Tree Allometrics

Picea rubens / Stem biomass

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

Stem biomassPicea rubens · PinaceaeCanadaRead from the original paper
Photo of Picea rubens
© Douglas Goldman · CC BY-SA · iNaturalist
Equation

As printed (Eq. 3)

y wood = β wood1D βwood2Hβwood3 + ewood

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

Stem biomass = 0.0143 * D^1.6441 * H^1.4065 + 0.0274 * D^2.0188
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. Height drops out of the bark 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
Red spruce bwood1 0.0143
Equation · Table 4, Red spruce
bwood2 1.6441
Equation · Table 4, Red spruce
bwood3 1.4065
Equation · Table 4, Red spruce
bbark1 0.0274
Equation · Table 4, Red spruce
bbark2 2.0188
Equation · Table 4, Red spruce
bbark3 —
Equation · Table 4, Red spruce
Red spruce 55 22.9±1.2 15.9±0.4 207.7±22.4
Trees measured · Table 2 (No. of trees)
(6.5;43.5) (8.0;21.2) (9.1;811.7)
Smallest DBH · Table 2, Red spruce (ranges of dbh, height, total biomass)
Stem 0.0630 0.97 22.8 2.74 0.0052 0.98 19.8 3.35
R² · Table 5, Red spruce (AdjRSq in the dbh- and height-based set, second block)
Trees measured
55
DBH range
6.5–43.5 cm
Height range
8–21.2 m
R²
0.98
Method
Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total
Where
Quebec, Canada (ENFOR archival data, early 1980s)
Last checked
2026-11-03
Calculate
Height from
100
Stem biomass (kg)
47.2
Carbon (kg), ×0.47
173
CO₂e (kg), ×44/12
Fitted DBH range050100150200250300350510152025303540DBH (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 = 15100100Computed from the printed form
computed from the published form at dbh = 20 cm, H = 15 m

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