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Above ground biomass and leaf area models based on a non destructive method for urban trees of two communes in Central Chile

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Above ground biomass and leaf area models based on a non destructive method for urban trees of two communes in Central Chile
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    BOSQUE32(3):287-296,2011DOI:10.4067/S0717-92002011000300010 Above ground biomass and leaf area models based on a non destructive method for urban trees of two communes in Central Chile EcuacionesdebiomasaaéreayáreafoliarbasadasenmétodosnodestructivosparaárbolesurbanosdedoscomunasdeChileCentral Cynnamon Dobbs a , Jaime Hernández b *, Francisco Escobedo c a UniversityofMelbourne,AustralianResearchCentreforUrbanEcology,Melbourne,Australia. *CorrespondingAuthor: b UniversidaddeChile,FacultaddeCienciasForestalesyConservacióndelaNaturaleza,Laboratoriode GeomáticayEcologíadelPaisaje(GEP),Santiago,Chile,casilla9206,tel.:56-02-9785873, jhernand@uchile.cl  c UniversityofFlorida–IFASSchoolofForestResouercesandConservation,Gainesville,FL,USA. SUMMARY Biomass is regarded as an important indicator of ecological and management processes in urban vegetation, difcult to measure buteasytointerpret.Existenceandgrowingratesofbiomasscanbeusedtocalculatecarbonstorageandsequestration,estimatedrydepositionofairpollutionorvolatileorganiccompoundemissions.Incities,managementpracticesalsoaffecttheamountanddistributionofbiomasscomponentswithinatreeandlocalcalibratedequationsshouldbeused.However,traditionaldestructivemethodstogatherthedatanecessarytobuildsuchequationsarelesspracticalinurbanenvironments.ThemainobjectiveofthisworkwastodevelopabovegroundbiomassandleafareamodelsbyusingnondestructivemethodsforcommonurbantreesinSantiago,Chile.Weusedrandomisedbranchsampling(RBS),anon-destructivemethod,andeasilymeasuredvariablessuchasDBHandtotalheighttoestimatecrownbiomassandleafareaforthe11mostcommonurbantreespeciesinSantiago.Resultsusingequationsdevelopedinthisstudyyieldedcrownbiomassestimates,comparableandwithintherangeofvaluesreportedinliteratureandwithin those obtained from urban forest structure models. Leaf area results yielded more reasonable estimates when compared to eld data andurbanforeststructuremodels.TheseequationscanbeincorporatedintourbanforestfunctionmodelsformorepreciseestimatesofLatinAmericantemperateurbanforestfunction.WithincreasedsamplingintensitytheRBSsamplingmethodcouldbepresentedasanon-destructiveandrepeatablemethodforestimatingdifferenttypesofurbantreecrowncharacteristics. Key words: non-destructivemethod,randomisedbranchsampling,allometry.RESUMENLabiomasaesconsideradaunimportanteindicadordelosprocesosecológicosydemanejoqueocurrenenlavegetaciónurbana. Es difícil de medir pero fácil de interpretar, pues reeja las condiciones del sitio y de los recursos edácos, hídricos y de radiación solardisponiblesenél.Enlasciudades,lasprácticasdemanejosobrelosárbolesafectanladistribucióndelabiomasaensuinterioryesnecesariousarecuacionescalibradaslocalmenteparapoderevaluarcadacomponente.Sinembargo,losmétodosdestructivostradicionales,queseusanpararecopilarlosdatosnecesariosenlaconstruccióndetalesmodelos,sonpocoaplicablesenambientesurbanos.Enesteestudioseutilizóelmuestreoaleatorioderamas(RBS),unmétodoprobabilísticonodestructivo,yvariablesdendrométricasdefácilmedicióncomoDAPyalturatotalparaestimarlabiomasaaéreayeláreafoliardeárbolesurbanosmáscomunesenSantiago,Chile.Losresultadosdelestudioarrojaronestimacionesdebiomasaaéreacomparables,ydentrodelrangodevalores,alosreportadosenlaliteraturainternacional,parabosquesyárbolesurbanos.Lasestimacionesparaáreafoliararrojaronvaloresmásrazonablesencomparaciónconlosdatosdecampoyreferenciasinternacionales.EstasecuacionespuedenserincorporadasenlosmodelosforestalesurbanosincluyendoestimacionesmásprecisasyajustadasalarealidaddeAméricaLatina.AumentandolaintensidaddemuestreodemétodoRBSsepodríausarcomounmétodono-destructivo,replicable,paraestimardiferentestiposdecaracterísticasenárbolesurbanos. Palabras