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1、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(
2、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
3、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,antingShahzadMuh
4、ammadKhurramHussainAmnaHePeiJiangLichun(KeyLaboratoryofSustainableForestEcosystemManagementOfMinistryofEducationSchlofForcstry,NorthcastForestryUniversityHarbin150040)Abstract:ObjectiveStemtaperfunctionsareimportantcomponentsinforestmanagementandplanningsystems.Currently,thereisnotaperfunctionforBel
5、ulaplatyphyllainnortheastChina,therefore,itisnecessarytodevelopthetaperfunctionforthisspecies.Eightcommonlyusedtaperfunctionsinforestrywerecomparedtoevaluatewhichprovidedabetterpredictionfordiametera(aspecificheightandtotalvolumeforBetulaplatyphyllainnortheastChina.MethodThedatausedinthisstudywereco
6、llectedfrom253destructivelyfelledsampletreeswith3795diameter/heightmeasurementsinthenorthwestofthenorthernslopeofYilehuliMountainsofnortheastChina.Afirst-ordercontinuousautoregressiveerrorstructurewasusedtomodeltheerrortermandaccountforautocorrelation.Multicollinearitywasalsoevaluatedwithconditionnu
7、mber.Coefficientofdetennination(/?2),Meanabsolutebias(MAB),rootmeansquaeerror(RMSE),andmeanpercentageofbias(MPB)wereselectedasevaluationcriteriaofmodels.ComPariSonofthetapermodelswascarriedoutusinggoodness-of-fitstatistics,boxplotsofdiameterandvolumeresidualdistributions,andvalidationstatistics.Resu
8、lt1)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)aremoreaccurateind
9、iameterandvolumepredictionwithsmallererrorsandalmostsimilarresidualdiameterandvolumedistribution.ThemodelsofSharmaetal.(2001),Sharmaetal.(2004),Sharmaetal.(2(X)9)andKozak(2004)-1havenonhomogeneousdistributionofthediameterresidualsalongdifferentsectionsofthestem.3)Modelvalidationalsoconfirmed(hatMaxe
10、tal.(1976),KoZak(2004)-2,andFangetal.(2000)showedbelterperformance.Ingeneral,themodelofKozak(2004)-2showedconsistentperformanceandwassuperiortoothertapermodelsinpredictingdiameterandvolume.ConclusionBasedontheevaluationstatisticsoffittingandvalidation,graphicanalysis,andconditionnumber,(hemodelofKoz
11、ak(2004)-2wasrecommendedIbrestimatingdiameterataspecificheight,totalvolumeandmerchantablevolumeforwhitebirchinNortheastChina.Keywords:Betulaplatyphyllataper：volume：autocorrelation：multicollinearityTapermodelsareoneoftheessentialcomponentincurrentsystemsofforestmanagementandplanning(Heidarssonetal.,2
12、011).Recently,theestimationoftreevolumebyusingtaperequationshasgainedpopularity.Asreportedinpreviousstudies,taperfunctionsareavaluabletooltoestimatethetreecontentsforawiderangeofproducts.Tapermodels,owingtotheirflexibility,areextensivelyappliedinforestinventoriestoestimatediameterandmerchantablestem
13、volume.Merchantablestemvolumeisofgreaterconcernsinceitenablestheclassificationoftimberproductsbymerchantabledimensions.Additionally,itwasindicatedbyLietal.(2010)andde-Migueletal.(2012)thattaperequationsstayaheadofexistingvolumetablesinvolumeestimation.Thisbenefitisattributedtotheabilityoftaperfuncti
14、onstopredictthediameter(overbarkorinsidebark)accuratelyatanyheightalongstem.Asaresultofwhich,calculationofmerchantablevolumeforanyrequiredspecificationiseasilymadepossible.Besidesthepredictionoftimbervolumeavailability(Zhangetal.,2006),stemtaperasaregressorvariable,hasalsobeenappliedtodeterminethenu
15、mberofgrowthringsincrosssection(Wilhelmsson,2006)andtoevaluatethecorrectsamplingdesignforthecollectionofstemdiameterdata(Newtonetal.,2008).Whitebirch(BetulaplatyphyllaisextensivelydistributedinnortheastChina.Currently,thereisnotaperfunctionforthisspeciesinnortheastChina.Apracticalstemtaperequationis
16、requiredtoestimatewoodvolumeofwhitebirch.Objectivesofthisstudyweretoevaluateselectedexistingtaperfunctionsandtodevelopataperequationforthepredictionofdiameter,totalvolumeandmerchantablevolumeofwhitebirch.1 Materialsandmethods1.1 DataDatausedinthisstudywerecollectedfromuneven-agedwhitebirchstandsinth
17、enorthwestofthenorthernslopeofYilehuliMountainsofnortheastChina.Atotalof253treescoveringtheexistingrangeofstandconditionsanddensitieswereselectedfordestructivesampling.Beforefelling,diameteratbreastheight(D,1.3mabovegroundlevel)wasmeasuredforalltrees.Summarystatisticsfortreediameterandtotalheightare
