{"id":"lambert-2005-balsam-fir","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, balsam fir, dbh only (sum of wood, bark, branches, foliage; Table 3)","output":{"quantity":"agb"},"expression":"0.0534 * D^2.403 + 0.0115 * D^2.3484 + 0.007 * D^2.5406 + 0.084 * D^1.6695","published":{"expression":"0.0534 * dbh^2.403 + 0.0115 * dbh^2.3484 + 0.007 * dbh^2.5406 + 0.084 * dbh^1.6695","units":{"dbh":"cm"},"variables":{"dbh":"D"},"output_unit":"kg"},"taxon":{"level":"species","name":"Abies balsamea","family":"Pinaceae","group":"conifer"},"region":{"scope":"national","countries":["CA"],"place":"Canada: Alberta, Manitoba, Newfoundland and Labrador, Nova Scotia, Ontario, Quebec, Saskatchewan (ENFOR archival data, early 1980s)","biomes":["boreal","temperate"]},"fit":{"n_trees":639,"dbh_min_cm":1.5,"dbh_max_cm":42.4,"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":"y branches = β branches1D βbranches2 + e branches","locator":"Eq. 2"},{"field":"expression","quote":"y foliage = β foliage1D βfoliage2 + efoliage","locator":"Eq. 2"},{"field":"expression","quote":"Balsam fir bwood1 0.0534","locator":"Table 3, Balsam fir"},{"field":"expression","quote":"bwood2 2.4030","locator":"Table 3, Balsam fir"},{"field":"expression","quote":"bbark1 0.0115","locator":"Table 3, Balsam fir"},{"field":"expression","quote":"bbark2 2.3484","locator":"Table 3, Balsam fir"},{"field":"expression","quote":"bbranches1 0.0070","locator":"Table 3, Balsam fir"},{"field":"expression","quote":"bbranches2 2.5406","locator":"Table 3, Balsam fir"},{"field":"expression","quote":"bfoliage1 0.0840","locator":"Table 3, Balsam fir"},{"field":"expression","quote":"bfoliage2 1.6695","locator":"Table 3, Balsam fir"},{"field":"fit.n_trees","quote":"Balsam fir              639     16.4±0.4     12.2±0.2      103.4±4.7","locator":"Table 2 (No. of trees)"},{"field":"fit.dbh_min_cm","quote":"(1.5;42.4)   (1.6;52.2)     (0.5;649.0)","locator":"Table 2, Balsam fir (ranges of dbh, height, total biomass)"},{"field":"fit.r2","quote":"Total 0.0047 0.97 20.1 3.63 0.0073 0.98 17.6 3.38","locator":"Table 5, Balsam fir (AdjRSq in the dbh-based set, first block)"}],"check":[{"inputs":{"D":20},"expected":111.124,"origin":"computed","note":"computed from the published form at dbh = 20 cm"}],"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). 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."}