# Canadian national equation, beech, dbh and height (sum of wood, bark, branches, foliage; Table 4)

Aboveground biomass equation for Fagus grandifolia, Canada, from Lambert et al. 2005. 177 trees, DBH 1.8–46.3 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. 3):

> y wood = β wood1D βwood2Hβwood3 + ewood

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#equation

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

```
Aboveground biomass = 0.0432 * D^2.0378 * H^0.7 + 0.0049 * D^1.9057 * H^0.677 + 0.0355 * D^2.3749 + 0.0452 * D^1.5567
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 0.0432 * dbh^2.0378 * H^0.7 + 0.0049 * dbh^1.9057 * H^0.677 + 0.0355 * dbh^2.3749 + 0.0452 * dbh^1.5567, with dbh in cm, H in m; output in kg.
Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#canonical

## What it covers

- Output: Aboveground biomass, kg
- Taxon: Fagus grandifolia (species), family Fagaceae; broadleaf
- Where: Ontario and Quebec, Canada (ENFOR archival data, early 1980s). Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#where
- Biomes: temperate
- Stand: not stated
- Trees measured: 177. Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#n_trees
- DBH range: 1.8–46.3 cm. Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#dbh
- Height range: 2.9–26.5 m. Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#height
- R²: 0.91. Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#r2
- Method: Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total. Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#method
- Verification: read in the original source
- Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#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-beech-dbh-h/#source

## The facts, in the source's words

**Equation** (Eq. 3):

> y wood = β wood1D βwood2Hβwood3 + ewood

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#equation

**Equation** (Eq. 3):

> y bark = β bark1D βbark2Hβbark3 + e bark

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

**Equation** (Eq. 3):

> y branches = β branches1D βbranches2Hβbranches3 + e branches

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

**Equation** (Eq. 3):

> y foliage = β foliage1D βfoliage2Hβfoliage3 + efoliage

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

**Equation** (Table 4, Beech):

> Beech bwood1 0.0432

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#quote-expression-4

**Equation** (Table 4, Beech):

> bwood2 2.0378

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#quote-expression-5

**Equation** (Table 4, Beech):

> bwood3 0.7000

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#quote-expression-6

**Equation** (Table 4, Beech):

> bbark1 0.0049

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#quote-expression-7

**Equation** (Table 4, Beech):

> bbark2 1.9057

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#quote-expression-8

**Equation** (Table 4, Beech):

> bbark3 0.6770

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#quote-expression-9

**Equation** (Table 4, Beech):

> bbranches1 0.0355

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#quote-expression-10

**Equation** (Table 4, Beech):

> bbranches2 2.3749

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#quote-expression-11

**Equation** (Table 4, Beech):

> bbranches3 —

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#quote-expression-12

**Equation** (Table 4, Beech):

> bfoliage1 0.0452

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#quote-expression-13

**Equation** (Table 4, Beech):

> bfoliage2 1.5567

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#quote-expression-14

**Equation** (Table 4, Beech):

> bfoliage3 —

Cite: https://treeallometry.org/equations/lambert-2005-beech-dbh-h/#quote-expression-15

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

> Beech                   177     23.5±0.9     17.5±0.4      405.4±27.3

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

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

> (1.8;46.3)   (2.9;26.5)     (0.7;1372.5)

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

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

> Total 0.4720 0.90 115.9 2.92 0.1702 0.91 111.0 3.18

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

**Our note:** Total aboveground biomass = wood + bark + branches + foliage, each fitted as its own equation; the total is their sum (additivity by construction). Height drops out of the branches, foliage term: the paper leaves its height exponent blank (—, not significantly different from zero). 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 | 187 | 187 | Computed from the printed form: computed from the published form at dbh = 20 cm, H = 15 m |

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