Tree Allometrics

Pinus patula / Root biomass

Pinus patula Belowground (root) biomass from D and H (Table 5)

Root 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)

Root biomass = exp(-6.4835 + 1.716 * 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.

Source
β0 6.4835, β1 1.7160, R2 0.9848
Equation · Table 5, model (1) (CSV table download; p. 166 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
0.9848
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
1.53
Root biomass (kg)
0.718
Carbon (kg), ×0.47
2.63
CO₂e (kg), ×44/12
Fitted DBH range0510152025510152025303540DBH (cm)Root biomass (kg)Root 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 = 71.531.53Computed from the printed form
computed from the published form
D = 13, H = 128.868.86Computed from the printed form
computed from the published form
D = 22, H = 1843.843.8Computed from the printed form
computed from the published form

Report a problem with this equation · JSON

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