1
Imp o emen in accu acy o abo eg ound biomass es ima ion in 1
Eucalyp us ni ens plan a ions: e ec o bole sampling in ensi y and 2
explana o y a iables 3
Césa Pé ez-C uzado1,2,*, Roque Rod íguez-Soallei o1,2 4
1 Sus ainable Fo es Managemen Uni , Uni e si y o San iago de Compos ela, 5
2C op P oduc ion Depa men , Uni e si y o San iago de Compos ela, 6
E-27002 Lugo, Spain 7
* Co esponding au ho . Tel.: (+34) 982 285900 Ex 23108; ax: (+34) 982 285926 8
E-mail add ess: cesa .[email p o ec ed] 9
10
11
12
13
14
15
16
17
18
19
20
*Manusc ip
Click he e o download Manusc ip : P ez-C uzado & Rod guez-Soallei o (2011).doc Click he e o iew linked Re e ences
2
Imp o emen in accu acy o abo eg ound biomass es ima ion in 1
Eucalyp us ni ens plan a ions: e ec o bole sampling in ensi y and 2
explana o y a iables 3
Césa Pé ez-C uzado1,2,*, Roque Rod íguez-Soallei o1,2 4
1Uni o Sus ainable Fo es Managemen , Uni e si y o San iago de Compos ela, 5
2C op P oduc ion Depa men , Uni e si y o San iago de Compos ela, 6
E-27002 Lugo, Spain 7
* Co esponding au ho . Tel.: (+34) 982 285900 Ex 23108; ax: (+34) 982 285926 8
E-mail add ess: [email p o ec ed] 9
10
Abs ac : 11
Two se s o abo eg ound biomass equa ions we e i ed o s em only and s em plus 12
c own p edic i e a iables in Eucalyp us ni ens plan a ions in No he n Spain. A sample o 40 13
ees was chosen a e a comple e s udy o a ia ion in ee heigh and diame e in he egion. 14
The ees we e elled and he biomass was di ided in o he ollowing componen s: wood, 15
ba k, hick b anches, hin b anches, wigs, lea es and dead b anches along he s em. Bole 16
biomass was es ima ed by sys ema ic subsampling o one 5 cm- hick disk e e y 0.5 m. Such 17
in ensi e subsampling enabled de e mina ion o he e ec o subsampling in ensi y on 18
accu acy and bias o wood es ima ion, conside ing wo a io- ype es ima o s: s em weigh o 19
d y ma e , de e mined by he comple e weighing (CW) me hod (i.e. o he esh weigh o he 20
en i e s em) and olume o d y ma e , de e mined by he pa ial weighing (PW) me hod. The 21
changes in mois u e con en and basic densi y along he s em explained he se ious isk o d y 22
mass o weigh o e es ima ion when a sys ema ic subsample is conside ed. The a e age basic 23
densi y was usually ound a a ela i e heigh o 30-35% along he s em. The de aul choice o 24
3
he bo om disk o log as he i s sec ion esul ed in o e es ima ions o he CW me hod and 1
unde es ima ions o he PW one. The biomass equa ions we e i ed by seemingly un ela ed 2
eg ession, wi h co ec ions o he e oscedas ici y ca ied ou by weigh ed i ing. Diame e a 3
b eas heigh was he bes explana o y a iable, and he inclusion o heigh did no imp o e 4
he accu acy, excep o wood. The inclusion o c own a iables imp o ed he p edic i e 5
abili y o c own ac ions, inc easing he accu acy o es ima ing hick b anches (by 10.8%), 6
wigs (by 19.1%) and lea es (by 17.3%). The biomass o each ac ion dec eased in he 7
ollowing o de : wood>ba k> hick b anches>dead b anches along he s em>lea es> hin 8
b anches> wigs. The changes in hese pe cen ages wi h diame e class and he p edic i e 9
abili y o he i ed equa ions we e also s udied. 10
Keywo ds: Eucalyp us ni ens, biomass, a io ype es ima o s, wood basic densi y, wood 11
mois u e; c own a iables 12
13
1. In oduc ion 14
Des uc i e sampling and subsequen eg ession analysis is he mos common me hod 15
used o es ima e ee biomass (Pa esol, 1999). Biomass es ima ion a ee le el is a necessa y 16
i s s age in es ima ing s and biomass, and he main sou ces o e o in his p ocess a e: i) 17
selec ion o ees o sampling; ii) measu emen o independen and dependen a iables in 18
sampling ees; iii) choice o a sui able o m o he allome ic ela ionship and alues o any 19
adjus able pa ame e s in he equa ion; i ) ield measu emen o he independen a iables in 20
he objec i e popula ion, and ) applica ion o allome ic equa ions o objec i e popula ions 21
o indi idual ee biomass es ima ion and summa ion o ob ain s and es ima es (Cunia, 1987, 22
Ke e ings e al., 2001). Each o hese s eps has an associa ed e o ha mus be minimized; 23
he e o s in ol ed in s ep ii a e he leas well s udied (Sa oo and Madgwick, 1982, Cunia, 24
1987, Pa esol, 1999, Ke e ings e al., 2001). 25
4
The e o s in he assessmen o sample ee dependen a iables a e s ongly in luenced 1
by he p ocedu e (Cunia, 1987): i) subsampling selec ion, ii) esh and d y weigh es ima ion, 2
and iii) subsampling in ensi y. Wi h small ees, esh and d y weighing o he en i e ee is 3
no ime consuming no expensi e and is he e o e ecommended (Pa esol, 2001). Howe e , 4
di ec measu emen becomes mo e expensi e as ee size inc eases, and subsampling becomes 5
