Tree Allometrics

Betula alleghaniensis / Aboveground biomass

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

Aboveground biomassBetula alleghaniensis · BetulaceaeCanadaRead from the original paper

Photo of Betula alleghaniensis

Equation

As printed (Eq. 3)

y wood = β wood1D βwood2Hβwood3 + ewood

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

Aboveground biomass = 0.0259 * D^1.9044 * H^0.9715 + 0.0069 * D^2.0834 * H^0.5371 + 0.0325 * D^2.3851 + 0.1683 * D^1.2764

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 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

Yellow birch bwood1 0.0259

Equation · Table 4, Yellow birch

bwood2 1.9044

Equation · Table 4, Yellow birch

bwood3 0.9715

Equation · Table 4, Yellow birch

bbark1 0.0069

Equation · Table 4, Yellow birch

bbark2 2.0834

Equation · Table 4, Yellow birch

bbark3 0.5371

Equation · Table 4, Yellow birch

bbranches1 0.0325

Equation · Table 4, Yellow birch

bbranches2 2.3851

Equation · Table 4, Yellow birch

bbranches3 —

Equation · Table 4, Yellow birch

bfoliage1 0.1683

Equation · Table 4, Yellow birch

bfoliage2 1.2764

Equation · Table 4, Yellow birch

bfoliage3 —

Equation · Table 4, Yellow birch

Yellow birch 280 25.7±0.9 16.4±0.3 494.4±34.4

Trees measured · Table 2 (No. of trees)

(0.8;70.3) (2.7;25.6) (0.1;2951.4)

Smallest DBH · Table 2, Yellow birch (ranges of dbh, height, total biomass)

Total 2.8971 0.94 145.5 2.34 0.9527 0.94 135.6 2.59

R² · Table 5, Yellow birch (AdjRSq in the dbh- and height-based set, second block)

Trees measured: 280
DBH range: 0.8–70.3 cm
Height range: 2.7–25.6 m
R²: 0.94
Method: Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total
Where: Canada: Newfoundland and Labrador, Ontario, Quebec (ENFOR archival data, early 1980s)
Last checked: 2026-11-03

Calculate

DBH (cm)Height (m)

Height from

172

Aboveground biomass (kg)

80.9

Carbon (kg), ×0.47

297

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	172	172	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: Betulaceae 0.50–0.59 spg (Table 5) · Chojnacky et al. 2014 · DBH
White birch aboveground biomass from D only (MS-2) (sum of components, Table 5) · Dong et al. 2018 · DBH
White birch aboveground biomass from D and H (MS-3) (sum of components, Table 6) · Dong et al. 2018 · DBH + Height
Canadian national equation, grey birch, dbh and height (sum of wood, bark, branches, foliage; Table 4) · Lambert et al. 2005 · DBH + Height
Canadian national equation, grey birch, dbh only (sum of wood, bark, branches, foliage; Table 3) · Lambert et al. 2005 · DBH
Canadian national equation, white birch, dbh and height (sum of wood, bark, branches, foliage; Table 4) · Lambert et al. 2005 · DBH + Height
Canadian national equation, white birch, dbh only (sum of wood, bark, branches, foliage; Table 3) · Lambert et al. 2005 · DBH
Canadian national equation, yellow birch, 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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