# Canadian national equation, jack pine, dbh only (sum of wood, bark, branches, foliage; Table 3)

Aboveground biomass equation for Pinus banksiana, Canada, from Lambert et al. 2005. 364 trees, DBH 1.7–41 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Lambert et al. 2005 (Eq. 2):

> y wood = β wood1 D^βwood2 + ewood … y bark = β bark1 D^βbark2 + e bark … y foliage = β foliage1 D^βfoliage2 … y branches = β branches1 D^βbranches2

Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#equation

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

```
Aboveground biomass = 0.0804 * D^2.4041 + 0.0184 * D^2.0703 + 0.0079 * D^2.4155 + 0.0389 * D^1.729
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: 0.0804 * dbh^2.4041 + 0.0184 * dbh^2.0703 + 0.0079 * dbh^2.4155 + 0.0389 * dbh^1.729, with dbh in cm; output in kg.
Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#canonical

## What it covers

- Output: Aboveground biomass, kg
- Taxon: Pinus banksiana (species), family Pinaceae; conifer
- Where: Canada (ENFOR archival data, early 1980s). Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#where
- Biomes: boreal
- Stand: natural
- Trees measured: 364. Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#n_trees
- DBH range: 1.7–41 cm. Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#dbh
- R²: 0.94. Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#r2
- Method: Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total. Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#method
- Verification: read in the original source
- Last checked: 2026-11-01. Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#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

Lambert, M.-C., Ung, C.-H., Raulier, F. (2005). Canadian national tree aboveground biomass equations. Canadian Journal of Forest Research, 35(8), 1996–2018.

- DOI: https://doi.org/10.1139/x05-112
- Access: paywalled
- Copy we read: https://www.esf.edu/quest/documents/Lambertetal.2005.Canadatreebiomass.pdf
- Every equation from this source: https://treeallometry.org/sources/lambert-2005/
- Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#source

## The facts, in the source's words

**Equation** (Eq. 2):

> y wood = β wood1 D^βwood2 + ewood … y bark = β bark1 D^βbark2 + e bark … y foliage = β foliage1 D^βfoliage2 … y branches = β branches1 D^βbranches2

Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#equation

**Equation** (Table 3, Jack pine (rows transcribed)):

> bwood1 0.0804 bwood2 2.4041 bbark1 0.0184 bbark2 2.0703 bbranches1 0.0079 bbranches2 2.4155 bfoliage1 0.0389 bfoliage2 1.729

Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#quote-expression

**Equation** (Table 3):

> Jack pine bwood1 0.0804 0.0042

Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#quote-expression-2

**Trees measured** (Table 2 (No. of trees; dbh range in parentheses)):

> Jack pine 364

Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#quote-fit-n-trees

**R²** (Table 5, dbh-based set (σ̂ii, AdjRSq, RMSE in kg)):

> Jack pine Total 0.0227 0.94 37.5

Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#quote-fit-r2

**Our note:** Total aboveground biomass = wood + bark + branches + foliage, each a power function of dbh (cm), kg dry mass; the total is the sum of the four compartment equations (additivity by construction). r2 is the adjusted R² of the total. The paper also gives dbh+height equations (Table 4). Ung et al. (2008) later revised parameters for some species with BC data; not used here.

## 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 = 20 | 135 | 135 | Computed from the printed form: computed from the published form at dbh = 20 cm |

Cite: https://treeallometry.org/equations/lambert-2005-jack-pine/#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: Lambert, M.-C., Ung, C.-H., Raulier, F. (2005). Canadian national tree aboveground biomass equations. Canadian Journal of Forest Research, 35(8), 1996–2018. https://doi.org/10.1139/x05-112

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Canadian national equation, jack pine, dbh only (sum of wood, bark, branches, foliage; Table 3)", checked 2026-11-01, https://treeallometry.org/equations/lambert-2005-jack-pine/. 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/lambert-2005-jack-pine.json
Report a problem: email info@restorationscope.com with the equation id (lambert-2005-jack-pine) and where the right value appears.