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Error Analysis on the Five Stand Biomass Growth Estimation Methods for a Sub-Alpine Natural Pine Forest in Yunnan, Southwestern China

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Guoqi Chen at Central South University of Forestry and Technology
Guoqi Chen
Xilin Zhang
Xilin Zhang
Xilin Zhang
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Chunxiao Liu
Chunxiao Liu
Chunxiao Liu
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Chang Liu
Chang Liu
Chang Liu
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Abstract and Figures

Forest biomass measurement or estimation is critical for forest monitoring at the stand scale, but errors among different estimations in stand investigation are unclear. Thus, the Pinus densata natural forest in Shangri-La City, southwestern China, was selected as the research object to investigate the biomass of 84 plots and 100 samples of P. densata. The stand biomass was calculated using five methods: stand biomass growth with age (SBA), stem biomass combined with the biomass expansion factors (SB+BEF), stand volume combined with biomass conversion and expansion factors (SV+BCEF), individual tree biomass combined with stand diameter structure (IB+SDS), and individual tree biomass combined with stand density (IB+SD). The estimation errors of the five methods were then analyzed. The results showed that the suitable methods for estimating stand biomass are SB+BEF, M+BCEF, and IB+SDS. When using these three methods (SB+BEF, SV+BCEF, and IB+SDS) to estimate the biomass of different components, wood biomass estimation using SB+BEF is unsuitable, and root biomass estimation employing the IB+SDS method was not preferred. The SV+BCEF method was better for biomass estimation. Except for the branches, the mean relative error (MRE) of the other components presented minor errors in the estimation, while MRE was lower than other components in the range from −0.11%–28.93%. The SB+BEF was more appealing for branches biomass estimation, and its MRE is only 0.31% lower than SV+BCEF. The stand biomass strongly correlated with BEF, BCEF, stand structure, stand age, and other factors. Hence, the stand biomass growth model system established in this study effectively predicted the stand biomass dynamics and provided a theoretical basis and practical support for accurately estimating forest biomass growth.
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Forests2022,13,1637.https://doi.org/10.3390/f13101637www.mdpi.com/journal/forests
Article
ErrorAnalysisontheFiveStandBiomassGrowthEstimation
MethodsforaSub‐AlpineNaturalPineForestinYunnan,
SouthwesternChina
GuoqiChen
1,2
,XilinZhang
1,2
,ChunxiaoLiu
1,2
,ChangLiu
1,2
,HuiXu
1,2
andGuanglongOu
1,2,
*
1
CollegeofForestry,SouthwestForestryUniversity,Kunming650224,China
2
KeyLaboratoryofStateForestryAdministrationonBiodiversityConservationinSouthwestChina,
SouthwestForestryUniversity,Kunming650224,China
*Correspondence:olg2007621@swfu.edu.cn
Abstract:Forestbiomassmeasurementorestimationiscriticalforforestmonitoringatthestand
scale,buterrorsamongdifferentestimationsinstandinvestigationareunclear.Thus,thePinusden‐
satanaturalforestinShangri‐LaCity,southwesternChina,wasselectedastheresearchobjectto
investigatethebiomassof84plotsand100samplesofP.densata.Thestandbiomasswascalculated
usingfivemethods:standbiomassgrowthwithage(SBA),stembiomasscombinedwiththebio‐
massexpansionfactors(SB+BEF),standvolumecombinedwithbiomassconversionandexpansion
factors(SV+BCEF),individualtreebiomasscombinedwithstanddiameterstructure(IB+SDS),and
individualtreebiomasscombinedwithstanddensity(IB+SD).Theestimationerrorsofthefive
methodswerethenanalyzed.Theresultsshowedthatthesuitablemethodsforestimatingstand
biomassareSB+BEF,M+BCEF,andIB+SDS.Whenusingthesethreemethods(SB+BEF,SV+BCEF,
andIB+SDS)toestimatethebiomassofdifferentcomponents,woodbiomassestimationusing
SB+BEFisunsuitable,androotbiomassestimationemployingtheIB+SDSmethodwasnotpre‐
ferred.TheSV+BCEFmethodwasbetterforbiomassestimation.Exceptforthebranches,themean
relativeerror(MRE)oftheothercomponentspresentedminorerrorsintheestimation,whileMRE
waslowerthanothercomponentsintherangefrom−0.11%–28.93%.TheSB+BEFwasmoreappeal‐
ingforbranchesbiomassestimation,anditsMREisonly0.31%lowerthanSV+BCEF.Thestand
biomassstronglycorrelatedwithBEF,BCEF,standstructure,standage,andotherfactors.Hence,
thestandbiomassgrowthmodelsystemestablishedinthisstudyeffectivelypredictedthestand
biomassdynamicsandprovidedatheoreticalbasisandpracticalsupportforaccuratelyestimating
forestbiomassgrowth.
Keywords:above‐groundbiomass;biomassgrowth;erroranalysis;Pinusdensataforests
1.Introduction
Theforestisfundamentaltotheglobalcarboncycleandplaysavitalroleinmain‐
tainingtheglobalgreenhousegasbalance[1–5].Biomassdataisthebasisforstudying
forestryandecologicalproblems,andaccuratelyestimatingbiomassisanessentialissue
inforestmanagementandforestryresearch[6–8].Primarilyduetoglobalwarmingand
thecarbondioxidefixedbyplantsinphotosynthesis,accuratelymeasuringthebiomass
oftreecomponents(wood,bark,branches,leaves,androots)hasattractedsignificantre‐
searchattention[9].Thus,forestbiomassmeasurement,estimation,andgrowthatthe
standscalearecrucialtoanalyzingforestcarbon.
Measuringorestimatingthestandbiomassmainlyincludesdirectharvesting,vol‐
umeconversion,andbiomassequationmethods.Theharvestingmethodwasfirstdevel‐
oped,wherethebiomassofeachcomponentisdirectlyobtainedbycuttingandweighing
alltreesorestimatingthebiomassbydirectlymeasuringthebiomassofthestandardtrees
Citation:Chen,G.;Zhang,X.;
Liu,C.;Liu,C.;Xu,H.;Ou,G.Error
AnalysisontheFiveStandBiomass
GrowthEstimationMethodsfora
Sub‐AlpineNaturalPineForestin
Yunnan,SouthwesternChina.
Forests2022,13,1637.https://doi.org/
10.3390/f13101637
AcademicEditor:GiorgioVacchiano
Received:7August2022
Accepted:3October2022
Published:6October2022
Publisher’sNote:MDPIstaysneu‐
tralwithregardtojurisdictional
claimsinpublishedmapsandinstitu‐
tionalaffiliations.
Copyright:©2022bytheauthors.Li‐
censeeMDPI,Basel,Switzerland.
Thisarticleisanopenaccessarticle
distributedunderthetermsandcon‐
ditionsoftheCreativeCommonsAt‐
tribution(CCBY)license(https://cre‐
ativecommons.org/licenses/by/4.0/).
Forests2022,13,16372of20
[10].Thedirectharvestingmethodischaracterizedbyhighprecisionbutrequiresalotof
humanandmaterialresourceswhilecausingunavoidabledamagetotheforestandthe
environment[11].Thismethodisnotallowedwhenestimatinglarge‐scaleforestbiomass.
Inthiscase,thevolumeconversionandbiomassequationmethodsareapplicable[12].
Thevolumeconversionmethodcanbeconductedduetothesignificantcorrelationbe‐
tweenthestandvolumeandbiomass,[13–16],whichistherecommendedbiomassesti‐
mationtechniquebytheIntergovernmentalPanelonClimateChange(IPCC)[17,18].This
techniquemainlyincludesbiomassexpansionfactors(BEF)andbiomassconversionand
expansionfactors(BCEF).Nevertheless,usingaconstantBEForBCEFdoesnotprovide
anaccurateestimateofforestbiomassastheyarerelatedtostanddensity,standage,and
siteconditions[19–22].Therefore,thebiomassconversionfactorcontinuousfunction
methodwasusedtoimproveandachievebetterresults[23–26].Moreover,thebiomass
equationatthestandscaleisastandardmethodtoestimatethetotalordifficult‐to‐meas‐
urestandbiomassbyeasilymeasurableforestvariables[27–29].
Biomassgrowthmodelscandescribechangesinanindividualtreeorstandsizeover
time[9].Thesemodelscanbedividedintoindividualtreegrowth,standdiameterstruc‐
ture,andwholestandmodels[30].Morethan3000biomassmodelsexist[31],whereusu‐
ally,theindependentmodelvariablesarecommonfactorsinforestsurveys,suchasdi‐
ameteratbreastheight(DBH),treeheight(H),andage.Moreover,sitequality,standden‐
sity,andmanagementmeasurementsareincorporatedintothegrowthmodelstoimprove
theirpredictionaccuracyoranalyzetheenvironmentaleffects.Amongthem,biomass
equationsonlyusingtheindependentvariableDBHorbothindependentvariablesDBH
andHarewidelyusedattheindividualtreeorstandscale[32–34].Moreover,theindi‐
vidualtreemodelsincorporatingtheagingvariableareestablishedtodescribebiomass
growth[22,35].
Moreover,whenthestructureanddynamicsofthestandcanbedescribedinmore
detail[36],thegrowthofthestandcanbesimulatedbasedontheindividualtreemodel
[37–40].Thewhole‐standmodelusuallyprovidesawell‐behavedoutputatthestandlevel
butlacksinformationaboutthestand’sstructure[41].Connectingindividualtreesandthe
standlevelincludesconstraintparameters,disaggregation,andcombinationmethods
[42].Althoughthesemethodsarewidelyusedtoconnectindividualtreesandstandlevels
[43–45],theerrorsinestimatingthestandbiomassusingtheindividualtreebiomass
growthcombinedwiththestandstructurearealmostnotquantified[41,45–47].