clave :métodonodestructivo,muestreoaleatorioderamas,alometría. INTRODUCTIONtreehealth,leafareaandbiomass.Forestfunctionsaredeterminedbyforeststructure,includingawiderangeof A simple but efcient way to assess and monitor ur  -environmentalandecosystemservicessuchasairpollubanvegetationistoconsiderexplicitlyitsstructureandtionremovalandcoolerairtemperatures(Nowak et al. functionsinagivenurbanlandscape.Foreststructureis2002).Consequently,forestvaluesareanestimateoftheameasureofvariousphysicalattributesofurbanvegeta-economicworthofthevariousforestfunctions.Inseveraltion,suchastreespeciescomposition,numberoftrees,countries,recentlegislationandformalagreementshave287  BOSQUE32(3):287-296,2011Biomassequationsforurbantrees increasedfocusonutilisingtheurbanforesttoreduceCO 2 emissions(McHale et al .2007).Tobeabletocalculatecurrentcarbonstorage,biomassforsingletreeshastobecalculatedusingequationsfromliteratureandmeasuredtreedata.Unfortunately,veryoften,theseequationsarenotavailableortheyhavenotbeencalibratedforlocalconditions.Tomeasurethestructureoftheurbanforestthe“urbanforesteffects”model(UFORE)hasbeenwidelyused,andseveralmanagementregimeshavebeenbasedonitsresults.UnfortunatelythismodelisbuiltonallometricequationsandurbanforestfunctionalmodelsdevelopedintheUnitedStatesofAmerica(DelaMaza et al. 2005).Inurbanareas,mostanalysesofforeststructurearebasedonthismodel,thereforetheylackindirectmeasurements(McPhersonandSimpson2001).Alsothevariablesthataffecturbantreegrowth( i.e. soil,water,solarresources)aredifferentamongcities,thereforeallometricrelationshipswithinthoseurbantreesvary(McHale et al .2009).Crownbiomassandleafareacanbeestimatedusingallometricequationsandmeasuredtreedimensionvariablessuchassapwoodarea,diameteratbreastheight(DBH),totalheight,andothercrownmeasurements(Nowak1996,McPherson1998,PeperandMcPherson1998,Turner et al. 2000,McHale et al .2009).Sapwoodareahasbeenfoundtobehighlyrelatedwithwholetreeabovegroundbiomassandleafareaformanytreespecies(Turner et al .2000).However,leafbiomassandleafareaequationsinurbanareashavetobedevelopedusingnondestructivemethodsduetoliabilityandpublicvalues(McPherson1998).Nowak(1996)forexampleestimatedleafbiomassforopengrownurbantreesusingeasilymeasureddimensionssuchasDBH,totalheight,crownheightandwidth,andashadingfactorforeachsampledspecies.TheauthorfoundthatestimatesbasedoncrownwidthhadasmallermeansquareerrorthanestimatespresentedbymodelsbasedonDBH.Othermethodssuchasrandomisedbranchsampling(RBS)usetheindividualtreeasapopulationanduseitsbranchstructuretodevelopasamplingmodel(Gregoire et al. 1995).Randomisedbranchsamplingisanon-destructive,multistageprobabilitysamplingmethodintroducedbyJessen(1955)fortheestimationoffruitquantityonorangetrees.Thesamplingmethodusesatree’sbranchingstructuretotakemeasurementsalongsequentialbranchesinacrownwithconsiderablylesseffortthanthatneededforweighingallbranchesorpilingandreselectingthembyarandomisedsubsample.Foliarbiomassisestimatedbymeasuringthefoliageofthesampledbranchesandnottheentirecrown(Gregoire et al. 1995).PeperandMcPherson(1998)comparedrandomisedbranchsamplingandothermethodsforestimatingurbantreefoliarbiomassinSacramento,California,againstmeasuredactualfoliarbiomassandfound no signicant difference. Treeleafareaisalsoimportantforstudyingseveralphysiologicalprocessessuchasphotosynthesis,transpiration,evapotranspiration,andproductivity.Leafareaisoftenestimatedusingtheleafareaindexortheleafgreenarearepresentingtheprojectionofone-sidedleafareainrelationtosurfaceunitarea(Hardin