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

Stem volume equation for Quercus alba, United States, from Westfall et al. 2024. 705 trees, DBH 2.54–106.68 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Westfall et al. 2024 (Example 4, p. 21):

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

Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#equation

In this library's units, ready to compute (stem volume in m³):

```
Stem volume = 0.028316846592 * 0.002062931814 * (D/2.54)^1.852527628718 * (H/0.3048)^1.09312644716
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 0.002062931814 * DBH^1.852527628718 * HT^1.09312644716, with DBH in in, HT in ft; output in ft3.
Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#canonical

## What it covers

- Output: Stem volume, m³
- Taxon: Quercus alba (species), family Fagaceae; broadleaf
- Where: FIA ecodivision M220, Hot Continental Mountains (mapped in GTR fig. 1). Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#where
- Biomes: temperate, montane
- Stand: not stated
- Trees measured: 705. Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#n_trees
- DBH range: 2.54–106.68 cm. Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#dbh
- 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. Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#method
- Verification: read in the original source
- Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#checked_at

A missing fit statistic is one the source doesn't state, or that we haven't recorded; it is never estimated. Outside the stated DBH range or region, the equation is an extrapolation.

## 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: https://doi.org/10.2737/WO-GTR-104
- Access: open access
- Copy we read: https://research.fs.usda.gov/download/treesearch/66998.pdf
- Every equation from this source: https://treeallometry.org/sources/westfall-2024/
- Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#source

## The facts, in the source's words

**Equation** (Example 4, p. 21):

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

Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#equation

**Taxon** (Example 4, p. 21):

> a live white oak (Quercus alba; SPCD = 802) tree having D = 18.1 inches, H = 65 feet

Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#quote-taxon

**Where** (Example 4, p. 21):

> growing in the Hot Continental Mountains (DIVISION = M220)

Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#quote-region

**Equation** (Eq. 1, p. 2):

> yi = a × Di^b × Hi^c + εi

Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#quote-expression

**Units** (Methods, Model development, p. 2):

> Di is diameter (inches) at breast height (4.5 feet), Hi is total tree height (feet)

Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#quote-published-units

**published.output unit** (Examples of tree-level calculations, p. 8):

> units for volume and biomass predictions are cubic feet and pounds, respectively

Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#quote-published-output-unit

**Output** (Methods, Data, p. 2):

> total stem was defined as groundline to tree tip

Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#quote-output

**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):

> "Total Stem Wood Volume","ST_WD_CV_TOT","802","M220","HOT_CONTINENTAL_REGIME_MOUNTAINS",705,12.2829787234043,1,42

Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#quote-fit

**Fit** (Methods, Model development, p. 6):

> key modeling statistics such as sample sizes (n), tree diameter distributions (minimum, mean, and maximum)

Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#quote-fit-2

**Our note:** 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).

## Checks this equation passes

On every build, the library's form and the source's own form (in its units) must both give these values within 1%.

| Inputs | Expected | We get | From |
| --- | --- | --- | --- |
| D = 45.974, H = 19.812 | 1.2 | 1.2 | Value 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 |

Cite: https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/#checks

## How to cite

Cite the source for the equation: 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. https://doi.org/10.2737/WO-GTR-104

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "NSVB white oak, Hot Continental Mountains (M220): total stem wood volume (inside bark), Schumacher-Hall model (Eq. 1)", checked 2026-11-03, https://treeallometry.org/equations/westfall-2024-quercus-alba-m220-volume/. Data CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Quotes are the authors' words.

Data for this equation: https://treeallometry.org/data/equations/westfall-2024-quercus-alba-m220-volume.json
Report a problem: email info@restorationscope.com with the equation id (westfall-2024-quercus-alba-m220-volume) and where the right value appears.