Tree Allometrics

Equations / Aboveground biomass

Dry miombo, total AGB, All 44 species (trees and shrubs), D, H and wood density

Aboveground biomassTrees and shrubs, 44 speciesTanzanianaturalRead from the original paper
Many species, no single photo
Equation

As printed (Table 2, total biomass, model 6)

Combined (N = 104); 44 species ... Total biomass ... (df = 101) 6 −8.8819 (0.139) 0.9497 (0.010) — 1.4–62 0.988 0.187 0.162 6.40

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

Aboveground biomass = 1.0176 * exp(-8.8819 + 0.9497 * ln(1000 * rho * D^2 * H))
rho
Wood density (oven-dry mass / green volume), g/cm³
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

ln-ln OLS (species models) or linear mixed model with species random effect (group models); total aboveground biomass is stump + stem and branches + twigs and leaves, so foliage is included. The paper states CF = exp(RMSE²/2) and that it was applied to predictions; the CF value (1.0176) is not printed and is computed here from the printed RMSE (0.187) by that stated formula, and applied in both forms. The R² shown for group models is the likelihood-ratio R² named in the Table 2 note; for species models it is adjusted R². Wood density is in kg/m³ per the table note (the text says g/cm³ in one place); the coefficients only give plausible values with kg/m³. The canonical form multiplies rho (g/cm³) by 1000.

Source
CF = exp⁡(RMSE2/2), which was applied to the predicted values of volume and biomass
Correction factor · Section 2.5 (Sprugel correction)
Y is volume (m3) or biomass (kg); Dbh is diameter at breast height (cm); ht is total height (m); and wd is wood density (kg m−3).
Units · Table 2 note
The minimum and maximum sizes of sample trees/shrubs were 1.4 cm and 62.0 cm in diameter at breast height
Largest DBH · Section 2.2 (study-wide)
Trees measured
104
DBH range
1.4–62 cm
Height range
2.5–18.2 m
R²
0.988
Correction factor
1.0176 (applied)
Method
linear mixed model on ln-transformed data (species random effect)
Where
Gangalamtumba Village Land Forest Reserve, Iringa, Tanzania (dry miombo woodland)
Last checked
2026-11-02
Calculate
Height from
162
Aboveground biomass (kg)
76.14
Carbon (kg), ×0.47
279.2
CO₂e (kg), ×44/12
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 = 10, rho = 0.6162162Computed from the printed form
hand-computed from the published form
D = 40, H = 14, rho = 0.7963963Computed from the printed form
hand-computed from the published form

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