# Pantropical height–diameter model with stress index E (Eq. 6a)

Height equation for Tropical trees (58 sites), Pantropical, from Chave et al. 2014. DBH 5–212 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Chave et al. 2014 (Eq. 6a, p. 3183):

> ln(H) = 0.893 − E + 0.760 ln(D) − 0.0340[ln(D)]²

Cite: https://treeallometry.org/equations/chave-2014-eq6a/#equation

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

```
Height = exp(0.893 - E + 0.760 * ln(D) - 0.0340 * (ln(D))^2)
```

Inputs: E = Environmental stress index (Chave et al. 2014); D = Diameter at breast height (1.3 m) (cm).
The source's own form: exp(0.893 - E + 0.760 * ln(D) - 0.0340 * (ln(D))^2), with D in cm, E in unitless; output in m.
Cite: https://treeallometry.org/equations/chave-2014-eq6a/#canonical

## What it covers

- Output: Height, m
- Taxon: Tropical trees (58 sites) (mixed species); broadleaf
- Where: 58 harvest sites across the tropics. Cite: https://treeallometry.org/equations/chave-2014-eq6a/#where
- Biomes: tropical, subtropical, dryland
- Stand: natural
- DBH range: 5–212 cm. Cite: https://treeallometry.org/equations/chave-2014-eq6a/#dbh
- Residual SE: 0.243. Cite: https://treeallometry.org/equations/chave-2014-eq6a/#rse
- Method: linear regression of ln(H) on E, ln(D) and ln(D)². Cite: https://treeallometry.org/equations/chave-2014-eq6a/#method
- Verification: read in the original source
- Last checked: 2026-11-01. Cite: https://treeallometry.org/equations/chave-2014-eq6a/#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

Chave, J., Réjou-Méchain, M., Búrquez, A., et al. (2014). Improved allometric models to estimate the aboveground biomass of tropical trees. Global Change Biology, 20(10), 3177–3190.

- DOI: https://doi.org/10.1111/gcb.12629
- Access: paywalled
- Copy we read: https://forestgeo.si.edu/sites/default/files/aboveground_biomass_protocol_accessible.pdf
- Every equation from this source: https://treeallometry.org/sources/chave-2014/
- Cite: https://treeallometry.org/equations/chave-2014-eq6a/#source

## The facts, in the source's words

**Equation** (Eq. 6a, p. 3183):

> ln(H) = 0.893 − E + 0.760 ln(D) − 0.0340[ln(D)]²

Cite: https://treeallometry.org/equations/chave-2014-eq6a/#equation

**Residual standard error** (Eq. 6a, p. 3183):

> (AIC = 47, RSE = 0.243, df = 3998)

Cite: https://treeallometry.org/equations/chave-2014-eq6a/#quote-fit-rse

**Note** (Eq. 6b, p. 3183):

> E = (0.178 × TS − 0.938 × CWD − 6.61 × PS) × 10⁻³

Cite: https://treeallometry.org/equations/chave-2014-eq6a/#quote-notes

**Largest DBH** (Introduction, p. 3178):

> for a total of 4004 trees with trunk diameter ranging from 5 to 212 cm

Cite: https://treeallometry.org/equations/chave-2014-eq6a/#quote-fit-dbh-max-cm

**Our note:** E is the bioclimatic stress index of Eq. 6b (TS temperature seasonality, CWD climatic water deficit, PS precipitation seasonality); a global gridded E layer is published by the authors. The paper prints the model on the log scale and gives no back-transform correction for H; expression is the plain exp() of Eq. 6a. Fitted on the harvest dataset (df = 3998); the paper does not state n separately for this fit.

## 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, E = 0 | 21.9 | 21.9 | Computed from the printed form: computed with python3 from the published form |
| D = 30, E = 0.5 | 13.3 | 13.3 | Computed from the printed form: computed with python3 from the published form |

Cite: https://treeallometry.org/equations/chave-2014-eq6a/#checks

## How to cite

Cite the source for the equation: Chave, J., Réjou-Méchain, M., Búrquez, A., et al. (2014). Improved allometric models to estimate the aboveground biomass of tropical trees. Global Change Biology, 20(10), 3177–3190. https://doi.org/10.1111/gcb.12629

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Pantropical height–diameter model with stress index E (Eq. 6a)", checked 2026-11-01, https://treeallometry.org/equations/chave-2014-eq6a/. 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/chave-2014-eq6a.json
Report a problem: email info@restorationscope.com with the equation id (chave-2014-eq6a) and where the right value appears.