Combining a finite mixture distribution model with

CombiningafinitemixturedistributionmodelwithindicatorkrigingtodelineateandmapthespatialpatternsofsoilheavymetalpollutioninChunghuaCounty,centralTaiwanLinYu-Pina,*,ChengBai-Youa,ShyuGuey-Shinb,ChangTsun-KuoaaDepartmentofBioenvironmentalSystemsEngineering,NationalTaiwanUniversity,1,Section4,RooseveltRoad,Da-anDistrict,TaipeiCity106,Taiwan,ROCbDepartmentofEnvironmentalManagement,TungnanUniversity,152,Section3,PeiShenRoad,ShenKeng,Taipei222,Taiwan,ROCEffectivelydeterminepollutionthresholdandmapcontaminatedareas.articleinfoArticlehistory:Received10December2008Receivedinrevisedform14July2009Accepted17July2009Keywords:FinitemixturedistributionmodelHeavymetalpollutionContaminationthresholdMultivariateindicatorkrigingGeographicalinformationsystemabstractThisstudyidentifiesthenaturalbackground,anthropogenicbackgroundanddistributionofcontami-nationcausedbyheavymetalpollutantsinsoilinChunghuaCountyofcentralTaiwanbyusingafinitemixturedistributionmodel(FMDM).Theprobabilitiesofcontaminatedareadistributionaremappedusingsingle-variableindicatorkrigingandmultiple-variableindicatorkriging(MVIK)withtheFMDMcut-offvaluesandregulationthresholdsforheavymetals.FMDMresultsindicatethatCr,Cu,NiandZncanbeindividuallyfittedbyamixturemodelrepresentingthebackgroundandcontaminationdistri-butionsofthefourmetalsinsoil.TheFMDMcut-offvaluesforcontaminationcausedbythemetalsareclosetotheregulationthresholds,exceptforthecut-offvalueofZn.Thereceiveroperatingcharacteristic(ROC)curvevalidatesthatindicatorkrigingandMVIKwithFMDMcut-offvaluescanreliablydelineateheavymetalscontamination,particularlyforareaslackingbackgroundinformationandhighheavymetalconcentrationsinsoil.2009ElsevierLtd.Allrightsreserved.1.IntroductionDataonheavymetalsinsoiloccasionallyexhibitcomplexspatialvariationsandpatterns,possiblycomplicatingeffortstoidentifythecharacteristicsofheavymetalpollutantsinsoil,particularlyinurbanandindustrialareas.Suchcomplexvariationsandpatternsareattributedtonaturalphenomena(naturalbackground)andhumanactivities(anthropogenicbackground)(Martı´netal.,2006;Mico´etal.,2006;ElSebaietal.,2007;Lin,2008).Anthropogenicactivities,suchasthedischargeofwastefrommetalprocessingplants,burningfossilfuelsandpesticidesuse,subsequentlycausedmostsoilpollution(Linetal.,2002a).Someoftheseanthropogenicbackground-relatedpracticeshelpdistinguishtheanthropogenicbackgroundfromanaturalbackground(Portier,2001).Otherissuesarerelatedtohowdataaboutanthropogenicbackgroundconcen-trationsmaybeaddressedinpolicydecisionsrelatedtopollutionremediation(Portier,2001),riskassessment,andenvironmentalmanagementininvestigatedsites.Thus,determiningprecisepollutionthresholdsdependsontheabilitytodevelopefficientanalyticalapproachesforidentifyingnaturalandanthropogenicbackgroundconcentrationsofheavymetalsinsoil.Suchthresholdscanthenbeusedtodelineateandmappollutedareas,aswellasdeterminethespatialdistributionsandvariabilityofheavymetalsinsoil,forenvironmentalpolicydecisionmakers.Theconcentrationsofvariouselements,includingheavymetalsinsoil,provideavaluablereferenceforestablishingthresholdvaluesoractionlevelsforscreeningstudydecisions(Portier,2001).Soilpollutionstudiesnormallytakesamplesfrommixturesofpollutedandunpollutedareaswithoutunderstandingthefullarealextentofcontamination.Therefore,thesoilsamplescontainamixtureincludingnaturalandanthropogenicconcentrationsofheavymetalsinsoil.Afinitemixturemodelassumesthatthesamplestakenfromamixturedistributionarecomposedbyseveralcomponentdistributionsofaninvestigatedvariableinanareaofinterest.Meanwhile,finitemixturesofdistributionscanbeusedinmathematicalapproachesforstatisticalmodelingofanextensivevarietyofrandomphenomena(McLachlanandPeel,2000).Therefore,amixturemodelofsoilsamplescanmodelcomplexdistributionsbychoosingthecomponents,i.e.,naturalandanthropogenicconcentrations,thatrepresentlocalareasintheactualdistributionsofsoilconcentrations.Soilpollutionstudiescanconceptualizeandmodeltheoverallbackgroundconcentrationdistributionasamixtureofanaturalbackgrounddistribution,ananthropogenicbackgrounddistributionandadistributiondesigned*Correspondingauthor.Tel.:þ886233663467;fax:þ886233663464.E-mailaddress:[e-mail](Y.-P.Lin).ContentslistsavailableatScienceDirectEnvironmentalPollutionjournalhomepage:www.elsevier.com/locate/envpol0269-7491/$–seefrontmatter2009ElsevierLtd.Allrightsreserved.doi:10.1016/j.envpol.2009.07.015EnvironmentalPollution158(2010)235–244toaccommodatethepotentialforcontaminationsitesamplesincludedinabackgroundsampleset(Portier,2001).Mappingpollutedareasbasedongivenpollutionthresholdsisessentialbecauserelatedinformationsignificantlycontributestoeffortstoformulateenvironmentalactionstrategies,suchastheremediationofsoilpollutedbyheavymetals,aftersamplingthesoilanddeterminingpollutionthresholds.Inindicatorkriging,assumptionsarenotmadeabouttheunderlyinginvariantdistri-bution,and0–1indicatortransformationsofdatarenderthepredictorrobusttooutliers(Cressie,1993).Indicatorkrigingiswidelyusedtomaptheprobabilitiesofestimatesthatexceedgiventhresholdlevelssuchasr