# NSVB slash pine (planted stands), species-level (all ecodivisions): total stem wood volume (inside bark), modified Wiley model (Eq. 4)

Stem volume equation for Pinus elliottii, United States, from Westfall et al. 2024. 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 (Table S1a (Table S1a_volib_coefs_spcd.csv, WO-GTR-104-Supp1), columns SPCD,DIVISION,STDORGCD,model,a,a1,b,b1,c,c1):

> 111,,1,4,0.001776285,,1.98252695,-0.009785143,1.022562887,

Cite: https://treeallometry.org/equations/westfall-2024-pinus-elliottii-planted-volume/#equation

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

```
Stem volume = 0.028316846592 * 0.001776285 * (D/2.54)^1.98252695 * (H/0.3048)^1.022562887 * exp(-(-0.009785143 * (D/2.54)))
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 0.001776285 * DBH^1.98252695 * HT^1.022562887 * exp(-(-0.009785143 * DBH)), with DBH in in, HT in ft; output in ft3.
Cite: https://treeallometry.org/equations/westfall-2024-pinus-elliottii-planted-volume/#canonical

## What it covers

- Output: Stem volume, m³
- Taxon: Pinus elliottii (species), family Pinaceae; conifer
- Where: United States, species-level fit (NSVB uses it wherever table S1a has no row for the tree's ecodivision). Cite: https://treeallometry.org/equations/westfall-2024-pinus-elliottii-planted-volume/#where
- Biomes: tropical, subtropical
- Stand: plantation
- Method: NSVB modified Wiley model (Eq. 4), coefficients for SPCD 111 (species-level row, no DIVISION), STDORGCD 1 from table S1a; fitted with weighted regression to destructively sampled trees. Cite: https://treeallometry.org/equations/westfall-2024-pinus-elliottii-planted-volume/#method
- Verification: read in the original source
- Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/westfall-2024-pinus-elliottii-planted-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-pinus-elliottii-planted-volume/#source

## The facts, in the source's words

**Equation** (Table S1a (Table S1a_volib_coefs_spcd.csv, WO-GTR-104-Supp1), columns SPCD,DIVISION,STDORGCD,model,a,a1,b,b1,c,c1):

> 111,,1,4,0.001776285,,1.98252695,-0.009785143,1.022562887,

Cite: https://treeallometry.org/equations/westfall-2024-pinus-elliottii-planted-volume/#equation

**Equation** (Eq. 4, p. 2):

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

Cite: https://treeallometry.org/equations/westfall-2024-pinus-elliottii-planted-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-pinus-elliottii-planted-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-pinus-elliottii-planted-volume/#quote-published-output-unit

**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):

> 111,slash pine,N,Pinus,elliottii,,,Pinus elliottii

Cite: https://treeallometry.org/equations/westfall-2024-pinus-elliottii-planted-volume/#quote-taxon

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

> total stem was defined as groundline to tree tip

Cite: https://treeallometry.org/equations/westfall-2024-pinus-elliottii-planted-volume/#quote-output

**stand** (Methods, Model development, p. 3):

> stand origins for planted (stand origin code (STDORGCD) = 1) and natural (STDORGCD = 0) stands may be fitted separately

Cite: https://treeallometry.org/equations/westfall-2024-pinus-elliottii-planted-volume/#quote-stand

**Where** (Results, p. 6):

> If a species occurs in an ecodivision not explicitly listed, the entry having no ecodivision noted is used.

Cite: https://treeallometry.org/equations/westfall-2024-pinus-elliottii-planted-volume/#quote-region

**Our note:** 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). The scorecards don't split loblolly and slash pine by stand origin, so n and DBH range are left out. Species-level row: NSVB applies it in every ecodivision that has no row of its own for this species in this table. Table S1a also lists these exact coefficients under DIVISION 230; this record stands for that row too.

## 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 = 30.48, H = 21.336 | 0.601 | 0.601 | Computed from the printed form: computed from the published form at D = 12 in, H = 70 ft, converted to cm, m and m3 |

Cite: https://treeallometry.org/equations/westfall-2024-pinus-elliottii-planted-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 slash pine (planted stands), species-level (all ecodivisions): total stem wood volume (inside bark), modified Wiley model (Eq. 4)", checked 2026-11-03, https://treeallometry.org/equations/westfall-2024-pinus-elliottii-planted-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-pinus-elliottii-planted-volume.json
Report a problem: email info@restorationscope.com with the equation id (westfall-2024-pinus-elliottii-planted-volume) and where the right value appears.