# NSVB spruce spp., species-level (all ecodivisions): total stem wood volume (inside bark), modified Wiley model (Eq. 4)

Stem volume equation for Picea, United States, from Westfall et al. 2024. 5,910 trees, DBH 4.06–101.85 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 (Table S1a (Table S1a_volib_coefs_spcd.csv, WO-GTR-104-Supp1), columns SPCD,DIVISION,STDORGCD,model,a,a1,b,b1,c,c1):

> 90,,,4,0.001359241,,1.876480245,0.009562428,1.207913332,

Cite: https://treeallometry.org/equations/westfall-2024-picea-spp-volume/#equation

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

```
Stem volume = 0.028316846592 * 0.001359241 * (D/2.54)^1.876480245 * (H/0.3048)^1.207913332 * exp(-(0.009562428 * (D/2.54)))
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 0.001359241 * DBH^1.876480245 * HT^1.207913332 * exp(-(0.009562428 * DBH)), with DBH in in, HT in ft; output in ft3.
Cite: https://treeallometry.org/equations/westfall-2024-picea-spp-volume/#canonical

## What it covers

- Output: Stem volume, m³
- Taxon: Picea (genus), 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-picea-spp-volume/#where
- Biomes: temperate, boreal, montane, dryland
- Stand: not stated
- Trees measured: 5,910. Cite: https://treeallometry.org/equations/westfall-2024-picea-spp-volume/#n_trees
- DBH range: 4.06–101.85 cm. Cite: https://treeallometry.org/equations/westfall-2024-picea-spp-volume/#dbh
- Method: NSVB modified Wiley model (Eq. 4), coefficients for SPCD 90 (species-level row, no DIVISION) from table S1a; fitted with weighted regression to destructively sampled trees. Cite: https://treeallometry.org/equations/westfall-2024-picea-spp-volume/#method
- Verification: read in the original source
- Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/westfall-2024-picea-spp-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-picea-spp-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):

> 90,,,4,0.001359241,,1.876480245,0.009562428,1.207913332,

Cite: https://treeallometry.org/equations/westfall-2024-picea-spp-volume/#equation

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

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

Cite: https://treeallometry.org/equations/westfall-2024-picea-spp-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-picea-spp-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-picea-spp-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):

> 90,spruce spp.,N,Picea,spp.,,,Picea spp.

Cite: https://treeallometry.org/equations/westfall-2024-picea-spp-volume/#quote-taxon

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

> total stem was defined as groundline to tree tip

Cite: https://treeallometry.org/equations/westfall-2024-picea-spp-volume/#quote-output

**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-picea-spp-volume/#quote-region

**Fit** (Table S13_component_spcd_scorecard.csv (WO-GTR-104-Supp1), columns VAR2,VAR3,SPCD,N,Avg_DBH,Min_DBH,Max_DBH):

> "Total Stem Wood Volume","ST_WD_CV_TOT","90",5910,11.9095939086294,1.6,40.1

Cite: https://treeallometry.org/equations/westfall-2024-picea-spp-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-picea-spp-volume/#quote-fit-2

**Our note:** 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 across ecodivisions (table S13). Species-level row: NSVB applies it in every ecodivision that has no row of its own for this species in this table.

## 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 | 0.616 | 0.616 | 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-picea-spp-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 spruce spp., 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-picea-spp-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-picea-spp-volume.json
Report a problem: email info@restorationscope.com with the equation id (westfall-2024-picea-spp-volume) and where the right value appears.