Tree Allometrics

Fraxinus pennsylvanica / Stem biomass

Canadian national equation, red ash, dbh only (stem wood plus stem bark; Table 3)

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

As printed (Eq. 2)

y wood = β wood1D βwood2 + ewood

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

Stem biomass = 0.1571 * D^2.1817 + 0.0416 * D^2.0509
D
Diameter at breast height (1.3 m), cm

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 βbark2 + e bark
Equation · Eq. 2
Red ash bwood1 0.1571
Equation · Table 3, Red ash
bwood2 2.1817
Equation · Table 3, Red ash
bbark1 0.0416
Equation · Table 3, Red ash
bbark2 2.0509
Equation · Table 3, 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)
Stem 2.6838 0.86 54.7 2.04 0.0155 0.95 34.1 3.35
R² · Table 5, Red ash (AdjRSq in the dbh-based set, first block)
Trees measured
27
DBH range
4.9–40.2 cm
R²
0.86
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
128
Stem biomass (kg)
60
Carbon (kg), ×0.47
220
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 = 20128128Computed from the printed form
computed from the published form at dbh = 20 cm

Report a problem with this equation · JSON

Related

Compare these curves