# Nothofagus antarctica inside-bark merchantable stem volume (to 15 cm top) from D and H (Schumacher-Hall, Cuadro 4)

Stem volume equation for Nothofagus antarctica, Argentina, from Lencinas et al. 2002. 251 trees, DBH 7.5–61 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Lencinas et al. 2002 (Ecuación (2), Modelo 2 (estándar tradicional, Schumacher-Hall)):

> V = (a / 10.000) · DAP^b · HT^c  (2)

Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#equation

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

```
Stem volume = 0.20379745 / 10000 * D^2.32092575 * H^0.71495048
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 0.20379745 / 10000 * DAP^2.32092575 * HT^0.71495048, with DAP in cm, HT in m; output in m3.
Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#canonical

## What it covers

- Output: Stem volume, m³
- Taxon: Nothofagus antarctica (species), family Nothofagaceae; broadleaf
- Where: Central Isla Grande de Tierra del Fuego, Argentina (15 sites). Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#where
- Biomes: temperate
- Stand: natural
- Trees measured: 251. Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#n_trees
- DBH range: 7.5–61 cm. Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#dbh
- Height range: 3.5–15 m. Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#height
- R²: 0.93. Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#r2
- Method: nonlinear regression. Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#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

Lencinas, M. V., Martínez Pastur, G., Cellini, J. M., Vukasovic, R., Peri, P., & Fernández, M. C. (2002). Incorporación de la altura dominante y la clase de sitio a ecuaciones estándar de volumen para Nothofagus antarctica (Forster f.) Oersted. Bosque, 23(2), 5-17.

- DOI: https://doi.org/10.4067/s0717-92002002000200002
- Access: open access
- Copy we read: https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0717-92002002000200002
- Every equation from this source: https://treeallometry.org/sources/lencinas-2002/
- Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#source

## The facts, in the source's words

**Equation** (Ecuación (2), Modelo 2 (estándar tradicional, Schumacher-Hall)):

> V = (a / 10.000) · DAP^b · HT^c  (2)

Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#equation

**Equation** (Cuadro 4):

> VFSC = volumen de fuste sin corteza (m3); Modelo 2: a = 0,20379745, b = 2,32092575, c = 0,71495048

Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#quote-expression

**Trees measured** (Resumen):

> Se utilizaron 251 árboles de Nothofagus antarctica a lo largo de Tierra del Fuego (Argentina) (DAP entre 7,5-61,0 cm y HT entre 3,5-15,0 m).

Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#quote-fit-n-trees

**R²** (Cuadro 4, Modelo 2):

> r2 0,93

Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#quote-fit-r2

**Our note:** Cuadro 4 and the formulas are images on SciELO; coefficients transcribed from them. V in m3, DAP in cm, HT total height in m. Coefficient a is divided by 10.000 in the printed formula. VFSC is the merchantable stem volume inside bark to a 15 cm minimum top diameter (Métodos: 'el fuste sin corteza de extracción hasta un diámetro mínimo de 15 cm'), not the whole stem. The paper also prints Models 3 and 5 (site class CS or stand dominant height HD) and per-stand local models; those need predictors outside the canonical variables and are not included.

## 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 = 8 | 0.0484 | 0.0484 | Computed from the printed form: computed from the published form (coefficients as printed; a divided by 10.000) |
| D = 30, H = 12 | 0.323 | 0.323 | Computed from the printed form: computed from the published form (coefficients as printed; a divided by 10.000) |
| D = 50, H = 14 | 1.18 | 1.18 | Computed from the printed form: computed from the published form (coefficients as printed; a divided by 10.000) |

Cite: https://treeallometry.org/equations/lencinas-2002-vfsc-sh/#checks

## How to cite

Cite the source for the equation: Lencinas, M. V., Martínez Pastur, G., Cellini, J. M., Vukasovic, R., Peri, P., & Fernández, M. C. (2002). Incorporación de la altura dominante y la clase de sitio a ecuaciones estándar de volumen para Nothofagus antarctica (Forster f.) Oersted. Bosque, 23(2), 5-17. https://doi.org/10.4067/s0717-92002002000200002

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Nothofagus antarctica inside-bark merchantable stem volume (to 15 cm top) from D and H (Schumacher-Hall, Cuadro 4)", checked 2026-11-02, https://treeallometry.org/equations/lencinas-2002-vfsc-sh/. 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/lencinas-2002-vfsc-sh.json
Report a problem: email info@restorationscope.com with the equation id (lencinas-2002-vfsc-sh) and where the right value appears.