Insummary,therearemanymethodsformeasuringforestbiomassandgrowth,but
theestimationaccuracyisuncertain,especiallyestimationfromanindividualtreetothe
standscale[41,45,46].Theestimationmethodsarelogicallyequivalent,whichmeansthat
differencesbetweenmethodsmaybeduetorandomornon‐randomprocessesrelatedto
samplingandmodeling.Especiallytheestimationerrorofthesemethodsisunclearfor
thevariousbiomasscomponents[46].Thus,quantifyingandcomparingtheestimation
accuracydifferencesbetweendifferentmethodshasessentialtheoreticalandpracticalsig‐
nificanceforaccuratelydescribingforestbiomassgrowth.
Inthisstudy,thePinusdensatanaturalforestinShangri‐Lawasusedastheresearch
subjecttoanalyzetheaccuracydifferencesinestimatingstandbiomassgrowthforthe
differentcomponentsusingfivemethods.Namely,thestandbiomassgrowthwithage
(SBA),standbiomassgrowthwithage(SBA),thestembiomasscombinedwiththebio‐
massexpansionfactors(SB+BEF),thestandvolumecombinedwithbiomassconversion
andexpansionfactors(SV+BCEF),theindividualtreebiomasscombinedwithstanddi‐
ameterstructure(IB+SDS),andindividualtreebiomasscombinedwithstanddensity
(IB+SD).Thesignificantcontributionsofthisworkwere:
(1) Toquantifytheerrorofthedifferentestimationmethodsforeachbiomasscompo‐
nent;
(2) Toestablishastandbiomassgrowthmodelsystem;
(3) Toexploretheapplicableestimationmethodsforforestbiomassgrowthunderdif‐
ferentconditions.
Forests2022,13,16373of20
2.MaterialsandMethods
2.1.EstimationMethods
Standbiomassispredictablebyusingtheindividualtreedataindirectlyorstanddata
directly,andthestandbiomassgrowthcanbeestimatedemployingbothdatatypes.In
thisstudy,wedesignedfiveestimationmethodsbasedondifferentoriginaldatatopre‐
dictforestbiomassgrowth(Figure1).AsillustratedinFigure1,asthestandbiomassof
differentcomponentswasobtained,thestandbiomassmodelwiththestandage(SBA)
couldbeconstructedtopredictforestbiomassgrowth.Thestembiomassdataisrelatively
easytomeasureorinvestigatecomparedwiththeothercomponents.Thegrowthmodels
thatcombinedstembiomassdatawithBEF(SB+BEF)couldpredictthechangeofthestand
biomassusingthestandage.Moreover,thestandvolume(SV)wasoneoftheessential
variablestodescribetheforestproductionandcharacteristicsand,therefore,hasgained
attraction.Alternatively,thestandvolumecombinedwiththechangeoftheBCEF
(SV+BCEF)couldalsopredictthestand’sbiomassgrowth.
Moreover,individualtreebiomassandstandstructurecouldalsoestimatethestand
biomass.Indeed,astheindividualtreestaticbiomassmodelwasestablished,thegrowth
ofthestandbiomasscouldbepredictedbycombiningtheindividualstaticbiomassmod‐
elswiththestanddiameterstructuredynamicchange(IB+SDS).Ifthebiomassgrowth
modelsoftheindividualtreehadbeenconstructed,thismethodcombinedwiththeindi‐
vidualtreebiomassgrowthmodelandstanddensity(IB+SD)couldbeusedtopredictthe
standbiomassgrowth.
Figure1.Thelistofstandbiomassgrowthestimationmodels.SBAisadirectestimationusingstand
biomassofthecomponents;SB+BEFisanestimationmethodusingstandstembiomassincorporat‐
ingBEFi;SV+BCEFisanestimationmethodusingstandvolumeincorporatingBCEFi;IB+SDSisan
estimationmethodusingstaticbiomassofthecomponentsforindividualtreeincorporatingdynam‐
icalestimationonstanddiameterstructure;IB+SDisanestimationmethodusingbiomassgrowth
ofthecomponentsforindividualtreeincorporatingstanddensity.Furthermore,IBiisthei‐thcom‐
ponentsbiomassofindividualtree;SBiisthei‐thcomponentsbiomassofstand;BEFiisthebiomass
expansionfactorsofthei‐thcomponentsbasedonstembiomassofstand;BCEFiisthebiomasscon‐
versionandexpansionfactorsofi‐thcomponentsbiomassbasedonstandvolume;SVisthestand
volume;DBHisthediameteratbreastheight;Rdisthediameterclasses;tistheageofthetreeor
Forests2022,13,16374of20
stand;SDisthestanddensity(trees∙ha−1);Nisthecumulativeprobabilityofthediameterclasses
fromminimumclass;pjistheestimationofthecumulativeprobabilitydistributionfunctionsfor
fittingthestanddiameterstructure.
2.2.StudyArea
ThePinusdensataforestinShangri‐LaCityintheNorthwestYunnanprovince,South‐
westChina,wasselectedastheresearchobject(Figure2).Thegeographicalcoordinates
ofShangri‐Lacityrangefrom99°20′Eto100°19′Eandfrom26°52′Nto28°52′ N,atthe
junctionofYunnan,Sichuan,andTibet.Thehighestaltitudeis5545mabovesealevel,
andthelowestis1503m(averageelevationis3459mabovesealevel).Thevegetation
coveragereaches89%,ofwhich59%isconiferousforest,15.6%broad‐leavedforest,18%
shrub,and3.7%grasslandandcrop.Theannualaveragetemperatureis5.4°C,withDe‐
cemberbeingthecoldestmonthinShangri‐LaCity.TheaveragetemperatureinDecember
isfrom−2°Cto6°Cwithanextrememinimumof−27.4°C,andJulyisthehoestmonth
withanaveragetemperaturefrom12°Cto14°Candanextrememaximumtemperature
of25.6°C[48].Theaverageannualrainfallisfrom268mmto945mm,andthefrost‐free
periodisfrom129to197days[49].Thesoiltypeismainlydarkbrownforestsoil[50].
Figure2.Thelocationofstudysitesandtheplots.
2.3.DataInvestigationandMeasurement
InAugustandSeptember2016,thebiomassof84plotsand100samplingtreeswere
investigatedandcalculated,withtheareapersampleplotbeing0.09ha.Werecordedeach
plot’slocationcoordinates,elevation,slopedegree,direction,andthemeasuredDBHand
Hofeachtreeinthesampleplots.Thenwecalculatedthestandaveragetreeheight,av‐
erageheightofthedominanttrees,averageDBH,andtheSD.Meanwhile,threestandard
treeswithasimilaraverageDBHandHintheplotwereselectedtodeterminethestand
age.Moreover,wemeasuredtheheightof3to6dominanttreesevenlydistributedinthe
Forests2022,13,16375of20
sampleplotandusedtheiraveragevalueasthemeandominantheight[51].Theaverage
heightsofthedominanttreesintheplotsrangedfrom3.60to29.00m.Themeanheight
ofthestandwasfrom2.82to24.30m,withtheirmeanvaluesbeing12.59and10.36m,
respectively.TheAGErangedfrom8to150a,thestanddensityfrom489to8500trees∙ha−1,
andtheSVfrom8.36to719.05m3ha−1(Table1).
Table1.Theprimarycharacteristicsoftheplots(n=84).Htistheaverageheightofdominanttrees
inthestand,Hmisthemeanheightofthestand,Dgisthediametercorrespondingwiththemean
basalareaatbreastheight,AGEistheageofstand,SDisthestanddensity,andSVisthestand
volume.
VariablesMinimumMaximumMeanStandardDevia‐
tion
Stand
Ht(m)3.60 29.00 12.59 4.70
Hm(m)2.82 24.30 10.36 4.13
Dg(cm)3.99 41.27 13.97 5.55
AGE(a)8 150 41 21
SD(treesha−1)489 8500 2888 1541
SV(m3ha−1)8.36 719.05 229.40 133.88
Biomass
Wood(tha−1)2.87 236.19 76.30 44.67
Bark(tha−1)0.51 28.24 10.65 6.18
Needles(tha−1)6.23 70.98 33.23 10.95
Branches(tha−1)1.51 23.00 6.17 2.55
Above‐ground(tha−1)11.12 344.38 126.35 60.45
Roots(tha−1)0.8031.4710.875.29
Total(tha−1)11.92 375.85 137.23 65.53
BEF
Wood0.762 0.926 0.873 0.030
Bark0.074 0.238 0.127 0.030
Needles0.141 2.006 0.536 0.366
Branches0.022 0.482 0.106 0.090
Above‐ground1.163 3.488 1.642 0.456
Roots0.080 0.257 0.140 0.036
Total1.265 3.7071.782 0.486
BCEF
Wood0.279 0.375 0.335 0.023
Bark0.030 0.092 0.048 0.010
Needles0.050 0.852 0.208 0.151
Branches0.008 0.205 0.041 0.037
Above‐ground0.413 1.482 0.632 0.197
Roots0.0320.0990.0550.014
Total0.449 1.5750.6860.210
Thesampletree’slengthwasmeasuredafterlogging,andtheDBH,H,andtreeage
weremeasured.Intotal,weharvested100sampletrees,withtheDBHrangingfrom3.99
to41.27cm(meanof13.97cm),thetreeheightfrom4.20to33.00m(meanof14.50m),and
thetree’sagerangedfrom18to258a(meanof60.17a).Thebiomasspercomponent
rangedfrom0.06to1652.72kg(Table2).Moreover,thebiomassofthetreecomponents
wasdestructivelymeasured,includingwood,bark,branches,needles,androots;stemdi‐
ametersandbarkthicknesswererecordedaccordingtothestemheightat0,0.5,1.5,and
2.5mtoobtainthestemvolume[39,40].Wemeasuredthefreshweightofthewoodand
barkin2msegments.Thenasampledisc,withabout4cmthicknesspersegment,was
sampledtoobtainthemoisturecontentandwoodorbarkdensity.Weweighedthe
branches(freshbiomass)andneedlesinthefieldandsampled(atleast5%oftheirfresh
mass)toassessdryweight.Allsamplesweredriedtoaconstantmassinthelaboratory
[52].Regardingwoodandbark,wecalculatedthedrymassusingthedisc’sdensityand
thecorrespondingvolumeperstemsegment.Forthebranchesandneedles,weusedthe
proportionsofthetotalfreshmassesandthemoisturecontentofthesamples[38].
