Tree Allometrics

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Pinus patula Total biomass (roots, stem, branches, foliage) from D and H (Table 3)

Total biomassPinus patula · PinaceaeMexiconaturalRead from the original paper
Photo of Pinus patula
© Lauu · CC BY · iNaturalist
Equation

As printed (Section 3.1 (Model 1, Table 1))

y = e(−β0 + β1 ln (D × TH))

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

Total biomass = exp(-4.7483 + 1.7395 * ln(D * H))
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

Printed form y = e^(−β0 + β1 ln(D × TH)); the tabulated β0 is positive and enters with a minus sign, as printed. Units are D in cm, TH in m, biomass in kg dry weight (Figure 3). No correction factor stated. Parameters read from the journal table CSV downloads. The paper also fits an additive simultaneous system (Table 6) with slightly different parameters; not added. The foliage model (Table 4: ϖ0 8.1986, ϖ1 1.6628, R2 0.9762) is not added here; the printed additive formula in Section 3.3 shows the foliage intercept without the minus sign, but Figure 3(d) (p. 166) prints the fitted foliage curve as y = e^(−8.198579+(1.66277 ln(D x TH))), n=25, so the sign is a typesetting slip and the model could be added as exp(−8.1986 + 1.6628 ln(D × TH)). Authors recommend use for 5 to 25 cm DBH. Total includes roots, stem, branches and foliage.

Source
β0 4.7483, β1 1.7395, R2 0.9886
Equation · Table 3, model (1) (CSV table download; p. 164 of the PDF)
a destructive analysis was made of 25 trees distributed in five diameter classes
Trees measured · Abstract
diameter at breast height (D) that varied from 3.5 cm to 25.7 cm, with a total height (TH) fluctuating from 4.32 m to 20.18 m
Smallest DBH · Section 3.1
Trees measured
25
DBH range
3.5–25.7 cm
Height range
4.32–20.18 m
R²
0.9886
Method
nonlinear regression (SAS PROC MODEL), exponential form
Where
Ixtlán de Juárez, Sierra Norte, Oaxaca (pine-oak forest)
Last checked
2026-11-02
Calculate
Height from
9.524
Total biomass (kg)
4.476
Carbon (kg), ×0.47
16.41
CO₂e (kg), ×44/12
Fitted DBH range050100150200510152025303540DBH (cm)Total biomass (kg)Total 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 = 8, H = 79.529.52Computed from the printed form
computed from the published form
D = 13, H = 1256.656.6Computed from the printed form
computed from the published form
D = 22, H = 18286.1286.1Computed from the printed form
computed from the published form

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