{"id":"lambert-2005-black-ash-stem","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, black ash, dbh only (stem wood plus stem bark; Table 3)","output":{"quantity":"stem_biomass"},"expression":"0.0941 * D^2.3491 + 0.0323 * D^2.0761","published":{"expression":"0.0941 * dbh^2.3491 + 0.0323 * dbh^2.0761","units":{"dbh":"cm"},"variables":{"dbh":"D"},"output_unit":"kg"},"taxon":{"level":"species","name":"Fraxinus nigra","family":"Oleaceae","group":"broadleaf"},"region":{"scope":"regional","countries":["CA"],"place":"Ontario and Quebec, Canada (ENFOR archival data, early 1980s)","biomes":["temperate"]},"fit":{"n_trees":73,"dbh_min_cm":2,"dbh_max_cm":43.1,"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 βwood2 + ewood","locator":"Eq. 2"},{"field":"expression","quote":"y bark = β bark1D βbark2 + e bark","locator":"Eq. 2"},{"field":"expression","quote":"Black ash bwood1 0.0941","locator":"Table 3, Black ash"},{"field":"expression","quote":"bwood2 2.3491","locator":"Table 3, Black ash"},{"field":"expression","quote":"bbark1 0.0323","locator":"Table 3, Black ash"},{"field":"expression","quote":"bbark2 2.0761","locator":"Table 3, Black ash"},{"field":"fit.n_trees","quote":"Black ash                73     16.2±1.2     14.4±0.6      142.0±21.6","locator":"Table 2 (No. of trees)"},{"field":"fit.dbh_min_cm","quote":"(2.0;43.1)   (2.6;22.9)     (1.0;926.4)","locator":"Table 2, Black ash (ranges of dbh, height, total biomass)"},{"field":"fit.r2","quote":"Stem 0.0182 0.97 30.8 3.43 0.2132 0.97 27.4 2.52","locator":"Table 5, Black ash (AdjRSq in the dbh-based set, first block)"}],"check":[{"inputs":{"D":20},"expected":123.3405,"origin":"computed","note":"computed from the published form at dbh = 20 cm"}],"verification":"original_read","checked_at":"2026-11-03","notes":"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."}