# Canadian national equation, eastern white pine, dbh and height (branches; Table 4) Branch biomass equation for Pinus strobus, Canada, from Lambert et al. 2005. 199 trees, DBH 1.5–68.7 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 branches = β branches1D βbranches2Hβbranches3 + e branches Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#equation In this library's units, ready to compute (branch biomass in kg): ``` Branch biomass = 0.0184 * D^3.1968 * H^(-1.0876) ``` Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m). The source's own form: 0.0184 * dbh^3.1968 * H^(-1.0876), with dbh in cm, H in m; output in kg. Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#canonical ## What it covers - Output: Branch biomass, kg - Taxon: Pinus strobus (species), family Pinaceae; conifer - Where: Ontario and Quebec, Canada (ENFOR archival data, early 1980s). Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#where - Biomes: temperate - Stand: not stated - Trees measured: 199. Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#n_trees - DBH range: 1.5–68.7 cm. Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#dbh - Height range: 2.3–38.5 m. Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#height - R²: 0.89. Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#r2 - Method: Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total. Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#method - Verification: read in the original source - Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#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-eastern-white-pine-dbh-h-branches/#source ## The facts, in the source's words **Equation** (Eq. 3): > y branches = β branches1D βbranches2Hβbranches3 + e branches Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#equation **Equation** (Table 4, Eastern white pine): > bbranches1 0.0184 Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#quote-expression **Equation** (Table 4, Eastern white pine): > bbranches2 3.1968 Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#quote-expression-2 **Equation** (Table 4, Eastern white pine): > bbranches3 –1.0876 Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#quote-expression-3 **Trees measured** (Table 2 (No. of trees)): > Eastern white pine 199 28.7±1.1 18.7±0.5 425.8±33.0 Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#quote-fit-n-trees **Smallest DBH** (Table 2, Eastern white pine (ranges of dbh, height, total biomass)): > (1.5;68.7) (2.3;38.5) (0.3;2183.1) Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#quote-fit-dbh-min-cm **R²** (Table 5, Eastern white pine (AdjRSq in the dbh- and height-based set, second block)): > Branches 0.0009 0.82 35.1 3.71 0.0000 0.89 27.3 4.66 Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#quote-fit-r2 **Our note:** All branches, cut at the stem base (live branches; dead branches excluded). 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 | 14 | 14 | Computed from the printed form: computed from the published form at dbh = 20 cm, H = 15 m | Cite: https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/#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, eastern white pine, dbh and height (branches; Table 4)", checked 2026-11-03, https://treeallometry.org/equations/lambert-2005-eastern-white-pine-dbh-h-branches/. 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-eastern-white-pine-dbh-h-branches.json Report a problem: email info@restorationscope.com with the equation id (lambert-2005-eastern-white-pine-dbh-h-branches) and where the right value appears.