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Fig. 1. Location of the experiments for modelling tree biomass for spruce and deciduous trees in Finland.

Table 1. Stand characteristics at the establishment of the experiments in 2021, and numbers of sampled biomass trees. For height, mean is presented with standard deviation in parentheses. For number of sampled biomass trees by tree species, the number of above-ground tree components is presented with the number of root samples in the parentheses.
Finland, Nastola Finland, Karkkila Finland, Tammela
Coordinates 60°55.417’N,
25o53.208’E 		60o33.783’N,
24o15.693’E 		60o51.140’N,
23o46.211’E
Number of sample plots 8 12 12
Sample plot size, m2 625 500 500
Number of stems, ha–1
   Planted spruce 2384 2235 1893
   Broadleaves trees 27 900 19 100 41 900
Height, m
   Planted spruce 0.95 (0.44) 1.34 (0.46) 1.02 (0.29)
   Deciduous trees 1.87 (0.78) 1.79 (0.77) 1.41 (0.68)
Number of sampled biomass trees:
   Norway spruce 16 (8) 8 (8) 20 (10)
   Silver birch 20 (10) 10 (10) 24 (12)
   Aspen 20 (10) - -
   Rowan - 10 (10) 24 (12)
Table 2. Characteristics of biomass sample trees gathered from the experiments.
N Stem diameter at stump height*, cm Tree height, m
Mean Range Mean Range
Norway spruce 44 2.4 0.7–4.2 1.3 0.5–2.6
Silver birch 54 2.5 0.6–5.3 2.2 0.6–4.3
Aspen 20 2.2 0.5–4.6 2.6 0.6–4.8
Rowan 34 1.4 0.6–2.7 1.4 0.6–2.3
* Measured at 0.1 m height.
Table 3. The parameter estimates of multi-response model for biomass of Norway spruce (kg). For the fixed parameters the standard error is given in parentheses. Variances and correlations of residual errors (enj) are given. The response variables are in logarithmic scale.
Stem Branches Foliage Stump Roots
Intercept –5.676 (0.405) –4.163 (0.092) –7.003 (0.194) –8.570 (0.479) –10.183 (0.775)
5.260 (0.874) 9.038 (0.323) 6.618 (0.677) 9.874 (1.219)
k 2 1.5 1 1
ln(ds) 2.285 (0.103)
ln(h) 1.288 (0.216) 0.795 (0.264)
var(enj) 0.062 0.067 0.037 0.096 0.083
e1j e2j e3j e4j e5j
e2j –0.37
e3j 0.04 0.59
e4j 0.26 0.50 0.34
e5j 0.20 0.42 0.65 0.71
Table 4. The parameter estimates of multi-response model for biomass of birch (kg). For the fixed parameters the standard error is given in parentheses. Variances and correlations of residual errors (enj) are given. The response variables are in logarithmic scale.
Stem Branches Foliage Stump Roots
Intercept –6.471 (0.320) –5.937 (0.084) –7.104 (0.118) –6.209 (0.120) –6.679 (0.286)
5.111 (0.911) 9.123 (0.248) 8.476 (1.933)
k 2 3 6
ln(ds) 2.293 (0.226) 2.157 (0.103)
ln(h) 1.599 (0.260) 0.655 (0.267) 1.418 (0.486)
var(enj) 0.071 0.104 0.058 0.096 0.076
e1j e2j e3j e4j e5j
e2j 0.30
e3j 0.41 0.67
e4j –0.56 –0.24 –0.25
e5j 0.15 0.18 0.21 –0.21
Table 5. The parameter estimates of multi-response model for biomass of aspen (kg). For the fixed parameters the standard error is given in parentheses. Variances and correlations of residual errors (enj) are given. The response variables are in logarithmic scale.
Stem Branches Foliage Stump Roots*
Intercept –4.489 (0.107) –15.326 (0.571) –4.809 (0.056) - –6.579 (0.260)
18.844 (1.211) 10.700 (0.647)
k 1 4
ln(ds) 1.873 (0.119) 2.169 (0.058)
h 0.345 (0.063) –0.314 (0.136)
var(enj) 0.022 0.204 0.026 0.116
e1j e2j e3j e4j e5j
e2j 0.05
e3j 0.01 0.52
e4j - - -
e5j 0.05 0.74 0.65 -
* Stump included.
Table 6. The parameter estimates of multi-response model for biomass of rowan (kg). For the fixed parameters the standard error is given in parentheses. Variances and correlations of residual errors (enj) are given. The response variables are in logarithmic scale.
Stem Branches Foliage Stump Roots
Intercept –4.443 (0.054) –14.193 (0.928) –7.809 (0.338) –8.292 (0.442) –7.586 (0.636)
14.980 (1.524) 8.700 (0.772) 8.054 (0.991) 9.690 (1.434)
k 1 2 2 2
ln(ds) 1.260 (0.145)
ln(h) 1.420 (0.160)
var(enj) 0.060 0.784 0.227 0.302 0.657
e1j e2j e3j e4j e5j
e2j 0.55
e3j 0.74 0.48
e4j 0.56 –0.11 0.41
e5j 0.76 0.48 0.52 0.68
2

Fig. 2. Predictions of the compiled biomass models for tree components as a function of tree height. Stump and roots are included to below-ground biomass.

3

Fig. 3. The biomass allocation to the biomass of the tree components based on the developed biomass models. Stump and roots are included to below-ground biomass.

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Fig. 4. The observed (circle marks) and predicted root-to-shoot ratio in the modelling data predicted by the developed models (MODEL) and models of Repola (2008, 2009).

Table 7. Bias (kg) of the predicted biomass of spruce and birch obtained by the developed (MODEL) and Repola (2008, 2009) models. Bias of the model based also on the crown variable are presented in parenthesis.
Spruce Birch
MODEL Repola 2009 MODEL Repola 2008
Stem –0.001 –0.029 0.001 0.003
Branches –0.001 0.059 (0.012) –0.001 –0.009 (0.010)
Foliage 0.006 0.185 (0.164) 0.000 0.101 (0.067)
Below-ground 0.005 –0.290 –0.008 –0.196
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Fig. 5. The observed (Obs.) and predicted spruce and birch above-ground biomass in the modelling data predicted by the developed models (Model) and models of Repola (2008, 2009). * Predictions of the model with the independent variables of diameter, height, crown length or crown ratio.

Fig. 6. The observed (Obs.) and expected spruce and birch below-ground biomass in the modelling data predicted by the developed models (Model) and models of Repola (2008, 2009).