Tree Allometrics

Picea rubens / Aboveground biomass

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

Aboveground biomassPicea rubens · PinaceaeCanadaRead from the original paper

Photo of Picea rubens

Equation

As printed (Eq. 3)

y wood = β wood1D βwood2Hβwood3 + ewood

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

Aboveground biomass = 0.0143 * D^1.6441 * H^1.4065 + 0.0274 * D^2.0188 + 0.0005 * D^3.3136 + 0.0106 * D^2.2709

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 bark, branches, 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

Lambert, M.-C., Ung, C.-H., Raulier, F. (2005). Canadian national tree aboveground biomass equations. Canadian Journal of Forest Research, 35(8), 1996–2018.

doi:10.1139/x05-112 · Paywalled · copy we read

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

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

bbranches1 0.0005

Equation · Table 4, Red spruce

bbranches2 3.3136

Equation · Table 4, Red spruce

bbranches3 —

Equation · Table 4, Red spruce

bfoliage1 0.0106

Equation · Table 4, Red spruce

bfoliage2 2.2709

Equation · Table 4, Red spruce

bfoliage3 —

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)

Total 0.0059 0.97 29.1 3.64 0.0196 0.98 25.9 3.12

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

DBH (cm)Height (m)

Height from

120

Aboveground biomass (kg)

56.5

Carbon (kg), ×0.47

207

CO₂e (kg), ×44/12

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%.

Inputs	Expected	We get	From
D = 20, H = 15	120	120	Computed from the printed form computed from the published form at dbh = 20 cm, H = 15 m

Report a problem with this equation · JSON

Related

North American taxa group: Picea ≥ 0.35 spg (Table 5) · Chojnacky et al. 2014 · DBH
North American taxa group: Picea < 0.35 spg (Table 5) · Chojnacky et al. 2014 · DBH
Norway spruce, Czech Republic: Total aboveground biomass from D and H/D (Table 2) · Čihák & Vejpustková 2018 · DBH + Height
Norway spruce, Czech Republic: Total aboveground biomass from D (Table 2) · Čihák & Vejpustková 2018 · DBH
European general equation, Picea abies, aboveground, diameter only (Eq. 3) · Forrester et al. 2017 · DBH
Canadian national equation, black spruce, dbh and height (sum of wood, bark, branches, foliage; Table 4) · Lambert et al. 2005 · DBH + Height
Canadian national equation, black spruce, dbh only (sum of wood, bark, branches, foliage; Table 3) · Lambert et al. 2005 · DBH
Canadian national equation, red spruce, dbh only (sum of wood, bark, branches, foliage; Table 3) · Lambert et al. 2005 · DBH
Canadian national equation, alpine fir, dbh only (branches; Table 3) · same paper · Branch biomass
Canadian national equation, alpine fir, dbh and height (branches; Table 4) · same paper · Branch biomass
Canadian national equation, alpine fir, dbh and height (foliage; Table 4) · same paper · Foliage biomass
Canadian national equation, alpine fir, dbh and height (stem wood plus stem bark; Table 4) · same paper · Stem biomass
Canadian national equation, alpine fir, dbh and height (sum of wood, bark, branches, foliage; Table 4) · same paper · Aboveground biomass
Canadian national equation, alpine fir, dbh only (foliage; Table 3) · same paper · Foliage biomass
Canadian national equation, alpine fir, dbh only (stem wood plus stem bark; Table 3) · same paper · Stem biomass
Canadian national equation, alpine fir, dbh only (sum of wood, bark, branches, foliage; Table 3) · same paper · Aboveground biomass

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