Tree Allometrics

Pinus contorta / Stem volume

NSVB lodgepole pine, Marine Regime Mountains (M240): total stem wood volume (inside bark), segmented model (Eq. 2), D ≥ 9 in (22.86 cm)

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

As printed (Table S1a (Table S1a_volib_coefs_spcd.csv, WO-GTR-104-Supp1), columns SPCD,DIVISION,STDORGCD,model,a,a1,b,b1,c,c1)

108,M240,,2,0.00288801,,1.955076824,1.692491493,1.005097398,

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

Stem volume = 0.028316846592 * 0.00288801 * 9^(1.955076824 - 1.692491493) * (D/2.54)^1.692491493 * (H/0.3048)^1.005097398
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. DBH is measured at 4.5 ft (1.37 m). 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 M240 (table S19) and cover the whole segmented model; the record's DBH limit at k is the segmentation point. Upper branch of the segmented model; pair with westfall-2024-pinus-contorta-m240-volume-small.

Source
yi = a × Di^b × Hi^c + εi; Di < k / yi = a × k^(b−b1) × Di^b1 × Hi^c + εi; Di ≥ k
Equation · Eq. 2, 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
108,lodgepole pine,N,Pinus,contorta,,,Pinus contorta
Taxon · FIADB REF_SPECIES.csv (FIA DataMart), columns SPCD,COMMON_NAME,SHARED_COMMON_NAME_IND,GENUS,SPECIES,VARIETY,SUBSPECIES,SCIENTIFIC_NAME: the species codes the NSVB tables use
total stem was defined as groundline to tree tip
Output · Methods, Data, 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
"Total Stem Wood Volume","ST_WD_CV_TOT","108","M240","MARINE_REGIME_MOUNTAINS",330,8.4069696969697,1.6,17.1
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
330
DBH range
22.86–43.43 cm
Method
NSVB segmented model (Eq. 2), coefficients for SPCD 108 in DIVISION M240 from table S1a; fitted with weighted regression to destructively sampled trees
Where
FIA ecodivision Marine Regime Mountains (M240), mapped in GTR fig. 1
Last checked
2026-11-03
Calculate
Height from
1.24
Stem volume (m³)
Fitted DBH range01234510203040506070DBH (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 = 38.1, H = 25.91.241.24Computed from the printed form
computed from the published form at D = 15 in, H = 85 ft, converted to cm, m and m3

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