大兴安岭白桦削度方程.docx

大兴安岭白桦削度方程ShahzadMuhammadKhurramHussainAmna何培姜立春(东北林业大学林学院森林生态系统可持续经营教仔部重点实验室哈尔滨I5OO4O)搞要：【目的】确定东北地区白桦预测不同高度直径和材积的最优削度方程，以弥补该地区没有白桦削度方程的不足。【方法】以伊勒呼里山北坡西北部立地亚区253株白桦伐倒木3795对直径/高度数据为基础，基于林业上广泛应用的8个削度方程，利用SAS软件的非线性回归SUR法对方程进行拟合。使用一阶连续自回归误差结构模拟方程误差项并解释空间自相关，采用条件数评价方程多重共线性，选择确定系数(R2)、均方根误差(RMSE)、平均误差绝对值(MAB)和相对误差绝对值(MPB)作为方程评价指标，运用拟合统计量、直径和材积残差分布的箱式图和检验统计量进行削度方程的综合比较。【结果】1)从各削度方程拟合统计量来看，Kozak(2004)2、Fang等(2000)和MaX等(1976)方程排在前3位，Sharma等(2001)方程表现最差；2)基于直径和材积残差分布的箱式图，Kozak(2004)-2、Fang等(2000).MaX等(1976)和Bi(2000)方程在预测直径和材积时误差较小且具有相似的等方差分布，Sharma等(2001)、Sharma等(2004)、Sharma等(2009)和KoZak(2004)/等方程具有较强的方差异质性：3)模型检验证实Kozak(2004)-2、Fang等(2000)和MaX等(1976)方程表现较好，Kozak(2004)-2削度方程在预测直径和材积方面表现出一致性，且优于其他削度方程。【结论】根据模型拟合和检验统计量、图形分析和条件数，Kozak(2004)-2方程被推荐用于预测东北地区H桦不同高度的直径、总材积和商品材积。关键词：白桦：削度：材积：自相关；多重共线性中图分类号，文献标识码：A文章编号：1001-7488(2020)00-0000-00StemTaperFunctionsforBetulaplatyphyllainDaxing,antingShahzadMuhammadKhurramHussainAmnaHePeiJiangLichun(KeyLaboratoryofSustainableForestEcosystemManagementOfMinistryofEducationSchlofForcstry,NorthcastForestryUniversityHarbin150040)Abstract:ObjectiveStemtaperfunctionsareimportantcomponentsinforestmanagementandplanningsystems.Currently,thereisnotaperfunctionforBelulaplatyphyllainnortheastChina,therefore,itisnecessarytodevelopthetaperfunctionforthisspecies.Eightcommonlyusedtaperfunctionsinforestrywerecomparedtoevaluatewhichprovidedabetterpredictionfordiametera(aspecificheightandtotalvolumeforBetulaplatyphyllainnortheastChina.MethodThedatausedinthisstudywerecollectedfrom253destructivelyfelledsampletreeswith3795diameter/heightmeasurementsinthenorthwestofthenorthernslopeofYilehuliMountainsofnortheastChina.Afirst-ordercontinuousautoregressiveerrorstructurewasusedtomodeltheerrortermandaccountforautocorrelation.Multicollinearitywasalsoevaluatedwithconditionnumber.Coefficientofdetennination(/?2),Meanabsolutebias(MAB),rootmeansquaeerror(RMSE),andmeanpercentageofbias(MPB)wereselectedasevaluationcriteriaofmodels.ComPariSonofthetapermodelswascarriedoutusinggoodness-of-fitstatistics,boxplotsofdiameterandvolumeresidualdistributions,andvalidationstatistics.Result1)Intermsofmodelt(ingstatistics,themodelsofKozak(2(X)4)-2,Fangetal.(20)andMaxetal.(1976)werethetopthreemodels.ThemodelofSharmaetal.(2001)showedthepoorestperformance.2)Basedontheboxplotsofdiameterandvolumeresiduals,themodelsofBi(2000),Maxetal.(1976).Kozak(2004)-2andFangetal.(2000)aremoreaccurateindiameterandvolumepredictionwithsmallererrorsandalmostsimilarresidualdiameterandvolumedistribution.ThemodelsofSharmaetal.(2001),Sharmaetal.(2004),Sharmaetal.(2(X)9)andKozak(2004)-1havenonhomogeneousdistributionofthediameterresidualsalongdifferentsectionsofthestem.3)Modelvalidationalsoconfirmed(hatMaxetal.(1976),KoZak(2004)-2,andFangetal.