5

Silva Balcanica, 16(2)/2015

Allometric relAtionships for Aboveground biomAss of juvenile blAck poplAr hybrids

Tatiana Stankova1, Veselka Gyuleva1, Emil Popov1, Katya Velinova1, Emiliya Velizarova1, Dimitar N. Dimitrov1, Kancho Kalmukov2, Mariya Glushkova1,

Proletka Dimitrova1, Hristina Hristova1, Ekaterina Andonova1, Georgi P. Georgiev1, Ivaylo Kalaydzhiev1

1 Forest Research Institute – SofiaBulgarian Academy of Sciences

Dept. Experimental Station for Fast Growing Tree Species of Svishtov State Forestry Estate – Svishtov

ABSTRACT

The main objectives of this study were to investigate the allometry of aboveground biomass of juvenile black poplar hybrids (Populus deltoides x P. nigra) traditionally cultivated for timber and cellulose production and to derive biologically plausible and statistically sound biometric models for stem, branch, leaf and total aboveground biomass prediction from easily measurable tree and stand characteristics.

We examined a number of model formulations based on breast height tree diameter and total tree or mean stand height as predictor variables of the above-ground tree biomass following a two-stage fitting procedure, and we considered a set of goodness-of-fit criteria to derive the allometric relationships. We used data collected in industrial poplar plantations to parameterize the functions and validation data from nursery stock for final model adjustment.

Two systems of compatible generic equations were developed to estimate stem, branch, leaf and total aboveground biomass of hybrid black poplars. Model system M1 uses only the two principal tree dimensions. It can therefore be applied for determination of aboveground biomass in single trees or harvested saplings when information on the stand height is absent. Model system M2, which is based on mean stand height and tree diameter, can be used to assess rapidly and accurately the bio-mass of standing poplar stock.

key words: Euro-American poplars, Populus deltoides × P. nigra, biomass equations, short-rotation plantations

6

INTROduCTION

The poplars are trees with many valuable characteristics, such as fast growth, ease of propagation, aptitude to hybridize, pleasing appearance and many uses, and the accumulated global knowledge and information on them could fill many volumes (Isebrands, Richardson, 2014). They are recognized as the fastest-growing forest tree species at temperate continental climate, called ‘the eucalypts of the temperate geographic belt’, and have also attracted the attention of Bulgarian foresters, primar-ily in pursue of intensified wood production. Numerous studies have been conduct-ed to fulfill the needs for modern poplar sylviculture in Bulgaria. An emphasis has been given to exploration of the optimal environmental growth conditions for Euro-American hybrid poplars (Fakirov, 1979) and to definition of the forest sites, appro-priate for poplar cultivation (Marinov et al., 1982). These have been accompanied with extended research on optimal clone-density-tending combinations at various growth conditions (Naydenova, 1962, 1963; Fakirov, 1972a, 1972b; Palashev et al., 1973; Ganchev et al., 1981; Kalchev, Kolarov, 1981). Relevant volume, assortment, growth and yield tables accounting for the different genotypes, plantation densities and sites have been developed for proper timber appraisal and management (Fakirov, 1964; Krastanov et al., 1984, 1986, 1987a, 1987b). However, the allometric patterns and biomass production potential of black poplar hybrids, particularly at early stages of growth and development and in relation to site quality, have not been investigated in Bulgaria.

Biomass estimation is essential for determining the amount of forest resourc-es, which is relevant to e.g. carbon sequestration, agroforestry system production, wildfire modeling, bioenergy supply. Biomass equations relate tree biomass (kg) or stand biomass (t/ha), as well as their components, with easily measurable tree and stand variables. Allometric relationships and tables for aboveground biomass evalu-ation by diameter classes have been developed in Bulgaria for Scots pine (Dimitrov et al., 1986), Austrian black pine (Dimitrov et al., 1992), Norway spruce (Dimitrov, 1983), Douglas fir (Yonov, 1992) and Hornbeam (Dimitrov et al., 1990). The main objectives of this study were to investigate the allometry of aboveground biomass of juvenile black poplar hybrids (Populus deltoides × P. nigra) traditionally used for timber and cellulose production and to derive biologically plausible and statistically sound biometric models for stem, branch, leaf and total aboveground biomass esti-mation from easily measurable tree and stand characteristics.

mATERIAlS ANd mEThOdS

data collectionCollection of data and samples for model parameterization took place in 1- to

5-year-old plantations for timber production, established through planting of one-year-old ramets (Table 1). Fifteen permanent sample plots, of at least 40 trees each,

7

Tabl

e 1

Dat

a fr

om in

dust

rial p

lant

atio

ns u

sed

for m

odel

par

amet

eriz

atio

n*

plot

Clo

neSc

hem

e (m

× m

)**

Age

(y

ears

)Sa

mpl

ed

tree

sdb

h (c

m)

h (m

)h

(m)

ws (

kg)

wb (

kg)

wl (

kg)

wt (

kg)

p1A

gath

e6×

52

23.

0-4.

13.

8-4.

14

0.72

3-1.

392

0.14

2-0.

231

0.17

9-0.

