# Height from DBH, Quadratic model, both forests pooled

Height equation for Mixed Amazonian forest trees (367 species in terra-firme, 65 in várzea), Brazil, from Baia et al. 2025. 1,962 trees, DBH 1–139.5 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Baia et al. 2025 (Table 1 (form) and Table 2, Both forests block):

> H = exp(a + b × ln(DBH) + c × ln(DBH)²) + ε ; Table 2: Quadratic a 0.48064 0.092 4.937 0.75 11,838.5 | b 1.16793 0.059 | c −0.10905 0.009

Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#equation

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

```
Height = exp(0.48064 + 1.16793 * ln(D) - 0.10905 * ln(D)^2)
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: exp(0.48064 + 1.16793 * ln(DBH) - 0.10905 * ln(DBH)^2), with DBH in cm; output in m.
Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#canonical

## What it covers

- Output: Height, m
- Taxon: Mixed Amazonian forest trees (367 species in terra-firme, 65 in várzea) (mixed species); mixed
- Where: Terra-firme (NFA) and várzea (Mazagão) forests, Amapá, Brazil. Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#where
- Biomes: tropical
- Stand: natural
- Trees measured: 1,962. Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#n_trees
- DBH range: 1–139.5 cm. Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#dbh
- Height range: 1.2–51.9 m. Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#height
- R²: 0.75. Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#r2
- Method: nonlinear least squares height-diameter model; R2 is the adjusted pseudo R2. Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#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

Baia, A.L.P., Nascimento, H.E.M., Guedes, M., Hilário, R., Toledo, J.J. (2025). Tree height-diameter allometry and implications for biomass estimates in Northeastern Amazonian forests. PeerJ, 13, e18974.

- DOI: https://doi.org/10.7717/peerj.18974
- Access: open access
- Copy we read: https://europepmc.org/article/MED/40093411
- Every equation from this source: https://treeallometry.org/sources/baia-2025/
- Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#source

## The facts, in the source's words

**Equation** (Table 1 (form) and Table 2, Both forests block):

> H = exp(a + b × ln(DBH) + c × ln(DBH)²) + ε ; Table 2: Quadratic a 0.48064 0.092 4.937 0.75 11,838.5 | b 1.16793 0.059 | c −0.10905 0.009

Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#equation

**Trees measured** (Abstract):

> we measured the diameter and height of 1,962 trees in both forests

Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#quote-fit-n-trees

**Smallest DBH** (Results, first paragraph):

> In the terra-firme sites, trees ranged from 1 to 109.1 cm DBH and 1.2 to 51.9 m in total height. In várzea sites, trees ranged from 5 to 139.5 cm DBH and 2.3 to 38.8 m in total height.

Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#quote-fit-dbh-min-cm

**R²** (Table 2, Both forests block):

> Adj. pseudo R2 0.75

Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#quote-fit-r2

**Our note:** Predicts total tree height from DBH. The quadratic form is read as a + b ln(DBH) + c (ln DBH)^2 inside exp(); Table 1 prints ln(DBH) with a superscript 2, and ln(DBH^2) would not be separable from the b term. RSE printed in Table 2 is 4.937 (height scale, m), so fit.rse is not stored. Ranges are those of the trees sampled at the site(s); the pooled block uses the min and max of the two forests' printed ranges. No correction factor is applied; the paper reports local models deviate 0.1% from measured heights.

## 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 | 13.4 | 13.4 | Computed from the printed form: computed from the published form (coefficients as printed) |
| D = 30 | 24.3 | 24.3 | Computed from the printed form: computed from the published form (coefficients as printed) |
| D = 60 | 31 | 31 | Computed from the printed form: computed from the published form (coefficients as printed) |

Cite: https://treeallometry.org/equations/baia-2025-both-quadratic/#checks

## How to cite

Cite the source for the equation: Baia, A.L.P., Nascimento, H.E.M., Guedes, M., Hilário, R., Toledo, J.J. (2025). Tree height-diameter allometry and implications for biomass estimates in Northeastern Amazonian forests. PeerJ, 13, e18974. https://doi.org/10.7717/peerj.18974

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Height from DBH, Quadratic model, both forests pooled", checked 2026-11-02, https://treeallometry.org/equations/baia-2025-both-quadratic/. 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/baia-2025-both-quadratic.json
Report a problem: email info@restorationscope.com with the equation id (baia-2025-both-quadratic) and where the right value appears.