# Canadian national equation, black spruce, dbh and height (sum of wood, bark, branches, foliage; Table 4) Aboveground biomass equation for Picea mariana, Canada, from Lambert et al. 2005. 1,534 trees, DBH 1.6–37.2 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-black-spruce-dbh-h/#equation In this library's units, ready to compute (aboveground biomass in kg): ``` Aboveground biomass = 0.0309 * D^1.7527 * H^1.0014 + 0.0115 * D^1.7405 * H^0.6589 + 0.038 * D^3.2558 * H^(-1.4218) + 0.2048 * D^2.5754 * H^(-1.3704) ``` Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m). The source's own form: 0.0309 * dbh^1.7527 * H^1.0014 + 0.0115 * dbh^1.7405 * H^0.6589 + 0.038 * dbh^3.2558 * H^(-1.4218) + 0.2048 * dbh^2.5754 * H^(-1.3704), with dbh in cm, H in m; output in kg. Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#canonical ## What it covers - Output: Aboveground biomass, kg - Taxon: Picea mariana (species), family Pinaceae; conifer - Where: Canada: Alberta, Manitoba, Newfoundland and Labrador, Nova Scotia, Northwest Territories, Ontario, Quebec, Saskatchewan, Yukon (ENFOR archival data, early 1980s). Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#where - Biomes: boreal, temperate - Stand: not stated - Trees measured: 1,534. Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#n_trees - DBH range: 1.6–37.2 cm. Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#dbh - Height range: 1.8–23.5 m. Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#height - R²: 0.97. Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-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-black-spruce-dbh-h/#method - Verification: read in the original source - Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-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-black-spruce-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-black-spruce-dbh-h/#equation **Equation** (Eq. 3): > y bark = β bark1D βbark2Hβbark3 + e bark Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression **Equation** (Eq. 3): > y branches = β branches1D βbranches2Hβbranches3 + e branches Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-2 **Equation** (Eq. 3): > y foliage = β foliage1D βfoliage2Hβfoliage3 + efoliage Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-3 **Equation** (Table 4, Black spruce): > Black spruce bwood1 0.0309 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-4 **Equation** (Table 4, Black spruce): > bwood2 1.7527 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-5 **Equation** (Table 4, Black spruce): > bwood3 1.0014 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-6 **Equation** (Table 4, Black spruce): > bbark1 0.0115 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-7 **Equation** (Table 4, Black spruce): > bbark2 1.7405 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-8 **Equation** (Table 4, Black spruce): > bbark3 0.6589 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-9 **Equation** (Table 4, Black spruce): > bbranches1 0.0380 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-10 **Equation** (Table 4, Black spruce): > bbranches2 3.2558 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-11 **Equation** (Table 4, Black spruce): > bbranches3 –1.4218 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-12 **Equation** (Table 4, Black spruce): > bfoliage1 0.2048 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-13 **Equation** (Table 4, Black spruce): > bfoliage2 2.5754 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-14 **Equation** (Table 4, Black spruce): > bfoliage3 –1.3704 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-expression-15 **Trees measured** (Table 2 (No. of trees)): > Black spruce 1534 13.9±0.2 11.6±0.1 73.3±1.9 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-fit-n-trees **Smallest DBH** (Table 2, Black spruce (ranges of dbh, height, total biomass)): > (1.6;37.2) (1.8;23.5) (0.6;556.1) Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-dbh-h/#quote-fit-dbh-min-cm **R²** (Table 5, Black spruce (AdjRSq in the dbh- and height-based set, second block)): > Total 0.0091 0.96 15.2 3.55 0.0093 0.97 12.5 3.38 Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-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). 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 | 126 | 126 | Computed from the printed form: computed from the published form at dbh = 20 cm, H = 15 m | Cite: https://treeallometry.org/equations/lambert-2005-black-spruce-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, black spruce, dbh and height (sum of wood, bark, branches, foliage; Table 4)", checked 2026-11-03, https://treeallometry.org/equations/lambert-2005-black-spruce-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-black-spruce-dbh-h.json Report a problem: email info@restorationscope.com with the equation id (lambert-2005-black-spruce-dbh-h) and where the right value appears.