# Canadian national equation, red pine, dbh only (branches; Table 3)

Branch biomass equation for Pinus resinosa, Canada, from Lambert et al. 2005. 371 trees, DBH 1.3–55.1 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

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

> y branches = β branches1D βbranches2 + e branches

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

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

```
Branch biomass = 0.0033 * D^2.7515
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: 0.0033 * dbh^2.7515, with dbh in cm; output in kg.
Cite: https://treeallometry.org/equations/lambert-2005-red-pine-branches/#canonical

## What it covers

- Output: Branch biomass, kg
- Taxon: Pinus resinosa (species), family Pinaceae; conifer
- Where: Canada: Nova Scotia, Ontario, Quebec (ENFOR archival data, early 1980s). Cite: https://treeallometry.org/equations/lambert-2005-red-pine-branches/#where
- Biomes: boreal, temperate
- Stand: not stated
- Trees measured: 371. Cite: https://treeallometry.org/equations/lambert-2005-red-pine-branches/#n_trees
- DBH range: 1.3–55.1 cm. Cite: https://treeallometry.org/equations/lambert-2005-red-pine-branches/#dbh
- R²: 0.8. Cite: https://treeallometry.org/equations/lambert-2005-red-pine-branches/#r2
- Method: Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total. Cite: https://treeallometry.org/equations/lambert-2005-red-pine-branches/#method
- Verification: read in the original source
- Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/lambert-2005-red-pine-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-red-pine-branches/#source

## The facts, in the source's words

**Equation** (Eq. 2):

> y branches = β branches1D βbranches2 + e branches

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

**Equation** (Table 3, Red pine):

> bbranches1 0.0033

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

**Equation** (Table 3, Red pine):

> bbranches2 2.7515

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

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

> Red pine               371     22.4±0.6     16.4±0.3     216.5±12.6

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

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

> (1.3;55.1)   (1.8;34.4)    (0.3;1572.6)

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

**R²** (Table 5, Red pine (AdjRSq in the dbh-based set, first block)):

> Branches 0.0000 0.80 18.2 4.49 0.0002 0.87 14.7 3.95

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

**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 | 12.5 | 12.5 | Computed from the printed form: computed from the published form at dbh = 20 cm |

Cite: https://treeallometry.org/equations/lambert-2005-red-pine-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, red pine, dbh only (branches; Table 3)", checked 2026-11-03, https://treeallometry.org/equations/lambert-2005-red-pine-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-red-pine-branches.json
Report a problem: email info@restorationscope.com with the equation id (lambert-2005-red-pine-branches) and where the right value appears.