ine i able (Sa oo and Madgwick, 1982, Pa esol, 1999). F esh weigh can be measu ed 6
di ec ly o es ima ed by se e al me hods. One o he mos commonly used me hods o 7
de e mining he esh weigh o ees and es ima ing he d y weigh is o use a io- ype 8
es ima o s (B iggs e al., 1987), in which he ela ionships be ween d y/ esh weigh o d y 9
weigh / esh olume a e assessed in a sample and applied o he es o he ee o d y weigh 10
es ima ion. The main ad an age o hese me hods is he simplici y o applica ion and 11
de e mina ion, al hough i is well known ha a io es ima o s a e biased (Cunia, 1979, 12
Valen ine e al., 1984). 13
Some me hods p o ide unbiased, e icien es ima ions, such as andomized-b anch 14
sampling (RBS) and impo ance sampling (IS) me hods, which use auxilia y in o ma ion o 15
selec elemen s in he sample o educe he a iance o he es ima o (Valen ine e al., 1984, 16
Pa esol, 1999). RBS is a ype o mul i-s age p obabili y sampling, which is used o selec a 17
pa h so ha esul an segmen s o he pa h comp ise a p obabili y sampling o he en i e ee. 18
IS is a con inuous analog in ol ing sampling disc e e uni s wi h p obabili y p opo ional o 19
size (G egoi e e al., 1995). These me hods a e o in e es o es ima ing ac ions such as 20
b anches o oliage, al hough in p ac ice hey a e ime-consuming and di icul o apply. 21
To apply a io ype es ima o s, s ems can be weighed and disks emo ed o de e mine 22
mois u e con en (by he comple e esh weighing, CW me hod) o olume can be es ima ed 23
and sho sample logs weighed o ob ain olume o mass con e sion ac o s (by he pa ial 24
weighing, PW me hod). Subsampling ac oss he bole can be done by andom s a i ied 25
5
sampling, as ca ied ou by B iggs e al. (1987), al hough mos esea che s use a ixed numbe 1
o sec ions ac oss he s em, wi h he posi ion chosen sys ema ically (i.e. (Sain -And é e al., 2
2005)), andomly, o wi h a p obabili y p opo ional o a gi en dimension. This was he case 3
o Kleinn and Pelz, (1987), who chose disks wi h a p obabili y o selec ion p opo ional o 4
es ima ed olume. On he o he hand, he PW me hod is p e e ed o la ge ees in si es wi h 5
di icul access, as esh weighing o he whole s em is qui e labo ious and ime consuming 6
(Snowdon e al., 2000). In he CW me hod, he dis ibu ion o mois u e along he s em is he 7
main sou ce o e o o d y weigh es ima ion, whe eas in he PW me hod, i is he a ia ion 8
in basic densi y along he bole heigh ha a ec s ha e o . In bo h cases, sampling in ensi y 9
and dis ibu ion should gua an ee a sui able desc ip ion o he a iabili y in mois u e con en 10
and speci ic densi y. 11
Diame e a b eas heigh (d) and o al heigh (h) a e he mos common dependen 12
a iables used in biomass eg ession, because o hei ease o measu emen and p edic i e 13
capaci y (Pa esol, 1999, Snowdon e al., 2000). Howe e , because o he cu en inc easing 14
in e es in ob aining accu a e p edic ions o c own ac ions o bioene gy, nu ien s abili y 15
and sil icul u al o ecological s udies, he e is a co esponding inc easing in e es in c own 16
biomass modelling. Some au ho s ha e obse ed ha he use o c own a iables as 17
explana o y a iables imp o es he accu acy o biomass equa ions (Sa oo and Madgwick, 18
1982, An ónio e al., 2007). In biomass s udies in which high p ecision is equi ed o c own 19
ac ions, and des uc i e sampling canno be applied, highly accu a e models a e equi ed. 20
The objec i es o he p esen s udy we e: i) o ob ain biomass es ima ion ools o a as 21
g owing species, Eucalyp us ni ens, in no hwes e n Spain, conside ing he mos comple e se 22
o abo eg ound componen s; ii) o e alua e he bias and accu acy o wood biomass es ima ion 23
o di e en in ensi ies o sys ema ic subsampling ac oss he s em and wo a io- ype 24
es ima o s (d y/ esh weigh and d y mass/ esh olume), iii) o e alua e he inc eased 25

6
accu acy de i ed om he inclusion o c own a iables in he es ima ion o indi idual ee 1
biomass componen s, and i ) o e alua e he abili y o he p oposed equa ions o es ima e he 2
p opo ion o each biomass componen o e o al abo eg ound biomass, o a ange o 3
diame e classes. 4
2. Ma e ials and me hods 5
2.1. S udy si e and ees sampled 6
This s udy was ca ied ou in no hwes e n Spain, in an inland a ea loca ed a ele a ions 7
o 500 o 1000m, wi h a e age p ecipi a ion o 900-1200 mm and a e age annual empe a u e 8
o 12-13ºC (Ma ínez Co izas and Pé ez Albe i, 1999). Al hough os occu ence limi s 9
plan ing o he mos common Eucalyp us species in Spain (Eucalyp us globulus Labill.), 10
Eucalyp us ni ens (Deane & Maiden) Maiden was success ully in oduced in he mid 1990s, 11
p o iding yields o 15-50 m3 ha-1 y -1 (Pé ez-C uzado, 2009). 12
