Tree Allometrics

Pinus sylvestris / Aboveground biomass

Scots pine total above-ground biomass, Model 1a (Eq. 9)

Aboveground biomassPinus sylvestris · PinaceaeFinlandmixedRead from the original paper
Photo of Pinus sylvestris
© Douglas Goldman · CC BY-SA · iNaturalist
Equation

As printed (Eq. 9, p. 631)

ln(yki) = b0 + b1 dSki/(dSki + 12) + b2 hki/(hki + 20) + uk + eki

In this library's units, ready to compute (kg)

Aboveground biomass = exp(-3.198 + 9.547 * (2 + 1.25*D)/((2 + 1.25*D) + 12) + 3.241 * H/(H + 20) + (0.009 + 0.010)/2)
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

Total above-ground biomass of the stem wood, bark, living and dead branches and needles. dS = 2 + 1.25d is a transformation of dbh (cm), not a stump diameter. The variance correction (var(uk)+var(eki))/2 = 0.0095 is added to the intercept as the paper prescribes, in both published and canonical forms. Sample trees spanned d 1.5–35.8 cm and h 2.0–28.6 m (Table 3, all 908 trees); the total equation used a subset of 285 trees, so no fit range is stated. Mineral-soil stands, Finland.

Source
Total Eq. 9 N = 285 b0 –3.198 b1 9.547 b2 3.241 var(uk) 0.009 var(eki) 0.010
Equation · Table 5, p. 632
dSki = 2 + 1.25 dki
Equation · variable definitions
a variance correction term, (σu² + σe²)/2 … should be added to the intercept
Correction factor · Section 2.4 (2009) / Section 3 (2008)
Trees measured
285
Correction factor
1.00955 (applied)
Method
Multivariate linear mixed model on ln(biomass) with stand random effects (fitted jointly with component equations); fixed part shown, with variance correction (var(u)+var(e))/2 added to the intercept
Where
Finland, mineral-soil stands (mostly southern and central Finland)
Last checked
2026-11-01
Calculate
Height from
142
Aboveground biomass (kg)
66.8
Carbon (kg), ×0.47
245
CO₂e (kg), ×44/12
0100200300400500510152025303540DBH (cm)Aboveground biomass (kg)Aboveground biomass

Shaded: the DBH range the model was fitted on. Other inputs held at the values above.

Checks this equation passes

On every build, the library's form and the paper's own form (in its units) must both give these values within 1%.

InputsExpectedWe getFrom
D = 20, H = 18142142Computed from the printed form
computed from the published form (with variance correction) at d = 20 cm, h = 18 m

Report a problem with this equation · JSON

Related

Compare these curves