Tree Allometrics

Equations / Stem volume

NSVB spruce spp., Subarctic Regime Mountains (M130): total stem wood volume (inside bark), modified Wiley model (Eq. 4)

Stem volumePicea · PinaceaeUnited StatesRead from the original paper
Covers the whole genus
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)

90,M130,,4,0.001590526,,1.831495104,0.006044958,1.184669479,

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

Stem volume = 0.028316846592 * 0.001590526 * (D/2.54)^1.831495104 * (H/0.3048)^1.184669479 * exp(-(0.006044958 * (D/2.54)))
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

FIA's SPCD 90 (Picea spp.) is for trees recorded only to genus, so this is a genus record. 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 M130 (table S19).

Source
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
90,spruce spp.,N,Picea,spp.,,,Picea spp.
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","90","M130","SUBARCTIC_REGIME_MOUNTAINS",2028,10.4501972386588,3.2,27.4
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
2,028
DBH range
8.13–69.6 cm
Method
NSVB modified Wiley model (Eq. 4), coefficients for SPCD 90 in DIVISION M130 from table S1a; fitted with weighted regression to destructively sampled trees
Where
FIA ecodivision Subarctic Regime Mountains (M130), mapped in GTR fig. 1
Last checked
2026-11-03
Calculate
Height from
0.609
Stem volume (m³)
Fitted DBH range00.511.522.5102030405060DBH (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 = 30.5, H = 21.30.6090.609Computed from the printed form
computed from the published form at D = 12 in, H = 70 ft, converted to cm, m and m3

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