Forests2022,13,16376of20
Moreover,accordingtothemethodologyguidelinesfromtheIPCC[18],theBEFval‐
uesofeachcomponentperplotwerecalculatedusingtheproportionsofthebiomassof
eachcomponenttothestembiomass.TheBCEFvalueswerecalculatedbytheratiosof
thebiomassofeachcomponenttothestandvolumeforeachbiomasscomponent(includ‐
ingwood,bark,needles,branches,roots,above‐ground,andtotalbiomass).
BEFi=Bi/Bstem(1)
BCEFi=Bi/SV(2)
whereBEFiistheBEFvalueofthei‐thcomponent,Biisthebiomassofthei‐thcomponent,
Bstenisthestandstembiomass,BCEFiistheBCEFvalueofthei‐thcomponent,andSVis
thestandvolume.
Table2.Theprimarycharactersofthesamplingtrees(n=100).nisthenumberoftrees,Histhetree
height,DBHisthediameteratbreastheight,andageisthetreeage.
VariablesMinimumMaximumMeanStandard
Deviation
n100100100‐
H(m)4.2033.0014.506.65
DBH(cm)5.6058.9023.3014.03
age(a)1825860.1745.08
Woodbiomass(kg)2.551088.25191.55270.71
Barkbiomass(kg)0.25134.6021.9233.31
Needlesbiomass(kg)0.0634.846.417.26
Branchesbiomass(kg)0.21160.9139.3744.36
Above‐groundbiomass(kg)4.031398.68259.24347.27
Rootsbiomass(kg)1.51275.3851.9066.47
Totalbiomass(kg)5.541652.72311.14412.94
2.4.ModelFitting
Amongthe84sampleplots,werandomlyselected63formodeling,andtheremain‐
ing21sampleplotswereusedfortesting.Amongthe100sampletrees,75sampletrees
wererandomlychosenformodeling,andtheother25sampletreeswereusedfortesting.
Thepowerfunctionwasselectedtoconstructtheindividualbiomassstaticmodels[53,54],
andtheRichards,Logistic,Gompertz,Korf,andWeibulldistributionswereemployedto
modelindividualtreebiomassgrowthandstandbiomass,whileBEFsandBCEFschanged
withthestandage[51].
ThesemodelswereconstructedusingtheRstatisticalsoftware[55].Thenumberof
treesinthecorrespondingdiameterclasseswasobtained,andthenthepercentageofthe
correspondingdiameterclassesandcumulativepercentageofthediameterclasseswere
calculated.ThecumulativediameterstructureofeachplotwasbasedontheRichards
function,andtheparameterpredictionmodelwasusedtodescribethedynamicchange
lawofthestanddiameterdistribution.Finally,thenonlinearfittingmethodinthe1stOpt
software[56]wasusedtofindtheoptimalfunctionalrelationshipbetweenitsparameters,
thestandage,andthestanddensityindex.
Thebiomassequationsorgrowthmodelscouldbeevaluatedbasedonseveralstatis‐
ticalindicators.Forinstance,Zengetal.[57,58]selectedseveralindicatorstoassessthe
model’sperformance,withthecoefficientofdetermination(R2)andtherootmeansquare
error(RMSE)usedastheessentialindexesofmodelselection.
𝑅1∑󰇛
𝑦𝑦󰇜

∑󰇛
𝑦𝑦󰇜
 (3)
Forests2022,13,16377of20
RMSE ∑󰇛
𝑦𝑦󰇜
𝑛1(4)
%100×)
ˆ
ˆ
(
1
=EE 1=
∑－
N
ii
ii
y
y
y
N(5)
%100×
ˆ
ˆ
1
=RMA 1=
∑ －
N
ii
ii
y
yy
N
(6)
whereyiistheobservedvalueofy,i
y
ˆisthepredictedvalueofy,
y
isthemeanofy,nis
thenumberofsamples,andNisthesamplesize.
2.5.MethodEvaluation
Wechosetwoerrorindexes,themeanrelativeerror(MRE)andthemeanrelative
absoluteerror(MRAE),toevaluatetheestimationperformanceoffivemethodsusingdif‐
ferentstandcomponents.AllstatisticalindicatorsutilizestheSPSSsoftware[59].
%100×)(
1
=∑∧
∧
－
MRE
i
ii
y
yy
n
(7)
%100×
ˆ
ˆ
1
=∑－
MRAE
i
ii
y
yy
n
(8)
whereyiistheobservedvalueoftheresponsevariable,i
y
ˆisthepredictedvalueofthe
responsevariable,andnisthesamplesizeofthevalidationdata.
3.Results
3.1.ModelEvaluation
3.1.1.StandBiomassofDifferentComponents(SBA)
Thestandbiomassgrowthmodels(SBA)werebuiltusingtheindependentvariable
ofstandagetoestimatethestandbiomassgrowthforthedifferentcomponentsaccording
to
SB
𝑓
󰇛𝑡󰇜(9)
whereSBiisthestandbiomasspercomponentandtisthestandage,whilethefunctions
aretheRichards,Logistic,Gompertz,Korf,andWeibull.
DuetothehighestR2andlowestRMSEpercomponent,thelogisticfunctionwas
selectedtofitthegrowthofthewood,roots,andtheabove‐groundbiomass,theKorf
functionwasemployedtofitthegrowthofbarkbiomass,andtheRichardsfunctiontofit
thegrowthofthebranchesandneedlesbiomass.Allmodelsandtheirestimationresults
arereportedinTable3.
TheR2rangedfrom0.401to0.655,withthecorrespondingvalueforthewoodbio‐
massbeingthehighestandtheneedlesbeingthelowest.However,theneedleshadthe
smallestRMSE(1.383).Theaveragerelativeerror(EE)rangedfrom16.749to30.628,all
positive,indicatingthattheequationestimationwasonthehighside,andtheabsolute
meanrelativeerror(RMA)wasabove32.101(Table3).

Forests2022,13,16378of20
Table3.TheestimationresultoftheSBA.Wisthebiomassofeachcomponent(wood,bark,needles,
andbranches),above‐ground,androotsbiomassofthestand.Nisthestanddensity,andAGEis
thestandage.
ComponentsModelFormsFittingTest
nR2RMSEnEERMA
Wood
W
112.24
1exp
󰇧
4.32-0.113
󰇡
N
1000
󰇢
0.188 AGE
630.65524.1982130.62845.761
BarkW24.607exp
-83.459󰇡
N
1000󰇢-0.011 AGE-1.259
630.5834.0662116.74937.444
NeedlesW5.1611-exp-0.345󰇡
N
1000󰇢-0.942AGE
1-exp-0.345󰇡
N
1000󰇢-0.942202.782
630.4011.3832124.32732.101
Branches
W
23.987
⎝
⎜
⎛
1-exp
󰇧
-0.185
󰇡
N
1000
󰇢
-0.647 AGE
1-exp
󰇧
-0.185
󰇡
N
1000
󰇢
-0.647 20
⎠
⎟
⎞
3.209
630.4977.7882116.12425.024
Above‐groundW173.25
1exp3.281-0.093󰇡
N
1000󰇢0.217AGE630.61134.8492123.39334.989
RootsW30.514
1exp3.626-0.141󰇡
N
1000󰇢0.05AGE630.5616.8492120.00831.577
3.1.2.StandStemBiomassCombinedwithBiomassExpansionFactors(SB+BEF)
Basedonthegrowthrelationshipofthestandstembiomass(SBstem)andbiomassex‐
pansionfactors(BEFi)withstandage(t),thestandbiomassofthedifferentcomponentsat
acertainagewaspredictedusingtheproductofSBstemandthecorrespondingBEFvalues.
ThecorrespondingequationispresentedinEquation(10),revealingthatthestandbio‐
massgrowthcanbeestimatedbycombiningthestandstembiomasswithbiomassexpan‐
sionfactors(SB+BEF).
󰇱SB
𝑓
󰇛𝑡󰇜
BEF
𝑓
󰇛𝑡󰇜
SBSB∙BEF(10)
whereSBstemisthestandstembiomass,BEFiisthebiomassexpansionfactor,SBiisthe
standbiomasspercomponent,andtisthestandage.Thefunctionsarelogistic,linear,
power,andlogarithm.
Thelogisticfunctionwasselectedtofitthestem’sgrowth,andthelinearfunction
fittedthegrowthofwood,bark,needles,andabove‐ground.Thepowerfunctionfitted
thegrowthofthebranches,andthelogarithmfunctionwasselectedtofitthegrowthof
theroots.AllmodelsandtheestimatedresultsarereportedinTable4.
