NSVB Pacific silver fir, Marine Division (240): total stem wood volume (inside bark), modified Wiley model (Eq. 4)

Stem volumeAbies amabilis · PinaceaeUnited StatesRead from the original paper

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)

11,240,,4,0.001314136,,2.037385804,0.014090669,1.156702494,

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

Stem volume = 0.028316846592 * 0.001314136 * (D/2.54)^2.037385804 * (H/0.3048)^1.156702494 * exp(-(0.014090669 * (D/2.54)))

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 240 (table S19).

Source

Westfall, J.A., Coulston, J.W., Gray, A.N., Shaw, J.D., Radtke, P.J., Walker, D.M., Weiskittel, A.R., et al. (2024). A national-scale tree volume, biomass, and carbon modeling system for the United States. Gen. Tech. Rep. WO-104. Washington, DC: USDA Forest Service. 37 p.

doi:10.2737/WO-GTR-104 · Open access · copy we read

yi = a × Di^b × Hi^c × exp(−(b1 × Di)) + εi

Equation · Eq. 4, 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

11,Pacific silver fir,N,Abies,amabilis,,,Abies amabilis

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

"Total Stem Wood Volume","ST_WD_CV_TOT","11","240","MARINE_DIVISION",179,16.6,5.7,44.1

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: 179
DBH range: 14.48–112.01 cm
Method: NSVB modified Wiley model (Eq. 4), coefficients for SPCD 11 in DIVISION 240 from table S1a; 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

DBH (cm)Height (m)

Height from

0.676

Stem volume (m³)

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%.

Inputs	Expected	We get	From
D = 30.5, H = 21.3	0.676	0.676	Computed from the printed form computed from the published form at D = 12 in, H = 70 ft, converted to cm, m and m3

Report a problem with this equation · JSON

NSVB Pacific silver fir, Warm Continental Regime Mountains (M210): total stem wood volume (inside bark), modified Wiley model (Eq. 4) · Westfall et al. 2024 · DBH + Height
NSVB Pacific silver fir, Marine Regime Mountains (M240): total stem wood volume (inside bark), modified Wiley model (Eq. 4) · Westfall et al. 2024 · DBH + Height
NSVB Pacific silver fir, species-level (all ecodivisions): total stem wood volume (inside bark), modified Wiley model (Eq. 4) · Westfall et al. 2024 · DBH + Height
NSVB balsam fir, Subarctic Division (130): total stem wood volume (inside bark), segmented model (Eq. 2), D ≥ 9 in (22.86 cm) · Westfall et al. 2024 · DBH + Height
NSVB balsam fir, Subarctic Division (130): total stem wood volume (inside bark), segmented model (Eq. 2), D < 9 in (22.86 cm) · Westfall et al. 2024 · DBH + Height
NSVB balsam fir, Warm Continental Division (210): total stem wood volume (inside bark), segmented model (Eq. 2), D ≥ 9 in (22.86 cm) · Westfall et al. 2024 · DBH + Height
NSVB balsam fir, Warm Continental Division (210): total stem wood volume (inside bark), segmented model (Eq. 2), D < 9 in (22.86 cm) · Westfall et al. 2024 · DBH + Height
NSVB balsam fir, Hot Continental Division (220): total stem wood volume (inside bark), segmented model (Eq. 2), D ≥ 9 in (22.86 cm) · Westfall et al. 2024 · DBH + Height
NSVB Pacific silver fir, species-level (all ecodivisions): total aboveground biomass (without foliage), Schumacher-Hall model (Eq. 1) · same paper · Aboveground biomass, without leaves
NSVB Pacific silver fir, species-level (all ecodivisions): branch biomass (wood and bark), Schumacher-Hall model (Eq. 1) · same paper · Branch biomass
NSVB Pacific silver fir, Warm Continental Regime Mountains (M210): total stem wood volume (inside bark), modified Wiley model (Eq. 4) · same paper · Stem volume
NSVB Pacific silver fir, Marine Regime Mountains (M240): total stem wood volume (inside bark), modified Wiley model (Eq. 4) · same paper · Stem volume
NSVB Pacific silver fir, species-level (all ecodivisions): total stem wood volume (inside bark), modified Wiley model (Eq. 4) · same paper · Stem volume
NSVB balsam fir, Subarctic Division (130): total stem wood volume (inside bark), segmented model (Eq. 2), D ≥ 9 in (22.86 cm) · same paper · Stem volume
NSVB balsam fir, Subarctic Division (130): total stem wood volume (inside bark), segmented model (Eq. 2), D < 9 in (22.86 cm) · same paper · Stem volume
NSVB balsam fir, Warm Continental Division (210): total aboveground biomass (without foliage), segmented model (Eq. 2), D ≥ 9 in (22.86 cm) · same paper · Aboveground biomass, without leaves

Compare these curves

NSVB Pacific silver fir, Marine Division (240): total stem wood volume (inside bark), modified Wiley model (Eq. 4)

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