Tree Allometrics

Equations / Stem biomass

Lodgepole pine bole biomass, simple SUR (D only)

Stem biomassPinus contorta · PinaceaeUnited StatesmixedRead from the original paper
Photo of Pinus contorta
© Alison Northup · CC BY · iNaturalist
Equation

As printed (Eqs. 2-5 (X1 = ln DBH) and Table 3, Simple SUR, Lodgepole pine)

Bole = exp(a11 + a12*X1); a11 = -2.374, a12 = 2.373

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

Stem biomass = exp(-2.374 + 2.373 * ln(D))
D
Diameter at breast height (1.3 m), cm

Read from the author's accepted manuscript (draft, manuscript ID cjfr-2015-0256.R1), not the typeset article; values may differ from the final print. Fitted in original scale (nonlinear SUR), so no log back-transform correction. DBH in cm, biomass in kg (Eq. 2-5 text). Bole is stem wood; bark is reported as a separate component (not provided here as there is no matching output quantity). Extended SUR models using height and crown length are not included (crown length is not a canonical variable).

Source
22 Douglas-fir (Pseudotsuga menziesii (Mirbel) Franco) and 33 lodgepole pine (Pinus contorta) trees
Trees measured · Materials and Methods, Data and Study Area
Trees measured
33
DBH range
13.5–42.9 cm
Method
seemingly unrelated regression (simple SUR), component equations constrained to sum to total, fitted in original scale
Where
Oregon, USA (several forests)
Last checked
2026-11-02
Calculate
57.52
Stem biomass (kg)
27.04
Carbon (kg), ×0.47
99.13
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 = 1557.557.5Computed from the printed form
computed from the published form (coefficients as printed)
D = 25193.3193.3Computed from the printed form
computed from the published form (coefficients as printed)
D = 40589.8589.8Computed from the printed form
computed from the published form (coefficients as printed)

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