# Merchantable stem volume from DBH and height (Model 6, Table 7)

Stem volume equation for Pterocarpus angolensis, Namibia, Angola, from De Cauwer et al. 2020. 340 trees, DBH 5–92 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in De Cauwer et al. 2020 (Table 7, Model 6):

> Vmer = exp(a + b 1 *(lnDBH)2 + b 2 *(lnDBH)3+ b 3 *lnH) ... -7.821 *** 0.599 *** -0.064 *** 0.800 ***

Cite: https://treeallometry.org/equations/de-cauwer-2020-vmer-d-h/#equation

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

```
Stem volume = exp(-7.821 + 0.599 * ln(D)^2 - 0.064 * ln(D)^3 + 0.800 * ln(H))
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: exp(-7.821 + 0.599 * ln(DBH)^2 - 0.064 * ln(DBH)^3 + 0.800 * ln(H)), with DBH in cm, H in m; output in m3.
Cite: https://treeallometry.org/equations/de-cauwer-2020-vmer-d-h/#canonical

## What it covers

- Output: Stem volume, m³
- Taxon: Pterocarpus angolensis (species), family Fabaceae; broadleaf
- Where: Baikiaea-Pterocarpus woodlands of northern Namibia and southern Angola (MAP 480-700 mm). Cite: https://treeallometry.org/equations/de-cauwer-2020-vmer-d-h/#where
- Biomes: tropical, dryland
- Stand: natural
- Trees measured: 340. Cite: https://treeallometry.org/equations/de-cauwer-2020-vmer-d-h/#n_trees
- DBH range: 5–92 cm. Cite: https://treeallometry.org/equations/de-cauwer-2020-vmer-d-h/#dbh
- R²: 0.95. Cite: https://treeallometry.org/equations/de-cauwer-2020-vmer-d-h/#r2
- Method: Regression on ln scale with Baskerville correction in intercept; adjusted R2. Cite: https://treeallometry.org/equations/de-cauwer-2020-vmer-d-h/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/de-cauwer-2020-vmer-d-h/#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

De Cauwer, V., Beeckman, H., Kleinn, C., Moses, M., Nott, A., Seifert, T., Muys, B. (2020). Improving the knowledge base for tropical dry forest management in southern Africa: Regional volume models for Pterocarpus angolensis. Forest Ecology and Management, 477, 118485.

- DOI: https://doi.org/10.1016/j.foreco.2020.118485
- Access: open access
- Copy we read: https://lirias.kuleuven.be/retrieve/00adf4e9-cc77-4da0-88bc-0454a2f00a1c
- Every equation from this source: https://treeallometry.org/sources/de-cauwer-2020/
- Cite: https://treeallometry.org/equations/de-cauwer-2020-vmer-d-h/#source

## The facts, in the source's words

**Equation** (Table 7, Model 6):

> Vmer = exp(a + b 1 *(lnDBH)2 + b 2 *(lnDBH)3+ b 3 *lnH) ... -7.821 *** 0.599 *** -0.064 *** 0.800 ***

Cite: https://treeallometry.org/equations/de-cauwer-2020-vmer-d-h/#equation

**Trees measured** (Table 7 caption):

> Data of 340 trees were used for Model 6 and 356 trees for all other models. DBH range is between 5 and 92 cm.

Cite: https://treeallometry.org/equations/de-cauwer-2020-vmer-d-h/#quote-fit-n-trees

**Our note:** Merchantable (saw wood) over-bark volume of the bole, excluding the stump; the bole is the stem up to the first branch, so mapped to stem_volume. Table 7 caption: intercept a includes the Baskerville correction factor, so nothing is added (no CF value printed). Quadratic and cubic terms of ln(DBH) as printed. Paper's RSE is on the volume scale (m3), so fit.rse is left out; R2 is the printed adjusted R2.

## 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 = 20, H = 8 | 0.0819 | 0.0819 | Computed from the printed form: hand-computed from the published form |
| D = 50, H = 14 | 0.688 | 0.688 | Computed from the printed form: hand-computed from the published form |

Cite: https://treeallometry.org/equations/de-cauwer-2020-vmer-d-h/#checks

## How to cite

Cite the source for the equation: De Cauwer, V., Beeckman, H., Kleinn, C., Moses, M., Nott, A., Seifert, T., Muys, B. (2020). Improving the knowledge base for tropical dry forest management in southern Africa: Regional volume models for Pterocarpus angolensis. Forest Ecology and Management, 477, 118485. https://doi.org/10.1016/j.foreco.2020.118485

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Merchantable stem volume from DBH and height (Model 6, Table 7)", checked 2026-11-02, https://treeallometry.org/equations/de-cauwer-2020-vmer-d-h/. 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/de-cauwer-2020-vmer-d-h.json
Report a problem: email info@restorationscope.com with the equation id (de-cauwer-2020-vmer-d-h) and where the right value appears.