# Canadian national equation, red oak, dbh only (stem wood plus stem bark; Table 3) Stem biomass equation for Quercus rubra, Canada, from Lambert et al. 2005. 117 trees, DBH 1.1–55.3 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. 2): > y wood = β wood1D βwood2 + ewood Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#equation In this library's units, ready to compute (stem biomass in kg): ``` Stem biomass = 0.1754 * D^2.1616 + 0.0381 * D^2.0991 ``` Inputs: D = Diameter at breast height (1.3 m) (cm). The source's own form: 0.1754 * dbh^2.1616 + 0.0381 * dbh^2.0991, with dbh in cm; output in kg. Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#canonical ## What it covers - Output: Stem biomass, kg - Taxon: Quercus rubra (species), family Fagaceae; broadleaf - Where: Ontario, Canada (ENFOR archival data, early 1980s). Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#where - Biomes: temperate - Stand: not stated - Trees measured: 117. Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#n_trees - DBH range: 1.1–55.3 cm. Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#dbh - R²: 0.87. Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#r2 - Method: Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total. Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#method - Verification: read in the original source - Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/lambert-2005-red-oak-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-red-oak-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-red-oak-stem/#equation **Equation** (Eq. 2): > y bark = β bark1D βbark2 + e bark Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#quote-expression **Equation** (Table 3, Red oak): > Red oak bwood1 0.1754 Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#quote-expression-2 **Equation** (Table 3, Red oak): > bwood2 2.1616 Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#quote-expression-3 **Equation** (Table 3, Red oak): > bbark1 0.0381 Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#quote-expression-4 **Equation** (Table 3, Red oak): > bbark2 2.0991 Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#quote-expression-5 **Trees measured** (Table 2 (No. of trees)): > Red oak 117 22.6±1.0 15.3±0.4 311.4±29.2 Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#quote-fit-n-trees **Smallest DBH** (Table 2, Red oak (ranges of dbh, height, total biomass)): > (1.1;55.3) (2.5;23.0) (0.4;1977.5) Cite: https://treeallometry.org/equations/lambert-2005-red-oak-stem/#quote-fit-dbh-min-cm **R²** (Table 5, Red oak (AdjRSq in the dbh-based set, first block)): > Stem 0.1560 0.87 73.0 3.07 0.0524 0.95 43.4 3.09 Cite: https://treeallometry.org/equations/lambert-2005-red-oak-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 | 134 | 134 | Computed from the printed form: computed from the published form at dbh = 20 cm | Cite: https://treeallometry.org/equations/lambert-2005-red-oak-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, red oak, dbh only (stem wood plus stem bark; Table 3)", checked 2026-11-03, https://treeallometry.org/equations/lambert-2005-red-oak-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-red-oak-stem.json Report a problem: email info@restorationscope.com with the equation id (lambert-2005-red-oak-stem) and where the right value appears.