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

Aboveground biomass equation for Fraxinus nigra, Canada, from Lambert et al. 2005. 73 trees, DBH 2–43.1 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 wood = β wood1D βwood2 + ewood

Cite: https://treeallometry.org/equations/lambert-2005-black-ash/#equation

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

```
Aboveground biomass = 0.0941 * D^2.3491 + 0.0323 * D^2.0761 + 0.0448 * D^1.9771 + 0.0538 * D^1.3584
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: 0.0941 * dbh^2.3491 + 0.0323 * dbh^2.0761 + 0.0448 * dbh^1.9771 + 0.0538 * dbh^1.3584, with dbh in cm; output in kg.
Cite: https://treeallometry.org/equations/lambert-2005-black-ash/#canonical

## What it covers

- Output: Aboveground biomass, kg
- Taxon: Fraxinus nigra (species), family Oleaceae; broadleaf
- Where: Ontario and Quebec, Canada (ENFOR archival data, early 1980s). Cite: https://treeallometry.org/equations/lambert-2005-black-ash/#where
- Biomes: temperate
- Stand: not stated
- Trees measured: 73. Cite: https://treeallometry.org/equations/lambert-2005-black-ash/#n_trees
- DBH range: 2–43.1 cm. Cite: https://treeallometry.org/equations/lambert-2005-black-ash/#dbh
- R²: 0.96. Cite: https://treeallometry.org/equations/lambert-2005-black-ash/#r2
- Method: Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total. Cite: https://treeallometry.org/equations/lambert-2005-black-ash/#method
- Verification: read in the original source
- Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/lambert-2005-black-ash/#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-black-ash/#source

## The facts, in the source's words

**Equation** (Eq. 2):

> y wood = β wood1D βwood2 + ewood

Cite: https://treeallometry.org/equations/lambert-2005-black-ash/#equation

**Equation** (Eq. 2):

> y bark = β bark1D βbark2 + e bark

Cite: https://treeallometry.org/equations/lambert-2005-black-ash/#quote-expression

**Equation** (Eq. 2):

> y branches = β branches1D βbranches2 + e branches

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

**Equation** (Eq. 2):

> y foliage = β foliage1D βfoliage2 + efoliage

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

**Equation** (Table 3, Black ash):

> Black ash bwood1 0.0941

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

**Equation** (Table 3, Black ash):

> bwood2 2.3491

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

**Equation** (Table 3, Black ash):

> bbark1 0.0323

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

**Equation** (Table 3, Black ash):

> bbark2 2.0761

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

**Equation** (Table 3, Black ash):

> bbranches1 0.0448

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

**Equation** (Table 3, Black ash):

> bbranches2 1.9771

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

**Equation** (Table 3, Black ash):

> bfoliage1 0.0538

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

**Equation** (Table 3, Black ash):

> bfoliage2 1.3584

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

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

> Black ash                73     16.2±1.2     14.4±0.6      142.0±21.6

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

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

> (2.0;43.1)   (2.6;22.9)     (1.0;926.4)

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

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

> Total 0.0085 0.96 35.6 3.82 0.1349 0.97 32.9 2.76

Cite: https://treeallometry.org/equations/lambert-2005-black-ash/#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). 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 | 143 | 143 | Computed from the printed form: computed from the published form at dbh = 20 cm |

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