et al. 2007).Directmethodsincludecollectionoffoliageandlitterfall,below-canopylightinterceptionmeasurements,andothermoredestructivemethodssuchassapwoodareameasurements(Turner et al. 2000).Theleafareaindexiscommonlyobtainedusingtherelationshipbetweenfoliarmassandsapwoodarea for specic species (Turner et al. 2000).Nowak(1996) developedallometricequationsforpredictingleafareaforopen-grownurbandeciduoustreesbasedonstemdiameterandothercrownparameters.PeperandMcPherson(1998)listedotherindirectmethodsincludingaerialimageryandgapfractionanalysisandtheuseofvideoimages,andfoundthatimageprocessingdemonstratedthehighestprobabilityofaccuratelysamplingtheleafareaindex. By developing site-specic equations of crown biomass andleafarea,LatinAmericancitiescanbetterunderstandthefunctionoftheirurbanforestandassesstheroleoftreesontheurbanenvironment.Asmentionedbefore,tohavelocalcalibratedbiomassequationsiscrucialtohave unbiassed and more precise estimations. The specic ob  jectivesofthisstudywere:1)todevelopregressionequationstopredictcrownbiomassandleafareaforthe11mostcommonurbantreespeciesincentralChile,and2)toassesstheuseoftherandomisedbranchsamplingmethodsforestimatingcrownbiomass( e.g. thesumofbranchandleafbiomass)andleafareaforurbantreesincentralChile.Thestudydidverifyresultswithleafandbranchbiomassandleafareaequationsfromliteratureandthoseusedin an urban forest structure model. It is expected to nd sig  nicant differences between site specic biomass and leaf areaequationsandliteraturemodelsestimationsthatmake valuable the development of site specic models for crown biomassandleafarea.METHODSThe11mostcommonurbantreespeciesinSantiago,Chile,weremeasuredandsampledforleafandbranchbiomassduringthemonthsofOctoberandNovemberof2004.Thedateswerechosenbecauseoftreephenology,tohaveacompletedevelopmentoftheleafysection.Santiagoislocatedbetween450mand900mabovesealevel,at32°55’and34°19’Southlatitude,at69°46’and71°39’Westlongitude.Averageannualprecipitationisabout400mmandischaracterisedbyatemperate,semi-arid,Mediterraneanclimatewithanaverageannualhightemperatureof22ºCandaverageannuallowtemperatureof7ºC.Sampledtreespeciesincludedeightnonnative:  Ailanthus al-tissima Mill.,  Robinia pseudoacacia L., Prunus cerasifera Ehrh.,  Acacia melanoxylon R.Br.,  Acacia dealbata Link.,  Acer negundo L.,  Liquidambar styracilua L., Platanus x acerifolia Muenchh.,andthreenativeones: Schinus molle Raddi., Quillaja saponaria Molina,  Maytenus boaria Mo288  linaspeciesofcentralChile.Seeappendixforageneraldescriptionofallspecies.Sampleswereobtainedfromtwomunicipalitieswherepermissionwasgranted(LoBarnecheaandLaReina),thuslimitingsamplingtotheseareasofSantiago.Sampledtreeswereopen-grownwithoutevidenceofpruning,waterstress,ormechanicaldamage.TentreesperspecieswereselectedforsamplingandrepresenttherangeofsizesfoundinSantiago.TherangeforheightandDBHforeachspeciesisshownintable1.Similarsamplesizes(DBHrange11-53cm)havebeenusedbyNowak(1996)forestimatingtreebiomassandleafarea.Individualtreestemdiameteratbreastheight,130cm,andatcrownbasewasmeasured,asalsoweretotalheight,heighttocrownbase,andcrownwidthalongnorth-southandeast-westaxes.Thegreatestandsmallestdiameterofeachbranchsectionandthelengthofbranchsectionwerealsomeasuredforeachsampledtree.  