Tree Allometrics

Quercus rubra / Branch biomass

Canadian national equation, red oak, dbh and height (branches; Table 4)

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

As printed (Eq. 3)

y branches = β branches1D βbranches2Hβbranches3 + e branches

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

Branch biomass = 0.0013 * D^3.0637 * H^0.3153
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

All branches, cut at the stem base (live branches; dead branches excluded). 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
bbranches1 0.0013
Equation · Table 4, Red oak
bbranches2 3.0637
Equation · Table 4, Red oak
bbranches3 0.3153
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)
Branches 0.0029 0.85 46.6 3.94 0.0021 0.90 37.0 4.04
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
0.9
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
29.6
Branch biomass (kg)
13.9
Carbon (kg), ×0.47
50.9
CO₂e (kg), ×44/12
Fitted DBH range050100150200250510152025303540DBH (cm)Branch biomass (kg)Branch 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 = 1529.629.6Computed from the printed form
computed from the published form at dbh = 20 cm, H = 15 m

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