Tree Allometrics

Acer rubrum / Stem volume

NSVB red maple, species-level: total stem wood volume (inside bark), Schumacher-Hall model (Eq. 1)

Stem volumeAcer rubrum · SapindaceaeUnited StatesRead from the original paper
Photo of Acer rubrum
mefisher · CC0 · iNaturalist
Equation

As printed (Example 2, p. 12)

VtotibGross = 0.001983918881 × 11.1^1.810559393287 × 38^1.129417635145 = 9.427112777611

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

Stem volume = 0.028316846592 * 0.001983918881 * (D/2.54)^1.810559393287 * (H/0.3048)^1.129417635145
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. Species-level coefficients (no ecodivision): Example 2 says table S1a has no red maple row for its division (M210), so the species-level row applies. NSVB uses division-specific coefficients where table S1a has a row for the tree's division. 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 across ecodivisions (table S13). DBH is measured at 4.5 ft (1.37 m).

Source
Assume a red maple (Acer rubrum; SPCD = 316)
Taxon · Example 2, p. 12
If a species occurs in an ecodivision not explicitly listed, the entry having no ecodivision noted is used.
Where · Results, p. 6
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","316",3068,9.40677966101695,1,41.8
Fit · Table S13_component_spcd_scorecard.csv (WO-GTR-104-Supp1), columns VAR2,VAR3,SPCD,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
3,068
DBH range
2.54–106.17 cm
Method
NSVB Schumacher-Hall model (Eq. 1), coefficients for SPCD 316, species-level row (no DIVISION) from table S1a (the total stem wood volume (inside bark) table used in Example 2); fitted with weighted regression to destructively sampled trees
Where
United States: red maple's species-level stem volume fit across ecodivisions, which NSVB uses wherever table S1a has no row for the tree's ecodivision
Last checked
2026-11-03
Calculate
Height from
0.267
Stem volume (m³)
Fitted DBH range00.20.40.60.811020304050DBH (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 = 28.2, H = 11.60.2670.267Value printed in the paper
Example 2 (p. 12) prints 9.427112777611 ft3 for D = 11.1 in, H = 38 ft; inputs and expected converted to cm, m, m3

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