Tree Allometrics

Equations / Aboveground biomass

Douglas-fir total aboveground biomass, simple SUR (D only)

Aboveground biomassPseudotsuga menziesii · PinaceaeUnited StatesmixedRead from the original paper
Photo of Pseudotsuga menziesii
© Danny Steaven · CC BY-SA · iNaturalist
Equation

As printed (Eq. 6 and Table 3, Simple SUR, Douglas-fir)

Total = Σ exp(aij + aij*X1 ...) over bole, bark, branch and foliage; simple SUR uses X1 = ln(DBH) only

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

Aboveground biomass = exp(-0.349 + 1.925 * ln(D)) + exp(-3.247 + 1.919 * ln(D)) + exp(-2.604 + 1.942 * ln(D)) + exp(-3.242 + 1.758 * 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. Total is the sum of the four component equations (bole, bark, branch, foliage) from the constrained SUR system, so it includes foliage and bark. Fitted in original scale, no correction factor. Extended SUR models (height, crown length) not included.

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
22
DBH range
19.3–114 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
270
Aboveground biomass (kg)
126.9
Carbon (kg), ×0.47
465.3
CO₂e (kg), ×44/12
Fitted DBH range02004006008001,0001,200510152025303540DBH (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 = 20270270Computed from the printed form
computed from the published form (coefficients as printed)
D = 501,5711,571Computed from the printed form
computed from the published form (coefficients as printed)
D = 1005,9565,956Computed from the printed form
computed from the published form (coefficients as printed)

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