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

Aboveground biomassFraxinus nigra · OleaceaeCanadaRead from the original paper

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Equation

As printed (Eq. 3)

y wood = β wood1D βwood2Hβwood3 + ewood

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

Aboveground biomass = 0.0306 * D^2.1836 * H^0.574 + 0.0897 * D^2.2634 * H^(-0.567) + 0.0994 * D^2.163 * H^(-0.4809) + 0.0124 * D^1.0325 * H^0.8747

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). 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

Black ash bwood1 0.0306

Equation · Table 4, Black ash

bwood2 2.1836

Equation · Table 4, Black ash

bwood3 0.5740

Equation · Table 4, Black ash

bbark1 0.0897

Equation · Table 4, Black ash

bbark2 2.2634

Equation · Table 4, Black ash

bbark3 –0.5670

Equation · Table 4, Black ash

bbranches1 0.0994

Equation · Table 4, Black ash

bbranches2 2.1630

Equation · Table 4, Black ash

bbranches3 –0.4809

Equation · Table 4, Black ash

bfoliage1 0.0124

Equation · Table 4, Black ash

bfoliage2 1.0325

Equation · Table 4, Black ash

bfoliage3 0.8747

Equation · Table 4, Black ash

Black ash 73 16.2±1.2 14.4±0.6 142.0±21.6

Trees measured · Table 2 (No. of trees)

(2.0;43.1) (2.6;22.9) (1.0;926.4)

Smallest DBH · Table 2, Black ash (ranges of dbh, height, total biomass)

Total 0.0085 0.96 35.6 3.82 0.1349 0.97 32.9 2.76

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

Trees measured: 73
DBH range: 2–43.1 cm
Height range: 2.6–22.9 m
R²: 0.97
Method: Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total
Where: Ontario and Quebec, Canada (ENFOR archival data, early 1980s)
Last checked: 2026-11-03

Calculate

DBH (cm)Height (m)

Height from

138

Aboveground biomass (kg)

64.8

Carbon (kg), ×0.47

238

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	138	138	Computed from the printed form computed from the published form at dbh = 20 cm, H = 15 m

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

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