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

Aboveground biomass equation for Fraxinus americana, Canada, from Lambert et al. 2005. 109 trees, DBH 2.4–53.7 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-white-ash-dbh-h/#equation

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

```
Aboveground biomass = 0.0224 * D^1.7438 * H^1.1899 + 0.0126 * D^1.6456 * H^0.7893 + 0.0354 * D^2.3046 + 0.0195 * D^1.0509 * H^0.7836
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 0.0224 * dbh^1.7438 * H^1.1899 + 0.0126 * dbh^1.6456 * H^0.7893 + 0.0354 * dbh^2.3046 + 0.0195 * dbh^1.0509 * H^0.7836, with dbh in cm, H in m; output in kg.
Cite: https://treeallometry.org/equations/lambert-2005-white-ash-dbh-h/#canonical

## What it covers

- Output: Aboveground biomass, kg
- Taxon: Fraxinus americana (species), family Oleaceae; broadleaf
- Where: Ontario and Quebec, Canada (ENFOR archival data, early 1980s). Cite: https://treeallometry.org/equations/lambert-2005-white-ash-dbh-h/#where
- Biomes: temperate
- Stand: not stated
- Trees measured: 109. Cite: https://treeallometry.org/equations/lambert-2005-white-ash-dbh-h/#n_trees
- DBH range: 2.4–53.7 cm. Cite: https://treeallometry.org/equations/lambert-2005-white-ash-dbh-h/#dbh
- Height range: 3.9–26.9 m. Cite: https://treeallometry.org/equations/lambert-2005-white-ash-dbh-h/#height
- R²: 0.93. Cite: https://treeallometry.org/equations/lambert-2005-white-ash-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-white-ash-dbh-h/#method
- Verification: read in the original source
- Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/lambert-2005-white-ash-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-white-ash-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-white-ash-dbh-h/#equation

**Equation** (Eq. 3):

> y bark = β bark1D βbark2Hβbark3 + e bark

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

**Equation** (Eq. 3):

> y branches = β branches1D βbranches2Hβbranches3 + e branches

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

**Equation** (Eq. 3):

> y foliage = β foliage1D βfoliage2Hβfoliage3 + efoliage

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

**Equation** (Table 4, White ash):

> White ash bwood1 0.0224

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

**Equation** (Table 4, White ash):

> bwood2 1.7438

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

**Equation** (Table 4, White ash):

> bwood3 1.1899

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

**Equation** (Table 4, White ash):

> bbark1 0.0126

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

**Equation** (Table 4, White ash):

> bbark2 1.6456

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

**Equation** (Table 4, White ash):

> bbark3 0.7893

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

**Equation** (Table 4, White ash):

> bbranches1 0.0354

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

**Equation** (Table 4, White ash):

> bbranches2 2.3046

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

**Equation** (Table 4, White ash):

> bbranches3 —

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

**Equation** (Table 4, White ash):

> bfoliage1 0.0195

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

**Equation** (Table 4, White ash):

> bfoliage2 1.0509

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

**Equation** (Table 4, White ash):

> bfoliage3 0.7836

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

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

> White ash              109     22.3±1.1     17.6±0.4     296.2±28.5

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

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

> (2.4;53.7)   (3.9;26.9)    (1.2;1850.1)

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

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

> Total 0.0363 0.91 91.0 3.62 0.0491 0.93 78.5 3.38

Cite: https://treeallometry.org/equations/lambert-2005-white-ash-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 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 | 158 | 158 | Computed from the printed form: computed from the published form at dbh = 20 cm, H = 15 m |

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