# Canadian national equation, lodgepole pine, dbh and height (stem wood plus stem bark; Table 4) Stem biomass equation for Pinus contorta var. latifolia, Canada, from Lambert et al. 2005. 201 trees, DBH 2.5–39 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-lodgepole-pine-dbh-h-stem/#equation In this library's units, ready to compute (stem biomass in kg): ``` Stem biomass = 0.0202 * D^1.7179 * H^1.2078 + 0.0099 * D^1.6049 * H^0.7456 ``` Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m). The source's own form: 0.0202 * dbh^1.7179 * H^1.2078 + 0.0099 * dbh^1.6049 * H^0.7456, with dbh in cm, H in m; output in kg. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#canonical ## What it covers - Output: Stem biomass, kg - Taxon: Pinus contorta var. latifolia (species), family Pinaceae; conifer - Where: Alberta and Yukon, Canada (ENFOR archival data, early 1980s). Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#where - Biomes: boreal - Stand: not stated - Trees measured: 201. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#n_trees - DBH range: 2.5–39 cm. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#dbh - Height range: 2.5–25.9 m. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#height - R²: 0.99. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#r2 - Method: Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#method - Verification: read in the original source - Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-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-lodgepole-pine-dbh-h-stem/#source ## The facts, in the source's words **Equation** (Eq. 3): > y wood = β wood1D βwood2Hβwood3 + ewood Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#equation **Equation** (Eq. 3): > y bark = β bark1D βbark2Hβbark3 + e bark Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#quote-expression **Equation** (Table 4, Lodgepole pine): > Lodgepole pine bwood1 0.0202 Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#quote-expression-2 **Equation** (Table 4, Lodgepole pine): > bwood2 1.7179 Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#quote-expression-3 **Equation** (Table 4, Lodgepole pine): > bwood3 1.2078 Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#quote-expression-4 **Equation** (Table 4, Lodgepole pine): > bbark1 0.0099 Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#quote-expression-5 **Equation** (Table 4, Lodgepole pine): > bbark2 1.6049 Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#quote-expression-6 **Equation** (Table 4, Lodgepole pine): > bbark3 0.7456 Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#quote-expression-7 **Trees measured** (Table 2 (No. of trees)): > Lodgepole pine 201 15.0±0.6 12.7±0.4 99.0±8.8 Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#quote-fit-n-trees **Smallest DBH** (Table 2, Lodgepole pine (ranges of dbh, height, total biomass)): > (2.5;39.0) (2.5;25.9) (0.8;694.4) Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#quote-fit-dbh-min-cm **R²** (Table 5, Lodgepole pine (AdjRSq in the dbh- and height-based set, second block)): > Stem 0.0250 0.96 21.0 3.18 0.0004 0.99 11.6 4.13 Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#quote-fit-r2 **Taxon** (Appendix B, Table B1): > Lodgepole pine Pin lodgepole Pinus contorta var. latifolia Engelm. Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-stem/#quote-taxon **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, H = 15 | 101 | 101 | Computed from the printed form: computed from the published form at dbh = 20 cm, H = 15 m | Cite: https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-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, lodgepole pine, dbh and height (stem wood plus stem bark; Table 4)", checked 2026-11-03, https://treeallometry.org/equations/lambert-2005-lodgepole-pine-dbh-h-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-lodgepole-pine-dbh-h-stem.json Report a problem: email info@restorationscope.com with the equation id (lambert-2005-lodgepole-pine-dbh-h-stem) and where the right value appears.