkindofdamageanalysisinclimatechange

riskconditions.Finally,inenvironmentaldecisionmakingsector,itcouldprovideusefulguidancefor

naturalresourceplansbasedonthelevelofprobabledamageindifferentlocations.

Ontheotherhandtheworkcanbeimprovedinsomeaspectsasfollows.Monetarycomputations

inexpectedutilityvariationcausedbytheriskandbytheadaptationcostworkundertheassumption

thatallpricesandcosts(timber,labour,interest,regeneration,etc.)areconstantovertimeaccording

totheclassicalFaustmannmodel.Howeverinrealforestry,timberandinputpricesaresubjectto

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(extremeevent,increaseintemperature,etc.).Similarly,inFaustmannformulaanassumptionisthat

theinterestrateisknownandconstantovertheperiod.

In ordertoovercometheselimitstheintegrationofriskinclimatechangedamageestimation

canbeachievedalsobytheadditionofapremiumtothediscountrate(Hanewinkeletal.,2010a).

InastudycarriedoutbyKnokeandHahn(2007)simulationapproachdevelopedthroughMonte

CarloanalysiswasusedtointroduceriskevaluationinFaustmannformula.Uncertaintyrelatedto

timberpricescanbetakenintoaccountbymeansofstochasticdynamicprogramming(Lohmander,

2000).OnLEV reductionviewpointotherstudyestimatevalueclosetotheonesdepictedinthis

research,e.g.forsouthwestGermanyNorwayspruce,theapplicationofFaustmannprocedurelinked

bygeneralizedlinearmodelandsingle-treegrowthsimulatordeﬁnedanaverageLEVreductionof

521D /havs.326D /haofthepresentresearch(Hanewinkeletal.,2010b).

Furthermorethemodelassumesthatalsodamageandmitigationsworkperpetuallyandwith

con-stantquantiﬁcation.Inordertoconsiderpossibleﬂuctuationofclimatechange,ecosysteminteractions

andtheirconsequencesonforestcrops,process-basedapproachescanbeasolution.Dynamicsprocess

inparticularlandscapeandvegetationdynamicsorplantphysiologymodelsaresomesuitable

exam-plesofthese.Finallyrecentmethodologicaladvanceshavebeenusedtoconsiderhighlyvariableand

incompleteandnoisycharacteristicsofmostdisturbancedatasets(e.g.,machinelearningalgorithms

suchasrandomforestsandartiﬁcialneuralnetwork)(Seidletal.,2011).

Furtherfuturedevelopmentofthemodelcouldinvolvetheextensionofanalysistonon-market

datainordertoachieveamoreholisticframeworktosupportdecisionsinclimatechangeplanning.

Acknowledgements

AuthorsthanktwoanonymousreviewersaswellasDr.M.BracaliniandDr.E.Locandrofortheir

helpfulandstimulatingcommentsandsuggestions.

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