# Commercial stem volume from DBH, Husch log model (MV1)

Stem volume equation for 20 commercial tree species of a managed forest (DBH >= 50 cm), Brazil, from Romero et al. 2020. 223 trees, DBH 50.4–149.9 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Romero et al. 2020 (Table 1, MV1 (Husch 1963; logarithmic)):

> ln(V) = β0 + β1 ln(d) + ε

Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#equation

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

```
Stem volume = exp(-6.5125) * D^1.88558 * 1.0527
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: exp(-6.5125) * d^1.88558 * 1.0527, with d in cm; output in m3.
Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#canonical

## What it covers

- Output: Stem volume, m³
- Taxon: 20 commercial tree species of a managed forest (DBH >= 50 cm) (mixed species); broadleaf
- Where: Fazenda Antimari I and II, Porto Acre, Acre. Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#where
- Biomes: tropical
- Stand: natural
- Trees measured: 223. Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#n_trees
- DBH range: 50.4–149.9 cm. Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#dbh
- R²: 0.67. Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#r2
- Correction factor: 1.0527 (applied). Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#cf
- Method: Linear regression on ln(V) vs ln(d), back-transformed with correction factor. Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#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

Romero, F. M. B., Jacovine, L. A. G., Ribeiro, S. C., Torres, C. M. M. E., Silva, L. F. da, Gaspar, R. de O., et al. (2020). Allometric Equations for Volume, Biomass, and Carbon in Commercial Stems Harvested in a Managed Forest in the Southwestern Amazon: A Case Study. Forests, 11(8), 874.

- DOI: https://doi.org/10.3390/f11080874
- Access: open access
- Copy we read: https://www.mdpi.com/1999-4907/11/8/874/htm
- Every equation from this source: https://treeallometry.org/sources/romero-2020/
- Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#source

## The facts, in the source's words

**Equation** (Table 1, MV1 (Husch 1963; logarithmic)):

> ln(V) = β0 + β1 ln(d) + ε

Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#equation

**R²** (Table 3 (β0, β1, RMSE, R2, AIC, MAD, CF)):

> MV1 −6.51250 * 1.88558 * 2.318 0.67 1011.70 1.621 1.0527

Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#quote-fit-r2

**Smallest DBH** (Table 2 (n, DBH range and mean, wood density range and mean)):

> Total 223 50.4–149.9 79.6 ± 19.8 0.27–0.89 0.56 ± 0.16

Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#quote-fit-dbh-min-cm

**Our note:** Commercial stem volume over bark (Smalian) in m3. Coefficients and CF as printed; the CF multiplies the back-transformed estimate. R2 is on the log scale. Applies to commercial stems only (stump at 30 cm, buttresses removed, crown left in the forest) of trees with DBH >= 50 cm; do not use for whole-tree totals. The authors selected the equations with commercial stem length l as the best ones; these are the ones that use only canonical variables.

## 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 = 60 | 3.52 | 3.52 | Computed from the printed form: computed from the published form |
| D = 100 | 9.23 | 9.23 | Computed from the printed form: computed from the published form |

Cite: https://treeallometry.org/equations/romero-2020-mv1-husch-log/#checks

## How to cite

Cite the source for the equation: Romero, F. M. B., Jacovine, L. A. G., Ribeiro, S. C., Torres, C. M. M. E., Silva, L. F. da, Gaspar, R. de O., et al. (2020). Allometric Equations for Volume, Biomass, and Carbon in Commercial Stems Harvested in a Managed Forest in the Southwestern Amazon: A Case Study. Forests, 11(8), 874. https://doi.org/10.3390/f11080874

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Commercial stem volume from DBH, Husch log model (MV1)", checked 2026-11-02, https://treeallometry.org/equations/romero-2020-mv1-husch-log/. 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/romero-2020-mv1-husch-log.json
Report a problem: email info@restorationscope.com with the equation id (romero-2020-mv1-husch-log) and where the right value appears.