{"id":"lambert-2005-red-oak-dbh-h","source":{"id":"lambert-2005","citation":"Lambert, M.-C., Ung, C.-H., Raulier, F. (2005). Canadian national tree aboveground biomass equations. Canadian Journal of Forest Research, 35(8), 1996–2018.","title":"Canadian national tree aboveground biomass equations","authors":["Lambert, M.-C.","Ung, C.-H.","Raulier, F."],"year":2005,"venue":"Canadian Journal of Forest Research","doi":"10.1139/x05-112","url":"https://doi.org/10.1139/x05-112","read_url":"https://www.esf.edu/quest/documents/Lambertetal.2005.Canadatreebiomass.pdf","access":"paywalled","checked_at":"2026-11-03","status":"current","notes":"All 33 species are entered, each with total aboveground, stem (wood + bark), branch and foliage equations, for both the dbh-only set (Table 3) and the dbh + height set (Table 4). The paper's hardwood, softwood and all-species equations are not entered: they are meant for species outside the 33, and this library shows pooled fits only on the pages of species they name. Ung, Bernier & Guo (2008, CJFR 38:1123–1132, doi:10.1139/X07-224) re-estimated parameters for six species after adding British Columbia data and added eight BC species; no legal open copy of that paper was found (NRCan's repository lists it without a file), so Lambert 2005 parameters are used here."},"name":"Canadian national equation, red oak, dbh and height (sum of wood, bark, branches, foliage; Table 4)","output":{"quantity":"agb"},"expression":"0.0285 * D^1.8501 * H^1.0204 + 0.0326 * D^1.81 * H^0.4153 + 0.0013 * D^3.0637 * H^0.3153 + 0.0582 * D^1.5438","published":{"expression":"0.0285 * dbh^1.8501 * H^1.0204 + 0.0326 * dbh^1.81 * H^0.4153 + 0.0013 * dbh^3.0637 * H^0.3153 + 0.0582 * dbh^1.5438","units":{"dbh":"cm","H":"m"},"variables":{"dbh":"D"},"output_unit":"kg"},"taxon":{"level":"species","name":"Quercus rubra","family":"Fagaceae","group":"broadleaf"},"region":{"scope":"regional","countries":["CA"],"place":"Ontario, Canada (ENFOR archival data, early 1980s)","biomes":["temperate"]},"fit":{"n_trees":117,"dbh_min_cm":1.1,"dbh_max_cm":55.3,"h_min_m":2.5,"h_max_m":23,"r2":0.97,"method":"Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total"},"evidence":[{"field":"expression","quote":"y wood = β wood1D βwood2Hβwood3 + ewood","locator":"Eq. 3"},{"field":"expression","quote":"y bark = β bark1D βbark2Hβbark3 + e bark","locator":"Eq. 3"},{"field":"expression","quote":"y branches = β branches1D βbranches2Hβbranches3 + e branches","locator":"Eq. 3"},{"field":"expression","quote":"y foliage = β foliage1D βfoliage2Hβfoliage3 + efoliage","locator":"Eq. 3"},{"field":"expression","quote":"Red oak bwood1 0.0285","locator":"Table 4, Red oak"},{"field":"expression","quote":"bwood2 1.8501","locator":"Table 4, Red oak"},{"field":"expression","quote":"bwood3 1.0204","locator":"Table 4, Red oak"},{"field":"expression","quote":"bbark1 0.0326","locator":"Table 4, Red oak"},{"field":"expression","quote":"bbark2 1.8100","locator":"Table 4, Red oak"},{"field":"expression","quote":"bbark3 0.4153","locator":"Table 4, Red oak"},{"field":"expression","quote":"bbranches1 0.0013","locator":"Table 4, Red oak"},{"field":"expression","quote":"bbranches2 3.0637","locator":"Table 4, Red oak"},{"field":"expression","quote":"bbranches3 0.3153","locator":"Table 4, Red oak"},{"field":"expression","quote":"bfoliage1 0.0582","locator":"Table 4, Red oak"},{"field":"expression","quote":"bfoliage2 1.5438","locator":"Table 4, Red oak"},{"field":"expression","quote":"bfoliage3 —","locator":"Table 4, Red oak"},{"field":"fit.n_trees","quote":"Red oak                117     22.6±1.0     15.3±0.4     311.4±29.2","locator":"Table 2 (No. of trees)"},{"field":"fit.dbh_min_cm","quote":"(1.1;55.3)   (2.5;23.0)    (0.4;1977.5)","locator":"Table 2, Red oak (ranges of dbh, height, total biomass)"},{"field":"fit.r2","quote":"Total 0.0344 0.91 92.3 3.64 0.0618 0.97 59.1 3.25","locator":"Table 5, Red oak (AdjRSq in the dbh- and height-based set, second block)"}],"check":[{"inputs":{"D":20,"H":15},"expected":173.5584,"origin":"computed","note":"computed from the published form at dbh = 20 cm, H = 15 m"}],"verification":"original_read","checked_at":"2026-11-03","notes":"Total aboveground biomass = wood + bark + branches + foliage, each fitted as its own equation; the total is their sum (additivity by construction). Height drops out of the foliage 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."}