As he aim o he p esen s udy was o cons uc biomass models ha a e as 13
ep esen a i e as possible, sampling consis ed o wo phases: 1) s udy o he a iabili y o he 14
mos commonly used independen a iables in biomass equa ions a ee le el (d and h, see 15
below) ac oss he dis ibu ion a ea, and 2) des uc i e sampling o ees co e ing he obse ed 16
ange (Pa esol, 1999). Fo his pu pose, 76 plo s we e es ablished (see loca ion in Fig. 1), 17
co e ing he obse ed ange o ages and si e quali ies, wi h a minimum plo size o 314 m2, 18
which is gene ally sui able o biomass es ima ion p ocedu es in plan a ions (Sa oo and 19
Madgwick, 1982). 20
A sample size o 40 ees was chosen because o he low a iabili y in si e condi ions 21
and densi ies o plan a ions, mos o which we e es ablished wi h he MacAlis e p o enance. 22
The sampled ees we e chosen in wo s eps, wo ees pe diame e and heigh class we e i s 23
selec ed, and 16 addi ional ees we e hen chosen, conside ing he ela i e impo ance o each 24
diame e class in he popula ion. The aim o his p ocedu e was o co e he ull ange o ee 25
7
size, which is shown o heigh and diame e in Fig. 2. T ees we e elled in 12 plo s, in which 1
he alues o he quad a ic mean diame e and d o he ees sampled was simila ; undamaged, 2
heal hy ees ha ep esen ed he dominan and codominan s a a, we e chosen. The a e age 3
s anda d de ia ion and ange o ep esen a i e s and and single ee a iables, o bo h he 4
popula ion and he sample a e shown in Table 1. The a iabili y in c own a iables was 5
simila o ha obse ed in s em a iables, unlike in o he s udies (Sa oo and Madgwick, 6
1982). 7
The ollowing a iables we e measu ed in he sample ees while s ill s anding: diame e 8
a b eas heigh (d, cm) and s ump diame e a 0.15 m (ds , cm), bo h measu ed in wo 9
pe pendicula di ec ions o he nea es mm; o al heigh (h, m) and li e c own base heigh , 10
de ined as he heigh o he i s li e b anch inse ion in he s em (hcb, m), bo h measu ed o 11
he nea es dm; c own diame e (dc, m) measu ed in wo pe pendicula di ec ions ollowing 12
he ca dinal poin s o he nea es cm. Li ing c own leng h (hc, m) was es ima ed as di e ence 13
be ween o al heigh (h) and li e c own basis heigh (hcb, m). C own olume ( c) was 14
calcula ed om hc and dc by assimila ing he c own shape o an ellipsoid (1). Desc ip i e 15
s a is ics o hese a iables a e shown in Table 2. 16












223
42
cc
c
hd

(1)
17
2.2. Ra io ype es ima o s and subsampling 18
The elled ees we e cu in o 0.5 m logs o a small-end diame e o 7 cm. The logs we e 19
weighed esh and a sys ema ic subsample o one 5 cm-disk in he bo om pa o each log 20
was aken, also conside ing a u he disk a he op o he s em. Sample disks we e weighed 21
esh and anspo ed o he labo a o y in plas ic bags. The o e and unde -ba k diame e s o 22
8
he disks we e measu ed in wo di ec ions and he ba k and wood we e hen sepa a ed and 1
weighed. 2
Fo each disk, he d y wood weigh was measu ed a e o en d ying a 105ºC o cons an 3
weigh and he a io o he d y/ esh weigh o he wood was de e mined. Only one composi e 4
sample pe ee was conside ed o he ba k. F esh ba k o all disks was weighed join ly, and 5
d ied o de e mine d y ba k weigh , hus enabling he a io o d y/ esh weigh o ba k o be 6
ob ained o each ee. 7
The d y weigh o wood and o ba k in each log was calcula ed om he a e age a ios 8
calcula ed o he delimi ing disks. The o al wood (Ww, o a small-end diame e o e ba k o 9
7cm) and ba k (Wb, e alua ed ill he h eshold diame e conside ed o wood) d y biomass in 10
each ee was calcula ed as sum o he biomass o each log. 11
Fou biomass ac ions we e conside ed o he c own: hick b anches (WTb, diame e s 12
o e ba k 2-7cm), which also include he ops o he boles, hin b anches (W b, diame e s o e 13
ba k 0.5-2cm), wigs (W , diame e less han 0.5 cm) and lea es (Wl). Dead b anches in he 14
s em (Wdb) is also an impo an ac ion in Eucalyp us ni ens. C own biomass was i s 15
ac ioned in he ield in o h ee g oups: WTb, Wdb and he sum o W b, W and Wl, and hen 16
weighed esh, wi h a balance, o he nea es 10g. A subsample o 10-15% o esh weigh o 17
each ac ion was aken o ep esen he op, medium and bo om pa o he c own. These 18
subsamples we e weighed in he ield, wi h scales, o he nea es 0.01g. 19
The composi e subsample o W b, W and Wl, was ac ioned and weighed in he 20
labo a o y and he p opo ion o each ac ion was de e mined o enable es ima ion o he 21
esh weigh o each c own ac ion. The d y weigh o each ac ion was hen es ima ed om 22
he d y/ esh weigh a ios. 23
2.3. Me hodologies o bole mass es ima ion 24
9
The in o ma ion ob ained enabled compa ison o wo me hods o es ima ing bole mass 1
o weigh a a ange o sampling in ensi ies. The CW me hod consis ed o de e mining he 2