Randomised branch sampling (RBS). AccordingtoGregoire et al. (1995)itisaniterativeprobabilitysamplingapproachwhichusesapaththatconsistsofaseriesofbranchsectionsendinginterminalbranches(Gove et al. 2002).FollowingGregoire et al. (1995) denition, a  branch is dened as a complete stem system from lateral toterminalbudswithadiameterinferiorto2.5cm.The section is dened as the part of the branch located between twoconsecutivenodeswithoutdifferentiatingstemorlateralbranches.Apathisgivenbyasequenceofsections.Randomisedbranchsamplingselectsadatacollectionpathfromthebasetotheendofatreeortoarandomlyselectedterminalbranch.Theresultingsumoftheprobabilityofsampleoftheentiretreeorbranchisthenusedtoestimatecrownbiomassorthesumofleafandbranchbiomassintheindividualtreecrown.Inthisstudy,twopathspertreewereselectedsothat Table 1. Diameteratbreastheight(DBH)andtotalheight(H)rangesusedforeachspecies. Rangosdediámetroalaalturadelpecho(DBH)yalturatotal(H)delasespeciesutilizadas. SpeciesDBH(cm)Rangeof H(m)  Ailanthus altissima 6-455-22  Acer negundo 7-454-10  Acacia dealbata 10-353-9  Acacia melanoxylon 12-403-9 Prunus cerasifera 7-424-13  Robinia pseudoacacia 7-604-15  Liquidambar styracilua 6-304-10 Platanus acerifolia 20-808.5-25 Schinus molle 8-452.5-9 Quillaja saponaria 6-253-6  Maytenus boaria 8-214-6 BOSQUE32(3):287-296,2011Biomassequationsforurbantrees thestandarderrorandvariancecouldbecalculated(Gregoire et al. 1995,Gove et al. 2002).Eachpathconsistedofarandomlychosenbranchfromeachnodebeginning at the base of the sampled tree (gure 1). The probability ofselectingavariableneedstobehighlycorrelatedwiththeparametertobeestimated.Thereforetheconditionalprobabilityassociatedwitheachbranchwasassignedbasedonthesquarediameterofthebranchmultipliedbyitslengthandthendividedbythesumofthesquareddiametermultipliedbytherespectivelengthofallbranchesatthatnode(Gregoire et al. 1995).Thisisreferredtoasaconditionalprobabilitybecausetheselectionofonebranchatanodedependsonthepaththathasbeenfollowedandthisisinturndependentonthenodefromwhichthatbranchemanates.Theconditionalprobability( q k  )wasdetermined using a random number generator to dene the sampling path.Usingrandomisedbranchsampling,theunconditionalprobability( Q )ofselectingthe r  th sectionofabranchsamplewasdeterminedby: r Q r = ∏ q k [1] k  = 1 SampledpathNode2Node1Node3 Figure 1. TheRandomisedbranchsamplingmethod.Thesamplepathrequiresallmaterialtobecollected,includingmiddlebranchesalongthepath.Node1hasaprobabilityofeachselectedpathofq 1 =1,node2hasaprobabilityforeachselectedbranchofq 2 = 1  /  4 andnode3hasaprobabilityofeachselectedbranchofq 3 = 1  /  3 .Notethattheprobabilitiesofselectionassignedtothesampledbranchesshouldsumto1. Métododemuestreoaleatorioderamas(RBS).Elcaminodemuestreorequierequetodoelmaterialseaevaluado,incluidaslasramasintermedias.Elnodo1tieneunaprobabilidaddecadacaminoseleccionadodeq 1 =1,elnodo2tieneunaprobabilidadparacadaramaseleccionadadeq 2 = 1  /  4 yelnodo3tieneunaprobabilidaddecadaramaseleccionadadeq 3 = 1  /  3 .Notequelasprobabilidadesdeselecciónasignadasalasramasdelamuestradebensumar1. 289  BOSQUE32(3):287-296,2011Biomassequationsforurbantrees Biomass( b ˆ )amountwasdeterminedusingGregoire et al. (1995)methodbasedonequation[2],whereb r istheamountofbiomassmeasuredonthe r  th branchand b ˆ representstheestimatedamountofbiomassofatreecomponent( i.e. branches,leaves)orthewholetree: r  b ˆ = ∑   Qb r [2]Biomasswasthencalculatedasthesumofthebiomassofeachsectiondividedbyacumulativeprobability(Gregoire et al. 1995).Theunbiasedestimateofleafandbranchbiomasswasdeterminedusingequation[3]: b ˆ =  1 ∑   m b ˆ i [3] m i = 1 where, m =numberofpathsmeasuredonatree. Variancewasthenestimatedusingequation[4] m =2where: Varb ( )   ˆ =   m ( m 1 − 1 ) ∑ ( b ˆ i  −   b ˆ ) 2 [4]Finally,eachsampledpathwasseparatedintobranchesandleavesandovendriedat75ºCfor62hourstoconstantweight.Thetotaldryweightwasobtainedbysummingtheweightsofallbranchesandleaves.Thebiomassandleafareamodelswereselectedaprioribeforedatawereobtainedandselectioncriteriaarebasedontheiruseinthecitedliterature.Foreachtreespeciesthefollowingbiomassequations[5-9]andparameterswerecalculatedusingleastsquareslinearregressionswitha P <0.05:  B t =   a *  DBH  b + ε    [5]  B t =   e a +    DBH * e b + ε    [6]  B t =   a +   b *  DBH 2 *  H  t + ε    [7]  B t =   a +   b *( π     *  DBH 2 ) + ε    [8] 4  B t =  a *  H  t b + ε    [9]where,  B t =crownbiomasscomponenttobeestimated(thesum ofleafandbranchbiomass). a, b = equationvariables. ε = error that has a mean of 0 and a variance of σ  2 . e =exponentterm.  