Tree Allometrics

Picea rubens / Stem biomass

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

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

As printed (Eq. 2)

y wood = β wood1D βwood2 + ewood

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

Stem biomass = 0.0989 * D^2.2814 + 0.022 * D^2.0908
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 spruce bwood1 0.0989
Equation · Table 3, Red spruce
bwood2 2.2814
Equation · Table 3, Red spruce
bbark1 0.0220
Equation · Table 3, Red spruce
bbark2 2.0908
Equation · Table 3, 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-based set, first block)
Trees measured
55
DBH range
6.5–43.5 cm
R²
0.97
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
103
Stem biomass (kg)
48.6
Carbon (kg), ×0.47
178
CO₂e (kg), ×44/12
Fitted DBH range0100200300400500510152025303540DBH (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 = 20103103Computed from the printed form
computed from the published form at dbh = 20 cm

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