comple e s em weigh and es ima ing d y weigh om disks. Disk subsampling in ensi y was 3
modi ied conside ing a se ies o in e -disk dis ances which we e mul iples o 0.5. Fo each 4
in e -disk dis ance es ed, he e we e se e al solu ions, depending on he heigh o he i s 5
sec ion conside ed. Fo he logs be ween wo disks, he d y weigh es ima ion was calcula ed 6
om he a e age d y weigh wood a io o each disk, and o basal and e minal logs he disks 7
immedia ely abo e o below he log we e conside ed. 8
Fo he PW me hod, i was conside ed ha only one pa o he s em was weighed, and 9
o he es o he ee he olume was calcula ed om diame e unde ba k measu ed e e y 10
0.5 m along he s em and by use o he Smalian o mula. The leng h o he weighed and cubed 11
log was made o ange be ween 0.5m and he o al s em heigh (up o a small-end diame e o 12
7cm), conside ing a a iable posi ion o he log along he s em. The esh weigh o he log 13
was ans o med o d y weigh by conside ing he mois u e con en de i ed om he whole se 14
o disks aken each 0.5 m. Volume o d y weigh a ios we e hen used o es ima e he o al 15
d y mass o he s em by mul iplying by he calcula ed olumes. 16
Bo h me hods and sampling in ensi ies we e compa ed wi h he esul s ob ained by he 17
CW me hod and disk equidis ance o 0.5 m, conside ing he ela i e di e ence in he biomass 18
es ima ion o each ee (2). 19
 
100

W
WW
ˆ
RD
(2)
whe e
W
ˆ
is he p edic ed bole mass alue wi h each sampling me hodology and in ensi y. 20
The combina ions o in e -disk dis ances, weighed log leng hs and s a ing poin along 21
he bole p o ided a ela i e di e ence alue, and hese we e plo ed agains subsampling 22
in ensi y o di e en diame e classes. The 95% con idence in e als we e ob ained 23
16
3.3. P opo ions o each biomass componen 1
The s a is ics o he d y weigh biomass ac ions conside ed in he p esen s udy a e 2
shown in Table 1. Wood is pa icula ly impo an in he o al biomass, ep esen ing abou 3
70% o o al d y weigh o he a e age ee size, which emphasizes he impo ance o i s 4
accu a e es ima ion. The nex ac ions in impo ance a e ba k (10%) and hick b anches, d y 5
b anches, lea es, hin b anches and wigs. The ela i e p opo ions o each componen , 6
plo ed agains diame e , including a se o 8 small ees which we e no used o i ing, a e 7
shown in Fig. 11. The p opo ion o some o hese componen s in ees o di e en diame e 8
class ha e been used as pa ame e s in physiological g ow h models, and accu a e es ima ion 9
by use o he models p oposed in his pape is desi able. 10
The p opo ion o each componen ela ed o o al abo eg ound biomass is becoming 11
c i ical in a scena io o inc easing ha es ing o biomass componen s ha we e p e iously le 12
in place in o es soils. The p opo ion o wood, commonly e e ed o as he ha es index, 13
inc eased wi h diame e (Fig. 11), al hough he end was no con inuous because o he need 14
o conside a h eshold diame e . Consequen ly, he componen o hick b anches may accoun 15
o a la ge sha e o o al abo eg ound biomass o ees wi h a diame e s ill oo small o ha e 16
a signi ican wood ac ion. The ba k ac ion was de ined as he ba k ac ion in he s em, and 17
he ba k o sec ions less han 7 cm in diame e was included in hick o hin b anches, which 18
explains he low pe cen ages shown o diame e s less han 12 cm. As a esul , he equa ions 19
p esen ed he e would p o ide easonable es ima es o biomass componen pe cen ages o 20
diame e s la ge han 12 cm. Fo smalle diame e s, exclusi e use o he equa ion p edic ing 21
o al biomass is ecommended. 22
4. Discussion 23

17
4.1. S em biomass es ima ion 1
The esul s o his s udy show ha he e o may be impo an , and will depend on he 2
in ensi y o subsampling, when a io- ype es ima o s a e used o es ima e d y weigh . The 3
e o also depends on he me hod used (comple e esh weigh o pa ial esh weigh ) and on 4
he a e age ee size. O he au ho s ha e obse ed ha a io- ype es ima o s p o ide biased 5
es ima es (Cunia, 1979, Valen ine e al., 1984, B iggs e al., 1987). These o e es ima es a e as 6
la ge as he dec eases in bo h subsampling in ensi y and a e age ee size. O e es ima ion is 7
clea ly a mo e se ious e o han unde es ima ion (Sa oo and Madgwick, 1982) because i 8
does no e on he side o sa e y i.e. o ca bon accoun ing p ocedu es. 9
Wood mois u e con en and basic densi y change along he s em (Sa oo and Madgwick, 10
1982) (Figs. 5 and 6), and a ec he es ima ion o d y biomass by he CW and PW me hods 11
espec i ely. Minimum mois u e con en and basic densi y occu in he basal pa o he s em, 12
which is ob iously whe e mos o he accumula ed weigh and olume occu . This e ec mus 13
he e o e be aken in o accoun wi h a su icien and well dis ibu ed numbe o subsamples 14