261

1.04

5-1.

884

p2I 4

5 51

5×5

53

96.5

-10.

94.

2-8.

27

3.03

8-11

.07

1.34

2-6.

168

1.03

2-3.

153

5.41

2-19

.70

p3I 2

146×

55

410

.7-1

4.3

9.0-

11.1

1112

.81-

24.6

81.

945-

4.45

81.

056-

3.65

115

.98-

32.7

9p4

I 214

6×5

66

13.6

-21.

210

.8-1

3.8

1423

.47-

69.8

94.

059-

31.1

13.

013-

10.4

730

.54-

111.

5p5

I 214

6×5

22

3.2.

8-3.

63.

0-3.

13

0.47

9-0.

609

0.19

9-0.

369

0.25

5-0.

484

0.93

3-1.

463

p6I 2

146×

36

415

.3-2

1.0

13.5

-15.

116

36.4

9-66

.29

11.8

6-35

.01

4.41

9-6.

854

52.7

8-10

1.8

p7I 4

5 51

5×5

53

15.0

-19.

313

.8-1

4.7

1438

.43-

61.8

06.

122-

13.8

25.

205-

11.2

349

.76-

86.8

5p8

I 214

5×5

53

9.7-

14.2

10.2

-11.

411

13.1

8-30

.79

3.37

5-9.

717

3.26

1-6.

939

19.8

1-47

.50

p9I 4

5 51

5×5

33

2.2-

3.1

3.8-

4.5

40.

369-

0.76

80.

014-

0.03

70.

073-

0.18

00.

456-

0.98

4

p10

NN

DV

5×5

23

2.9-

3.6

4.4-

5.0

50.

682-

1.17

10.

078-

0.14

20.

196-

0.31

80.

953-

1.63

0

p11

MC

5×5

35

2.9-

9.7

4.3-

9.2

90.

725-

12.4

60.

078-

1.21

60.

151-

1.73

20.

953-

15.4

1

p12

Aga

the

5×5

43

12.8

-15.

511

.7-1

2.6

1327

.24-

36.1

38.

100-

8.82

25.

282-

6.45

140

.82-

49.7

7

p13

I 214

5×5

23

2.3-

3.0

3.7-

4.7

40.

412-

0.91

30.

029-

0.03

90.

091-

0.12

50.

565-

1.07

4

p14

I 214

5×5

63

6.0-

10.7

6.3-

9.9

103.

078-

13.6

11.

136-

4.96

01.

171-

3.94

95.

385-

22.2

9

p15

I 214

5×5

43

3.6-

5.0

5.1-

6.1

61.

132-

2.41

20.

211-

0.32

50.

352-

0.64

41.

695-

3.38

1

Abb

revi

atio

ns: d

bh –

bre

ast h

eigh

t dia

met

er o

f the

tree

(cm

), h

– to

tal t

ree h

eigh

t (m

); H

- av

erag

e hei

ght o

f the

stan

d/st

ock

to th

e nea

rest

met

er (m

); w

s – d

ry

biom

ass o

f ste

m (k

g); w

b – d

ry b

iom

ass o

f bra

nche

s (kg

); w

l – d

ry b

iom

ass o

f lea

ves (

kg);

wt –

tota

l abo

vegr

ound

dry

bio

mas

s of t

he tr

ee (k

g). *

Dat

a ra

nge

(min

imum

– m

axim

um) o

f the

prin

cipa

l tre

e an

d st

and

varia

bles

is sh

own.

**

Estim

ated

pla

nt a

ge w

as th

e su

m o

f the

yea

rs fr

om p

lant

atio

n es

tabl

ishm

ent

plus

one

, whi

ch w

as th

e ag

e of

the

plan

ted

sam

plin

gs.

8

were installed in hybrid black poplar (Populus deltoides × P. nigra) plantations along the banks of rivers Danube (Northern Bulgaria) and Maritsa and its tributaries (South-eastern Bulgaria) on Fluvisols (Fig. 1). Information for the poplar clone was available from plantation records and planting scheme was determined in the field. Soil types were classified according to the World Reference Base for Soil Resources (WGWRB, 2014). All breast-height tree diameters and 50% of total tree heights within the plots were measured. Two to six trees were sampled in the vicinity of each plot considering the pooled diameter distribution determined from the plot. Each sample tree was cut to the ground at 5 cm maximum stump height and the stem length and breast-height tree diameter were measured with 1.0 cm and 0.1 cm preci-sion, respectively. The stem, branches and leaves of each tree were separated and weighted in situ with 0.005 kg precision. Five stem samples were assembled from discs extracted on three places along the trunk: from the middle of the stem and at 1 m distance from the top and from the base of the tree. Three samples of around 200-300 g, proportionally combining branches of different weight and size, and two samples of leaves were obtained per tree.

