# Longleaf pine above-stump biomass, model 9 (DBH + ln(H.DBH))

Aboveground biomass equation for Pinus palustris, United States, from Farias et al. 2019. 100 trees, DBH 0.81–54.3 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Farias et al. 2019 (Table 4):

> 9th: ln (W ) = − 1.7709 + 0.0544. ( DBH ) + 0.6273.ln ( H .DBH )

Cite: https://treeallometry.org/equations/farias-2019-m9/#equation

In this library's units, ready to compute (aboveground biomass in kg):

```
Aboveground biomass = exp(-1.7709 + 0.0544 * D + 0.6273 * ln(H * D))
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: exp(-1.7709 + 0.0544 * DBH + 0.6273 * ln(H * DBH)), with DBH in cm, H in m; output in kg.
Cite: https://treeallometry.org/equations/farias-2019-m9/#canonical

## What it covers

- Output: Aboveground biomass, kg
- Taxon: Pinus palustris (species), family Pinaceae; conifer
- Where: Fort Benning, Camp Lejeune and Polk County, southeastern United States. Cite: https://treeallometry.org/equations/farias-2019-m9/#where
- Biomes: temperate, subtropical
- Stand: mixed
- Trees measured: 100. Cite: https://treeallometry.org/equations/farias-2019-m9/#n_trees
- DBH range: 0.81–54.3 cm. Cite: https://treeallometry.org/equations/farias-2019-m9/#dbh
- Height range: 0.55–30.4 m. Cite: https://treeallometry.org/equations/farias-2019-m9/#height
- R²: 0.9784. Cite: https://treeallometry.org/equations/farias-2019-m9/#r2
- Residual SE: 0.3641. Cite: https://treeallometry.org/equations/farias-2019-m9/#rse
- Method: ordinary least squares on ln(W). Cite: https://treeallometry.org/equations/farias-2019-m9/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/farias-2019-m9/#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

Farias, A.A., Gezan, S.A., Carvalho, M.P., et al. (2019). Allometric Equations to Predict Pinus palustris Biomass in the Southeastern United States. Floresta e Ambiente, 26(Spec No 1), e20180403.

- DOI: https://doi.org/10.1590/2179-8087.040318
- Access: open access
- Copy we read: http://www.scielo.br/pdf/floram/v26nspe1/2179-8087-floram-26-spe01-e20180403.pdf
- Every equation from this source: https://treeallometry.org/sources/farias-2019/
- Cite: https://treeallometry.org/equations/farias-2019-m9/#source

## The facts, in the source's words

**Equation** (Table 4):

> 9th: ln (W ) = − 1.7709 + 0.0544. ( DBH ) + 0.6273.ln ( H .DBH )

Cite: https://treeallometry.org/equations/farias-2019-m9/#equation

**Trees measured** (Section 2):

> The dataset consisted of measures of 100 longleaf pine trees, obtained from three different sites

Cite: https://treeallometry.org/equations/farias-2019-m9/#quote-fit-n-trees

**Largest DBH** (Table 1 (mean, SD, min, max)):

> DBH cm 16.0 13.7 0.81 54.3

Cite: https://treeallometry.org/equations/farias-2019-m9/#quote-fit-dbh-max-cm

**h max m** (Table 1 (mean, SD, min, max)):

> H m 11.5 7.7 0.55 30.4

Cite: https://treeallometry.org/equations/farias-2019-m9/#quote-fit-h-max-m

**R²** (Table 2, model 9 (Sy.x, adjusted R2)):

> 9 0.3641 0.9784

Cite: https://treeallometry.org/equations/farias-2019-m9/#quote-fit-r2

**Our note:** W is total above-stump biomass (kg); the paper does not say which components are included. Natural log; no back-transformation correction factor is stated, so none is applied. r2 is the adjusted R2 and rse is Sy.x as printed in Table 2. ln(H.DBH) is read as ln of the product H x DBH. The paper also prints stand-level models (Eqs. 15 and 16, needing basal area, trees per hectare and quadratic diameter), which are not captured because those inputs are not canonical variables.

## 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, H = 8 | 4.58 | 4.58 | Computed from the printed form: hand-computed from the Table 4 coefficients |
| D = 30, H = 20 | 48.1 | 48.1 | Computed from the printed form: hand-computed from the Table 4 coefficients |

Cite: https://treeallometry.org/equations/farias-2019-m9/#checks

The calculator on the page shows carbon as biomass × 0.47 (IPCC 2006 Guidelines, Vol. 4, Ch. 4, Table 4.3) and CO₂e as carbon × 44/12.

## How to cite

Cite the source for the equation: Farias, A.A., Gezan, S.A., Carvalho, M.P., et al. (2019). Allometric Equations to Predict Pinus palustris Biomass in the Southeastern United States. Floresta e Ambiente, 26(Spec No 1), e20180403. https://doi.org/10.1590/2179-8087.040318

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Longleaf pine above-stump biomass, model 9 (DBH + ln(H.DBH))", checked 2026-11-02, https://treeallometry.org/equations/farias-2019-m9/. 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/farias-2019-m9.json
Report a problem: email info@restorationscope.com with the equation id (farias-2019-m9) and where the right value appears.