Tree Allometrics

Pseudotsuga menziesii / Stem volume

NSVB Douglas-fir, Marine Division (240): total stem wood volume (inside bark), segmented model (Eq. 2), D ≥ 9 in (22.86 cm)

Stem volumePseudotsuga menziesii · PinaceaeUnited StatesRead from the original paper
Photo of Pseudotsuga menziesii
© Danny Steaven · CC BY-SA · iNaturalist
Equation

As printed (Example 1, p. 8)

VtotibGross = 0.001929099661 × 9^(2.162413104203 – 1.690400253097) × 20^1.690400253097 × 110^0.985444005253 = 88.452275544288

In this library's units, ready to compute (m³)

Stem volume = 0.028316846592 * 0.001929099661 * 9^(2.162413104203 - 1.690400253097) * (D/2.54)^1.690400253097 * (H/0.3048)^0.985444005253
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

Output is gross total stem wood volume inside bark, groundline to tip (VtotibGross), before cull or broken-top deductions. Coefficients for Douglas-fir in the Marine Division (240) only; NSVB uses other coefficients for Douglas-fir elsewhere (tables S1a–S9a). Upper branch of the segmented model; pair with westfall-2024-pseudotsuga-menziesii-240-volume-small. Paper units: in, ft, ft3; expression converts D cm→in (/2.54), H m→ft (/0.3048) and ft3→m3 (×0.028316846592). n and the DBH range are from the scorecard for ST_WD_CV_TOT in 240 (table S19), which covers the whole segmented model; this record's DBH limit at k is the segmentation point. DBH is measured at 4.5 ft (1.37 m).

Source
a Douglas-fir (Pseudotsuga menziesii; SPCD = 202)
Taxon · Example 1, p. 8
growing in the Marine Division (DIVISION = 240)
Where · Example 1, p. 8
yi = a × k^(b−b1) × Di^b1 × Hi^c + εi; Di ≥ k
Equation · Eq. 2, p. 2
k is a set segmentation point that is 9.0 inches for softwoods (SPCD<300) and 11.0 inches for hardwoods (SPCD≥300)
Equation · Methods, Model development, p. 2
Di is diameter (inches) at breast height (4.5 feet), Hi is total tree height (feet)
Units · Methods, Model development, p. 2
units for volume and biomass predictions are cubic feet and pounds, respectively
published.output unit · Examples of tree-level calculations, p. 8
total stem was defined as groundline to tree tip
Output · Methods, Data, p. 2
"Total Stem Wood Volume","ST_WD_CV_TOT","202","240","MARINE_DIVISION",2386,13.4212489522213,1.3,59.6
Fit · Table S19_component_division_spcd_scorecard.csv (WO-GTR-104-Supp1), columns VAR2,VAR3,SPCD,DIVISION,DIVISION_DESCRIPTION,N,Avg_DBH,Min_DBH,Max_DBH
key modeling statistics such as sample sizes (n), tree diameter distributions (minimum, mean, and maximum)
Fit · Methods, Model development, p. 6
Trees measured
2,386
DBH range
22.86–151.38 cm
Method
NSVB segmented model (Eq. 2), coefficients for SPCD 202 in DIVISION 240 from table S1a (the total stem wood volume (inside bark) table used in Example 1); fitted with weighted regression to destructively sampled trees
Where
FIA ecodivision Marine Division (240), mapped in GTR fig. 1
Last checked
2026-11-03
Calculate
Height from
2.5
Stem volume (m³)
Fitted DBH range024681020406080100DBH (cm)Stem volume (m³)Stem volume

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 = 50.8, H = 33.52.52.5Value printed in the paper
Example 1 (p. 8) prints 88.452275544288 ft3 for D = 20 in, H = 110 ft; inputs and expected converted to cm, m, m3

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