along he s em. One way o add essing his p oblem, when ape unc ions a e a ailable, is he 15
densi y in eg al app oach (Pa esol and Thomas, 1989). The weighed a e age is an al e na i e 16
me hod ha gi es mo e impo ance o hose obse a ions in he lowe pa o he s em, and 17
he e o e mo e closely ela ed o olume. 18
Cha e e al. (2001) epo ed ha he biomass alues o he smalles ees s ongly a ec 19
he alues o he model pa ame e s in he allome ic ela ion. This e ec is e en s onge 20
when a weigh ed adjus men me hodology is used, because he smalles ees, which a e less 21
a iable, a e mo e impo an han he la ges ees because o he e oscedas ici y co ec ion. I 22
is he e o e ad isable o ob ain he comple e d y weigh o he s em o small ees. 23
The deg ee o accu acy equi ed depends on he objec i e o he es ima ion, al hough 24
equilib ium be ween sampling in ensi y and he le el o p ecision mus be ensu ed (B own e 25
18
al., 1995). I a io- ype es ima o s a e chosen o s em d y biomass es ima ion, a ela i ely 1
in ensi e subsampling scheme should be implemen ed, as o he s au ho s indica ed o bo h 2
a io- ype and densi y-in eg al me hods (Pa esol, 1999). Compa ing he me hods conside ed 3
he e, he CW me hod p oduced be e esul s o he la ges dimensional class han he PW 4
me hod (Figs. 3 and 4). This is because, o a gi en leng h o cubed and weighed pa , he 5
p opo ion o e o al s em (as an indica o o sampling in ensi y) di e s depending on ee 6
size, and he e o e becomes less impo an as ee size inc eases. This mus be aken in o 7
accoun because he PW me hod is usually used o la ge ees in which comple e weighing is 8
ime-consuming. 9
The esul s clea ly show he ends in ela i e e o s de i ed om a de aul 10
conside a ion o he bo om disk o he bo om log as he i s sec ion o measu e. I is 11
ad isable, i sys ema ic sampling is o be used, o es ablish he subsampling in ensi y be o e 12
andomizing he posi ion along he s em o he i s disk o log o be measu ed. In he case o 13
he PW me hod i is no ecommended o ake only one sample log pe ee, al hough his was 14
he app oach used in his s udy. The subsampling in ensi y should be spli along he s em, and 15
a good ep esen a ion o he bole a ea whe e a e age basic densi y is likely o be ound is 16
ad isable. Mos published pape s do no p o ide in o ma ion abou he p opo ion o weighed 17
and cubed logs o hei dis ibu ion along he s em, al hough he mos easonable dis ibu ion 18
would be sys ema ic o andom, wi h he subsampling in ensi y chosen on he basis o 19
s a is ical c i e ia. 20
21
4.2. Biomass equa ions om s em and c own a iables 22
Al hough i is known ha d, h and W a e closely ela ed (Sa oo and Madgwick, 1982), h 23
is no always included in biomass equa ions oge he wi h d because bo h a e co ela ed and 24
inclusion o h adds only negligible accu acy (Jokela e al., 1986, Te -Mikaelian and 25
19
Ko zukhin, 1997, Johansson, 1999, Ve wijs and Telenius, 1999, Snowdon e al., 2000, 1
B own, 2002, Po é e al., 2002, Jenkins e al., 2003). In his s udy, inclusion o h oge he 2
wi h d only esul ed in imp o ed accu acy in he case o wood, al hough o he au ho s ha e 3
epo ed signi ican imp o emen o se e al ac ions (Loomis e al., 1966, Pea son e al., 4
1984, Ba elink, 1996, Reed and Tomé, 1998, Monse ud and Ma shall, 1999). In hei s udy 5
on Eucalyp us globulus, An ónio e al. (2007) obse ed imp o emen s in he sum o esidual 6
squa es o 72%, 8%, 12% and 10% o wood, ba k, lea es and b anches espec i ely, a e 7
inclusion o h oge he wi h d. I is possible ha in he p esen s udy he ee sample was no 8
ep esen a i e o he en i e a iabili y in heigh o a gi en diame e . 9
Some s udies included h and d in biomass models, oge he wi h densi y, age and si e 10
index (Te -Mikaelian and Pa ke , 2000, An ónio e al., 2007), and hese models a e he e o e 11
sui able o compa ing di e en si es (Ke e ings e al., 2001). O he s udies included age as 12
an independen a iable in biomass equa ions (Po é e al., 2002, Sain -And é e al., 2005), 13
hus p oducing dynamic models wi h which biomass inc emen s can be es ima ed by 14
de i a i e analysis. Al hough indi idually ds wo ked well as a p edic o , i is seldom 15
measu ed in o es in en o ies. On he o he hand, i is some imes use ul o es ima e d y 16
biomass when ees a e al eady cu down and only s ump dimensions a e a ailable. 17
I has been obse ed ha some c own a iables wo k well as p edic o s o c own 18
ac ions (Cla k, 1982, Sa oo and Madgwick, 1982, Ca alho and Pa esol, 2003). In he 19
p esen s udy, inclusion o c own a iables imp o ed he RMSE by 1.8%, 10.8%, 19.1% and 20
17.3% o espec i ely dead b anches, hick b anches, wigs and lea es, in he indi idual i . 21
