# NSVB red maple, species-level: total aboveground biomass, modified Wiley model (Eq. 4)

Aboveground biomass equation (without leaves) for Acer rubrum, United States, from Westfall et al. 2024. 468 trees, DBH 2.54–85.6 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 2, p. 15):

> AGBPredicted = 0.31573027567 × 11.1^1.853839844372 × 38^0.740557378679 × exp(-(-0.024745684975 × 11.1)) = 532.584798820042

Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#equation

In this library's units, ready to compute (aboveground biomass, without leaves in kg):

```
Aboveground biomass, without leaves = 0.45359237 * 0.31573027567 * (D/2.54)^1.853839844372 * (H/0.3048)^0.740557378679 * exp(-(-0.024745684975 * (D/2.54)))
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 0.31573027567 * DBH^1.853839844372 * HT^0.740557378679 * exp(-(-0.024745684975 * DBH)), with DBH in in, HT in ft; output in lb.
Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#canonical

This total leaves out leaves (foliage), as the source defines it.

## What it covers

- Output: Aboveground biomass, without leaves, kg
- Taxon: Acer rubrum (species), family Sapindaceae; broadleaf
- Where: United States, species-level fit (NSVB uses it wherever table S8a has no row for the tree's ecodivision). Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#where
- Biomes: subtropical, temperate, montane
- Stand: not stated
- Trees measured: 468. Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#n_trees
- DBH range: 2.54–85.6 cm. Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#dbh
- Method: NSVB modified Wiley model (Eq. 4), coefficients for SPCD 316 species-level row (no DIVISION) from table S8a (the total aboveground biomass table used in Example 2); fitted with weighted regression to destructively sampled trees. Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#method
- Verification: read in the original source
- Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#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-acer-rubrum-agb/#source

## The facts, in the source's words

**Equation** (Example 2, p. 15):

> AGBPredicted = 0.31573027567 × 11.1^1.853839844372 × 38^0.740557378679 × exp(-(-0.024745684975 × 11.1)) = 532.584798820042

Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#equation

**Taxon** (Example 2, p. 12):

> Assume a red maple (Acer rubrum; SPCD = 316)

Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#quote-taxon

**check** (Example 2, p. 12):

> growing in the Warm Continental Mountains (DIVISION = M210)

Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#quote-check

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

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

Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#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-acer-rubrum-agb/#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-acer-rubrum-agb/#quote-published-output-unit

**output.excludes** (Methods, Model development, p. 4):

> total aboveground biomass (without foliage)

Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#quote-output-excludes

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

> "Total Tree Wood+Bark","TT_WDBK_DW_ADJ","316",468,6.57200854700855,1,33.7

Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#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-acer-rubrum-agb/#quote-fit-2

**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-acer-rubrum-agb/#quote-region

**Our note:** Output is gross AGB without foliage (AGBPredicted), before NSVB's cull and broken-top reductions. Species-level coefficients (no ecodivision): table S8a in the supplement has no red maple row for M210, the division of the tree in Example 2, so the example uses the species-level row; NSVB uses division-specific coefficients where table S8a has a row for the tree's division. These are the coefficients NSVB applies to red maple in the Warm Continental Mountains (M210). Paper units: in, ft, lb; expression converts D cm→in (/2.54), H m→ft (/0.3048) and lb→kg (×0.45359237). n and the DBH range are from the scorecard for TT_WDBK_DW_ADJ across ecodivisions (table S13). For AGB the scorecard rates NSVB's harmonized total (TT_WDBK_DW_ADJ), not this model alone; only its n and DBH range are used. 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 = 28.194, H = 11.5824 | 242 | 242 | Value printed in the paper: Example 2 (p. 15) prints 532.584798820042 lb for D = 11.1 in, H = 38 ft; inputs and expected converted to cm, m, kg |

Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/#checks

The calculator on the page shows carbon as biomass × 0.47 (IPCC 2006 Guidelines, Vol. 4, Ch. 4, Table 4.3) and CO₂e as carbon × 44/12.

## 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 red maple, species-level: total aboveground biomass, modified Wiley model (Eq. 4)", checked 2026-11-03, https://treeallometry.org/equations/westfall-2024-acer-rubrum-agb/. 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-acer-rubrum-agb.json
Report a problem: email info@restorationscope.com with the equation id (westfall-2024-acer-rubrum-agb) and where the right value appears.