# Cerrado total volume with bark from DBH and height, Goal Programming (model 1)

Total volume equation for Cerrado sensu stricto and campo cerrado woody species (99 species), Brazil, from Morais et al. 2014. 696 trees. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Morais et al. 2014 (Eq. 1, p. 232):

> Ln (Yi) = B0+ B1Ln(X1i) + B2Ln(X2i) ± Ln (Ɛi)

Cite: https://treeallometry.org/equations/morais-2014-vol-m1-gp/#equation

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

```
Total volume = exp(-9.79192 + 2.44091 * ln(D) + 0.46566 * ln(H))
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: exp(-9.79192 + 2.44091 * ln(DBH) + 0.46566 * ln(Ht)), with DBH in cm, Ht in m; output in m3.
Cite: https://treeallometry.org/equations/morais-2014-vol-m1-gp/#canonical

## What it covers

- Output: Total volume, m³
- Taxon: Cerrado sensu stricto and campo cerrado woody species (99 species) (mixed species); mixed
- Where: 20 forest fragments, Minas Gerais (Inventário Florestal de Minas Gerais). Cite: https://treeallometry.org/equations/morais-2014-vol-m1-gp/#where
- Biomes: tropical
- Stand: natural
- Trees measured: 696. Cite: https://treeallometry.org/equations/morais-2014-vol-m1-gp/#n_trees
- Method: Goal Programming (lpsolve simplex) on ln-transformed Schumacher-Hall model. Cite: https://treeallometry.org/equations/morais-2014-vol-m1-gp/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/morais-2014-vol-m1-gp/#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

Morais, V.A., Mello, J.M., Gomide, L.R., et al. (2014). Influence of diameter measuring height on the adjustment of volume and biomass equations of cerrado in Minas Gerais. Ciência e Agrotecnologia, 38(3), 230-239.

- DOI: https://doi.org/10.1590/s1413-70542014000300002
- Access: open access
- Copy we read: https://www.scielo.br/j/cagro/a/GmNTJwsTrNFjgqbmyTQp8MM/?lang=en&format=pdf
- Every equation from this source: https://treeallometry.org/sources/morais-2014/
- Cite: https://treeallometry.org/equations/morais-2014-vol-m1-gp/#source

## The facts, in the source's words

**Equation** (Eq. 1, p. 232):

> Ln (Yi) = B0+ B1Ln(X1i) + B2Ln(X2i) ± Ln (Ɛi)

Cite: https://treeallometry.org/equations/morais-2014-vol-m1-gp/#equation

**Equation** (Table 2, p. 234):

> Total volume with bark, model 1, GP: β0 -9.79192; β1 2.44091; β2 0.46566

Cite: https://treeallometry.org/equations/morais-2014-vol-m1-gp/#quote-expression

**input** (Table 1, p. 232):

> DBH (1.30 meters from the soil)

Cite: https://treeallometry.org/equations/morais-2014-vol-m1-gp/#quote-input

**Trees measured** (Methods, p. 233):

> adjustment data used for model adjustment [696 trees]

Cite: https://treeallometry.org/equations/morais-2014-vol-m1-gp/#quote-fit-n-trees

**Our note:** Natural-log model as printed; the paper states no back-transformation correction factor, so none is applied. Volume is total volume with bark. Ht is total height. R² is the adjusted R² from the OLS rows (the paper leaves it blank for GP). The 868 trees were split into 696 for fitting and 172 for validation.

## 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 = 10, H = 5 | 0.0326 | 0.0326 | Computed from the printed form: computed from the Table 2 coefficients |
| D = 20, H = 8 | 0.221 | 0.221 | Computed from the printed form: computed from the Table 2 coefficients |

Cite: https://treeallometry.org/equations/morais-2014-vol-m1-gp/#checks

## How to cite

Cite the source for the equation: Morais, V.A., Mello, J.M., Gomide, L.R., et al. (2014). Influence of diameter measuring height on the adjustment of volume and biomass equations of cerrado in Minas Gerais. Ciência e Agrotecnologia, 38(3), 230-239. https://doi.org/10.1590/s1413-70542014000300002

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Cerrado total volume with bark from DBH and height, Goal Programming (model 1)", checked 2026-11-02, https://treeallometry.org/equations/morais-2014-vol-m1-gp/. 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/morais-2014-vol-m1-gp.json
Report a problem: email info@restorationscope.com with the equation id (morais-2014-vol-m1-gp) and where the right value appears.