Tree Allometrics

Abies lasiocarpa / Aboveground biomass

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

Aboveground biomassAbies lasiocarpa · PinaceaeCanadaRead from the original paper
Photo of Abies lasiocarpa
© Kaden Slone · 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 = 0.0268 * D^1.7579 * H^0.9871 + 0.0009 * D^1.446 * H^1.8839 + 0.047 * D^2.9288 * H^(-1.1588) + 0.0551 * D^1.7585
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
Alpine fir bwood1 0.0268
Equation · Table 4, Alpine fir
bwood2 1.7579
Equation · Table 4, Alpine fir
bwood3 0.9871
Equation · Table 4, Alpine fir
bbark1 0.0009
Equation · Table 4, Alpine fir
bbark2 1.4460
Equation · Table 4, Alpine fir
bbark3 1.8839
Equation · Table 4, Alpine fir
bbranches1 0.0470
Equation · Table 4, Alpine fir
bbranches2 2.9288
Equation · Table 4, Alpine fir
bbranches3 –1.1588
Equation · Table 4, Alpine fir
bfoliage1 0.0551
Equation · Table 4, Alpine fir
bfoliage2 1.7585
Equation · Table 4, Alpine fir
bfoliage3 —
Equation · Table 4, Alpine fir
Alpine fir 60 19.6±1.3 14.8±0.8 158.4±19.5
Trees measured · Table 2 (No. of trees)
(2.1;36.5) (2.2;23.7) (1.7;461.8)
Smallest DBH · Table 2, Alpine fir (ranges of dbh, height, total biomass)
Total 0.2380 0.96 30.8 2.44 0.0313 0.97 26.7 3.00
R² · Table 5, Alpine fir (AdjRSq in the dbh- and height-based set, second block)
Trees measured
60
DBH range
2.1–36.5 cm
Height range
2.2–23.7 m
R²
0.97
Method
Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total
Where
Alberta, Canada (ENFOR archival data, early 1980s)
Last checked
2026-11-03
Calculate
Height from
110
Aboveground biomass (kg)
51.8
Carbon (kg), ×0.47
190
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 = 15110110Computed from the printed form
computed from the published form at dbh = 20 cm, H = 15 m

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