# NSVB yellow-poplar, Hot Continental Regime Mountains (M220): total aboveground biomass (without foliage), modified Wiley model (Eq. 4)

Aboveground biomass equation (without leaves) for Liriodendron tulipifera, United States, from Westfall et al. 2024. 59 trees, DBH 2.79–56.9 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 S8a (Table S8a_total_biomass_coefs_spcd.csv, WO-GTR-104-Supp1), columns SPCD,DIVISION,STDORGCD,model,a,a1,b,b1,c,c1):

> 621,M220,,4,0.154317349,,2.568115687,0.011588086,0.543413156,

Cite: https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-agb/#equation

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

```
Aboveground biomass, without leaves = 0.45359237 * 0.154317349 * (D/2.54)^2.568115687 * (H/0.3048)^0.543413156 * exp(-(0.011588086 * (D/2.54)))
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 0.154317349 * DBH^2.568115687 * HT^0.543413156 * exp(-(0.011588086 * DBH)), with DBH in in, HT in ft; output in lb.
Cite: https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-agb/#canonical

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

## What it covers

- Output: Aboveground biomass, without leaves, kg
- Taxon: Liriodendron tulipifera (species), family Magnoliaceae; broadleaf
- Where: FIA ecodivision Hot Continental Regime Mountains (M220), mapped in GTR fig. 1. Cite: https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-agb/#where
- Biomes: temperate, montane
- Stand: not stated
- Trees measured: 59. Cite: https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-agb/#n_trees
- DBH range: 2.79–56.9 cm. Cite: https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-agb/#dbh
- Method: NSVB modified Wiley model (Eq. 4), coefficients for SPCD 621 in DIVISION M220 from table S8a; fitted with weighted regression to destructively sampled trees. Cite: https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-agb/#method
- Verification: read in the original source
- Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-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-liriodendron-tulipifera-m220-agb/#source

## The facts, in the source's words

**Equation** (Table S8a (Table S8a_total_biomass_coefs_spcd.csv, WO-GTR-104-Supp1), columns SPCD,DIVISION,STDORGCD,model,a,a1,b,b1,c,c1):

> 621,M220,,4,0.154317349,,2.568115687,0.011588086,0.543413156,

Cite: https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-agb/#equation

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

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

Cite: https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-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-liriodendron-tulipifera-m220-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-liriodendron-tulipifera-m220-agb/#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):

> 621,yellow-poplar,N,Liriodendron,tulipifera,,,Liriodendron tulipifera

Cite: https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-agb/#quote-taxon

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

> total aboveground biomass (without foliage)

Cite: https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-agb/#quote-output-excludes

**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 Tree Wood+Bark","TT_WDBK_DW_ADJ","621","M220","HOT_CONTINENTAL_REGIME_MOUNTAINS",59,10.1898305084746,1.1,22.4

Cite: https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-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-liriodendron-tulipifera-m220-agb/#quote-fit-2

**Our note:** Output is gross AGB without foliage (AGBPredicted), before NSVB's cull and broken-top reductions and harmonization with components. DBH is measured at 4.5 ft (1.37 m). 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 in M220 (table S19). 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.

## 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 | 362 | 362 | Computed from the printed form: computed from the published form at D = 12 in, H = 70 ft, converted to cm, m and kg |

Cite: https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-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 yellow-poplar, Hot Continental Regime Mountains (M220): total aboveground biomass (without foliage), modified Wiley model (Eq. 4)", checked 2026-11-03, https://treeallometry.org/equations/westfall-2024-liriodendron-tulipifera-m220-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-liriodendron-tulipifera-m220-agb.json
Report a problem: email info@restorationscope.com with the equation id (westfall-2024-liriodendron-tulipifera-m220-agb) and where the right value appears.