Inthebiomassgrowthequationconstructedbybiomassexpansionfactors(BEF),the
effectofwoodandbarkwasnotideal,withR2=0.006butRMSE=0.032,whichwasthe
smallest.Exceptforthewoodbiomass,themeanrelativeerrorsoftheothercomponents
(bark,needles,branches,above‐ground,androots)wereallnegative,andRMAranged
from2.532to30.082(Table4).
Table4.TheestimationresultoftheSB+BEF.SBstemisthestembiomass,Nisthestanddensity,AGE
isthestandage,yisthebiomassexpansionfactorsofeachcomponent(wood,bark,needles,
branches),andabove‐groundandrootsbiomassexpansionfactors.
VariablesModelFormsFittingTest
nR2RMSEnEERMA
StembiomassSB155.663
1 exp 󰇧4.946-0.107 󰇡
N
1000󰇢0.288 AGE󰇨630.62536.8032133.55049.434
BEFWood𝑦=0.875-0.0000979AGE630.0060.032210.5902.532
Forests2022,13,16379of20
Bark𝑦=0.1250.0000979AGE630.0060.03221−3.88217.008
Needles𝑦=4.42/AGE-0.024630.6740.05821−13.50030.082
Branches𝑦=16.069AGE−0.959630.7000.22421−17.07124.432
Above‐ground𝑦=22.546/AGE-0.979630.6940.28221−5.7218.774
Roots𝑦=0.936-0.168ln(AGE)630.5150.08721−5.12914.425
3.1.3.StandVolumeCombinedwithBiomassConversionandExpansionFactors
(SV+BCEF)
Bymodelingtherelationshipofthestandvolume(SV)andtheBCEFsofeachcom‐
ponentwithstandage,thestandbiomassofthedifferentcomponentsatacertainage
couldbepredictedusingtheproductofSVandthecorrespondingBCEFvalues.Thestand
biomassgrowthwasestimatedusingthemethodofstandvolumecombinedwiththebi‐
omassconversionandexpansionfactors(SV+BCEF)usingtheequationbelow:
󰇱SV
𝑓
󰇛𝑡󰇜
BCEF
𝑓
󰇛𝑡󰇜
SBSV ∙𝐵𝐶𝐸𝐹(11)
whereSVisthestandvolume,BCEFiisthebiomassconversionandexpansionfactors,SBi
isthestandbiomassofeachcomponent,andtisthestandage.Thefunctionsarelogistic,
linear,power,andlogarithm.
Thelogisticfunctionwasselectedtofitthestandvolumegrowth,thelinearfunction
tofitthegrowthofwood,bark,needles,andbranches,thepowerfunctiontofittheabove‐
groundgrowth,andthelogarithmfunctionwasselectedtofitthegrowthofroots.All
modelsandtheirestimationresultsarereportedinTable5.
InthebiomassgrowthequationconstructedbyBCEF,theR2ofwoodandbarkwere
small,0.151and0.031,respectively,andthemeanrelativeerrorsofthefivecomponents
wereallnegative,indicatingthattheestimationofeachequationwasgenerallylow.The
RMAofwoodasthesmallestat4.339(Table5).
Table5.TheestimationresultoftheSV+BCEF.SVisthestandvolume,Nisthestanddensity,AGE
isthestandage,yisthebiomassconversionandexpansionfactorsofeachcomponent(wood,bark,
needles,branches),andabove‐groundandrootsbiomassconversionandexpansionfactors.
VariablesModelFormsFittingTest
nR2RMSEnEERMA
StandvolumeSV404.278
1exp
󰇧
4.887-0.113󰇡
N
1000󰇢0.236 AGE
󰇨
630.64792.2972132.33947.855
BCEF
Wood𝑦=-0.00037AGE+0.351630.1510.02421−1.5404.339
Bark𝑦=exp(-3.07+2.011/AGE)630.0310.01121−4.92315.257
Needles𝑦=−0.012+1.827/AGE630.6830.02321−15.42830.720
Branches𝑦=−0.013+7.531/AGE630.7050.09221−16.15424.151
Above‐
ground𝑦=4.294AGE−0.535630.7120.11921−6.61011.013
Roots𝑦=0.387−0.072ln(AGE)630.5930.03221−6.67014.019
3.1.4.IndividualBiomassStaticModelsCombinedwithStandDiameterStructure
(IB+SDS)
Forthestaticbiomassmodelsofthecomponents,weusedthepowerfunctionasthe
primaryformofthemodeltoconstructthePinusdensataindividualtreebiomassmodel.
WebuiltthePinusdensataindividualtreebiomassmodelbasedonthetreeheightand
diameteratbreastheightastheindependentvariablesofeachdimensionofthebiomass
model.Moreover,theheightcurveswerefittedtoobtainthetreeheightcorresponding
withtheDBHclasses.Thebasicmodelswerealsoselectedasthepowerfunction,logistic
Forests2022,13,163710of20
equation,Korfequation,andRichardsequation.Theonepresentingthebestfittingand
predictionaccuracyperformancewasusedfurther.
Thestandbiomassgrowthwasestimatedbyusingtheindividualbiomassstatic
modelcombinedwiththestanddiameterstructure(IB+SDS):
⎩
⎪
⎨
⎪
⎧
IB
f
󰇛DBH, 𝐻󰇜,and 𝐻
f
󰇛DBH󰇜
PDF󰇛DBH󰇜
f
󰇛DBH󰇜
𝑝f󰇛AGE, SD󰇜
SB𝑁∙𝑝∙IB,
(12)
whereIBiistheindividualbiomass,andthebasicfunctionconsidersusingfourpower
functionmodels.TheindependentvariablesareDBH,H,andDBH2H(pseudovolume).
DBHisthediameteratbreastheight,Histhetreeheight,AGEisthestandage,SDisthe
standdensity,Nisthecumulativeprobabilityofthediameterclassesfromminimumclass,
pjistheestimationofthecumulativeprobabilitydistributionfunctionsforfittingthestand
diameterstructure,andSBiisthestandbiomassofeachcomponent.Thefunctionsofthe
treeheightcurvearelogistic,power,Bates,Wykoff,andRichards.
Forthestanddiameterstructuremodels,weusedtheRichardsfunction(Equation
(13)),fittingthecumulativepercentagealongwiththediameterclassesperplot.Table6
reportsthefittingresultswiththeR2valuesofallplotsexceeding0.9,indicatinganexcel‐
lentfittingeffectthatbetterreflectedtheactualsituationofastanddiameteraccumulation
distribution(Table6).Then,theestimationparametersbandcwereestimatedutilizing
thestandageandstanddensity,thuspredictingthediameterclassdistributionataspe‐
cifictime.
()
c
d
R∙by －）（exp1= (13)
whereyisthecumulativepercentageofthestand’sdiameterclasses,Rdisthediameter
class(cm),andbandcaretheparameterstobeestimated.
Table6.Thestatisticsoftheestimationparametersofthecumulativedistributionfunctionofthe
standdiameterstructureforallplots.
ParametersMinimumMaximumMeanStandard
Deviation
b0.0441.5790.3260.275
c1.307402.31126.42560.700
R20.9051.0000.9770.018
RMSE0.1180.8960.4270.180
Finally,thetotalbiomassperdiameterclassisobtainedfromthetreenumberwith
differentdiameterclassesandthecorrespondingcomponentbiomass.Then,thebiomass
ofalltreesforeachcomponentorthetotalstandbiomassisobtainedbyaddingalldiam‐
eterclasses.
Foreachcomponent,thestaticbiomassgrowthmodelofanindividualtreewasesti‐
matedbyapowerfunctionequation,withmodelsandestimationresultslistedinTable7.
AsreportedinTable7,theR2ofthebiomassgrowthmodelpercomponentofthe
woodwasappealing,buttheR2oftheneedlesas0.674,lowerthantheothercomponents.
Themeanrelativeerrors(EE)ofeachcomponentwereallnegative,indicatingthatthe
errorestimatingeachequationwasgenerallylow.TheEEoftheparameters(b,c)wasalso
negative(Table7).

Forests2022,13,163711of20
Table7.TheestimationresultoftheIB+SDS.IBistheindividualtreebiomassofeachcomponent
(wood,bark,needles,branches),above‐ground,androotindividualtreebiomass.DBHisthediam‐
eteratbreastheight,HisthevaluecorrespondingtoDBHonthetreeheightcurve,bandcarethe
standdiameterstructureparameters,x1representstheAGEofthestandage,andx2representsthe
standdensity.
VariablesModelFormsFittingTest
nR2RMSEnEERMA
Individualtreebio‐
mass
WoodIB=0.030×DBH1.746×H1.021750.99028.92125−2.70112.067
BarkIB=0.0034×DBH1.222×H1.640750.89811.17525−9.79631.204
NeedlesIB=0.045×DBH2.498×H−1.143750.6744.3892513.11541.071
BranchesIB=0.170×DBH2.007×H−0.386750.83118.98925−18.63542.069
Above‐groundIB=0.075×DBH1.700×H0.875750.99036.14525−5.80215.163
RootsIB=0.025×DBH2.221×H0.082750.9992.49525−2.3576.368
Treeheightcurve
H
41.133
15.809exp
󰇛
-0.048DBH
󰇜
750.8772.34925−1.51115.523
Standdiameters
structureparame‐
ters
b
b(-122275-4884.247∙x1+337.997∙x2-
53.09∙x12-0.109∙x22+6.29∙x1∙x2)/(1-18670.
