Tree Allometrics

Quercus rubra / Aboveground biomass

Canadian national equation, red oak, dbh and height (sum of wood, bark, branches, foliage; Table 4)

Aboveground 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)

Aboveground biomass = 0.0285 * D^1.8501 * H^1.0204 + 0.0326 * D^1.81 * H^0.4153 + 0.0013 * D^3.0637 * H^0.3153 + 0.0582 * D^1.5438
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

Total aboveground biomass = wood + bark + branches + foliage, each fitted as its own equation; the total is their sum (additivity by construction). 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
y bark = β bark1D βbark2Hβbark3 + e bark
Equation · Eq. 3
y branches = β branches1D βbranches2Hβbranches3 + e branches
Equation · Eq. 3
y foliage = β foliage1D βfoliage2Hβfoliage3 + efoliage
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
bbranches1 0.0013
Equation · Table 4, Red oak
bbranches2 3.0637
Equation · Table 4, Red oak
bbranches3 0.3153
Equation · Table 4, Red oak
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)
Total 0.0344 0.91 92.3 3.64 0.0618 0.97 59.1 3.25
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
0.97
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
174
Aboveground biomass (kg)
81.6
Carbon (kg), ×0.47
299
CO₂e (kg), ×44/12
Fitted DBH range0200400600800510152025303540DBH (cm)Aboveground biomass (kg)Aboveground 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 = 15174174Computed from the printed form
computed from the published form at dbh = 20 cm, H = 15 m

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