Measurements and samples collected in three one-year-old nursery stocks, in-cluding various poplar clones, were used for model validation (Table 2). Biomass data of stems and leaves were only available due to established cultural practices, involving removal of branches during the first year of growth. Therefore, this data source did not provide sufficient information for incorporation into the parametriza-tion data set, but was appropriate for selection of a model adjusted to the young-est plant data. The first nursery stock (NP1-NP4) was positioned in South-eastern Bulgaria near Maritsa river on Fluvisols, the second was situated in South-western Bulgaria near Struma river on Fluvisols (NP5-NP6), and the third nursery stock was located along the bank of Danube river in Northern Bulgaria on Haplic kastanozem (NP7-NP10) (Table 2, Fig. 1). Total heights and breast height diameters of 50 sap-lings positioned in 10-plant-strips arranged consecutively along five adjacent rows, were measured. Three to five of these plants were sampled, according to the pooled diameter distribution, for determination of the fresh weight. One stem sample and one sample of leaves were taken from each tree.

Mean stand/stock height was determined from the plot data according to Lo-rey’s formula.

Fresh weight of the samples was measured in the field; they were packed in paper bags and transported to the laboratory. The samples were oven-dried at 105° to constant weight, which was measured with 0.001 kg precision. Proportion of dry mass relative to the fresh sample weight was averaged from the samples of each fraction within the tree and was used to estimate the total amount of dry mass of the respective tree compartment.

Analytical method and model developmentBiomass models for aboveground compartments of individual trees common-

9

Tabl

e 2

Dat

a fr

om n

urse

ry st

ock

used

for m

odel

val

idat

ion*

plot

Clo

neSc

hem

e (m

× m

)A

ge (y

ears

)Sa

mpl

ed

tree

sdb

h (c

m)

h (m

)h

(m)

ws (

kg)

wl (

kg)

NS1

Gua

rdi

1×0.

41

41.

7-2.

43.

5-4.

74

0.25

0-0.

505

0.11

3-0.

170

NS2

I 37

611×

0.4

15

1.3-

2.3

2.8-

4.0

40.

138-

0.45

60.

065-

0.17

8N

S3A

194

1×0.

41

52.

2-3.

04.

1-4.

85

0.44

1-0.

741

0.19

4-0.

268

NS4

I 214

1×0.

41

41.

2-2.

02.

8-3.

74

0.13

2-0.

377

0.06

6-0.

140

NS5

NN

DV

3.6×

0.25

15

1.1-

1.5

2.2-

2.6

20.

118-

0.18

9N

S6A

194

3.6×

0.25

14

1.2-

1.9

2.2-

3.0

20.

108-

0.26

8N

S7I 2

141.

35×0

.33

13

1.5-

2.2

3.3-

3.8

40.

183-

0.35

60.

068-

0.10

8N

S8A

gath

e1.

35×0

.33

13

1.4-

2.2

3.1-

3.8

30.

188-

0.39

10.

072-

0.10

1N

S9B

L1.

35×0

.33

13

1.5-

2.2

3.1-

3.7

30.

179-

0.34

00.

085-

0.13

3N

S10

I 214

1.35

×0.3

31

31.

5-2.

22.

5-3.

13

0.14

0-0.

276

0.06

5-0.

123

Abb

revi

atio

ns: d

bh –

bre

ast h

eigh

t dia

met

er o

f the

tree

(cm

), h

– to

tal t

ree

heig

ht (m

); H

- av

erag

e he

ight

of t

he st

and/

stoc

k to

the

near

est m

eter

(m);

ws –

dr

y bi

omas

s of s

tem

(kg)

; wb –

dry

bio

mas

s of b

ranc

hes (

kg);

wl –

dry

bio

mas

s of l

eave

s (kg

); w

t – to

tal a

bove

grou

nd d

ry b

iom

ass o

f the

tree

(kg)

. * D

ata

rang

e (m

inim

um –

max

imum

) of t

he p

rinci

pal t

ree

and

stoc

k va

riabl

es is

show

n.

10

Fig.

1. G

eogr

aphi

cal d

istri

butio

n of

the

sam

ple

plot

s (lo

ngitu

de 2

3 - 2

6E a

nd la

titud

e 41

- 44

N)

11

ly utilize two principle tree dimensions as predictor variables: diameter at breast height (dbh, cm) and total tree height (h, m) (Clutter et al. 1983; Burkhart, Tomé, 2012). It has been asserted that the tree height provides insignificant improvement of a diameter-only equation (Ter-Mikaelian, Korzukhin, 1997; Bond-Lamberty et al., 2002) and the models are often simplified to a power function of diameter (Zianis et al., 2005; Blujdea et al., 2012; Paul et al., 2013a, 2013b), known as the allometric equation (Huxley, 1972). Other tree parameters that are considered as independent variables in some of the biomass models are age and live crown length (Bond-Lam-berty, 2002; Porté et al., 2002; de-Miguel et al., 2014). The amount of branches in poplars, which has been of interest primarily to assess the timber harvest and has been estimated in percentage of stem volume, has been regarded as dependent on tree age, crown length and stem diameter (Naydenova, 1961).