These imp o emen s a e smalle han hose ob ained by An ónio e al. (2007) o Eucalyp us 22
globulus in Po ugal, p obably because o he lowe gene ic a iabili y in he plan a ions 23
conside ed in ha s udy. The bes imp o emen was o lea es, which implies be e 24
es ima ions o a ac ion ha is e y di icul o p edic and is e y impo an as ega ds 25
20
nu i ion and ecology. O e all, he esul s indica e a low accu acy o es ima ion o he ba k 1
ac ion in he p esen s udy, in compa ison wi h epo s o o he species o Eucalyp us. 2
Wood, ba k and hin b anches depend on he same a iables in bo h sys ems o equa ions, and 3
he esul s ob ained by simul aneous i ing we e gene ally only sligh ly less accu a e. Fo 4
lea es, he educ ion in R2Adj de i ed om simul aneous i ing was 6.3%. 5
The abili y o he i ed biomass equa ions o e alua e he p opo ion o each 6
abo eg ound biomass componen o a ange o diame e s has seldom been s udied. The 7
p opo ions a e o en conside ed as pa ame e s o ecophysiological models, pa icula ly o 8
small diame e s (Sands and Landsbe g, 2002). The p esen esul s show ha , i a h eshold 9
diame e is conside ed o de ining a wood componen , minimum b eas heigh diame e mus 10
be conside ed o de ine he ange o use o he biomass componen s equa ions, i sound 11
es ima ion o hese pe cen ages is sough . 12
5. Conclusions 13
Two sys ems o equa ions we e i ed o abo eg ound biomass componen s o 14
Eucalyp us ni ens. The inclusion o c own a iables as p edic i e a iables p o ided poo e 15
esul s o o al biomass, wood and hin b anches, bu imp o ed he accu acy o es ima ion o 16
wigs, lea es, hick b anches and dead b anches. 17
S em subsampling a ec s es ima ion o he wood ac ion. I a sys ema ic subsample o 18
disks o logs is aken, he a ia ion in mois u e con en o basic densi y along he s em should 19
be conside ed. Less in ensi e sampling usually leads o o e es ima ion o biomass wi h bo h 20
me hods (comple e esh weighing o pa ial esh weighing). The minimum subsampling 21
in ensi y o an assumed ±5% RD in wood d y biomass es ima ion depends on he ee 22
diame e class, wi h a ange o 0.75 o 0.95 disks m-1 in he CW me hod. Use o he PW 23
me hod would equi e e y in ense subsampling o educe he ela i e e o , independen ly o 24
21
ee size. The a e age basic densi y usually occu s a a ela i e heigh o 30-35% along he 1
s em. I is no always ad isable o choose he i s sec ion o s udy a he bo om o he s em. 2
Acknowledgemen s 3
The au ho s hank Elena Fe nández-Ri as, Fe nando Pé ez-Rod íguez and Juan Gab iel 4
Al a ez o assis ing wi h ieldwo k and da a analysis. The s udy was unded by he Spanish 5
Minis y o Educa ion and Science (SUM2006-00006-00-00) and a FPU-MEC Spanish 6
Fellowship awa ded o he co esponden au ho . 7
Re e ences 8
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Cunia, T., Cons uc ion o ee biomass ables by linea eg ession echniques, 1987. Wha on, 1 E.H., Cunia, T., (Eds.), In: Es ima ing T ee Biomass Reg essions and hei E o : 2 P oceedings o he Wo kshop on T ee Biomass Reg ession Funk ions and hei 3 Con ibu ion o he E o o Fo es In en o y Es ima es. USDA Fo es Se ice, 27-36. 4 G egoi e, T.G., Valen ine, H.T., Fu ni al, G.M., 1995. Sampling me hods o es ima e oliage 5 and o he cha ac e is ics o indi idual ees. Ecology. 76, 1181-1194. 6 Ha ey, A.C., 1976. Es ima ing Reg ession Models wi h Mul iplica i e He e oscedas ici y. 7 Econome ica. 44, 461-465. 8 Jenkins, J.C., Chojnacky, D.C., Hea h, L.S., Bi dsey, R.A., 2003. Na ional-Scale Biomass 9 Es ima o s o Uni ed S a es T ee Species. Fo . Sci. 49, 13-35. 10 Johansson, T., 1999. Biomass equa ions o de e mining ac ions o pendula and pubescen 11 bi ches g owing on abandoned a mland and some p ac ical implica ions. Biomass & 12 Bioene gy. 16, 223-238. 13 Jokela, E.J., Van G up, K.P., B iggs, R.D., Whi e, E.H., 1986. Biomass es ima ion equa ions 14 o no way sp uce in New Yo k. Can. Jou . Fo . Res. 16, 413-415. 15 Ke e ings, Q.M., Coe, R., an Noo dwijk, M., Ambagau, Y., Palm, C.A., 2001. Reducing 16 unce ain y in he use o allome ic biomass equa ions o p edic ing abo e-g ound ee 17 biomass in mixed seconda y o es s. Fo . Ecol. Manage. 146, 199-209. 18 Kleinn, C., Pelz, D.R., 1987. Subsampling ees o biomass. In: Wha on, E.H., Cunia, T., 19 (Eds.).Es ima ing T ee Biomass Reg essions and hei E o : P oceedings o he 20 Wo kshop on ee Biomass Reg ession Func ions and hei Con ibu ion o he E o o 21 Fo es In en o y Es ima es. USDA Fo es Se ice, B oomall, PA: U.S., pp. 225-227. 22 Loomis, R.M., Pha es, R.E., C osby, J.S., 1966. Es ima ing oliage and b anchwood quan i ies 23 in sho lea pine. Fo . Sci. 12, 30-39. 