# Canadian national equation, yellow birch, dbh and height (branches; Table 4) Branch biomass equation for Betula alleghaniensis, Canada, from Lambert et al. 2005. 280 trees, DBH 0.8–70.3 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-yellow-birch-dbh-h-branches/#equation In this library's units, ready to compute (branch biomass in kg): ``` Branch biomass = 0.0325 * D^2.3851 ``` Inputs: D = Diameter at breast height (1.3 m) (cm). The source's own form: 0.0325 * dbh^2.3851, with dbh in cm, H in m; output in kg. Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-dbh-h-branches/#canonical ## What it covers - Output: Branch biomass, kg - Taxon: Betula alleghaniensis (species), family Betulaceae; broadleaf - Where: Canada: Newfoundland and Labrador, Ontario, Quebec (ENFOR archival data, early 1980s). Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-dbh-h-branches/#where - Biomes: boreal, temperate - Stand: not stated - Trees measured: 280. Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-dbh-h-branches/#n_trees - DBH range: 0.8–70.3 cm. Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-dbh-h-branches/#dbh - Height range: 2.7–25.6 m. Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-dbh-h-branches/#height - R²: 0.81. Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-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-yellow-birch-dbh-h-branches/#method - Verification: read in the original source - Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-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-yellow-birch-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-yellow-birch-dbh-h-branches/#equation **Equation** (Table 4, Yellow birch): > bbranches1 0.0325 Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-dbh-h-branches/#quote-expression **Equation** (Table 4, Yellow birch): > bbranches2 2.3851 Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-dbh-h-branches/#quote-expression-2 **Equation** (Table 4, Yellow birch): > bbranches3 — Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-dbh-h-branches/#quote-expression-3 **Trees measured** (Table 2 (No. of trees)): > Yellow birch 280 25.7±0.9 16.4±0.3 494.4±34.4 Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-dbh-h-branches/#quote-fit-n-trees **Smallest DBH** (Table 2, Yellow birch (ranges of dbh, height, total biomass)): > (0.8;70.3) (2.7;25.6) (0.1;2951.4) Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-dbh-h-branches/#quote-fit-dbh-min-cm **R²** (Table 5, Yellow birch (AdjRSq in the dbh- and height-based set, second block)): > Branches 0.0004 0.81 76.3 4.48 0.0005 0.81 76.5 4.45 Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-dbh-h-branches/#quote-fit-r2 **Our note:** All branches, cut at the stem base (live branches; dead branches excluded). Height drops out of the branches term: the paper leaves its height exponent blank (—, not significantly different from zero). 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 | 41.2 | 41.2 | Computed from the printed form: computed from the published form at dbh = 20 cm, H = 15 m | Cite: https://treeallometry.org/equations/lambert-2005-yellow-birch-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, yellow birch, dbh and height (branches; Table 4)", checked 2026-11-03, https://treeallometry.org/equations/lambert-2005-yellow-birch-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-yellow-birch-dbh-h-branches.json Report a problem: email info@restorationscope.com with the equation id (lambert-2005-yellow-birch-dbh-h-branches) and where the right value appears.