DBH  =diameteratbreastheight(1.3m)incentimeters.  H  =totalheightinmeters. Equationswerecalculatedforeachspeciesusing n =10treesperspecies;similarsamplesizewasusedbyNowak(1996).Equationswerebasedonthehypothesisthatdatawerehighlycorrelatedwithalpha=0.05.Theselectionoftheappropriatemodelwasbasedontheanalysisoftheresidualsofthedependentandindependentvariablesas well as the analysis of the goodness of t (adjusted R  2 )andmeansquareerror.Residualswerealsotestedusingscatter  plots, the sum of errors, goodness of t, mean, deviation, andthesumofnormalisedresiduals.FurthertestsandresidualanalysescanbefoundinDobbs(2005).Todevelopleafareaequations,thetreecrownwasdividedintothreestrata.Foreachtree,totalverticalcrownheightwasmeasuredanddividedinto3equalpartsoranupper,middleandlowercrownstratum.Foreachstratum,asubsampleof50leaveswasrandomlycollectedforato tal of 150 leaves per tree. A total of ve trees per species weresampledbothintheinnerandouterportionsofthecrown.Leafareasampleswerecollectedduringthelatesummer,southernlatitudemonthsofFebruaryandMarchof2005.Thosedateswerechosentomatchtheseasonofurbanforesteffectsmodeldatacollection.Theonesidedleafsurfacewascalculatedusingascannedimageofeachindividualleaf(HewlettPackard®Scanjet2400Scanner)witharesolutionof300dpiandablack/whitebinaryscalethatcalculatedtheportionofpixelsbelongingtotheleafrelativetotheentirescannedimage.Usingthesurfacecoveredby1gramofleaf,thetotalleafareawasobtainedbytransformingthesevaluesusingatotalleafweighttoleafsurfacerelationship.Totalleafweightwasobtainedusingtherandomisedbranchsamplingmethod.Foreachtreespecies,leafareaequationsweredevelopedusingequations4-8andadjustedusingleastsquareslinearregressionswitha P < 0.05. Verication .Availableequationsfromliteratureandequationsusedintheurbanforesteffects(UFORE)model(Nowak1996,Nowak et al .2002,Jenkins et al .2003)wereusedtoverifyleafbiomassandleafarearesults.Distributionoftreebiomasswasalsousedtocomparetheresultsofourmethodswithliteratureforabovegroundwholetreebiomassallocation.Sincestembiomasswasneeded for verication and could not be obtained using destruc tivesampling,thestembiomassforallsampledspecieswasestimatedusingpublishedovendrywooddensities(Anderson2004)andmeasuredstemvolume(V)usingaSmalianformula:290  g a +   g b   [10] V =  *  L 2 where, g =crosssectionalareaofthelower( a )andtheupper( b ) sectionofthestem.  L =lengthofthesteminmeters. Totalwholetreeabovegroundbiomasswasthesumoftheestimatesusingthedifferentequationsforallcrowncomponents( i.e. branchesandleaves)andstembiomass.WooddensityvaluesandsourcesfromliteraturearepresentedinDobbs(2005).RESULTS  Branch biomass. Equationsyieldedbetterestimatesforsixofthe11sampledspecies,whereahighcorrelation(R 2 >0.60, P <0.05)ispresentforthreeofthespeciesandmediumcorrelationswereobservedfortheremaindingfour(R 2 =[0.40-0.6], P <0.05).Resultsindicateunbiasedestimatesasexhibitedbynormallydistributedresidualsandmeanstendingtowards0.ScatterplotsforthevaluesobtainedusingrandomisedbranchsamplingandtheestimatesbytheDobbs(2005),i.e.thisstudy’sequations,Nowak(1996)andJenkins et al .(2003)equa tions, are presented in gure 2 and table 2. ResultsobtainedforbranchbiomassequationsforDBH<30cmandR 2 >0.60generallygavesimilarvalues as other equations from literature (gure 2; Nowak 1996, Jenkins et al. 2003).ForDBH>30cmmostequations Table 2.  