28∙x1+86.892∙x2-541.006∙x12-0.426∙x22
+56.942∙x1∙x2)
630.8830.10521−4.02927.853
cc21.949-0.0026∙x2+478.319∙exp(-exp(-(
x1-14.209)/-1.378)-(x1-14.209)/-1.378+1)630.87425.20321−40.69251.911
3.1.5.IndividualBiomassGrowthModelsCombinedwithStandDensity(IB+SD)
Theindividualbiomassgrowthmodelscombinedwiththestanddensity(IB+SD)can
predictthestandbiomassgrowth.Theindividualtreebiomassgrowthmodelpercompo‐
nentisconstructed,andtheproductoftheindividualbiomassandstanddensityiscalcu‐
latedtoobtainthecomponents’standbiomassataspecifictime(Equation(14)).Thestand
densityofeachplotisassumednottochangewiththestandgrowth.
IB
𝑓
󰇛𝑡󰇜
SB𝑁∙IB(14)
whereIBiistheindividualbiomass,tisthestandage,Nisthestanddensity,andSBiisthe
standbiomassofeachcomponent.ThefunctionsemployedfortheIBiareRichards,Lo‐
gistic,andKorf.
TheRichardsfunctionwasselectedtofitthegrowthofthewood,needles,branches,
androotsbiomass,andthelogisticfunctionfittedthebarkbiomassgrowth.TheKorf
functionwasselectedtofitthegrowthoftheabove‐groundbiomass.Themodelsandthe
correspondingestimationresultsarereportedinTable8.
Thebestindividualtreebiomassgrowthmodelforthedifferentcomponentsislisted
inTable8,wheretheR2ofallmodelsexceeded0.45.Specifically,wood,bark,above‐
ground,androotsattainedavaluegreaterthan0.8,andtheneedlespresentedthelowest
valueof0.454.Themeanrelativeerrorsofeachcomponentwereallnegative.
Table8.TheestimationresultoftheIB+SD.TheIBistheindividualtreebiomassofeachcomponent
(wood,bark,needles,branches),above‐ground,androottreebiomass.Theageisthetreeage.
VariablesModelFormsFittingTest
nR2RMSEnEERMA
Individualtree
biomass
WoodIB 1378 1-exp󰇛-0.0111age󰇜2.880750.88992.08825−19.70046.527
BarkIB 92.881
1 exp󰇛4.87 - 0.057age󰇜750.80115.62225−16.90450.969
NeedlesIB 17.262 1-exp󰇛-0.03age󰇜3.743750.4545.68425−27.90553.246
BranchesIB 131.534 1-exp󰇛-0.025age󰇜3.96750.73323.87025−16.73057.181
Above‐
groundIB 1291.748 exp-5.876exp󰇛-0.021age󰇜750.892121.08525−22.06744.151
Forests2022,13,163712of20
RootsIB 253.572 1-exp󰇛-0.015age󰇜3.105750.85526.29625−16.21253.203
3.2.MethodComparison
TheMREandMRAEwereusedtoevaluatetheerrorofallfivemethods.Asillus‐
tratedinFigure3,theMREvaluesofbothSB+BEFandSV+BCEFforallcomponentswere
notsignificantlydifferentfromzero(exceptforthewoodbiomassestimatedbythe
SB+BEFmethodandthetotalbiomassbytheSV+BCEFmethod).InboththeSBAand
IB+SDmethods,theMREvalueswereextremelysignificanttozero.However,forthe
IB+SDS,thedifference’ssignificancevarieddependingonthebiomasscomponent,with
theMREoftherootsandthetotalstandbiomasssignificantlydifferenttozero.However,
theothercomponents’differencesbetweenMREandzerowereinsignificant.Moreover,
amongthefivemethods,theMREofthebiomass(eachcomponent,above‐ground,roots,
totalbiomass)estimatedbytheSBAmethodwassignificantlylargerthanthatofthe
IB+SDmethod.FortheMREofthewoodbiomass,thebiomassestimatedbySBA,SB+BEF,
andSV+BCEFwassignificantlydifferentfromtheonecalculatedbyIB+SDSandIB+SD.
Thesignificanceofthemeanrelativeerroroftheabove‐ground,roots,andtotalbiomass
isdepictedintheFigure3.
Figure3.Meanrelativeerror(MRE)offivemethodsforthedifferentcomponents.Thestatistical
testresultsofthesignificantdifferencesofMREsfromzero:*and**representthesignificancelevels
of0.05and0.01,respectively.Thelettersa,ab,andbindicatethesignificanceofthesamecomponent
betweendifferentmethodsatthesignificancelevelsof0.05.
Inaddition,fortheIB+SDmethod,thevalueoftheMREofthedifferentcomponents
rangedfrom−44.044to−7.019%,thevalueofthetotalbiomassisthelowest,andtheMRE
valueis−7.019%.ThebiomassMREusingtheSV+BCEFmethodwaspositive,exceptfor
thetotalbiomass.TheMRErangedfrom−6.914to28.582%.RegardingIB+SDS,theMRE
rangedfrom−13.84to16.649%,whiletheMREofeachbiomasscomponentestimatedby
theSBAmethodandtheSB+BEFmethodrangedfrom16.124to30.087%fortheSBA
Forests2022,13,163713of20
method.TheMRErangewas0.397to33.183%fortheSB+BEFmethod.TheMREvalues
wereallpositive,indicatingthatthebiomassestimatedbythesetwomethodswassmaller
thanthemeasuredvalue.
ComparedwithMRE,MRAEreflectedtheabsolutebiasbetweentheobservedand
predictedvalues,andtherewasnooffsetbetweenpositiveandnegative.Asdepictedin
Figure4,exceptforthesignificantdifferencebetweentheMRAEofneedles,biomasses‐
timatedbytheSBAmethod,andzero,theMRAEoftheremainingcomponents(wood,
bark,branches,roots),above‐ground,andtotalbiomasswassignificantlydifferentfrom
zero.FortheMRAEofbranchbiomass,theMRAEofbiomassestimatedbytheIB+SD
methodwassignificantlylargerthantheMRAEofthebiomassestimatedbytheremain‐
ingthreemethods(SBA,SB+BEF,andSV+BCEF)exceptfortheIB+SDSmethod.Forthe
totalbiomass,theMRAEofthebiomassestimatedusingSBAandSB+BEFwassignifi‐
cantlylargerthanthatestimatedusingtheotherthreemethods(SV+BCEF,IB+SDS,and
IB+SD).
Amongthebiomasscomponentsestimatedbythefivemethods,theMRAEvaluesof
thewoodbiomasswerealllarger(exceptfortheneedlesbiomass,whichhadthelargest
MRAEvalueoftheIB+SDSmethod).TheSV+BCEFandIB+SDmethodshadthelowest
MRAEvaluesfortheestimatedtotalbiomass,andthebrancheshadthelowestMRAE
valuesestimatedbytheotherthreemethods.
Figure4.Meanrelativeabsoluteerror(MRAE)offivemethodsforthedifferentcomponents.The
statisticaltestresultsofthesignificantdifferencesofMRAEsfromzero:*and**representthesig‐
nificancelevelsof0.05and0.01,respectively.Thelettersa,ab,andbindicatethesignificanceofthe
samecomponentbetweendifferentmethodsatthesignificancelevelsof0.05.
4.Discussion
4.1.EstimationComparison
Thisstudyusedfivemethodstocalculatetheabove‐groundbiomass,rootsbiomass,
andbiomassofdifferentcomponentsofthePinusdensata.Forthecalculations,weused
themeasuredsampleplotdataofPinusdensataandsimulatedthedynamicgrowthmodel
Forests2022,13,163714of20
systemofthePinusdensatabiomass.Themodelsystemreflectedtheeffectsofstandden‐
sity,DBH,standvolume,andbiomassfactorsonbiomass.Overall,thisstudy’sresults
revealedthatthestembiomasscombinedwiththebiomassexpansionfactors(BEF)
method,thestandvolumecombinedwiththebiomassconversionandexpansionfactors
(BCEF)method,andthemethodofcombiningindividualtreebiomasswiththestanddi‐
ameterstructurepresentedlesserrorsandahigherpredictionaccuracy.Thestandbio‐
masswasrelatedtothebiomassexpansionfactors,standvolume,biomassconversion,
expansionfactor,andstanddiameterstructure[60–62].Moreover,thestandbiomasswas
relatedtothestandvolume,whileintroducingthestandvolumeasavariabletocalculate
thebiomassreducedthemodel’suncertainty[11].Therefore,manymodelshavebeenes‐
tablishedtoderivebiomassfromthestandvolume[10,63],significantlyaffectingthestand
biomass.ThesefindingswereconsistentwiththeconclusionsofZengetal.[64],Donget
al.[21],andJagodzińskietal.[16,39,40]onbiomassandaccumulationofLarixdecidua
Mill.,AbiesalbaMill.,PinussylvestrisL.
