Tree Allometrics

Quercus alba / Stem biomass

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

Stem biomassQuercus alba · FagaceaeCanadaRead from the original paper
Photo of Quercus alba
© 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 = 0.0442 * D^1.6818 * H^1.031 + 0.0308 * D^1.7479 * H^0.3504
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
White oak bwood1 0.0442
Equation · Table 4, White oak
bwood2 1.6818
Equation · Table 4, White oak
bwood3 1.0310
Equation · Table 4, White oak
bbark1 0.0308
Equation · Table 4, White oak
bbark2 1.7479
Equation · Table 4, White oak
bbark3 0.3504
Equation · Table 4, White oak
White oak 61 23.9±2.1 11.5±0.6 325.4±63.1
Trees measured · Table 2 (No. of trees)
(2.2;74.3) (2.8;21.5) (1.3;2385.5)
Smallest DBH · Table 2, White oak (ranges of dbh, height, total biomass)
Stem 0.0003 0.82 133.4 4.92 0.0266 0.98 43.8 3.20
R² · Table 5, White oak (AdjRSq in the dbh- and height-based set, second block)
Trees measured
61
DBH range
2.2–74.3 cm
Height range
2.8–21.5 m
R²
0.98
Method
Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total
Where
Ontario, Canada (ENFOR archival data, early 1980s)
Last checked
2026-11-03
Calculate
Height from
126
Stem biomass (kg)
59.3
Carbon (kg), ×0.47
217
CO₂e (kg), ×44/12
Fitted DBH range0100200300400500510152025303540DBH (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 = 15126126Computed from the printed form
computed from the published form at dbh = 20 cm, H = 15 m

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