Tree Allometrics

Fraxinus pennsylvanica / Aboveground biomass

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

Aboveground biomassFraxinus pennsylvanica · OleaceaeCanadaRead from the original paper
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Equation

As printed (Eq. 3)

y wood = β wood1D βwood2Hβwood3 + ewood

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

Aboveground biomass = 0.0224 * D^1.7845 * H^1.066 + 0.0219 * D^1.419 * H^0.8963 + 0.0176 * D^2.3313 + 0.0761 * D^1.3077
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 branches, 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 ash bwood1 0.0224
Equation · Table 4, Red ash
bwood2 1.7845
Equation · Table 4, Red ash
bwood3 1.0660
Equation · Table 4, Red ash
bbark1 0.0219
Equation · Table 4, Red ash
bbark2 1.4190
Equation · Table 4, Red ash
bbark3 0.8963
Equation · Table 4, Red ash
bbranches1 0.0176
Equation · Table 4, Red ash
bbranches2 2.3313
Equation · Table 4, Red ash
bbranches3 —
Equation · Table 4, Red ash
bfoliage1 0.0761
Equation · Table 4, Red ash
bfoliage2 1.3077
Equation · Table 4, Red ash
bfoliage3 —
Equation · Table 4, Red ash
Red ash 27 21.1±1.8 18.0±1.1 207.9±33.6
Trees measured · Table 2 (No. of trees)
(4.9;40.2) (7.2;26.7) (5.8;587.8)
Smallest DBH · Table 2, Red ash (ranges of dbh, height, total biomass)
Total 6.2881 0.88 61.2 1.87 0.0130 0.95 39.5 3.51
R² · Table 5, Red ash (AdjRSq in the dbh- and height-based set, second block)
Trees measured
27
DBH range
4.9–40.2 cm
Height range
7.2–26.7 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
124
Aboveground biomass (kg)
58.5
Carbon (kg), ×0.47
215
CO₂e (kg), ×44/12
Fitted DBH range0100200300400500510152025303540DBH (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 = 15124124Computed from the printed form
computed from the published form at dbh = 20 cm, H = 15 m

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