Tree Allometrics

Fraxinus americana / Branch biomass

Canadian national equation, white ash, dbh and height (branches; Table 4)

Branch biomassFraxinus americana · OleaceaeCanadaRead from the original paper
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Equation

As printed (Eq. 3)

y branches = β branches1D βbranches2Hβbranches3 + e branches

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

Branch biomass = 0.0354 * D^2.3046
D
Diameter at breast height (1.3 m), cm

All branches, cut at the stem base (live branches; dead branches excluded). Height drops out of the branches 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
bbranches1 0.0354
Equation · Table 4, White ash
bbranches2 2.3046
Equation · Table 4, White ash
bbranches3 —
Equation · Table 4, White ash
White ash 109 22.3±1.1 17.6±0.4 296.2±28.5
Trees measured · Table 2 (No. of trees)
(2.4;53.7) (3.9;26.9) (1.2;1850.1)
Smallest DBH · Table 2, White ash (ranges of dbh, height, total biomass)
Branches 0.0019 0.74 44.6 3.97 0.0017 0.75 43.6 3.99
R² · Table 5, White ash (AdjRSq in the dbh- and height-based set, second block)
Trees measured
109
DBH range
2.4–53.7 cm
Height range
3.9–26.9 m
R²
0.75
Method
Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total
Where
Ontario and Quebec, Canada (ENFOR archival data, early 1980s)
Last checked
2026-11-03
Calculate
35.3
Branch biomass (kg)
16.6
Carbon (kg), ×0.47
60.8
CO₂e (kg), ×44/12
Fitted DBH range050100150200510152025303540DBH (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 = 1535.335.3Computed from the printed form
computed from the published form at dbh = 20 cm, H = 15 m

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