Tree Allometrics

Fagus grandifolia / Stem biomass

Canadian national equation, beech, dbh and height (stem wood plus stem bark; Table 4)

Stem biomassFagus grandifolia · FagaceaeCanadaRead from the original paper
Photo of Fagus grandifolia
© Douglas Goldman · CC BY-SA · iNaturalist
Equation

As printed (Eq. 3)

y wood = β wood1D βwood2Hβwood3 + ewood

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

Stem biomass = 0.0432 * D^2.0378 * H^0.7 + 0.0049 * D^1.9057 * H^0.677
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

Stem from ground level to tree top, stem wood plus stem bark; the stem is the sum of the two compartment equations. r2 is the adjusted R² (AdjRSq) of this compartment in Table 5. Fitted on the original scale (weighted nonlinear seemingly unrelated regression), so there is no back-transform correction. Dead branches, cones and fruits are not part of aboveground biomass in this work (Materials). Stand type was not always recorded. Ung, Bernier & Guo (2008) later revised parameters for some species with British Columbia data; not used here.

Source
y bark = β bark1D βbark2Hβbark3 + e bark
Equation · Eq. 3
Beech bwood1 0.0432
Equation · Table 4, Beech
bwood2 2.0378
Equation · Table 4, Beech
bwood3 0.7000
Equation · Table 4, Beech
bbark1 0.0049
Equation · Table 4, Beech
bbark2 1.9057
Equation · Table 4, Beech
bbark3 0.6770
Equation · Table 4, Beech
Beech 177 23.5±0.9 17.5±0.4 405.4±27.3
Trees measured · Table 2 (No. of trees)
(1.8;46.3) (2.9;26.5) (0.7;1372.5)
Smallest DBH · Table 2, Beech (ranges of dbh, height, total biomass)
Stem 0.3312 0.90 84.7 2.86 0.0215 0.91 79.9 3.61
R² · Table 5, Beech (AdjRSq in the dbh- and height-based set, second block)
Trees measured
177
DBH range
1.8–46.3 cm
Height range
2.9–26.5 m
R²
0.91
Method
Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total
Where
Ontario and Quebec, Canada (ENFOR archival data, early 1980s)
Last checked
2026-11-03
Calculate
Height from
138
Stem biomass (kg)
64.9
Carbon (kg), ×0.47
238
CO₂e (kg), ×44/12
Fitted DBH range0100200300400500600510152025303540DBH (cm)Stem biomass (kg)Stem 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 = 15138138Computed from the printed form
computed from the published form at dbh = 20 cm, H = 15 m

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