# Height from DBH, Michaelis-Menten (Table 3, best fit)

Height equation for Mixed tree species of ombrophilous/seasonal forest ecotone (65 fallen trees), Brazil, from Barbosa et al. 2019. 65 trees, DBH from 10 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Barbosa et al. 2019 (Table 3):

> Michaelis-Menten Y = β0 × X / β1 + X 45.8528 32.8330 - 3.347 0.7149 157.09

Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#equation

In this library's units, ready to compute (height in m):

```
Height = 45.8528 * D / (32.833 + D)
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: 45.8528 * X / (32.833 + X), with X in cm; output in m.
Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#canonical

## What it covers

- Output: Height, m
- Taxon: Mixed tree species of ombrophilous/seasonal forest ecotone (65 fallen trees) (mixed species); mixed
- Where: Maracá Ecological Station (PPBio grid), Roraima, northern Brazilian Amazonia. Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#where
- Biomes: tropical
- Stand: natural
- Trees measured: 65. Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#n_trees
- DBH range: from 10 cm. Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#dbh
- Height range: 11.7–37.7 m. Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#height
- R²: 0.7149. Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#r2
- Method: Nonlinear/linear regression (CurveExpert/R) on 65 directly measured fallen trees; r2 is the adjusted R² printed in Table 3; Syx = 3.347 m. Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#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

Barbosa, R.I., Ramírez-Narváez, P.N., Fearnside, P.M., Villacorta, C.D.A., Carvalho, L.C. da S. (2019). Allometric models to estimate tree height in northern Amazonian ecotone forests. Acta Amazonica, 49(2), 81-90.

- DOI: https://doi.org/10.1590/1809-4392201801642
- Access: open access
- Copy we read: https://www.scielo.br/j/aa/a/Csx7XwJFd3whWsjNzDSSQpw/?lang=en
- Every equation from this source: https://treeallometry.org/sources/barbosa-2019/
- Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#source

## The facts, in the source's words

**Equation** (Table 3):

> Michaelis-Menten Y = β0 × X / β1 + X 45.8528 32.8330 - 3.347 0.7149 157.09

Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#equation

**Trees measured** (Material and Methods, Sampling design):

> A total of 65 individual trees were sampled

Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#quote-fit-n-trees

**Smallest DBH** (Material and Methods, Sampling design):

> with stem diameter ≥10 cm

Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#quote-fit-dbh-min-cm

**h min m** (Results, paragraph on Figure 3):

> (mean ± CI 0.05 = 24.1 ± 1.5 m; range = 11.7 - 37.7 m)

Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#quote-fit-h-min-m

**R²** (Table 3 column header):

> R² adj

Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#quote-fit-r2

**Our note:** Best model by the authors' ranking (lowest Syx, highest adjusted R²). Y = β0·X/(β1+X), with the printed layout a fraction. Stem diameter was measured at 1.30 m, or 0.5 m above buttresses, on recently fallen trees (live or dead). The paper reports no maximum DBH in the text (see Table S1), so dbh_max is left out. Table 3 ranks five models; this is one of the four with fully legible coefficients (the Modified Hoerl row, with b1 = 0.000035, was not used).

## 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 | 17.4 | 17.4 | Computed from the printed form: hand-computed from the published coefficients in Table 3 |
| D = 40 | 25.2 | 25.2 | Computed from the printed form: hand-computed from the published coefficients in Table 3 |
| D = 70 | 31.2 | 31.2 | Computed from the printed form: hand-computed from the published coefficients in Table 3 |

Cite: https://treeallometry.org/equations/barbosa-2019-michaelis-menten/#checks

## How to cite

Cite the source for the equation: Barbosa, R.I., Ramírez-Narváez, P.N., Fearnside, P.M., Villacorta, C.D.A., Carvalho, L.C. da S. (2019). Allometric models to estimate tree height in northern Amazonian ecotone forests. Acta Amazonica, 49(2), 81-90. https://doi.org/10.1590/1809-4392201801642

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Height from DBH, Michaelis-Menten (Table 3, best fit)", checked 2026-11-02, https://treeallometry.org/equations/barbosa-2019-michaelis-menten/. 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/barbosa-2019-michaelis-menten.json
Report a problem: email info@restorationscope.com with the equation id (barbosa-2019-michaelis-menten) and where the right value appears.