The industrial plantations are usually subjected to replanting for replacement of the dead plants during the first three years from the establishment. Consequently, the trees in the plantation can differ in age by as much as 3 years, which is a signifi-cant variation considering the narrow age range investigated; therefore the inclusion of tree age as a predictor variable seemed unreliable. Our data collection took place on a variety of growth sites and soil types along the banks of rivers Danube, Maritsa and its tributaries and Struma. A very good indicator of the site quality that can serve also as a growth stage indicator instead of age is the average height of the stand or stock (Stankova, Shibuya, 2003). The bigger mean height will reflect both better

Table 3Selection of biomass models for the aboveground tree compartments

published models with two predictor variables **

1) Combined variable hdbhbby 210 += (Burkhart, Tomé, 2012)

2) Constant form factor hdbhby 21= (Burkhart, Tomé, 2012)

3)* Logarithmic 321

bb hdbhby = (Burkhart, Tomé, 2012)

4)* Generalized logarithmic 3210

bb hdbhbby += (Burkhart, Tomé, 2012)

5) Honer transformed variable

hbb

dbhy1

0 +=

(Burkhart, Tomé, 2012)

6) hbhbdbhbby 3210 )ln()ln()ln( +++= (de-Miguel et al., 2014)

7)* hbdbhbdbhbby 3210 )ln()ln( +++= (de-Miguel et al., 2014)

12

8) )ln()ln( 210 hdbhbby += (de-Miguel et al., 2014)

9)* )ln()ln()ln( 22

10 dbhbhdbhbby ++= (de-Miguel et al., 2014)

10)* ( )222

10 )ln()ln()ln( dbhbhdbhbby ++= (de-Miguel et al., 2014)

11)* ( ) )ln()ln()ln()ln( 32

210 hbdbhbdbhbby +++= (de-Miguel et al., 2014)

12) )ln()ln()ln( 32210 hbhdbhbdbhbby +++=

(de-Miguel et al., 2014)

13)* hbbdbh

dbhbby 32

10)ln( ++

+= (de-Miguel et al., 2014)

14) )ln()ln( 32

10 hbbdbh

dbhbby ++

+=(de-Miguel et al., 2014)

15) hbhbbdbh

dbhbby 432

10 )ln()ln( +++

+= (de-Miguel et al., 2014)

16) dbhbby 10 += (Albert et al., 2014)

17) dbhbbdbhby 210

+= (Albert et al., 2014)

18) hbbdbhby 210

+= (Albert et al., 2014)

19) 120

bhdbhby = (Albert et al., 2014)

20) 3210

bdbhbb hdbhby += (Albert et al., 2014)

21) 2210 dbhbdbhbby ++= (Albert et al., 2014)

22) )exp( 10 dbhbby = (Albert et al., 2014)

Abbreviations: dbh – breast height diameter (cm), h – either total height of the tree (m) or average height of the stand/stock (m); y – dry biomass (kg) of a tree compartment (stem, branches, leaves). * The models are tested also with the variable dbh alone;** - Models 1) – 5) and 16) – 22) are tested in log-transformed form.

13

site quality and tending on one hand and stronger growth potential due to genetic factors (intrinsic growth rate, resistance and tolerance to adverse conditions), on the other hand. Consequently, this stand characteristic can be viewed as a product of the interaction between the time and growth conditions and the mean stand/stock height (H, m) was considered as a composite quantitative variable. This stand parameter is strongly correlated with the tree height and their concomitant inclusion as predictors will probably lead to manifestation of multicollinearity. Therefore, either of them was used along with the tree diameter and was examined a set of model formula-tions suggested in studies by other investigators (Burkhart, Tomé, 2012; Albert et al., 2014; de-Miguel et al., 2014) (Table 3).

Graphical examination of the modeled variables against the predictors was employed to explore the nature of mean relation and variance distribution (Picard et al., 2012). The charts showed nonlinear mean relation and multiplicative, het-eroscedastic, lognormal error distribution for all dependent and independent vari-ables (Fig. 2-4). Therefore, linear regression on the log-transformed equation form was preferred to fit the final regression equations, as suggested by Xiao et al. (2011) and Sileshi (2014). Ordinary Least-Squares Method (OLS) of estimation was em-ployed and the model adequacy was assessed by a set of criteria (Table 4), e.g. tests

Table 4Criteria for model adequacy

Criterion Statistical test* Reference value(s)

Normality of er-rors Anderson-Darling test P > 0.05

Homoscedasticity of errors Breusch-Pagan test P > 0.05

Mean error t-test for mean absolute error different from zero P > 0.05

Model biassimultaneous F-test for slope equal to 1 and zero intercept of the linear regression relating observed and predicted values

P > 0.05

Collinearity Condition Number max 30Outliers Studentised residuals ∈[-2; 2] max 10% > |2|

Leverage points Leverage: 2(k+1)/n, k - number of predic-tors, n - sample size

max 10% > Leverage

Influential points Cook’s D: 4/n, n - sample size max 10% > D

Stability of param-eter estimate

Parameter Relative Standard Error (%): PRSE=100×SE/|b|, SE - standard error of parameter b

< 30%

* Selection based on Gadow, Hui 1999; Paressol 1999; Picard et al., 2012; Sileshi 2014

14

Fig.

