# Pinus densiflora needle (crown fuel) biomass from DBH (Table 3)

Foliage biomass equation for Pinus densiflora, South Korea, from Song et al. 2026. 67 trees, DBH 5–35.1 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Song et al. 2026 (Eq. 1):

> ln(Wt) = a ln(DBH) + b

Cite: https://treeallometry.org/equations/song-2026-needles/#equation

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

```
Foliage biomass = exp(1.893 * ln(D) - 3.835) * 1.028
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: exp(1.893 * ln(DBH) - 3.835) * 1.028, with DBH in cm; output in kg.
Cite: https://treeallometry.org/equations/song-2026-needles/#canonical

## What it covers

- Output: Foliage biomass, kg
- Taxon: Pinus densiflora (species), family Pinaceae; conifer
- Where: Seven sites across South Korea (Daegu, Yangyang, Yeongju, Bonghwa, Goryeong, Mungyeong, Seosan). Cite: https://treeallometry.org/equations/song-2026-needles/#where
- Biomes: temperate
- Stand: natural
- Trees measured: 67. Cite: https://treeallometry.org/equations/song-2026-needles/#n_trees
- DBH range: 5–35.1 cm. Cite: https://treeallometry.org/equations/song-2026-needles/#dbh
- Height range: 4.5–19.6 m. Cite: https://treeallometry.org/equations/song-2026-needles/#height
- Correction factor: 1.028 (applied). Cite: https://treeallometry.org/equations/song-2026-needles/#cf
- Method: OLS regression of ln(W) on ln(DBH), back-transformed with a correction factor. Cite: https://treeallometry.org/equations/song-2026-needles/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/song-2026-needles/#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

Song, J., Jang, M., Lee, B., et al. (2026). Allometric Equations for Estimating Crown Fuel Biomass of Pinus densiflora in South Korea. Forests, 17(5), 549.

- DOI: https://doi.org/10.3390/f17050549
- Access: open access
- Copy we read: https://www.mdpi.com/1999-4907/17/5/549
- Every equation from this source: https://treeallometry.org/sources/song-2026/
- Cite: https://treeallometry.org/equations/song-2026-needles/#source

## The facts, in the source's words

**Equation** (Eq. 1):

> ln(Wt) = a ln(DBH) + b

Cite: https://treeallometry.org/equations/song-2026-needles/#equation

**Equation** (Eq. 4):

> Wt = exp(a ln(DBH) + b) × CF

Cite: https://treeallometry.org/equations/song-2026-needles/#quote-expression

**Equation** (Table 3 (n, a, b, R2adj, s.e.e., correction factor)):

> Needles 67 1.893 (0.070) −3.835 (0.200) 0.917 0.236 1.028

Cite: https://treeallometry.org/equations/song-2026-needles/#quote-expression-2

**Trees measured** (Section 2.2):

> A total of 67 sample trees were selected across the seven study areas

Cite: https://treeallometry.org/equations/song-2026-needles/#quote-fit-n-trees

**Largest DBH** (Section 2.2):

> The average DBH and tree height were 18.1 cm (range: 5.0–35.1 cm) and 11.1 m (range: 4.5–19.6 m)

Cite: https://treeallometry.org/equations/song-2026-needles/#quote-fit-dbh-max-cm

**Our note:** Needle dry mass (crown fuel), a foliage-only equation. Printed R2adj is 0.917. In Table 3 column 'a' is the ln(DBH) slope and 'b' the intercept, per Eq. 1. Correction factor 1.028 as printed (exp(s.e.e.^2/2)). Natural forests with a mix of managed and unmanaged stands. The paper also prints branch diameter-class equations (<0.5, 0.5-1, 1-2, 2-4, >4 cm) and a total crown fuel equation (needles + branches, no stem); those are not added because they are partial-branch or crown-only totals with no matching output quantity.

## 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 | 1.74 | 1.74 | Computed from the printed form: computed from the Table 3 coefficients and correction factor |
| D = 25 | 9.84 | 9.83 | Computed from the printed form: computed from the Table 3 coefficients and correction factor |

Cite: https://treeallometry.org/equations/song-2026-needles/#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: Song, J., Jang, M., Lee, B., et al. (2026). Allometric Equations for Estimating Crown Fuel Biomass of Pinus densiflora in South Korea. Forests, 17(5), 549. https://doi.org/10.3390/f17050549

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Pinus densiflora needle (crown fuel) biomass from DBH (Table 3)", checked 2026-11-02, https://treeallometry.org/equations/song-2026-needles/. 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/song-2026-needles.json
Report a problem: email info@restorationscope.com with the equation id (song-2026-needles) and where the right value appears.