# South America Weibull height–diameter model

Height equation for Tropical forest trees (permanent plots), South America (Amazonia and Guiana Shield plots), from Feldpausch et al. 2012. 19,262 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 Feldpausch et al. 2012 (Eq. 5, p. 3387):

> H = a(1 − exp(−bD^c))

Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-south-america/#equation

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

```
Height = 42.574 * (1 - exp(-0.0482 * D^0.8307))
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: 42.574 * (1 - exp(-0.0482 * D^0.8307)), with D in cm; output in m.
Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-south-america/#canonical

## What it covers

- Output: Height, m
- Taxon: Tropical forest trees (permanent plots) (mixed species); mixed
- Where: South America (Amazonia and Guiana Shield plots). Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-south-america/#where
- Biomes: tropical
- Stand: natural
- Trees measured: 19,262. Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-south-america/#n_trees
- DBH range: from 10 cm. Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-south-america/#dbh
- Method: nonlinear Weibull H:D fit. Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-south-america/#method
- Verification: read in the original source
- Last checked: 2026-11-01. Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-south-america/#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

Feldpausch, T. R., Lloyd, J., Lewis, S. L., et al. (2012). Tree height integrated into pantropical forest biomass estimates. Biogeosciences, 9, 3381–3403.

- DOI: https://doi.org/10.5194/bg-9-3381-2012
- Access: open access
- Copy we read: https://bg.copernicus.org/articles/9/3381/2012/bg-9-3381-2012.pdf
- Every equation from this source: https://treeallometry.org/sources/feldpausch-2012/
- Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-south-america/#source

## The facts, in the source's words

**Equation** (Eq. 5, p. 3387):

> H = a(1 − exp(−bD^c))

Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-south-america/#equation

**Units** (Table 3 caption, p. 3393):

> Coefficients for Weibull-H region-, continent-specific and pantropical models (H = a(1−exp(−bD^c))) to estimate tree height (H, m) from diameter (D, cm) ≥ 10 cm in pantropical forests

Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-south-america/#quote-published-units

**Trees measured** (Table 3 (columns a, b, c, RSE, AIC, n), p. 3393):

> S. America 42.574 0.0482 0.8307 5.619 121 167 19 262

Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-south-america/#quote-fit-n-trees

**Our note:** Weibull height–diameter model; RSE 5.619 m (on the height scale, not log scale, so not stored in fit.rse). Fitted on concurrent H and D measurements in permanent plots, trees ≥ 10 cm D; the paper gives no maximum D for this fit. Table 3 footnote: models adapted from the pantropical H:D database of Feldpausch et al. (2011).

## 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 = 30 | 23.7 | 23.7 | Computed from the printed form: computed with python3 from the published form |
| D = 80 | 35.8 | 35.8 | Computed from the printed form: computed with python3 from the published form |

Cite: https://treeallometry.org/equations/feldpausch-2012-weibull-south-america/#checks

## How to cite

Cite the source for the equation: Feldpausch, T. R., Lloyd, J., Lewis, S. L., et al. (2012). Tree height integrated into pantropical forest biomass estimates. Biogeosciences, 9, 3381–3403. https://doi.org/10.5194/bg-9-3381-2012

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "South America Weibull height–diameter model", checked 2026-11-01, https://treeallometry.org/equations/feldpausch-2012-weibull-south-america/. 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/feldpausch-2012-weibull-south-america.json
Report a problem: email info@restorationscope.com with the equation id (feldpausch-2012-weibull-south-america) and where the right value appears.