2. G

raph

ical

exa

min

atio

n of

stem

dry

mas

s dat

a ag

ains

t bre

ast h

eigh

t dia

met

er (c

m),

tota

l tre

e he

ight

(m) a

nd a

vera

ge h

eigh

t of t

he st

and/

stoc

k (m

).

15

Fig.

3. G

raph

ical

exa

min

atio

n of

bra

nch

dry

mas

s dat

a ag

ains

t bre

ast h

eigh

t dia

met

er (c

m),

tota

l tre

e he

ight

(m) a

nd a

vera

ge h

eigh

t of t

he st

and/

stock

(m).

16

Fig.

4. G

raph

ical

exa

min

atio

n of

leaf

dry

mas

s dat

a ag

ains

t bre

ast h

eigh

t dia

met

er (c

m),

tota

l tre

e he

ight

(m) a

nd a

vera

ge h

eigh

t of t

he st

and/

stoc

k (m

).

17

for normality, homoscedasticity, unbiasedness (Gadow, Hui, 1999; Paressol, 1999; Picard et al., 2012; Sileshi, 2014). Beside them, goodness-of-fit of all regression models was evaluated also according to the requirement for logical behaviour of the fitted functions (i.e. if h2>h1, dbh2>dbh1 then w2>w1), by the adjusted coefficient of determination (Radj.), the root mean squared error (RMSE) and Akaike information criterion (AIC).

Fitting and selection of models for the aboveground tree compartments was carried out in two stages. On the first one, the model for each tree compartment sepa-rately was derived using the OLS method and applying the outlined goodness-of-fit criteria. On the next stage, the best models for each compartment were combined in a system of equations that were fitted simultaneously taking care of the system additivity, which requires that the estimate of the total aboveground biomass equals the sum of estimates of individual compartments. To assure this additivity, the total biomass equation was formulated as the sum of the equations for all aboveground tree fractions and Seemingly Unrelated Regression (SUR) was applied to account for the cross-equation correlations (Parresol, 1999; Burkhart, Tomé, 2012). Finally, to convert the predicted values to arithmetic, untransformed units, additional correc-tion for bias was required (Parresol, 1999) and the ratio correction (Clifford et al., 2013) was applied. It consists of multiplication of the back-transformed estimate with the quotient between the antilogarithms of the mean experimental and the mean predicted values of the dependent variable and suggests a good compromise between accuracy and simplicity, as can be concluded from the investigation by Clifford et al. (2013). Correction for bias was performed for each of the aboveground tree com-partments separately, followed by their summation to obtain unbiased estimate of the total biomass.

Errors of predictionMagnitude and distribution of prediction errors were analysed for the param-

eterization and the validation data sets in parallel. Two error terms were estimated for the predicted untransformed variables:

100ˆ

%y

yyRE −=

and

100ˆ

%y

yyARE

−= ,

where RE% is relative error, ARE% is absolute value of the relative error, y and y are observed and predicted variable values, respectively. Mean value, 10th, 50th, 75th and 90th percentiles of these errors were calculated for the predicted bio-

18

mass of each tree compartment and were compared for both data sets. Both error terms indicate the magnitude of prediction error relative to the predicted variable. Relative error distribution reveals the presence/absence of bias, while the absolute relative error distribution shows the error range.

RESulTS

Twelve models for stem biomass and ten models for leaf biomass showed adequate to describe the dry mass of the respective tree compartments as functions of tree diameter and either tree or mean stand height. Only five models for branch biomass passed the goodness-of-fit tests, the best two being functions of the diameter alone. Next, combinations of stem, branches, leaves and total biomass models were formulated and examined to derive systems of equations for prediction of the above-ground biomass of hybrid black poplar clones. Models S1-S6, were consecutively combined with models B1-B3 and L1-L5, starting from those of the best goodness-of-fit statistics (Table 5). Models S7-S12, on the other hand, were included in formu-lations with models B2-B5 and L6-L10. Our purpose was not only to derive adequate model systems of high predictive abilities, but also to allow flexibility of model implementation considering different predictor variables (i.e. either total tree height or mean stand/stock height). These systems of models were examined rigorously through the set of goodness-of-fit criteria applied to log-transformed model forms (Table 3) and through prediction errors estimated for the back-transformed data. The final test consisted of evaluation of relative errors for the validation data set and their comparison with those obtained for the parameterization data to allow model adjustment to the nursery stock data. Considerable difference in the error magnitude, revealing poor model fit for the one-year-old plant data, was sufficient to define an inadequate model. A dbh - h system of equations (M1) which satisfied all require-ments for model adequacy was easily obtained (Table 6). A dbh – H model system (M2) was also derived (Table 6) with the compromise that Relative Standard Error of parameter b2 slightly exceeded the reference value of 30% (PRSE(b2)=30.6%).

Branch biomass was modeled as a function of diameter by the allometric equation (Huxley, 1972) and the logarithmic equation form (Burkhart, Tomé, 2012, Table 3) described best stem and leaf biomass of model system M1 (Table 6). In the second model system (M2), the combined variable equation (Burkhart, Tomé, 2012, Table 3) showed most adequate to present the leaf dry weight, while stem dry weight was expressed by a power function of tree diameter (Table 6), which exponent con-sisted of a linear function of mean stand height (Eq. 18 in Table 3). All fitted regres-sion models explained more than 90% of the variation in dependent variable and the highest accuracy was manifested by stem models that was also reflected in improved goodness-of-fit of the total biomass models.

