{"id":"lambert-2005-red-oak","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":"2026-11-01","status":"current","notes":"Ung, Bernier & Guo (2008, CJFR 38:1123–1132, doi:10.1139/X07-224) re-estimated parameters for six species after adding British Columbia data; that paper was not reachable as open text, so Lambert 2005 parameters are used here."},"name":"Canadian national equation, red oak, dbh only (sum of wood, bark, branches, foliage; Table 3)","output":{"quantity":"agb"},"expression":"0.1754 * D^2.1616 + 0.0381 * D^2.0991 + 0.0085 * D^2.779 + 0.0373 * D^1.674","published":{"expression":"0.1754 * dbh^2.1616 + 0.0381 * dbh^2.0991 + 0.0085 * dbh^2.779 + 0.0373 * dbh^1.674","units":{"dbh":"cm"},"variables":{"dbh":"D"},"output_unit":"kg"},"taxon":{"level":"species","name":"Quercus rubra","family":"Fagaceae","group":"broadleaf"},"region":{"scope":"national","countries":["CA"],"place":"Canada (ENFOR archival data, early 1980s)","biomes":["temperate"]},"stand":"natural","fit":{"n_trees":117,"dbh_min_cm":1.1,"dbh_max_cm":55.3,"r2":0.91,"method":"Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total"},"evidence":[{"field":"expression","quote":"y wood = β wood1 D^βwood2 + ewood … y bark = β bark1 D^βbark2 + e bark … y foliage = β foliage1 D^βfoliage2 … y branches = β branches1 D^βbranches2","locator":"Eq. 2"},{"field":"expression","quote":"bwood1 0.1754 bwood2 2.1616 bbark1 0.0381 bbark2 2.0991 bbranches1 0.0085 bbranches2 2.779 bfoliage1 0.0373 bfoliage2 1.674","locator":"Table 3, Red oak (rows transcribed)"},{"field":"expression","quote":"Red oak bwood1 0.1754 0.0149","locator":"Table 3"},{"field":"fit.n_trees","quote":"Red oak 117","locator":"Table 2 (No. of trees; dbh range in parentheses)"},{"field":"fit.r2","quote":"Red oak Total 0.0344 0.91 92.3","locator":"Table 5, dbh-based set (σ̂ii, AdjRSq, RMSE in kg)"}],"check":[{"inputs":{"D":20},"expected":175.0508,"origin":"computed","note":"computed from the published form at dbh = 20 cm"}],"verification":"original_read","checked_at":"2026-11-01","notes":"Total aboveground biomass = wood + bark + branches + foliage, each a power function of dbh (cm), kg dry mass; the total is the sum of the four compartment equations (additivity by construction). r2 is the adjusted R² of the total. The paper also gives dbh+height equations (Table 4). Ung et al. (2008) later revised parameters for some species with BC data; not used here."}