(2000)showedbelterperformance.Ingeneral,themodelofKozak(2004)-2showedconsistentperformanceandwassuperiortoothertapermodelsinpredictingdiameterandvolume.ConclusionBasedontheevaluationstatisticsoffittingandvalidation,graphicanalysis,andconditionnumber,(hemodelofKozak(2004)-2wasrecommendedIbrestimatingdiameterataspecificheight,totalvolumeandmerchantablevolumeforwhitebirchinNortheastChina.Keywords:Betulaplatyphyllataper：volume：autocorrelation：multicollinearityTapermodelsareoneoftheessentialcomponentincurrentsystemsofforestmanagementandplanning(Heidarssonetal.,2011).Recently,theestimationoftreevolumebyusingtaperequationshasgainedpopularity.Asreportedinpreviousstudies,taperfunctionsareavaluabletooltoestimatethetreecontentsforawiderangeofproducts.Tapermodels,owingtotheirflexibility,areextensivelyappliedinforestinventoriestoestimatediameterandmerchantablestemvolume.Merchantablestemvolumeisofgreaterconcernsinceitenablestheclassificationoftimberproductsbymerchantabledimensions.Additionally,itwasindicatedbyLietal.(2010)andde-Migueletal.(2012)thattaperequationsstayaheadofexistingvolumetablesinvolumeestimation.Thisbenefitisattributedtotheabilityoftaperfunctionstopredictthediameter(overbarkorinsidebark)accuratelyatanyheightalongstem.Asaresultofwhich,calculationofmerchantablevolumeforanyrequiredspecificationiseasilymadepossible.Besidesthepredictionoftimbervolumeavailability(Zhangetal.,2006),stemtaperasaregressorvariable,hasalsobeenappliedtodeterminethenumberofgrowthringsincrosssection(Wilhelmsson,2006)andtoevaluatethecorrectsamplingdesignforthecollectionofstemdiameterdata(Newtonetal.,2008).Whitebirch(BetulaplatyphyllaisextensivelydistributedinnortheastChina.Currently,thereisnotaperfunctionforthisspeciesinnortheastChina.Apracticalstemtaperequationisrequiredtoestimatewoodvolumeofwhitebirch.Objectivesofthisstudyweretoevaluateselectedexistingtaperfunctionsandtodevelopataperequationforthepredictionofdiameter,totalvolumeandmerchantablevolumeofwhitebirch.1 Materialsandmethods1.1 DataDatausedinthisstudywerecollectedfromuneven-agedwhitebirchstandsinthenorthwestofthenorthernslopeofYilehuliMountainsofnortheastChina.Atotalof253treescoveringtheexistingrangeofstandconditionsanddensitieswereselectedfordestructivesampling.Beforefelling,diameteratbreastheight(D,1.3mabovegroundlevel)wasmeasuredforalltrees.SummarystatisticsfortreediameterandtotalheightareshowninTab.1.Tab.lDescriptivestatisticsforfittingandvalidationsampletreesowhitebirchDataVariableNooftreesMeanMin.Max.SDFittingD19118.185.043.88.26H19117.257.924.13.92ValidationD6216.845.236.38.00H6215.778.522.13.09D=diameteratbreastheightoverbark：H=totaltreeheight(m).1.2 Methods1.2.1 FunctionsselectedforcomparisonEightcommonlyusedtaperequationswereselected.Thesemodelsbelongtothecategoriesofsimpletaperfunctioni.e.Sharmaetal.(2001),segmentedtaperfunctionsi.e.Maxetal.(1976),Fangetal.(2000),andvariableformtaperfunctionsi.e.Bi(2000),Kozak(2004)-1and2,Sharmaetal.(2004),Sharmaetal.