Low prediction errors were estimated for the stem and the total biomass mod-els, 90% of which did not exceed 30% and were even less than 15% for the stem bio-

19

Table 5Individual models for the aboveground biomass compartments of hybrid black poplars

model Equation RmSE. Radj AICS1 lnws=ln(b0+b1dbh2h) 0.151 0.992 -186.9S2 lnws=b0+b1ln(dbh)+b2h 0.130 0.994 -201.1S3 lnws=b0+b1ln(dbh2h) 0.106 0.996 -222.6S4 lnws= b0+b1ln(dbh2)+ln(h) 0.101 0.997 -227.7S5 lnws=b0+b1ln(dbh)+b2ln(dbh/h2) 0.099 0.997 -227.9S6 lnws= b0+(b1+b2h)ln(dbh) 0.165 0.991 -177.3S7 lnws=ln(b0+b1dbh2H) 0.206 0.986 -155.9S8 lnws=b0+b1ln(dbh)+b2ln(H) 0.173 0.990 -172.5S9 lnws=ln(dbh2)-ln(b0+b1/H) 0.174 0.990 -173.0

S10 lnws=b0+b1ln(dbh)+b2ln(dbh/H2) 0.173 0.990 -172.5S11 lnws=b0+2ln(dbh)+b2ln(H) 0.172 0.990 -174.1S12 lnws=b0+b1ln(dbh2)+b2(dbh/H2) 0.162 0.991 -179.2B1 lnwb=b0+b1ln(dbh2)+ln(h) 0.591 0.931 -50.7B2 lnwb=b0+b1ln(dbh) 0.525 0.945 -62.4B3 lnwb=b0+b1ln(dbh2) 0.525 0.945 -62.4B4 lnwb=b0+b1ln(dbh)+ln(H) 0.577 0.934 -53.1B5 lnwb=b0+b1ln(dbh2)+ln(H) 0.577 0.934 -53.1l1 lnwl=ln(b0+b1dbh2h) 0.468 0.905 -73.9l2 lnwl=ln(b1hdbhb

2) 0.412 0.926 -86.7l3 lnwl=b0+b1ln(dbh2h) 0.400 0.931 -89.6l4 lnwl=b0+b1ln(dbh2)+b2ln(h) 0.412 0.926 -86.7l5 lnwl=b0+b1hln(dbh) 0.582 0.853 -52.2l6 lnwl=ln(b0+b1dbh2H) 0.473 0.903 -72.8l7 lnwl=ln(b1Hdbhb

2) 0.436 0.918 -81.0l8 lnwl=b0+b1ln(dbh2H) 0.414 0.926 -86.2l9 lnwl=b0+b1ln(dbh)+ln(H) 0.436 0.918 -81.0

l10 lnwl=b0+b1ln(dbh2)+ln(H) 0.436 0.918 -81.0

Abbreviations: dbh – breast height diameter of the tree (cm), h – total tree height (m); H - average height of the stand/stock to the nearest meter (m); ws – dry biomass of stem (kg); wb – dry biomass of branches (kg); wl – dry biomass of leaves (kg); RMSE –root mean squared error (kg); Radj - adjusted coefficient of determination; AIC – Akaike Information Criterion.

20

Fig. 6. Predicted (dotted lines) by model system M2 values vs. observed biomass values for a) b) stem dry mass; c) d) dry mass of leaves. Parametrization data is denoted by circles and validation data is

denoted by stars.

Fig. 5. Predicted (dotted lines) by model system M1 values vs. observed biomass values for a) b) stem dry mass; c) d) dry mass of leaves. Parametrization data is denoted by circles and validation data is

denoted by stars.

21

Tabl

e 6.

Sys

tem

s of m

odel

s for

the

abov

egro

und

biom

ass o

f hyb

rid b

lack

pop

lars

.

Mod

elR

MSE

M

ean

erro

r*

Rad

jA

ICC

FPa

ram

eter

s**

a 0a 1

b 0b 1

b 2c 0

c 1

M1

lnw

s=b 0+

b 1ln(d

bh2 )+

ln(h

)0.

100

0.01

30.

997

-228

.80.

993

-6.0

3 (0

.18)

3.07

(0

.08)

-3.5

5 (0

.04)

0.83

(0

.01)

-4.3

6 (0

.18)

0.76

(0

.03)

lnw

b=a 0+

a 1ln(d

bh))

0.52

6-0

.010

0.94

5-6

3.2

1.03

8ln

wl=

c 0+c 1ln

(dbh

2 h)

0.39

70.

018

0.93

2-9

1.4

1.00

5ln

wt=

ln(e

xp(a

0)db

ha 1+ex

p(b 0)

db

h2b1h

+exp

(c0)(

hdbh

2 )c 1)0.

166

-0.0

080.

