# Cerrado sensu stricto wood + bark dry mass from D30 (quadratic, Fig. 5)

Aboveground biomass equation for Cerrado sensu stricto woody species (47 species), Brazil, from Vale et al. 2002. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Vale et al. 2002 (Figura 5, p. 124):

> y = 26,501 - 7,0631*x + 0,5169*x2

Cite: https://treeallometry.org/equations/vale-2002-agb-d30/#equation

In this library's units, ready to compute (aboveground biomass in kg):

```
Aboveground biomass = 26.501 - 7.0631 * D30 + 0.5169 * D30^2
```

Inputs: D30 = Stem diameter at 30 cm (cm).
The source's own form: 26.501 - 7.0631 * x + 0.5169 * x^2, with x in cm; output in kg.
Cite: https://treeallometry.org/equations/vale-2002-agb-d30/#canonical

## What it covers

- Output: Aboveground biomass, kg
- Taxon: Cerrado sensu stricto woody species (47 species) (mixed species); mixed
- Where: Fazenda Água Limpa, Universidade de Brasília, Distrito Federal. Cite: https://treeallometry.org/equations/vale-2002-agb-d30/#where
- Biomes: tropical
- Stand: natural
- R²: 0.92. Cite: https://treeallometry.org/equations/vale-2002-agb-d30/#r2
- Method: Quadratic regression y = b0 + b1x + b2x2 (SAEG); best of 12 equations tested. Cite: https://treeallometry.org/equations/vale-2002-agb-d30/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/vale-2002-agb-d30/#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

Vale, A.T., Fiedler, N.C., Silva, G.F. (2002). Avaliação energética da biomassa do cerrado em função do diâmetro das árvores. Ciência Florestal, 12(2), 115-126.

- DOI: https://doi.org/10.5902/198050981686
- Access: open access
- Copy we read: https://periodicos.ufsm.br/cienciaflorestal/article/download/1686/962
- Every equation from this source: https://treeallometry.org/sources/vale-2002/
- Cite: https://treeallometry.org/equations/vale-2002-agb-d30/#source

## The facts, in the source's words

**Equation** (Figura 5, p. 124):

> y = 26,501 - 7,0631*x + 0,5169*x2

Cite: https://treeallometry.org/equations/vale-2002-agb-d30/#equation

**R²** (Figura 5, p. 124):

> R2 = 0,92

Cite: https://treeallometry.org/equations/vale-2002-agb-d30/#quote-fit-r2

**input** (Resumo):

> em função do diâmetro a 30 cm de altura do solo

Cite: https://treeallometry.org/equations/vale-2002-agb-d30/#quote-input

**Output** (Figura 5, p. 124):

> Massa seca total (kg/árv.)

Cite: https://treeallometry.org/equations/vale-2002-agb-d30/#quote-output

**Our note:** x is the stem diameter at 30 cm above ground (D30), not DBH. Total = wood plus bark of trunk and branches; branches under 3 cm basal diameter were removed before weighing, and the paper does not say how foliage was treated, so no exclusion is declared. The paper states 3 trees per diameter class in seven classes but not a total n, so n_trees and the fitted diameter range are left out.

## 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 |
| --- | --- | --- | --- |
| D30 = 10 | 7.56 | 7.56 | Computed from the printed form: computed from the printed Figure 5 equation |
| D30 = 20 | 92 | 92 | Computed from the printed form: computed from the printed Figure 5 equation |

Cite: https://treeallometry.org/equations/vale-2002-agb-d30/#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: Vale, A.T., Fiedler, N.C., Silva, G.F. (2002). Avaliação energética da biomassa do cerrado em função do diâmetro das árvores. Ciência Florestal, 12(2), 115-126. https://doi.org/10.5902/198050981686

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Cerrado sensu stricto wood + bark dry mass from D30 (quadratic, Fig. 5)", checked 2026-11-02, https://treeallometry.org/equations/vale-2002-agb-d30/. 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/vale-2002-agb-d30.json
Report a problem: email info@restorationscope.com with the equation id (vale-2002-agb-d30) and where the right value appears.