Jagodzińskietal.[38]researchedScotspine,andUsoltsevetal.[65]concludedthat
biomassexpansionandconversionwererelatedtothestandage,confirmingthisstudy’s
rationalityandthefeasibilityusingageasavariabletopredictbiomassgrowth.The
changeinBEFinresponsetothechangingrelationshipsofstemvolumeandbiomassto
totaltreevolumeandbiomasswiththeincreasingstandagewasanessentialconsidera‐
tioninbiomassestimates[66].Inthisstudy,BEF,BCEF,andstandagepresentedacertain
regularity,asBEFandBCEFdecreasedwiththeincreaseofstandageuntilreachinga
constantvalue[67,68].SimilartoJagodzińskietal.[38,69],whostudiedyoungbirch(Bet‐
ulapendula)andyoungScotspinestands,thechangesoftheBEFandBCEFwiththestand
ageconformedtothebiologicallawoftreegrowthbiomasschanges,i.e.,thebiomass
changedwiththegrowthofthetreesafterreachingacertainage,afterwhichthebiomass
saturated.Forthatreason,thebiomassofyoungtreestandscannotbecalculatedusing
theBCEFderivedforoldertreestands[69,70].Thisstudyavoidedthisissuebecausewe
modeledthevariationsofBEFandBCEFwithstandage.Becausethestandvolumeand
standdiameterstructure(SDS)weredirectlyrelatedtostandfactorssuchasdiameterat
breastheightandtreeheight,whichweredirectlyrelatedtotreegrowth,theydirectly
affectedthestandbiomassandcarbonstorage[71,72].Inaddition,thegrowthchangeof
stembiomasswithagewasalsosignificantlycorrelatedwithDBHandtreeheight,sothe
growthofstembiomasswasalsoinlinewiththebiologicalchangesintreegrowth.
Inthisstudy,amongthebiomassgrowthequationsconstructedusingtwomethods,
SB+BEFandSV+BCEF,themodelsforBEFandBCEFwereconstructedusingstandageas
theindependentvariable.TheR2valuesoftheconstructedequationsofBEFandBCEFfor
wood(R2=0.006inTable4andR2=0.151inTable5)andbark(R2=0.006inTable4and
R2=0.031inTable5)werealllow.Lehtonenetal.[68]usedstandageastheindependent
variabletoconstructsomeBEFmodels.ForNorwaysprucestands,theR2ofBEFmodels
rangedfrom0.2020to0.3622,andthevaluesforthebroadleavedstandsrangedfrom
0.0377to0.2399;then,theysuggestedapplyingtheconstantastheR2waslowerthan0.25.
Therefore,theproportionsofwoodandbarktothestemwererelativelyconstant,andthe
constantBEFvaluesshouldbeusedinspecificsituations,particularlywhenestimating
barkandwoodbiomass[69].Moreover,theSBAandIB+SDmethodspredictedbiomass
growthinmodelconstruction,asthesetwomethodswerecloselyrelatedtostanddensity.
Trees’biologicalcharacteristicsandbiomassallocationpatternschangewiththestand
growth,andthesechangesmayberelatedtothetreesizeincreaseswithageandchanges
instanddensity[73].Thestanddensitysignificantlychangestheverticalandhorizontal
standstructureandstanddensitycandramaticallyaffectthegrowthanddevelopmentof
stands.Theincreaseinstanddensityleadstointensifiedcompetitionamongtrees,result‐
inginintensifiedintra‐specificandinter‐specificcompetitioninitsupperandlowerparts,
therebychangingbiomassallocation[38,61,74].

Forests2022,13,163715of20
4.2.ApplicabilityAnalysisoftheEstimationMethods
Thefivestandbiomassestimationmethodsarelogicallyequivalent[46].Andthe
equivalencebetweenthefivemethodsmeansthatdifferencesbetweenmethodsmayarise
fromrandomornon‐randomprocessesassociatedwithsamplingandmodeling[75].In
thisstudy,consideringthedestructivenessofforestbiomassinvestigation,theclear‐cut‐
tingmethodwasnotusedtomeasurethetreesinthesampleplot,onlythebiomassofthe
standardtreewasmeasured.Andthemeasurementmethodsusedareconsistent.Further‐
more,thesamplingrangeofbothtreeandplotcoversthetreeorstandage,standdensity,
andtreesizeofPinusdensatainthestudyarea(Tables1and2).Thus,theequivalence
betweenthefivemethodsmeantthatthedifferencesbetweenmethodsmaybeduetothe
processrelatedtomodeling.Theindividualtree,wholestand,andthediameterdistribu‐
tionmodelswereused,andtheyhadadvantagesanddisadvantages[51,75].Thewhole
standmodelsprovidedbetterestimatesatthestandlevel,butsuchestimationresults
lackedstandstructureinformation[41].Itiswellknownthatbuildingmodelsfromthe
individualtreeleveltothewholestandleveltoestimatebiomasscanleadtoinaccurate
estimationresultsduetoaccumulatederrors[45,46].However,thereisalackofresearch
onthespecificerrorsize.Thisstudyquantifiedtheerrorsfromtheindividualtreelevelto
thestandlevel,andtheerrorsinestimatingthebiomassofeachcomponentusingdifferent
methodswerecompared.
Moreover,thebiomassgrowthestimationsystemofPinusdensataforestswascon‐
structedbasedonindividualtree,standdiameterstructure,andstanddata.Eachmethod
appliedtodifferentconditions.TheIB+SDSandIB+SDmethodscalculatedthestandbio‐
massofPinusdensatabycalculatingthebiomassofanindividualtreeandthencombining
thecorrespondingstandfactorstocalculatethestandbiomassofPinusdensata.Usingthe
individualtreebiomassmodelasthebasemodeltoestimate,thestandbiomassgrowth
couldbetterdescribethestand[41,45,47,76].Standdensityisanessentialfactoraffecting
thegrowthandproductivityofstand[11].
Theconsiderationofconstantstanddensityisbasedonthemethod’sapplicability.
BecausethePinusdensatastandsinthisstudywererelativelyhomogeneousandthehec‐
tarevaluesofthetrees(treesha−1)wasusedasthestanddensity,theIB+SDmethodwas
suitableforestimatingthebiomassofplantationswithaconsistentstandage.Whenthe
standstructureisrelativelycomplex,theintroductionofthestanddiameterstructurecan
betterfittheequationtoaccuratelyestimatebiomass,sointhiscase,theIB+SDSmethod
wasmoresuitableforestimatingPinusdensatastandbiomass.Generally,thedistribution
oftreesonthestandisrelativelyuniforminaplantation,andthehectarevaluesofthe
treesandtheaveragesizeofthestandarefrequentlyusedasindicatorsofstanddensity,
butstanddensitychangeswiththestandageortreesize[51].Thestanddensityindex
(SDI),proposedbyReineke,appliestoplantationsorapureforestofthesameagewitha
substantiallysimilarmanagementhistory[77].Inthisstudy,thestanddensitywasas‐
sumednottochangewiththestandgrowthintheestimationIB+SDandIB+SDSmethod.
Thefixedstanddensitymaybringerrorsinbiomassestimation,butthestandardDBHis
requiredfortheSDI,andthevalueisnotuniform[51].TheusualvalueinChineseforestry
is20cm[51,78],butReinekedefinesitas25.4cm[77],andJiangetal.usedavalueof12
cmintheirstudyonMassonPine[79].Moreover,thestandself‐thinningslopevarieswith
treespeciesandgeographicalarea.TheslopevalueinReineke’sstudywas−1.605,which
isafixedvalueformosttreespecies.Luisetal.[80]usedaslopevalueof−1.897.Zhanget
al.[81]studiedtheself‐thinningslopeoffirandshowedthatthemodelwithclimate‐sen‐
sitivityperformedbest.Nospecificvaluewasgivenfortheself‐thinningslopeofPinus
densata.Thus,theinappropriatestandardDBHandstandself‐thinningslopemaycause
moresignificanterrors[51].Furthermore,thespatialpatternoftreesinnaturalforestsis
nothomogeneous,whichmaymaketherelationshipbetweendiameteratbreastheight
andstanddensityunstable[51].Thus,theuseofthestanddensityindexmayproduce
unexpectedresults.Usingthestanddensityfornaturalforestsshouldbeappropriate.
Forests2022,13,163716of20
TheSBA,SB+BEF,andSV+BCEFestimationmethodswerethemodelconstructedat
thestandlevel.FortheSBAmethod,eachstandcomponentcalculatedthestandbiomass
growth.Therefore,theSBAmethodissuitableforplantationsorforestsofthesameage,
wherethestandageisrelativelyeasytoobtain.Itismoresuitabletocalculatethebiomass
growthbypoints;theSB+BEFmethodissuitableforthebiomassconversionfactorwhen
onlytreetrunkdatacanbeobtainedoriseasytoobtaininthesampleplot.TheSV+BCEF
methodissuitableforstandswhosestandvolumeiseasytomeasure,thestandbiomass
canbecalculatedbycombiningthestandvolumewiththebiomassconversionexpansion
factor.
Althoughmanyremotesensingmethodshavebeenusedtomeasureforestbiomass,
remotesensingobservationsstillneedtobecombinedwithgroundsurveydata[78].
Withinaspecificaccuracyrange,theresearchmethodinthispapercanmeetgroundsur‐
veys.Inaddition,theremotesensingmethodcanonlyobservetheabove‐groundbiomass.
Itcannotmeasuretherootbiomassoftheforest.However,therootsbiomassisalsoan
essentialpartoftheforestbiomass[9],sotheresearchinthispapercanbeusedinfuture
work—methodscombinedwithremotesensingmethodstoconductgroundsurveys.