24 Ma ínez Co izas, A., Pé ez Albe i, A., 1999. A las Climá ico De Galicia. Xun a de Galicia, 25 San iago de Compos ela. 26 Monse ud, R.A., Ma shall, J.D., 1999. Allome ic c own ela ions in h ee no he n Idaho 27 coni e species. Can. Jou . Fo . Res. 29, 521-535. 28 Ne e , J., Wasse man, W., Ku ne , M.H., William Wasse man, M.H.K., 1989. Applied Linea 29 Reg ession Models. I win Homewood, Ill, New Yo k. 30 Pa esol, B.R., 1993. Modeling mul iplica i e e o a iance: an example p edic ing ee 31 diame e om s ump dimensions in baldcyp ess. Fo . Sci. 39, 670-679. 32 Pa esol, B.R., 1999. Assessing T ee and S and Biomass: A Re iew wi h Examples and 33 C i ical Compa isons. Fo . Sci. 45, 573-593. 34 Pa esol, B.R., 2001. Addi i i y o nonlinea biomass equa ions. Can. J. Fo . Res. 31, 865-35 878. 36 Pa esol, B.R., Thomas, C.E., 1989. A densi y-in eg al app oach o es ima ing s em biomass. 37 Fo . Ecol. Manage. 26, 285-297. 38 Pea son, J.A., Fahey, T.J., Knigh , D.H., 1984. Biomass and lea a ea in con as ing lodgepole 39 pine o es s. Can. J. Fo . Res. 14, 259-265. 40 Pé ez-C uzado, C., 2009. He amien as de ges ión pa a plan aciones de Eucalyp us ni ens 41 (Deane & Maiden) Maiden con el obje i o de ijación de ca bono. Uni e si y o 42 San iago de Compos ela. 43 Po é, A., T iche , P., Be , D., Lous au, D., 2002. Allome ic ela ionships o b anch and ee 44 woody biomass o Ma i ime pine (Pinus pinas e Ai .). Fo . Ecol. Manage. 158, 71-83. 45 Reed, D., Tomé, M., 1998. To al abo eg ound biomass and ne d y ma e accumula ion by 46 plan componen in young Eucalyp us globulus in esponse o i iga ion. Fo . Ecol. 47 Manage. 103, 21-32. 48 Sain -And é, L., M'Bou, A.T., Mabiala, A., Mou ondy, W., Jou dan, C., Roupsa d, O., 49 Delepo e, P., Hamel, O., Nou ellon, Y., 2005. Age- ela ed equa ions o abo e-and 50
23
below-g ound biomass o a Eucalyp us hyb id in Congo. Fo . Ecol. Manage. 205, 199-1 214. 2 Sands, P.J., Landsbe g, J.J., 2002. Pa ame e isa ion o 3-PG o plan a ion g own Eucalyp us 3 globulus. Fo . Ecol. Manage. 163, 273-292. 4 SAS Ins i u e Inc, 2004. SAS/STAT 9.1 Use 's Guide. Ca y, N.C. 5 Sa oo, T., Madgwick, H.A.I., 1982. Fo es Biomass. 152. 6 Schaegel, B.E., 1982. Boxelde (Ace Negundo L.) Biomass Componen Reg ession Analysis 7 o he Mississippi Del a. Fo . Sci. 20, 617-628. 8 Snowdon, P., Eamus, D., Gibbons, P., Khanna, P.K., Kei h, H., Raison, R.J., Ki schbaum, 9 M.U.F., 2000. Syn hesis o Allome ics, Re iew o Roo Biomass and Design o Fu u e 10 Woody Biomass Sampling S a egies. Aus alian G eenhouse O ice, Canbe a. 11 Te -Mikaelian, M.T., Ko zukhin, M.D., 1997. Biomass equa ions o six y- i e No h 12 Ame ican ee species. Fo . Ecol. Manage. 97, 1-24. 13 Te -Mikaelian, M.T., Pa ke , W.C., 2000. Es ima ing biomass o whi e sp uce seedlings wi h 14 e ical pho o image y. New Fo es s. 20, 145-162. 15 Valen ine, H.T., T i on, L.M., Fu ni al, G.M., 1984. Subsampling ees o biomass, olume, 16 o mine al con en . Fo . Sci. 30, 673-681. 17 Ve wijs , T., Telenius, B., 1999. Biomass es ima ion p ocedu es in sho o a ion o es y. 18 Fo . Ecol. Manage. 121, 137-146. 19 Whi e, H., 1980. A he e ocedas ici y-consis en co a iance ma ix es ima o and a di ec es 20 o he e ocedas ici y. Econome ica. 48, 817-838. 21 Zianis, D., Mencuccini, M., 2004. On simpli ying allome ic analyses o o es biomass. Fo . 22 Ecol. Manage. 187, 311-332. 23 24 25
24
TABLES 1 2 Table 1. S a is ics o s and and single ee a iables in he popula ion (76 plo s, 3864 ees) 3 and he sample plo s (12 plo s, 40 ees). 4
S and a iables
Indi idual ee a iables
SI (m)
N (s ems ha-1)
Age (y )
d (cm)
h (m)
All plo s
A e age (S d. de .)
15.3 (4.4)
1089 (280)
9.5 (4.2)
18.5 (7.5)
20.2 (6.4)
Range
8.8 - 20.8
446 - 1560
2 - 18
1.0 - 59.6
2.2 - 48.3
Sample plo s
A e age (S d. de .)
15.7 (2.7)
1101 (223)
10.2 (2.8)
19.5 (7.7)
19.3 (5.5)
Range
9.8 - 18.9
446 - 1401
2 - 13
1.1 - 47.0
2.4 - 35.1
Whe e SI is he si e index (m a e e ence age o 6 yea s); N is s and densi y (s ems ha-1), d is 5 diame e a b eas heigh (cm), and h is he o al heigh (m). 6 7 Table 2. Desc ip i e s a is ics o sampled ees. 8
Va iable
A e age
Maximum
Minimum
S . De .
Independen a iables
d (cm)
20.84
41.55
3.95
10.04
ds (cm)
25.63
52.40
6.60
12.13
h (m)
19.94
30.80
4.40
7.27
hcb (m)
12.55
20.60
2.80
4.68
hc (m)
7.39
19.80
1.20
4.21
dc (cm)
3.50
8.55
1.25
1.66
c (m3)
81.78
566.5
1.00
129.3
Dependen a iables (kg ee-1)
Wl
10.73
48.85
0.28
12.94
W
4.15
23.33
0.18
5.10
W b
4.40
18.46
0.04
4.53
WTb
13.57
75.65
1.29
18.71
Ww
168.43
599.5
0
176.9
Wb
24.59
111.3
0
28.33
Wdb
11.29
68.28
0.03
13.64
W o
237.2
838.2
2.54
248.1
De ini ions o independen and dependen a iables a e gi en in sec ions 2.1 and 2.2, 9 espec i ely. W o e e s o o al abo eg ound biomass. 10 11 Table 3. Models selec ed o simul aneous i ing o each equa ion sys em. 12