(2009).MathematicalexpressionsofthesemodelsarepresentedinTab.2.Tab.2AnalyzedtaperfunctionsM(iclExpressionShWd=Dd(篝)(.卢+3+%巧Maxet.(l976)d=D21(-1)+b2(.q2-1)+b3(a1-q)2I1+4(2-)2I2=1.ifrotherwise2=l,if<7«2；0otherwiseD.breastheightdiameter(cm);H,totaltreeheight(m);h,heightabovegroundlevel(m);d.diameteroutsidebark(cm)atheight(m);0-02,0-¼,P,andpzaretheparameterstobeestimated;q=h!Ht=1.3H,Z=(H-h)Hm=0.01;X=(H-h)/(H-3).1.2.2ModelevaluationTwogoodness-of-fitstatisticswereused:coefficientofdetermination(R2)androotmeansquareerror(RMSE).Meanabsolutebias(MAB),rootmeansquareerror(RMSE),andmeanpercentageofbias(MPB)wereusedforvalidation.Theexpressionsofthesestatisticsareasfollows:(-)2R2=-(1)(x-)2Li=J>(yi-yi)2RMSE=卫(2)Vn-1lWhere,y.,yiandyarethemeasured,predictedandaveragevalues,respectively,nisthenumberofobservations.2ResultsInitially,taperfunctionswerefittedwithnon-linerleastsquaresmethodandautocorrelationwasnottakenintoaccount.AnexampleofobservedautocorrelationinthemodelofKozak(2004)-2isgiveninFigure1(firstrow).Asexpected,astrongpositiveautocorrelationwasobserved.AfterafirstordercontinuousautoregressiveerrorstructureCAR(1)wasincorporatedintothemodelofKozak(2004)-2,noobviouscorrelationtrendwasobserved,indicatingthatautocorrelationcanbereducedthroughCAR(I)(Fig.l,secondrow).10-101,1,J-10-5O5101.ag1ResidualsFig.ILaggedresidualsfortheKozak(2004)-2modelfittedwithoutconsideringtheautocorrelationparameters(firstrow),andusingcontinuous-timeautoregressiveerrorstructuresoffirstorder(secondrow).Tab.3Goodness<o11tstatistics,rankofmodels,andconditionnumberoftapermodelsModelsRMSER2RankCNBi(20)1.52870.97111.667113.45Sharmaetal.(2001)1.88510.95598.0LO(X)OSharmaetal.(2(X)4)1.57860.96912.527I.80Sharmaetal.(2(X)9)1.52820.97111.6628.9048Maxetal.(1976)1.49560.97231.123274.69Kozak(2004)-11.63060.96712.90530.220Kozak(24)-21.48870.97261.077.830Fangetal.(2(X)0)1.49240.97241.07483.083Theboxplotsofdresidualsversusrelativeheightclasses(Fig.2)indicatedthatthedistributionoferroralongthestemisnotsameamongdifferenttaperfunctions.ThemodelsofSharmaetal.(2001)andSharmaetal.(2004)overestimatedthediameterabove10%ofrelativeheight.ThemodelofSharmaetal.(2(X)9)overestimatedthediameterinthemiddlebolesection(10%-90%).ThemodelofKozak(2004)-1hasnonhomogeneousdistributionoftheresidualsalongdifferentsectionsofthestem.Itunderestimatesthemiddle(30%-70%)andoverestimatestheupperportions(>8()%)ofthestem.ThemodelsofBi(2000),Maxetal.(1976),Kozak(20()4)-2andFangetal.(2000)aremoreaccurateindiameterpredictionwithsmallererrorsandalmostsimilarresidualdiameterdistribution.Tab.4EvaluationstatisticswithrankingofdifferenttapermodelsinestimatingdiameterandvolumeModelsDiameterVblumeMPBMABRMSERankMPBMABRMSERankBi(2000)7.42830.98221.69691.61310.10240.02200.04682.081Sharmaetal.(2(X)1)10.71311.41652.33838.017.91310.03910.07078.000Shannaetal.(2OQ4)7.81431.03311.71492.18010.62140.02310.04812.445Sharmaetal.