Moreover,someresearchshowedthattheerrorestimatesinanextendedfactor
modelofbiomassconstructedwithageastheindependentvariableandthattheerror
rangewasspecies‐dependent[75].Thus,thisstudyincludedfiveestimationswithageas
theindependentvariable.Moreover,itisfeasibletouseageasavariabletopredictforest
biomassgrowth,andmanyscholarshavealsoconductedrelatedexplorationsinprevious
studies.Zavitkovski[82]showedthatagesignificantlyaffectedtherelationshipbetween
above‐groundroots,thebiomassofabove‐groundcomponents,andtreesize.Introducing
standageasanauxiliaryvariableintothemodelwithadiameteratbreastheight,diame‐
teratbreastheight,andtreeheightasindependentvariablescanimprovetheestimation
effectofthemodelandreducetheerrorintheallometricgrowthequationoftheabove‐
groundcomponents[80].Thebiomassgrowthmodelwithagehasahigherfittingaccu‐
racythanthegrowthmodelwithoutageasavariable[83].Peichletal.[66]studiedthe
allometricgrowthanddistributionofabove‐groundandrootstreebiomassoffourage
sequencesofwhitepine.Theyconsideredthatageaffectsthedistributionofbiomassof
eachstandingtreecomponentduringthegrowthprocess.Thiswasrelatedtocomparing
thebiomassmodelwithoutintroducingtheagefactor.Theintroductionoftheagevaria‐
blecanreducetheerrorofbiomassestimationofwoodsamplesofdifferentages.Xueet
al.[84]establishedanindividualtreebiomassgrowthmodelforthreetreespecieswith
standingtreeageasanindependentvariable,indicatingthattheproportionofabove‐
groundbiomassinthestandingtreegrowthcycleincreasedwithageandconstantly
changed.Constructingabiomassgrowthmodelincludingstandagecanrealizebiomass
estimationonaregionalscaleataspecifictime,whichcanbeusedforregional‐scalebio‐
massandcarbonstorageestimationandcarbonsinkpotentialassessment[85].Thisstudy
usedstandageasavariabletoconstructabiomassgrowthequation,whichprovided
modelsandmethodsforestimatingthebiomassandcarbonstorageofPinusdensatafor‐
estsinShangri‐La.
5.Conclusions
ThisstudyprovidedacomprehensiveoverviewofmethodsforestimatingPinusden‐
satastandbiomassinShangri‐LaCityinsouthwestChina.Fivemethodsforestimating
biomassgrowthwereestablishedandevaluated,andthemostsuitablemethodsforesti‐
matingthebiomassofdifferentcomponentsofPinusdensataforestswerescreenedout.
Thesemethodshavecertainbiologicalrationalityandaccuracy:thestandstembiomass
combinedwithBEF,thestandvolume(SV)combinedwithBCEF,andtheindividualtree
biomasscombinedwiththechangeofstanddiameterstructure(SDS).Overall,thesethree
methodsshowedgoodaccuracyinestimatingthetotalstandbiomass,above‐groundbio‐
mass,rootsbiomass,andbiomassofdifferentcomponentsofPinusdensataforestsinthis
area.
Forests2022,13,163717of20
However,choosingamethoddependsonthedataavailable.Asthestemdataiseasy
toobtainandthebiomassofothercomponentsisnoteasytoobtain,thestembiomasscan
becalculated.ByconstructingtheallometricgrowthequationofBEF,thestembiomass
combinedwithBEFcancalculatethechangeofthedifferentcomponentswithage.Ifstand
volumedataisnoteasytoobtain,thechangeinbiomassofdifferentcomponentswithage
canbepredictedbyconstructingtheallometricequationofstandvolumeandcombining
itwiththeBCEFvalue.Ifthebiomassofanindividualtreeiseasytoobtain,thechangeof
forestbiomasswithagecanbepredictedusingthebiomassofanindividualtreecombined
withthestanddiameterstructure.Overall,thisworkhasasignificantreferencevaluefor
thegrowthestimationofstandbiomassinafforestationandreforestation.
AuthorContributions:G.C.participatedinthecollectionoffielddata,conducteddataanalysis,and
wrotethedraftofthepaper;X.Z.andC.L.(ChunxiaoLiuand)participatedinthecollectionoffield
dataanddataanalysis;C.L.(ChangLiu)andH.X.helpedwithdataanalysisandwritingofthe
paper.G.O.supervisedandcoordinatedtheresearchproject,designedtheexperiment,andrevised
thepaper.Allauthorshavereadandagreedtothepublishedversionofthemanuscript.
Funding:ThestudywasfinanciallysupportedbytheNationalNaturalScienceFoundationofChina
(grantnumbers31560209and31760206)andtheTen‐ThousandTalentsProgramofYunnanProv‐
ince,China(YNWR‐QNBJ‐2018‐184).
Acknowledgments:TheauthorswouldliketothankthefacultyandstudentsattheCollegeofFor‐
estry,SouthwestForestryUniversity(SWFU),China,whoprovidedandcollectedthedataforthis
study.TheauthorswouldliketothankEditSprings(https://www.editsprings.cn)fortheexpertlin‐
guisticservices.
ConflictsofInterest:Theauthorsdeclarethattheyhavenoknowncompetingfinancialinterestsor
personalrelationshipsthatcouldhaveappearedtoinfluencetheworkreportedinthispaper.
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Full-text available
  • May 2022
[Objective] There are knowledge gaps on stand carbon stock growth model at present. This study developed a stand-level carbon stock growth model system to provide a method for dynamic estimation of regional forest carbon storage with time. [Method] Taking Larix olgensis plantation in Jilin Province of northeastern China as the research object, the site quality classification algorithm was used to divide all sample plots into three site grades, which were introduced into the model system as dummy variables. The stand carbon stock growth model system was established by simultaneous equations to link stand average height, basal area growth model and stand carbon stock model. The adjusted coefficient of determination (R2adj ), the standard error of the estimated value (SEE) and the average prediction error (MPE) were used to evaluate model performance. The growth process of stand carbon stock under different site grades and stand density index (SDI), and the influence of stand basal area and average height on stand carbon stock were analyzed. [Result] (1) The R2adj of stand average height growth model, basal area growth model and carbon stock model were 0.892, 0.979 and 0.960, respectively, and the MPEs were both less than 2%. (2) Both procedures in the model system (inventory- and model-derived stand average height and basal area) could accurately estimate the stand carbon stock, and the difference was only 0.02 t/ha, so the model system had great generality and stability. (3) Stand carbon stock growth increased with the increasing site grade of sample plots. When the site grade was the same, the growth was slow with SDI less than 1 500 plant/ha; but there were no differences in the growth process among different SDIs larger than 1 500 plant/ha after 40 years, and the optimal SDI for maximum stand carbon stock was about 1 500−2 000 plant/ha. (4) The stand carbon stock increased with the increase of stand basal area and average height, and stand basal area had larger effects on stand carbon than stand average height. [Conclusion] The growth of stand carbon stock is closely related to the site grade, stand average age, density, basal area and average height. The modeling approach of simultaneous equations is a feasible method for developing the stand carbon stock growth model system. The stand carbon stock growth model system developed by this study could effectively predict stand carbon stock, which providing a tool for understanding the growth of stand carbon stock and forest carbon sink assessment.
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Tree functional traits, forest biomass, and tree species diversity interact with site properties to drive forest soil carbon
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Full-text available
  • Mar 2022
Forests constitute important ecosystems in the global carbon cycle. However, how trees and environmental conditions interact to determine the amount of organic carbon stored in forest soils is a hotly debated subject. In particular, how tree species influence soil organic carbon (SOC) remains unclear. Based on a global compilation of data, we show that functional traits of trees and forest standing biomass explain half of the local variability in forest SOC. The effects of functional traits on SOC depended on the climatic and soil conditions with the strongest effect observed under boreal climate and on acidic, poor, coarse-textured soils. Mixing tree species in forests also favours the storage of SOC, provided that a biomass over-yielding occurs in mixed forests. We propose that the forest carbon sink can be optimised by (i) increasing standing biomass, (ii) increasing forest species richness, and (iii) choosing forest composition based on tree functional traits according to the local conditions. Forests constitute important ecosystems in the global carbon cycle. This study investigates how tree species influence soil organic carbon using a global dataset, showing the importance of tree functional traits and forest standing biomass to optimise forest carbon sink.
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Temporal and Spatial Variation of Aboveground Biomass of Pinus densata and Its Drivers in Shangri-La, CHINA
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Understanding the drivers of forest aboveground biomass (AGB) is essential to further understanding the forest carbon cycle. In the upper Yangtze River region, where ecosystems are incredibly fragile, the driving factors that make AGB changes differ from other regions. This study aims to investigate AGB’s spatial and temporal variation of Pinus densata in Shangri-La and decompose the direct and indirect effects of spatial attribute, climate, stand structure, and agricultural activity on AGB in Shangri-La to evaluate the degree of influence of each factor on AGB change. The continuous sample plots from National Forest Inventory (NFI) and Landsat time series were used to estimate the AGB in 1987, 1992, 1997, 2002, 2007, 2012, and 2017. The structural equation model (SEM) was used to analyze the different effects of the four factors on AGB based on five scales: entire, 1987–2002, 2007–2017, low population density, and high population density. The results are as follows: (1) The AGB of Pinus densata in Shangri-La decreased from 1987 to 2017, with the total amount falling from 9.52 million tons to 7.41 million tons, and the average AGB falling from 55.49 t/ha to 40.10 t/ha. (2) At different scales, stand structure and climate were the drivers that directly affect the AGB change. In contrast, the agricultural activity had a negative direct effect on the AGB change, and spatial attribute had a relatively small indirect effect on the AGB change. (3) Analyzing the SEM results at different scales, the change of the contribution of the agricultural activity indicates that human activity is the main negative driver of AGB change in Shangri-La, especially at the high population density region. In contrast, the change of the contribution of the stand structure and climate indicates that the loss of old trees has an important influence on the AGB change. Forest resources here and other ecologically fragile areas should be gradually restored by adhering to policies, such as strengthening forest protection, improving forest stand quality, and limiting agricultural production activities.