991

-176

.7

M2

lnw

s=b 0+

(b1+

b 2ln(H

))ln

(dbh

)0.

183

0.01

70.

989

-168

.30.

982

-6.1

5 (0

.17)

3.13

(0

.08)

-2.5

0 (0

.12)

1.96

(0

.12)

0.02

(0

.01)

0.11

(0

.02)

1.9×

10-3

(1

.6×

10-4

)

lnw

b=a 0+

a 1ln(d

bh)

0.53

6-0

.001

0.94

3-6

1.5

0.98

2ln

wl=

ln(c

0+c 1d

bh2 H

)0.

470

-0.0

030.

904

-74.

60.

911

lnw

t=ln

(exp

(a0)

dbha 1+

exp(

b 0)

dbh(

b 1+b2H

)+c 0+

c 1Hdb

h2 )0.

185

-0.0

060.

989

-165

.5

A

bbre

viat

ions

: dbh

– b

reas

t hei

ght d

iam

eter

of t

he tr

ee (c

m),

h –

tota

l tre

e he

ight

(m);

H -

aver

age

heig

ht o

f the

stan

d/st

ock

to th

e ne

ares

t met

er (m

); w

s –

dry

biom

ass o

f ste

m (k

g); w

b – d

ry b

iom

ass o

f bra

nche

s (kg

); w

l – d

ry b

iom

ass o

f lea

ves (

kg);

wt –

tota

l woo

dy b

iom

ass:

stem

+bra

nche

s (kg

); R

MSE

root

m

ean

squa

red

erro

r (kg

); R

adj

adj

uste

d co

effic

ient

of d

eter

min

atio

n; A

IC –

Aka

ike

Info

rmat

ion

Crit

erio

n, C

F –

corr

ectio

n fa

ctor

.*

Mea

n er

rors

are

not

sign

ifica

ntly

diff

eren

t for

m z

ero

in a

ll ca

ses.

** S

tand

ard

erro

rs a

re d

ispl

ayed

in b

rack

ets.

22

mass of model system M1. Error range of the validation data was wider for the stem model in M1, but was twice as narrow as that of the parameterization data for model system M2 (Table 7). The magnitude of errors for leaf biomass was comparable for the parameterization and the validation data sets. Prediction charts revealed that the lack of small-size trees in the data used for model derivation and parameterization has led to narrowing of the predicted values range of model system M2 (Fig. 6). Fig. 5 and Table 7, on the other hand, suggest the inference that the stem predictions of model system M1 are slightly worsen for the one-year-old saplings and the model underestimates their leaf biomass.

dISCuSSION

Model system M1, based on the two principal tree variables, revealed bet-ter goodness-of-fit and predictive power than M2, when applied to the parameter-ization data from plantation-grown plants (Table 6). It is composed of power-form relationships, which agree with the notion for the multiplicative nature of growth and which have been shown to provide the most adequate fit for the aboveground poplar biomass in studies by other investigators. Ajit et al. (2011), who designed predictive models for dry weight estimation of above and below ground biomass components of Populus deltoides in India, tested linear, allometric, Gompertz, Chap-man-Richards and logistic functions and reached the conclusion that the power func-tion on tree diameter fulfilled the validation criterions to the best possible extent. Zabek, Prescott (2006) concluded that the logarithmic equation, which is based on

Fig. 7. Distribution of the aboveground biomass compartments of hybrid black poplar clones.a) b) parameterization data; c) validation data.

23

Tabl

e 7

Rel

ativ

e er

rors

of p

redi

ctio

n fo

r the

par

amet

rizat

ion

and

the

valid

atio

n da

ta se

t

mod

elva

riab

leE

rror

pred

ictio

n da

tava

lidat

ion

data

Mea

nPe

rc10

Perc

50Pe

rc75

Perc

90M

ean

Perc

10Pe

rc50

Perc

75Pe

rc90

M1

ws

RE

-1.2

-12.

5-1

.76.

610

.76.

4-1

3.8

4.9

15.5

28.9

AR

E8.

01.

96.

710

.414

.312

.01.

311

.016

.328

.9

wb

RE

-17.

4-9

4.9

6.1

21.3

47.3

AR

E47

.16.

839

.365

.594

.9

wl

RE

-11.

6-5

4.6

0.1

22.5

35.4

22.9

-5.0

26.8

33.6

42.0

AR

E34

.13.

025

.536

.157

.626

.314

.626

.833

.642

.0

wt

RE

-0.7

-18.

1-0

.910

.418

.6A

RE

12.0

1.1

8.8

16.8

22.1

M2

ws

RE

-1.5

-28.

61.

011

.420

.41.

5-1

1.8

4.4

8.6

13.1

AR

E14

.22.

711

.220

.029

.88.

50.

35.

811

.616

.2

wb

RE

-12.

4-8

4.0

8.2

26.2

49.8

AR

E45

.86.

340

.264

.284

.0

wl

RE

-2.1

-59.

111

.238

.644

.6-1

3.5

-68.

2-1

1.2

15.9

28.2

AR

E39

.55.

733

.447

.763

.329

.16.