(2009)7.33180.96941.65691.35816.23600.03540.06676.817Maxetal.(1976)7.29400.96441.60521.1439.98010.02170.04712.039Kozak(2004)-18.46321.11901.81143.3428.77170.01910.04181.000Kozak(2004)-27.18530.95001.65191.1489.65300.02100.04551.745Fang&H.(2000)7.24950.95851.63491.17910.07830.02200.04642.0433 DiscussionNumeroustaperfunctionshavebeendevelopedformanyspecies.However,stemtapermodelsforwhitebirchhavenotbeendevelopedinNortheastChina.Inthepresentstudy,atotalof8commonlyusedstemtaperfunctionsfromthreegroups(simplepolynomial,segmentedandvariableformtaperfunctions)werefittedtoestimatethestemdiameterandtotalvolumeofwhitebirch.Autocorrelationandmulticollinearitywereconsideredinmodelfittingprocess.Itshouldbenotedthatinclusionofautocorrelationwastoimprovetheinterpretationofstatisticalpropertiesoftapermodels.Therewasnosubstantialdifferencebetweentheestimationofthemodelsfittedwithandwithoutautocorrelation.Multicollinearityisnotadecisivefactorforselectingabesttapermodel,however,modelswithlowerCNshouldbepreferred(Kozak,1997).4 ConclusionsInthisstudy,ataperequationforwhitebirchinnortheastChinawasdevelopedtoestimatediametersatanypositionalongthestem,totalandmerchantablevolume.Atotalofeightwell-knowntaperfunctionswereevaluated:simpletaperfunctionofSharmaetal.(2001),thesegmentedtaperfunctionsproposedbyMaxetal.(1976)andFangetal.(20(X),theCrignonmetricandvariableformtaperfunctionsproposedbyBi(2000),Kozak(2004),Shannaetal.(2004),andSharmaetal.(2009).ItisobviousfromthesummarystatisticsandgraphicalanalysisthatthemodelofKozak(2004)-2showedthebestperformancefollowedbyFangetal.(2000)withamarginaldifferenceinthepredictionofdiametersalongthestemandtotalstemvolume.Thus,themodelofKozak(2(X)4)-2wasrecommendedforestimatingdiameteratsspecificheightandtotalvolumeforwhitebirch.ReferencesAntaMB.Didguez-ArandaU.Casiedo-DoradoF.etal.2(X)7.MerchantablevolumesystemforpedunculateoakinnorthwesternSpain.AnnalsofForestScience,64:511-520.BclsleyDA.1991.Conditioningdiagnostics:Collincarityandweakdatainregression.JohnWiley&Sons,Inc.NewYork.396p.BiH.2000.Trigonometricvariable-formtaperequationsforAustralianeucalypls.ForestScience.46:397-409.Crecente-CanipoEAlborecaAR,Dieguez-ArandaU.2009.AmerchantablevolumesystemforPinussylvestrisL.inthemajormountainrangesofSpain.AnnalsofForestScience,66:1-12.de-MiguelS,MchtiitaloL,ShatcrZ,etal.2012.Evaluatingmarginalandconditionalpredictionsoftapernlc!sintheabsenceofcalibrationdata.CanadianJournalofForestResearch.42:1383-1394.HeidarssonL.PukkalaT2011.TaperfunctionsforIodgepolepine(Pinuscontorta)andSiberianlarch(Larixsibirica)inIceland.IcelandicAgriculturalSciences,24:3-11.JiangL.MaY.LiY.2016.Variable-exponenttapermodelsfordahurianlarchindifierentregionsofDaxing'anling.ScientiaSilvaeSinicae,52(2):17-25.(inChinese).KozakA.20Q4.Mylastwordsontaperequations.TheForestryChronicle,80:507-515.