Tree Allometrics

Quercus rubra / Stem biomass

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

Stem biomassQuercus rubra · FagaceaeCanadaRead from the original paper
Photo of Quercus rubra
© Sandy Wolkenberg · CC BY · iNaturalist
Equation

As printed (Eq. 3)

y wood = β wood1D βwood2Hβwood3 + ewood

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

Stem biomass = 0.0285 * D^1.8501 * H^1.0204 + 0.0326 * D^1.81 * H^0.4153
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
Red oak bwood1 0.0285
Equation · Table 4, Red oak
bwood2 1.8501
Equation · Table 4, Red oak
bwood3 1.0204
Equation · Table 4, Red oak
bbark1 0.0326
Equation · Table 4, Red oak
bbark2 1.8100
Equation · Table 4, Red oak
bbark3 0.4153
Equation · Table 4, Red oak
Red oak 117 22.6±1.0 15.3±0.4 311.4±29.2
Trees measured · Table 2 (No. of trees)
(1.1;55.3) (2.5;23.0) (0.4;1977.5)
Smallest DBH · Table 2, Red oak (ranges of dbh, height, total biomass)
Stem 0.1560 0.87 73.0 3.07 0.0524 0.95 43.4 3.09
R² · Table 5, Red oak (AdjRSq in the dbh- and height-based set, second block)
Trees measured
117
DBH range
1.1–55.3 cm
Height range
2.5–23 m
R²
0.95
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
138
Stem biomass (kg)
64.9
Carbon (kg), ×0.47
238
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 = 15138138Computed from the printed form
computed from the published form at dbh = 20 cm, H = 15 m

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