Tree Allometrics

Quercus alba / Stem volume

NSVB white oak, Hot Continental Mountains (M220): total stem wood volume (inside bark), Schumacher-Hall model (Eq. 1)

Stem volumeQuercus alba · FagaceaeUnited StatesRead from the original paper
Photo of Quercus alba
© Douglas Goldman · CC BY-SA · iNaturalist
Equation

As printed (Example 4, p. 21)

VtotibGross = 0.002062931814 × 18.1^1.852527628718 × 65^1.09312644716 = 42.277832913225

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

Stem volume = 0.028316846592 * 0.002062931814 * (D/2.54)^1.852527628718 * (H/0.3048)^1.09312644716
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 white oak in the Hot Continental Mountains (M220) only; other ecodivisions use other coefficients. 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 M220 (table S19). DBH is measured at 4.5 ft (1.37 m).

Source
a live white oak (Quercus alba; SPCD = 802) tree having D = 18.1 inches, H = 65 feet
Taxon · Example 4, p. 21
growing in the Hot Continental Mountains (DIVISION = M220)
Where · Example 4, p. 21
yi = a × Di^b × Hi^c + εi
Equation · Eq. 1, 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","802","M220","HOT_CONTINENTAL_REGIME_MOUNTAINS",705,12.2829787234043,1,42
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
705
DBH range
2.54–106.68 cm
Method
NSVB Schumacher-Hall model (Eq. 1), coefficients for SPCD 802 in DIVISION M220 from table S1a (the total stem wood volume (inside bark) table used in Example 4); fitted with weighted regression to destructively sampled trees
Where
FIA ecodivision M220, Hot Continental Mountains (mapped in GTR fig. 1)
Last checked
2026-11-03
Calculate
Height from
1.2
Stem volume (m³)
Fitted DBH range01234520406080DBH (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 = 46, H = 19.81.21.2Value printed in the paper
Example 4 (p. 21) prints 42.277832913225 ft3 for D = 18.1 in, H = 65 ft; inputs and expected converted to cm, m, m3

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