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

Aboveground biomass equation for Quercus rubra, Canada, from Lambert et al. 2005. 117 trees, DBH 1.1–55.3 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-red-oak/#equation

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

```
Aboveground biomass = 0.1754 * D^2.1616 + 0.0381 * D^2.0991 + 0.0085 * D^2.779 + 0.0373 * D^1.674
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: 0.1754 * dbh^2.1616 + 0.0381 * dbh^2.0991 + 0.0085 * dbh^2.779 + 0.0373 * dbh^1.674, with dbh in cm; output in kg.
Cite: https://treeallometry.org/equations/lambert-2005-red-oak/#canonical

## What it covers

- Output: Aboveground biomass, kg
- Taxon: Quercus rubra (species), family Fagaceae; broadleaf
- Where: Canada (ENFOR archival data, early 1980s). Cite: https://treeallometry.org/equations/lambert-2005-red-oak/#where
- Biomes: temperate
- Stand: natural
- Trees measured: 117. Cite: https://treeallometry.org/equations/lambert-2005-red-oak/#n_trees
- DBH range: 1.1–55.3 cm. Cite: https://treeallometry.org/equations/lambert-2005-red-oak/#dbh
- R²: 0.91. Cite: https://treeallometry.org/equations/lambert-2005-red-oak/#r2
- Method: Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total. Cite: https://treeallometry.org/equations/lambert-2005-red-oak/#method
- Verification: read in the original source
- Last checked: 2026-11-01. Cite: https://treeallometry.org/equations/lambert-2005-red-oak/#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-oak/#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-red-oak/#equation

**Equation** (Table 3, Red oak (rows transcribed)):

> bwood1 0.1754 bwood2 2.1616 bbark1 0.0381 bbark2 2.0991 bbranches1 0.0085 bbranches2 2.779 bfoliage1 0.0373 bfoliage2 1.674

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

**Equation** (Table 3):

> Red oak bwood1 0.1754 0.0149

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

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

> Red oak 117

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

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

> Red oak Total 0.0344 0.91 92.3

Cite: https://treeallometry.org/equations/lambert-2005-red-oak/#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 | 175 | 175 | Computed from the printed form: computed from the published form at dbh = 20 cm |

Cite: https://treeallometry.org/equations/lambert-2005-red-oak/#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 oak, dbh only (sum of wood, bark, branches, foliage; Table 3)", checked 2026-11-01, https://treeallometry.org/equations/lambert-2005-red-oak/. 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-oak.json
Report a problem: email info@restorationscope.com with the equation id (lambert-2005-red-oak) and where the right value appears.