124

.634

.368

.2

wt

RE

1.8

-22.

04.

812

.723

.3A

RE

13.7

1.9

9.9

20.1

28.3

Abb

revi

atio

ns: P

erc1

0, P

erc5

0, P

erc7

5 an

d Pe

rc90

den

ote

the

10th, 5

0th, 7

5th a

nd 9

0th p

erce

ntile

, res

pect

ivel

y; R

E –

rela

tive

erro

r in

%, A

RE

– ab

solu

te

valu

e of

the

rela

tive

erro

r in

%.

24

power terms of height and diameter (sensu Burkhart, Tomé, 2012), was superior to the polynomial, which consistently overestimated both stem and branch biomass of Populus trichocarpa Torr. and Gray × P. deltoides Marsh. hybrid trees from the small size classes. Johansson, Karačić (2011), who investigated 42 stands of various poplar hybrids on former farmland in Sweden, also found the power-form relation-ship as better describing the individual aboveground dry weight than the parabolic and Chapman-Richards functions.

It must be admitted that both derived model systems, except for the stem bio-mass model of system M2 (Table 7), under-evaluated stem and leaf biomass of the nursery stock. This outcome could has been expected considering that the saplings have been exposed to intensive care during their first vegetation period, consisting of systematic and ample watering, regular fertilization and weed control. In addi-tion, branches removal as a cultural practice leads to redistribution of the nutrient resources between stem and leaves and the balance between the aboveground plant mass and the tree dimensions is shifted during the first year of growth due to this human interference. Our explanation is supported also by the finding of Reffy et al. (1997) that the decrease in branch number induces increase of tree height, i.e. prun-ing favours height. Stem and leaf models of system M2 accounted for the improved site quality and accelerated plant growth due to tending by inclusion of the compos-ite variable mean stock height as a principal predictor. In addition, system M2 does not require information about the individual tree height, which is a variable more dif-ficult to measure, but takes advantage of the mean stand height, which is commonly available in forest inventories. The linear form of the mean height incorporation into the leaf model was not very satisfactory (Fig. 6d, Table 7), but the height-dependent exponent of the stem biomass model was particularly well fitted (Fig. 6b, Table 7).

Stem compartment accounted for the largest part of the biomass, attaining around 70% (68.9% on average) from the total dry weight (Fig. 7a). The total den-dromass of the plantation-grown poplars amounted to an average of 85% from the biomass (Fig. 7b), but both branches and leaves showed high dry weight variability and similar quantities (3.1-42% for branches and 4.9-33.1% for leaves). Broshtilova (1986) investigated the biological productivity and turnover of nitrogen and ash el-ements of 21-year-old plantation of Populus bachelieri, and found that the stem was up to 80% of the aboveground biomass, 16.6% of the dry weight consisted of branches and only 3.4% of the biomass was contained in the leaves. The difference in the biomass allocation pattern, observed in comparison to our study, is probably due to the age odds between the experimental plants. This understanding is supported by the notion that young trees undergo a period of exponential growth until reaching a relatively constant value when it becomes constrained by environmental limitations, i.e. competition for resources in the stand at more advanced age (Norby et al., 2001). Our conclusion is in line with the finding by Fakirov (1980) that the maximum leaf biomass of hybrid black poplars is reached at 8-10 years of age, around 5 years after

25

the canopy closure. Similar to the plantation-grown poplars, around 70% (71.4% on average) of the dry weight was contained in the stems of one-year-old saplings (Fig. 7c). The variation in their aboveground biomass compartments was relatively small (63.1-80.4% for stem and 19.6-36.9% for leaves), which is in concordance with the variability magnitude observed by Tsanov et al. (1986) for seven black poplar clones during the first year of their growth.

Taeroe et al. (2015), who investigated biomass allometry of a hybrid poplar clone Populus trichocarpa × Populus maximowiczii (OP42) across southern Scandi-navia using mixed-effects models to account for the variation due to site, found that inclusion of height increased the amount of explained variation and contributed for unbiased predictions for stands of different management systems and sites. We de-rived two systems of compatible generic equations to estimate stem, branch, leaf and total aboveground biomass of hybrid black poplars, which accounted for variability across sites, clones and ages by inclusion of two principal predictor variables: breast height diameter and either total tree or mean stand height. Model system M1 uses only the two principal tree dimensions. It can therefore be applied for determination of aboveground biomass in single trees or harvested saplings when information on the stand height is absent. Model system M2, based on mean stand height and tree diameter, can be used to assess rapidly and accurately the biomass of standing poplar stock.

Acknowledgements: We thank Dr L. Trichkov from the Executive Forest Agency, Prof. H. Tsakov from the Forest Research Institute, Sofia and the forestry officers from Svishtov, Strumyani, Parvomay and Svilengrad Forestry Estates for their cooperation and logistic support in carrying out the experimental work and data collection. We are grateful to the National Science Fund of Bulgaria that provided financial support for this work through the project ‘Comprehensive assessment of forest and agricultural species for establishment of energy crops in Bulgaria’ (Contract N DFNI-E01/6, 2012).

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