Tree Allometrics

Fraxinus nigra / Stem biomass

Canadian national equation, black ash, dbh and height (stem wood plus stem bark; Table 4)

Stem biomassFraxinus nigra · OleaceaeCanadaRead from the original paper
No openly licensed photo yet
Equation

As printed (Eq. 3)

y wood = β wood1D βwood2Hβwood3 + ewood

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

Stem biomass = 0.0306 * D^2.1836 * H^0.574 + 0.0897 * D^2.2634 * H^(-0.567)
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

Stem from ground level to tree top, stem wood plus stem bark; the stem is the sum of the two compartment equations. 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
Black ash bwood1 0.0306
Equation · Table 4, Black ash
bwood2 2.1836
Equation · Table 4, Black ash
bwood3 0.5740
Equation · Table 4, Black ash
bbark1 0.0897
Equation · Table 4, Black ash
bbark2 2.2634
Equation · Table 4, Black ash
bbark3 –0.5670
Equation · Table 4, Black ash
Black ash 73 16.2±1.2 14.4±0.6 142.0±21.6
Trees measured · Table 2 (No. of trees)
(2.0;43.1) (2.6;22.9) (1.0;926.4)
Smallest DBH · Table 2, Black ash (ranges of dbh, height, total biomass)
Stem 0.0182 0.97 30.8 3.43 0.2132 0.97 27.4 2.52
R² · Table 5, Black ash (AdjRSq in the dbh- and height-based set, second block)
Trees measured
73
DBH range
2–43.1 cm
Height range
2.6–22.9 m
R²
0.97
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
Height from
117
Stem biomass (kg)
55.2
Carbon (kg), ×0.47
202
CO₂e (kg), ×44/12
Fitted DBH range0100200300400500600510152025303540DBH (cm)Stem biomass (kg)Stem 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 = 15117117Computed from the printed form
computed from the published form at dbh = 20 cm, H = 15 m

Report a problem with this equation · JSON

Related

Compare these curves