# Radiata pine total AGB, log model Eq. 4 (ln D, (ln D)^2)

Aboveground biomass equation for Pinus radiata, New Zealand, from Moore 2010. 637 trees, DBH 0.7–80.6 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Moore 2010 (Section 2.2, Eq. 4):

> ln AGB = β0 + β1 ln D + β2 (ln D)2 (4)

Cite: https://treeallometry.org/equations/moore-2010-eq4/#equation

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

```
Aboveground biomass = exp(-0.5816 + 1.1240 * ln(D) + 0.2030 * ln(D)^2) * 1.113593
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: exp(-0.5816 + 1.1240 * ln(D) + 0.2030 * ln(D)^2) * 1.0273 * 1.084, with D in cm; output in kg.
Cite: https://treeallometry.org/equations/moore-2010-eq4/#canonical

## What it covers

- Output: Aboveground biomass, kg
- Taxon: Pinus radiata (species), family Pinaceae; conifer
- Where: New Zealand (13 studies, mainly North Island). Cite: https://treeallometry.org/equations/moore-2010-eq4/#where
- Biomes: temperate
- Stand: plantation
- Trees measured: 637. Cite: https://treeallometry.org/equations/moore-2010-eq4/#n_trees
- DBH range: 0.7–80.6 cm. Cite: https://treeallometry.org/equations/moore-2010-eq4/#dbh
- Height range: up to 42.1 m. Cite: https://treeallometry.org/equations/moore-2010-eq4/#height
- R²: 0.95. Cite: https://treeallometry.org/equations/moore-2010-eq4/#r2
- Residual SE: 0.2332. Cite: https://treeallometry.org/equations/moore-2010-eq4/#rse
- Correction factor: 1.113593 (applied). Cite: https://treeallometry.org/equations/moore-2010-eq4/#cf
- Method: linear mixed-effects model on ln-transformed data, back-transformed with modified smearing estimate cf1 x cf2. Cite: https://treeallometry.org/equations/moore-2010-eq4/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/moore-2010-eq4/#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

Moore, J. R. (2010). Allometric equations to predict the total above-ground biomass of radiata pine trees. Annals of Forest Science, 67(8), 806.

- DOI: https://doi.org/10.1051/forest/2010042
- Access: open access
- Copy we read: https://hal.science/hal-00883629
- Every equation from this source: https://treeallometry.org/sources/moore-2010/
- Cite: https://treeallometry.org/equations/moore-2010-eq4/#source

## The facts, in the source's words

**Equation** (Section 2.2, Eq. 4):

> ln AGB = β0 + β1 ln D + β2 (ln D)2 (4)

Cite: https://treeallometry.org/equations/moore-2010-eq4/#equation

**Equation** (Table II, row Eq. 4 (parameter estimates)):

> –0.5816 | 1.1240 | 0.2030

Cite: https://treeallometry.org/equations/moore-2010-eq4/#quote-expression

**Correction factor** (Table III, row Eq. 4 (cf1 | cf2)):

> 1.0273 | 1.0840

Cite: https://treeallometry.org/equations/moore-2010-eq4/#quote-fit-cf

**Trees measured** (Section 2.1):

> biomass measurements for 637 individual radiata pine trees from 13 different studies

Cite: https://treeallometry.org/equations/moore-2010-eq4/#quote-fit-n-trees

**R²** (Table II, R2 column, Eq. 4):

> 0.95

Cite: https://treeallometry.org/equations/moore-2010-eq4/#quote-fit-r2

**Our note:** D in cm, H in m, AGB in kg, natural log (the paper defines ln as natural). Back-transformed with the modified smearing estimate exp(Xb) cf1 cf2 (Eq. 11); cf1 and cf2 are as printed in Table III and applied as their product. Fit ranges are the pooled data (Table I overall; the text says height from 1.47 m while Table I says 0.32 m, so no h_min given). rse is the RMSE column for the log models. In Eq. 9 the text labels the quadratic coefficient β3 but Table II lists it in the third parameter column.

## 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 | 24.3 | 24.3 | Computed from the printed form: hand-computed from the published form |
| D = 25 | 190 | 190 | Computed from the printed form: hand-computed from the published form |
| D = 50 | 1,130 | 1,130 | Computed from the printed form: hand-computed from the published form |

Cite: https://treeallometry.org/equations/moore-2010-eq4/#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: Moore, J. R. (2010). Allometric equations to predict the total above-ground biomass of radiata pine trees. Annals of Forest Science, 67(8), 806. https://doi.org/10.1051/forest/2010042

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Radiata pine total AGB, log model Eq. 4 (ln D, (ln D)^2)", checked 2026-11-02, https://treeallometry.org/equations/moore-2010-eq4/. 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/moore-2010-eq4.json
Report a problem: email info@restorationscope.com with the equation id (moore-2010-eq4) and where the right value appears.