18、showninTab.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 Functionsselect
19、edforcomparisonEightcommonlyusedtaperequationswereselected.Thesemodelsbelongtothecategoriesofsimpletaperfunctioni.e.Sharmaetal.(2001),segmentedtaperfunctionsi.e.Maxetal.(1976),Fangetal.(2000),andvariableformtaperfunctionsi.e.Bi(2000),Kozak(2004)-1and2,Sharmaetal.(2004),Sharmaetal.(2009).Mathematical
20、expressionsofthesemodelsarepresentedinTab.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(yi-yi)2RMSE=卫(2)Vn-1lWhere,y.,yiandyarethemeasured,predictedandaveragevalues,respectively,nisthenumberofobservations.2Resu
21、ltsInitially,taperfunctionswerefittedwithnon-linerleastsquaresmethodandautocorrelationwasnottakenintoaccount.AnexampleofobservedautocorrelationinthemodelofKozak(2004)-2isgiveninFigure1(firstrow).Asexpected,astrongpositiveautocorrelationwasobserved.Afterafirstordercontinuousautoregressiveerrorstructu
22、reCAR(1)wasincorporatedintothemodelofKozak(2004)-2,noobviouscorrelationtrendwasobserved,indicatingthatautocorrelationcanbereducedthroughCAR(I)(Fig.l,secondrow).10-101,1,J-10-5O5101.ag1ResidualsFig.ILaggedresidualsfortheKozak(2004)-2modelfittedwithoutconsideringtheautocorrelationparameters(firstrow),
23、andusingcontinuous-timeautoregressiveerrorstructuresoffirstorder(secondrow).Tab.3Goodness8()%)ofthestem.ThemodelsofBi(2000),Maxetal.(1976),Kozak(20()4)-2andFangetal.(2000)aremoreaccurateindiameterpredictionwithsmallererrorsandalmostsimilarresidualdiameterdistribution.Tab.4Evaluationstatisticswithran
24、kingofdifferenttapermodelsinestimatingdiameterandvolumeModelsDiameterVblumeMPBMABRMSERankMPBMABRMSERankBi(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.(20
25、09)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 Discussion
26、Numeroustaperfunctionshavebeendevelopedformanyspecies.However,stemtapermodelsforwhitebirchhavenotbeendevelopedinNortheastChina.Inthepresentstudy,atotalof8commonlyusedstemtaperfunctionsfromthreegroups(simplepolynomial,segmentedandvariableformtaperfunctions)werefittedtoestimatethestemdiameterandtotalv
27、olumeofwhitebirch.Autocorrelationandmulticollinearitywereconsideredinmodelfittingprocess.Itshouldbenotedthatinclusionofautocorrelationwastoimprovetheinterpretationofstatisticalpropertiesoftapermodels.Therewasnosubstantialdifferencebetweentheestimationofthemodelsfittedwithandwithoutautocorrelation.Mu
28、lticollinearityisnotadecisivefactorforselectingabesttapermodel,however,modelswithlowerCNshouldbepreferred(Kozak,1997).4 ConclusionsInthisstudy,ataperequationforwhitebirchinnortheastChinawasdevelopedtoestimatediametersatanypositionalongthestem,totalandmerchantablevolume.Atotalofeightwell-knowntaperfu
29、nctionswereevaluated:simpletaperfunctionofSharmaetal.(2001),thesegmentedtaperfunctionsproposedbyMaxetal.(1976)andFangetal.(20(X),theCrignonmetricandvariableformtaperfunctionsproposedbyBi(2000),Kozak(2004),Shannaetal.(2004),andSharmaetal.(2009).Itisobviousfromthesummarystatisticsandgraphicalanalysist
30、hatthemodelofKozak(2004)-2showedthebestperformancefollowedbyFangetal.(2000)withamarginaldifferenceinthepredictionofdiametersalongthestemandtotalstemvolume.Thus,themodelofKozak(2(X)4)-2wasrecommendedforestimatingdiameteratsspecificheightandtotalvolumeforwhitebirch.ReferencesAntaMB.Didguez-ArandaU.Cas
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32、estScience.46:397-409.Crecente-CanipoEAlborecaAR,Dieguez-ArandaU.2009.AmerchantablevolumesystemforPinussylvestrisL.inthemajormountainrangesofSpain.AnnalsofForestScience,66:1-12.de-MiguelS,MchtiitaloL,ShatcrZ,etal.2012.Evaluatingmarginalandconditionalpredictionsoftapernlc!sintheabsenceofcalibrationda
33、ta.CanadianJournalofForestResearch.42:1383-1394.HeidarssonL.PukkalaT2011.TaperfunctionsforIodgepolepine(Pinuscontorta)andSiberianlarch(Larixsibirica)inIceland.IcelandicAgriculturalSciences,24:3-11.JiangL.MaY.LiY.2016.Variable-exponenttapermodelsfordahurianlarchindifierentregionsofDaxinganling.ScientiaSilvaeSinicae,52(2):17-25.(inChinese).KozakA.20Q4.Mylastwordsontaperequations.TheForestryChronicle,80:507-515.
