Tree Allometrics

Betula papyrifera / Stem biomass

Canadian national equation, white birch, dbh and height (stem wood plus stem bark; Table 4)

Stem biomassBetula papyrifera · BetulaceaeCanadaRead from the original paper
Photo of Betula papyrifera
Dezene Huber · CC0 · iNaturalist
Equation

As printed (Eq. 3)

y wood = β wood1D βwood2Hβwood3 + ewood

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

Stem biomass = 0.0338 * D^2.0702 * H^0.6876 + 0.008 * D^1.9754 * H^0.6659
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

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 βbark2Hβbark3 + e bark
Equation · Eq. 3
White birch bwood1 0.0338
Equation · Table 4, White birch
bwood2 2.0702
Equation · Table 4, White birch
bwood3 0.6876
Equation · Table 4, White birch
bbark1 0.0080
Equation · Table 4, White birch
bbark2 1.9754
Equation · Table 4, White birch
bbark3 0.6659
Equation · Table 4, White birch
White birch 606 16.4±0.4 13.3±0.2 152.0±7.1
Trees measured · Table 2 (No. of trees)
(1.5;43.6) (2.6;23.9) (0.4;1020.8)
Smallest DBH · Table 2, White birch (ranges of dbh, height, total biomass)
Stem 0.0113 0.94 32.2 3.62 0.0009 0.97 23.9 4.27
R² · Table 5, White birch (AdjRSq in the dbh- and height-based set, second block)
Trees measured
606
DBH range
1.5–43.6 cm
Height range
2.6–23.9 m
R²
0.97
Method
Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total
Where
Canada: Alberta, Manitoba, Newfoundland and Labrador, Nova Scotia, Ontario, Quebec, Saskatchewan (ENFOR archival data, early 1980s)
Last checked
2026-11-03
Calculate
Height from
125
Stem biomass (kg)
59
Carbon (kg), ×0.47
216
CO₂e (kg), ×44/12
Fitted DBH range0100200300400500600510152025303540DBH (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 = 20, H = 15125125Computed 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