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Analysis of spatio-temporal changes in forest biomass in China
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Full-text available
  • Apr 2021
Forests play a central role in the global carbon cycle. China's forests have a high carbon sequestration potential owing to their wide distribution, young age and relatively low carbon density. Forest biomass is an essential variable for assessing carbon sequestration capacity, thus determining the spatio-temporal changes of forest biomass is critical to the national carbon budget and to contribute to sustainable forest management. Based on Chinese forest inventory data (1999–2013), this study explored spatial patterns of forest biomass at a grid resolution of 1 km by applying a downscaling method and further analyzed spatio-temporal changes of biomass at different spatial scales. The main findings are: (1) the regression relationship between forest biomass and the associated influencing factors at a provincial scale can be applied to estimate biomass at a pixel scale by employing a downscaling method; (2) forest biomass had a distinct spatial pattern with the greatest biomass occurring in the major mountain ranges; (3) forest biomass changes had a notable spatial distribution pattern; increase (i.e., carbon sinks) occurred in east and southeast China, decreases (i.e., carbon sources) were observed in the northeast to southwest, with the largest biomass losses in the Hengduan Mountains, Southern Hainan and Northern Da Hinggan Mountains; and, (4) forest vegetation functioned as a carbon sink during 1999–2013 with a net increase in biomass of 3.71 Pg.
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How large is the difference in large-scale forest biomass estimations based on new climate-modified stand biomass models?
Article
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  • Jul 2021
  • ECOL INDIC
Accurate forest carbon service accounting is essential for climate change mitigation. At present, the knowledge about whether and how climate-sensitive stand biomass models could reduce the uncertainty of forest biomass/carbon estimation is lacking. Hence, the aim of this study is to develop climate-sensitive stand biomass models and quantify their differences. Data containing 539 sample plots of larch plantations in northern and northeastern China were utilized to develop two basic and the corresponding climate-sensitive stand biomass models. Owing to the uncertainty from predictors, the forecast combination method was used to combine the two basic models (FCMs) and the two climate-sensitive models (CS-FCMs) and to quantify the difference in biomass estimations at the plot and regional scales. Results showed that the adjusted R² values of the stand biomass models were greater than 0.85 and the relative root mean square errors ranged from 5.51% to 22.62%. The CS-FCMs produced more accurate biomass estimates than the FCMs. The difference in biomass estimations derived from biomass models with and without climatic variables was 411,549 tons or 0.27% at the regional scale, but the carbon value difference amounted to about $8.3 million. This study underlined the importance of accurate carbon accounting based on climate-modified stand biomass models for forest carbon management.
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Impact of Stand Density and Tree Social Status on Aboveground Biomass Allocation of Scots Pine Pinus sylvestris L.
Article
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  • Jul 2020
Stand density changes due to aging and thinning interventions. At the same time, the social status of trees develops and varies due to different genetic conditions as well as access to nutrients and light. Trees growing in diverse conditions gain their social status in the stand, which, in the end, influences their development and biomass allocation. The objective of this research was to discover if stand density or tree social status has an impact on a tree’s aboveground biomass allocation. The study was carried out in five premature and five mature pine stands, growing in the same soil conditions. The selected sample stands had a different growing density, from low to high. In each sample stand, 10 trees were selected to represent a different social status, according to the Schädelin classification. There were 100 trees felled in total (50 in the premature stands and 50 in the mature stands), for which the dry biomass of the stem, living and dead branches, needles, and cones was determined. The results showed that stand density only had an impact on the branches’ biomass fraction but not the stem and foliage fractions, while social status had an impact on all the fractions. Dominant and codominant trees, as well as those with developed crowns, had a smaller share of the stem and higher share of branches in comparison with trees of a lower social status.
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Biomass Models with Breast Height Diameter and Age for Main Nativetree Species in Guangdong Province
Article
Full-text available
  • Feb 2019
[Objective] In order to improve the monitoring efficiency and precisely calculate forest carbon sequestration in afforestation projects in Guangdong Province,this study selected major broad-leaved tree species in Guangdong,such as Cinnamomum camphora,Schima superba and Liquidambar formosana,and established aboveground biomass models with age and diameter as independent variables.[Method] All 270 sample trees with 90 sample trees for each tree species were obtained according to 10 diameter classes during the process of modeling,using destructive experiments and stem analysis method to obtain tree biomass and age data.Using the dummy variable method to distinguish the different origins (natural forests and plantations),single tree biomass models with the diameter of breast height (DBH) and age were established for the three species.Also the aboveground biomass components (stem wood and bark,branches,foliage) were established for natural forests and plantations based on dummy variable method.The additivity or compatibility of the components of the aboveground parts was solved by the nonlinear simultaneous equation systems.[Result] The determination coefficients Radj2 of the three above-ground biomass models of the three tree species are between 0.89 and 0.94.It is feasible to use biomass model (1) with DBH and age to estimate tree above-ground biomass.Model (1) has good estimation result and is easy to use.After adding the dummy variable,the three above-ground biomass models Radj2 of the three tree species all reached 0.90 or more.Model (4) can further improve biomass estimate accuracy and refine the model application conditions;for the B-D-T based compatible biomass model system (7) there are good performances in 3 tree species.Radj2 of stem biomass model is between 0.90 and 0.95,Radj2 of bark biomass model is between 0.84 and 0.94,and Radj2 of branch biomass model is between 0.73 and 0.91.The Radj2 of the leaf biomass model is between 0.63 and 0.75,and a compatible B-D-T biomass model system (8) with dummy variables is constructed.The stem biomass equation Radj2 is between 0.88 and 0.97,and the bark biomass equation Radj2 is between 0.82 and 0.93,the branch biomass equation Radj2 is between 0.84 and 0.90,and the leaf biomass equation Radj2 is between 0.62 and 0.69.The result further indicate that the biomass model with DBH and age is more effective than the DBH and tree height biomass models.[Conclusion] This study established the aboveground biomass model with diameter and age for three major native broad-leaved tree species in Guangdong Province.The biomass compatibility model of each component in the aboveground biomass part was established by simultaneous equations.The single tree aboveground biomass model with the DBH and age model (1) have higher fitting accuracy than the commonly used two DBH and height model (2) and (3) and the model (4) with dummy variable also have higher fitting accuracy than model (5) and (6).The precision of nonlinear simultaneous equations (8) with dummy variables is higher than that of model system (7) with B-D-T.Meanwhile,the precision index of the dummy variable simultaneous equations (8) with the DBH and age variable is also better than that of the dummy variables simultaneous equations (9) and (10) with the DBH high variable.The simultaneous equations (8) not only ensure the compatibility between the aboveground biomass of each component,but also obtain more optimal parameter estimates from different origins.The single-wood biomass model with DBH and age (1) and the aboveground biomass model considering the origin (4),the model system (7),the biomass compatibility equations for the above-ground components with the DBH and age,and considerations the above-ground biomass compatibility equations (8) have higher fitting precision than the commonly used above-ground biomass models of DBH and tree height,and are more suitable for artificial broad-leaved forest and carbon sink afforestation projects (arbon sink measurement,monitoring and evaluation) in practice.
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A theory to link relationships of stand volume, density, mean diameter and height in forestry data
Article
Full-text available
  • Dec 2019
In this study, a geometric model of a growing forest stand has been explored. The basic relationships considered link stand volume and stand density, diameter at breast height (DBH), mean DBH and mean height. The model provides simple formulas connecting the exponents of all the relationships. Application of the formulas to real forestry data provided a high level of predictions of an exponent from two others measured through regressions from empirical data. The Pinus sylvestris L. data were of a static nature, a collection of individual stands, while the Pseudotsuga menziesii (Mirb.) Franco data were dynamic, representing forest stand development over time. The ability of the model to predict exponents in the empirical data implies, on the one hand, a substantial level of similarity between the model and the forestry data. And, on the other hand, the model gives an example in which parameters of one relationship may be linked to parameters of another. Supposedly this kind of ‘relationship between relationships’ may be observed in forest stands undergoing active growth and competition-induced self-thinning.
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Evaluation of Stand Biomass Estimation Methods for Major Forest Types in the Eastern Da Xing’an Mountains, Northeast China
Article
Full-text available
  • Sep 2019
Currently, forest biomass estimation methods at the regional scale have attracted the greatest attention from researchers, and the development of stand biomass models has become popular a trend. In this study, a total of 5074 measurements on 1053 permanent sample plots were obtained in the Eastern Da Xing’an Mountains, and three additive systems of stand biomass equations were developed. The first additive system (M-1) used stand variables as the predictors (i.e., stand basal area and average height), the second additive system (M-2) utilized stand volume as the sole predictor, and the third additive system (M-3) included both stand volume and biomass expansion and conversion factors (BCEFs) as the predictors. The coefficients of the three model systems were estimated with nonlinear seemingly unrelated regression (NSUR), while the heteroscedasticity of the model residuals was solved with the weight function. The jackknifing technique was used on the residuals, and several statistics were used to assess the prediction performance of each model. We comprehensively evaluated four stand biomass estimation methods (i.e., M-1, M-2, M-3 and a constant BCEF (M-4)). Here, we showed that the (1) three additive systems of stand biomass equations showed good model fitting and prediction performance, (2) M-3 significantly improved the model fitting and performance and provided the most accurate predictions for most stand biomass components, and (3) the ranking of the four stand biomass estimation methods followed the order of M-3 > M-2 > M-4 > M-1. Our results demonstrated these additive stand biomass models could be used to estimate the stand aboveground and belowground biomass for the major forest types in the Eastern Da Xing’an Mountains, although the most appropriate method depends on the available data and forest type.
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