# All three forest types, Rio de Janeiro (local-generic), DBH and height (Schumacher and Hall, Model 3)

Aboveground biomass equation (without leaves) for Mixed Atlantic Forest trees (rainforest, semideciduous, restinga), Brazil, from Gaui et al. 2024. 172 trees. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Gaui et al. 2024 (Table 2 (model forms in Table 1)):

> Model 3 (Schumacher and Hall) General: B0 2 × 10−4, B1 1.519, B2 0.8251

Cite: https://treeallometry.org/equations/gaui-2024-general-model3/#equation

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

```
Aboveground biomass, without leaves = 1000 * 0.0002 * D^1.519 * H^0.8251
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 0.0002 * DBH^1.519 * Ht^0.8251, with DBH in cm, Ht in m; output in Mg.
Cite: https://treeallometry.org/equations/gaui-2024-general-model3/#canonical

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

## What it covers

- Output: Aboveground biomass, without leaves, kg
- Taxon: Mixed Atlantic Forest trees (rainforest, semideciduous, restinga) (mixed species); broadleaf
- Where: Rio de Janeiro state, Atlantic Forest Domain. Cite: https://treeallometry.org/equations/gaui-2024-general-model3/#where
- Biomes: tropical, subtropical
- Stand: natural
- Trees measured: 172. Cite: https://treeallometry.org/equations/gaui-2024-general-model3/#n_trees
- R²: 0.92. Cite: https://treeallometry.org/equations/gaui-2024-general-model3/#r2
- Method: non-linear regression, generalised least squares with varPower variance. Cite: https://treeallometry.org/equations/gaui-2024-general-model3/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/gaui-2024-general-model3/#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

Gaui, T. D., Cysneiros, V. C., de Souza, F. C., et al. (2024). Biomass Equations and Carbon Stock Estimates for the Southeastern Brazilian Atlantic Forest. Forests, 15(9), 1568.

- DOI: https://doi.org/10.3390/f15091568
- Access: open access
- Copy we read: https://www.mdpi.com/1999-4907/15/9/1568/htm
- Every equation from this source: https://treeallometry.org/sources/gaui-2024/
- Cite: https://treeallometry.org/equations/gaui-2024-general-model3/#source

## The facts, in the source's words

**Equation** (Table 2 (model forms in Table 1)):

> Model 3 (Schumacher and Hall) General: B0 2 × 10−4, B1 1.519, B2 0.8251

Cite: https://treeallometry.org/equations/gaui-2024-general-model3/#equation

**Trees measured** (Section 2.3):

> 172 trees

Cite: https://treeallometry.org/equations/gaui-2024-general-model3/#quote-fit-n-trees

**Our note:** Table 2 gives coefficients only; the model forms are from Table 1 (Husch y = B0 d^B1; Spurr y = B0 + B1 (d2 h); Schumacher and Hall y = B0 d^B1 h^B2), fitted by non-linear GLS with a varPower variance function. Output unit Mg is from the Figure 2 caption (AGB, Mg); the table itself does not state it, and 1000 x converts to kg. AGB was built from non-destructively measured wood volume (stem and branches) times basic wood density, so foliage is excluded. Coefficients are rounded as printed. Fit r2 is the printed Ryy (correlation of real and estimated values). DBH range of the 172 sample trees not stated. Authors judged Model 3 best for this data set.

## 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 = 15, H = 12 | 95 | 95 | Computed from the printed form: hand-computed from the published form (Mg x 1000 = kg) |
| D = 40, H = 22 | 695.3 | 695.3 | Computed from the printed form: hand-computed from the published form (Mg x 1000 = kg) |

Cite: https://treeallometry.org/equations/gaui-2024-general-model3/#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: Gaui, T. D., Cysneiros, V. C., de Souza, F. C., et al. (2024). Biomass Equations and Carbon Stock Estimates for the Southeastern Brazilian Atlantic Forest. Forests, 15(9), 1568. https://doi.org/10.3390/f15091568

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "All three forest types, Rio de Janeiro (local-generic), DBH and height (Schumacher and Hall, Model 3)", checked 2026-11-02, https://treeallometry.org/equations/gaui-2024-general-model3/. 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/gaui-2024-general-model3.json
Report a problem: email info@restorationscope.com with the equation id (gaui-2024-general-model3) and where the right value appears.