# Cerrado s.s. MG, Stem volume without bark, Schumacher-Hall log, regions 2 and 3 pooled

Stem volume equation for Cerrado sensu stricto tree species (mixed), Brazil, from Rufini et al. 2010. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Rufini et al. 2010 (Table 2, combination 23):

> Ln(VFsc) = -10,0185310695 + 1,595186012 * Ln(Dap) + 1,256733019 * Ln(H)

Cite: https://treeallometry.org/equations/rufini-2010-sh-r23-fvol-nobark/#equation

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

```
Stem volume = exp(-10.0185310695 + 1.595186012 * ln(D) + 1.256733019 * ln(H))
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: exp(-10.0185310695 + 1.595186012 * ln(Dap) + 1.256733019 * ln(H)), with Dap in cm, H in m; output in m3.
Cite: https://treeallometry.org/equations/rufini-2010-sh-r23-fvol-nobark/#canonical

## What it covers

- Output: Stem volume, m³
- Taxon: Cerrado sensu stricto tree species (mixed) (mixed species); mixed
- Where: Minas Gerais, Sao Francisco river basin, SF 5, 6, 10 and SF 7, 8, 9 sub-basins (regions 2 and 3 pooled). Cite: https://treeallometry.org/equations/rufini-2010-sh-r23-fvol-nobark/#where
- Biomes: tropical, dryland
- Stand: natural
- R²: 0.9681. Cite: https://treeallometry.org/equations/rufini-2010-sh-r23-fvol-nobark/#r2
- Method: log-transformed linear regression (Schumacher-Hall log) on pooled Huber rigorous cubing data, regions 2 and 3 (identity test accepted). Cite: https://treeallometry.org/equations/rufini-2010-sh-r23-fvol-nobark/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/rufini-2010-sh-r23-fvol-nobark/#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

Rufini, A.L., Scolforo, J.R.S., Oliveira, A.D. de, Mello, J.M. de (2010). Equações volumétricas para o cerrado sensu stricto, em Minas Gerais. CERNE, 16(1), 1-11.

- DOI: https://doi.org/10.1590/s0104-77602010000100001
- Access: open access
- Copy we read: https://www.scielo.br/j/cerne/a/n7hz4jCWRWRnMgBGSCpD8Vp/?lang=pt&format=pdf
- Every equation from this source: https://treeallometry.org/sources/rufini-2010/
- Cite: https://treeallometry.org/equations/rufini-2010-sh-r23-fvol-nobark/#source

## The facts, in the source's words

**Equation** (Table 2, combination 23):

> Ln(VFsc) = -10,0185310695 + 1,595186012 * Ln(Dap) + 1,256733019 * Ln(H)

Cite: https://treeallometry.org/equations/rufini-2010-sh-r23-fvol-nobark/#equation

**R²** (Table 2, combination 23):

> 96,81 (R2 %)

Cite: https://treeallometry.org/equations/rufini-2010-sh-r23-fvol-nobark/#quote-fit-r2

**Our note:** Pooled fit for regions 2 and 3 after the Graybill identity test found them similar. n for the pooled fit is not printed and is left out. Dap, H and volume units are not spelled out beside the model; read as Dap in cm, H in m, volume in m3 (consistent magnitudes). No back-transformation correction factor is stated, so none is applied. R2 printed as a percentage.

## 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 = 5, H = 3 | 0.00231 | 0.00231 | Computed from the printed form: hand-computed from the published form (coefficients as printed) |
| D = 10, H = 5 | 0.0133 | 0.0133 | Computed from the printed form: hand-computed from the published form (coefficients as printed) |
| D = 20, H = 8 | 0.0723 | 0.0723 | Computed from the printed form: hand-computed from the published form (coefficients as printed) |

Cite: https://treeallometry.org/equations/rufini-2010-sh-r23-fvol-nobark/#checks

## How to cite

Cite the source for the equation: Rufini, A.L., Scolforo, J.R.S., Oliveira, A.D. de, Mello, J.M. de (2010). Equações volumétricas para o cerrado sensu stricto, em Minas Gerais. CERNE, 16(1), 1-11. https://doi.org/10.1590/s0104-77602010000100001

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Cerrado s.s. MG, Stem volume without bark, Schumacher-Hall log, regions 2 and 3 pooled", checked 2026-11-02, https://treeallometry.org/equations/rufini-2010-sh-r23-fvol-nobark/. 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/rufini-2010-sh-r23-fvol-nobark.json
Report a problem: email info@restorationscope.com with the equation id (rufini-2010-sh-r23-fvol-nobark) and where the right value appears.