Tree Allometrics

Betula populifolia / Aboveground biomass

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

Aboveground biomassBetula populifolia · BetulaceaeCanadaRead from the original paper
Photo of Betula populifolia
© Homer Edward Price · CC BY · iNaturalist
Equation

As printed (Eq. 3)

y wood = β wood1D βwood2Hβwood3 + ewood

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

Aboveground biomass = 0.0295 * D^1.9064 * H^0.9139 + 0.0148 * D^1.8433 * H^0.5021 + 0.015 * D^3.0347 * H^(-0.7629) + 0.0455 * D^2.6447 * H^(-1.4955)
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
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
Grey birch bwood1 0.0295
Equation · Table 4, Grey birch
bwood2 1.9064
Equation · Table 4, Grey birch
bwood3 0.9139
Equation · Table 4, Grey birch
bbark1 0.0148
Equation · Table 4, Grey birch
bbark2 1.8433
Equation · Table 4, Grey birch
bbark3 0.5021
Equation · Table 4, Grey birch
bbranches1 0.0150
Equation · Table 4, Grey birch
bbranches2 3.0347
Equation · Table 4, Grey birch
bbranches3 –0.7629
Equation · Table 4, Grey birch
bfoliage1 0.0455
Equation · Table 4, Grey birch
bfoliage2 2.6447
Equation · Table 4, Grey birch
bfoliage3 –1.4955
Equation · Table 4, Grey birch
Grey birch 43 10.3±0.8 8.9±0.5 39.8±6.9
Trees measured · Table 2 (No. of trees)
(2.2;22.7) (2.3;14.9) (0.6;181.0)
Smallest DBH · Table 2, Grey birch (ranges of dbh, height, total biomass)
Total 0.0016 0.94 11.1 3.92 0.0050 0.96 9.0 3.33
R² · Table 5, Grey birch (AdjRSq in the dbh- and height-based set, second block)
Trees measured
43
DBH range
2.2–22.7 cm
Height range
2.3–14.9 m
R²
0.96
Method
Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total
Where
Nova Scotia, Canada (ENFOR archival data, early 1980s)
Last checked
2026-11-03
Calculate
Height from
139
Aboveground biomass (kg)
65.5
Carbon (kg), ×0.47
240
CO₂e (kg), ×44/12

Outside the data this model was fitted on: height above the fitted 14.9 m. Results may be unreliable.

Fitted DBH range0100200300400500600700510152025303540DBH (cm)Aboveground biomass (kg)Aboveground 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 = 15139139Computed from the printed form
computed from the published form at dbh = 20 cm, H = 15 m

Report a problem with this equation · JSON

Related

Compare these curves