# Canadian national equation, black ash, dbh only (stem wood plus stem bark; Table 3) Stem 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-stem/#equation In this library's units, ready to compute (stem biomass in kg): ``` Stem biomass = 0.0941 * D^2.3491 + 0.0323 * D^2.0761 ``` 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, with dbh in cm; output in kg. Cite: https://treeallometry.org/equations/lambert-2005-black-ash-stem/#canonical ## What it covers - Output: Stem 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-stem/#where - Biomes: temperate - Stand: not stated - Trees measured: 73. Cite: https://treeallometry.org/equations/lambert-2005-black-ash-stem/#n_trees - DBH range: 2–43.1 cm. Cite: https://treeallometry.org/equations/lambert-2005-black-ash-stem/#dbh - R²: 0.97. Cite: https://treeallometry.org/equations/lambert-2005-black-ash-stem/#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-stem/#method - Verification: read in the original source - Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/lambert-2005-black-ash-stem/#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-stem/#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-stem/#equation **Equation** (Eq. 2): > y bark = β bark1D βbark2 + e bark Cite: https://treeallometry.org/equations/lambert-2005-black-ash-stem/#quote-expression **Equation** (Table 3, Black ash): > Black ash bwood1 0.0941 Cite: https://treeallometry.org/equations/lambert-2005-black-ash-stem/#quote-expression-2 **Equation** (Table 3, Black ash): > bwood2 2.3491 Cite: https://treeallometry.org/equations/lambert-2005-black-ash-stem/#quote-expression-3 **Equation** (Table 3, Black ash): > bbark1 0.0323 Cite: https://treeallometry.org/equations/lambert-2005-black-ash-stem/#quote-expression-4 **Equation** (Table 3, Black ash): > bbark2 2.0761 Cite: https://treeallometry.org/equations/lambert-2005-black-ash-stem/#quote-expression-5 **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-stem/#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-stem/#quote-fit-dbh-min-cm **R²** (Table 5, Black ash (AdjRSq in the dbh-based set, first block)): > Stem 0.0182 0.97 30.8 3.43 0.2132 0.97 27.4 2.52 Cite: https://treeallometry.org/equations/lambert-2005-black-ash-stem/#quote-fit-r2 **Our note:** Stem from ground level to tree top, stem wood plus stem bark; the stem is the sum of the two compartment equations. 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 | 123 | 123 | Computed from the printed form: computed from the published form at dbh = 20 cm | Cite: https://treeallometry.org/equations/lambert-2005-black-ash-stem/#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 (stem wood plus stem bark; Table 3)", checked 2026-11-03, https://treeallometry.org/equations/lambert-2005-black-ash-stem/. 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-stem.json Report a problem: email info@restorationscope.com with the equation id (lambert-2005-black-ash-stem) and where the right value appears.