Tree Allometrics

Quercus rubra / Foliage biomass

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

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

As printed (Eq. 3)

y foliage = β foliage1D βfoliage2Hβfoliage3 + efoliage

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

Foliage biomass = 0.0582 * D^1.5438
D
Diameter at breast height (1.3 m), cm

Foliage is leaves and twigs. Height drops out of the foliage term: the paper leaves its height exponent blank (—, not significantly different from zero). 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
bfoliage1 0.0582
Equation · Table 4, Red oak
bfoliage2 1.5438
Equation · Table 4, Red oak
bfoliage3 —
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)
Foliage 0.0012 0.73 3.8 2.81 0.0008 0.72 3.8 2.98
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
0.72
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
5.94
Foliage biomass (kg)
2.79
Carbon (kg), ×0.47
10.2
CO₂e (kg), ×44/12
Fitted DBH range05101520510152025303540DBH (cm)Foliage biomass (kg)Foliage 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 = 155.945.94Computed from the printed form
computed from the published form at dbh = 20 cm, H = 15 m

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