Branchbiomassequationsforselectedspecies. Ecuacionesdebiomasaderamasdelasespeciesseleccionadas. SpecieModel R 2 MSE  Ailanthus altissima B=0.000007DBH 4.422943 0.71*69.17  Acer negundo B=7.130020+0.000938DBH 2 H0.51*16.24  Robinia  pseudoacacia B=2.050230H 1.686937 0.54*135.40  Liquidambar  styracilua B=0.000107H 5.102728 0.45*18.90 Schinus molle B=0.270671H 1.339925 0.70*24.10 Quillaja saponaria B=0.000306DBH 3.762624 0.71*24.50B:branchbiomass;DBH:diameteratbreastincentimetres;H:totalheightinmetres;R 2 : goodness of t; MSE: mean square error.OnlyspeciesandmodelswithR 2 >0.40arelisted(Fischer,*= P <0.05). B:biomasaderamas;DBH:diámetroalaalturadelpechoencentímetros;H:alturatotalenmetros;R 2 :bondaddelajuste;MSE:errorcuadráticomedio.SoloespeciesymodelosconR 2 >0,40sonlistados(Fischer,*= P <0,05). BOSQUE32(3):287-296,2011Biomassequationsforurbantrees overestimated the biomass when compared to eld data obtainedusingRBS.Someofthisstudyequationsalsooverestimatedbiomassinsmallertreesshowingnegativeandhigherresiduals(sumofresidues>0).Overestimationofbiomassforjuveniletreescouldbeduetofasterheightgrowthratesincomparisontothediametergrowthratesatearlystages,affectingthediameter-heightrelationsasseenfor  A. altissima ,  A. negundo and  R. pseudoacacia .Theinabilitytodistinguishbetweenmediumandsmallbranchsizeclassesoncertainspeciesresultedinpreventingthe t of an appropriate equation as is the case of  M. boaria .Residualvalueswerehowever,closertozero;so,increasingthenumberofsamplingpathscouldpossiblyreducevariance.  Leaf biomass .Leafbiomassequationsdevelopedarepre sented in table 3. For ve of the species, there was a better relationship(R 2 >0.60and P <0.05)betweenleafbiomassandDBH,orheight,thantheoneobtainedforbranchbiomass.Exceptionswere  A. dealbata ,  A. melanoxylon , P. acerifolia , P. cerasifera and  M. boaria. Thiscouldbe a result of the species-specic leaf size and crown charac  teristics. Results indicate a better relationship – as dened byhigherR 2 values-betweenleafbiomassandtotalheightthanforthebranchequations.Residualswerenormallydistributedandexhibitedaveragevaluesoflessthan1kilogram.ScatterplotsofleafbiomassestimatesusingrandomisedbranchsamplingandtheDobbs(2005),Jenkins et al. (2003)andNowak(1996)equationsarepresentedin gure 3 and table 3. The adjusted equations for leaf bio masspresentedalowerliabilityforsmall-leavedspecieswithsmallersizedleavesandwhereweight-arearelationshipwasgreater(table3),ascanbeobservedfor  M. boaria,  A. dealbata and  A. melanoxylon .Jenkins et al .(2003)andthisstudyequationsyieldedmorereliableestimateswhen compared to eld data. Estimates of leaf biomass for spe ciessuchas  M. boaria werenotasreliableasexpected  probably due to species-specic crown architecture.  Leaf area . Estimated species-specic leaf area equations arepresentedintable3.Resultsindicatethatgoodness of t coefcients for leaf area are similar to branch and leafbiomassequations(tables2and3).Threeofthespeciesshowedastrongcorrelation.Residualsremainedclosetozeroandwerenormallydistributed.Anequationfor S. Molle couldnotbedevelopedsincenoequationanalysedinthisstudyusingthisspeciesshowedanycorrelationbetweentheleafareaandtheDBHortotalheightofthe tree, within a goodness of t < 1. Leaf area models exhi bitedreasonableestimateswiththeexceptionof S. molle .SpecieswithR 2 >0.40showedsimilarresultswhencomparedtoNowak(1996)equation.Developedequations seem to underestimate leaf area when compared to eld data, nevertheless trends are similar (gure 4). DBH and height, however, were sufcient to estimate leaf area with theexceptionof S. molle .291
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