# Canadian national equation, lodgepole pine, dbh and height (branches; Table 4)

Branch biomass equation for Pinus contorta var. latifolia, Canada, from Lambert et al. 2005. 201 trees, DBH 2.5–39 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. 3):

> y branches = β branches1D βbranches2Hβbranches3 + e branches

Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#equation

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

```
Branch biomass = 0.044 * D^3.719 * H^(-2.0399)
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 0.044 * dbh^3.719 * H^(-2.0399), with dbh in cm, H in m; output in kg.
Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#canonical

## What it covers

- Output: Branch biomass, kg
- Taxon: Pinus contorta var. latifolia (species), family Pinaceae; conifer
- Where: Alberta and Yukon, Canada (ENFOR archival data, early 1980s). Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#where
- Biomes: boreal
- Stand: not stated
- Trees measured: 201. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#n_trees
- DBH range: 2.5–39 cm. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#dbh
- Height range: 2.5–25.9 m. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#height
- R²: 0.68. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#r2
- Method: Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#method
- Verification: read in the original source
- Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#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-lodgepole-pine-dbh-h-branches/#source

## The facts, in the source's words

**Equation** (Eq. 3):

> y branches = β branches1D βbranches2Hβbranches3 + e branches

Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#equation

**Equation** (Table 4, Lodgepole pine):

> bbranches1 0.0440

Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#quote-expression

**Equation** (Table 4, Lodgepole pine):

> bbranches2 3.7190

Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#quote-expression-2

**Equation** (Table 4, Lodgepole pine):

> bbranches3 –2.0399

Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#quote-expression-3

**Trees measured** (Table 2 (No. of trees)):

> Lodgepole pine         201     15.0±0.6     12.7±0.4      99.0±8.8

Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#quote-fit-n-trees

**Smallest DBH** (Table 2, Lodgepole pine (ranges of dbh, height, total biomass)):

> (2.5;39.0)   (2.5;25.9)    (0.8;694.4)

Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#quote-fit-dbh-min-cm

**R²** (Table 5, Lodgepole pine (AdjRSq in the dbh- and height-based set, second block)):

> Branches 0.0004 0.55 9.5 3.99 0.0006 0.68 8.0 3.60

Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#quote-fit-r2

**Taxon** (Appendix B, Table B1):

> Lodgepole pine Pin lodgepole Pinus contorta var. latifolia Engelm.

Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#quote-taxon

**Our note:** All branches, cut at the stem base (live branches; dead branches excluded). r2 is the adjusted R² (AdjRSq) of this compartment in Table 5. Fitted on the original scale (weighted nonlinear seemingly unrelated regression), so there is no back-transform correction. Dead branches, cones and fruits are not part of aboveground biomass in this work (Materials). Stand type was not always recorded. Ung, Bernier & Guo (2008) later revised parameters for some species with British Columbia 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, H = 15 | 12.1 | 12.1 | Computed from the printed form: computed from the published form at dbh = 20 cm, H = 15 m |

Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/#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, lodgepole pine, dbh and height (branches; Table 4)", checked 2026-11-03, https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-branches/. 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-lodgepole-pine-dbh-h-branches.json
Report a problem: email info@restorationscope.com with the equation id (lambert-2005-lodgepole-pine-dbh-h-branches) and where the right value appears.