S em equa ion sys em
C own equa ion sys em
F ac ion
Model
RMSE
MRES
R2 Adj
Model
RMSE
MRES
R2 Adj
W o

i o WW
37.9
2.86
0.98

i o WW
39.9
1.36
0.97
Wdb
1,2
b
1,1·db
10.6
0.32
0.40
2.3
2.2 b
cb
b
2.1 ·h·db
10.4
-0.04
0.42
Wb
1.4
b
1.3·db
15.3
0.72
0.71
2.5
b
2.4·db
15.3
0.30
0.71
Ww
1.71.6 bb
1.5 ·h·db
17.9
0.32
0.99
2.82.7 bb
2.6 ·h·db
18.2
-0.16
0.99
WTb
1.9
b
1.8·db
6.0
1.05
0.90
2.11
2.10 b
c
b
2.9 ·d·db
5.4
0.62
0.92
W b
1.11
b
1.10·db
2.2
0.13
0.76
2.13
b
2.12·db
2.4
0.24
0.71
W
1.13
b
1.12·db
2.1
0.07
0.83
2.16
2.15 b
c
b
2.14 ·d·db
1.7
0.26
0.89
Wl
1.15
b
1.14·db
5.6
0.25
0.81
2.19
2.18 b
c
b
2.17 ·h·db
4.6
0.15
0.87
25
De ini ions o he di e en ac ions a e gi en in sec ion 2.2. W o e e s o o al abo eg ound 1 biomass. 2 3 4 Table 4. Pa ame e s o simul aneous i ing o equa ions. 5
Pa ame e
Es ima e
App .SE
P > | |
Pa ame e
Es ima e
App .SE
P > | |
b1,1
0.145
0.05
0.0063
b2,1
0.0079
0.0077
0.3137
b1,2
1.403
0.12
<.0001
b2,2
1.279
0.313
0.0003
b1,3
0.013
0.0083
0.1177
b2,3
1.254
0.411
0.0044
b1,4
2.361
0.1892
<.0001
b2,4
0.0318
0.016
0.0545
b1,5
0.0094
0.0024
0.0004
b2,5
2.1079
0.156
<.0001
b1,6
2.0329
0.082
<.0001
b2,6
0.0149
0.0034
0.0001
b1,7
1.0562
0.1335
<.0001
b2,7
2.0515
0.081
<.0001
b1,8
0.000059
0.000064
0.3586
b2,8
0.8946
0.128
<.0001
b1,9
3.7599
0.2983
<.0001
b2,9
0.00082
0.0010
0.4124
b1,10
0.0128
0.005
0.0153
b2,10
2.6444
0.4403
<.0001
b1,11
1.8579
0.131
<.0001
b2,11
0.7627
0.265
0.0069
b1,12
0.00092
0.00049
0.07
b2,12
0.030047
0.0098
0.0042
b1,13
2.6322
0.159
<.0001
b2,13
1.590388
0.1168
<.0001
b1,14
0.0053
0.0034
0.1281
b2,14
0.006228
0.0028
0.0329
b1,15
2.3931
0.197
<.0001
b2,15
1.949093
0.1932
<.0001
b2,16
0.218899
0.01909
0.0259
b2,17
0.016847
0.0102
0.109
b2,18
1.515742
0.2651
<.0001
b2,19
0.774688
0.1934
0.0003
6 7 8 9 FIGURE CAPTIONS 10 11 Fig. 1. Loca ion o he measu ed plo s (do s) and he dis ibu ion o Eucalyp us ni ens in 12 no h-wes e n Spain (shaded a ea). 13 14 Fig. 2. Heigh -diame e dis ibu ion o Eucalyp us ni ens in an ini ial in en o y in no h-15 wes e n Spain. 16 17 Fig. 3. Rela i e di e ence o h ee dimensional classes: DC1 (d<14cm; n = 6922), DC2 18 (14<d<24cm; n = 17075) and DC3 (d>24cm; n = 18360), plo ed agains sampling in ensi y 19 (disks pe s em me e ) o he CW me hod. Con inuous black line: a e age alue o all da a; 20 do ed black lines: 95% con idence in e als o all da a; con inuous g ey line: a e age alue 21 o al e na i es ha include bo om log. n is he numbe o simula ed al e na i es o each 22 dimensional class. 23 24 Fig. 4. Rela i e di e ence o wo dimensional classes: DC2 (14<d<24cm; n = 7712) and 25 DC3 (d>24cm; n = 12001), plo ed agains sampling in ensi y ( ac ion o s em heigh 26 weighed) o he PW me hod. Con inuous black line: a e age alue o all da a; do ed black 27 lines: 95% con idence in e als o all da a; con inuous g ey line: a e age alue o 28 al e na i es ha include bo om log. n is he numbe o simula ed al e na i es o each 29 dimensional class. 30 31
6
W o
y = 1,0202x - 3,6567
R2 = 0,9804
0
200
400
600
800
1000
0200 400 600 800 1000
P edic ed
Obse ed
Ww
y = 1,0057x - 0,7481
R2 = 0,9894
0
100
200
300
400
500
600
700
0100 200 300 400 500 600 700
P edic ed
Obse ed
Wb
y = 0,9851x + 0,4452
R2 = 0,7088
0
20
40
60
80
100
120
020 40 60 80 100 120
P edic ed
Obse ed
Wdb
y = 0,918x + 0,8766
R2 = 0,4261
0
10
20
30
40
010 20 30 40
P edic ed
Obse ed
WTb
y = 1,0166x + 0,4047
R2 = 0,916
0
20
40
60
80
020 40 60 80
P edic ed
Obse ed
W b
y = 1,0061x - 0,0508
R2 = 0,7756
0
5
10
15
20
0 5 10 15 20
P edic ed
Obse ed
W
y = 1,0723x - 0,2395
R2 = 0,9048
0
5
10
15
20
25
0 5 10 15 20 25
P edic ed
Obse ed
Wl
y = 1,0407x - 0,3666
R2 = 0,8821
0
10
20
30
40
50
010 20 30 40 50
P edic ed
Obse ed
Fig. 10. Rela ionship be ween obse ed-p edic ed d y weigh alues o each biomass 1 componen (kg ee-1) in he C own sys em o equa ions. 2 3 4

7
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P opo ion o abo eg ound biomass (%)
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P ed, WTb
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P opo ion o abo eg ound biomass (%)
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P ed. W b
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P opo ion o abo eg ound biomass (%)
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P opo ion o abo eg ound biomass (%)
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Fig. 11. P opo ion o each biomass ac ion o e o al abo eg ound biomass. Open igu es: 1 ees used in de eloping biomass equa ions; illed igu es: addi ional small ees; lines: 2 p edic ion o biomass equa ions. 3 4 5 6