{"id":"lambert-2005-trembling-aspen-dbh-h-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, trembling aspen, dbh and height (stem wood plus stem bark; Table 4)","output":{"quantity":"stem_biomass"},"expression":"0.0142 * D^1.9389 * H^1.0572 + 0.0063 * D^2.0819 * H^0.6617","published":{"expression":"0.0142 * dbh^1.9389 * H^1.0572 + 0.0063 * dbh^2.0819 * H^0.6617","units":{"dbh":"cm","H":"m"},"variables":{"dbh":"D"},"output_unit":"kg"},"taxon":{"level":"species","name":"Populus tremuloides","family":"Salicaceae","group":"broadleaf"},"region":{"scope":"national","countries":["CA"],"place":"Canada: Alberta, Manitoba, Newfoundland and Labrador, Nova Scotia, Northwest Territories, Ontario, Quebec, Saskatchewan, Yukon (ENFOR archival data, early 1980s)","biomes":["boreal","temperate"]},"fit":{"n_trees":773,"dbh_min_cm":0.7,"dbh_max_cm":47.2,"h_min_m":1.8,"h_max_m":28.3,"r2":0.98,"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":"Trembling aspen bwood1 0.0142","locator":"Table 4, Trembling aspen"},{"field":"expression","quote":"bwood2 1.9389","locator":"Table 4, Trembling aspen"},{"field":"expression","quote":"bwood3 1.0572","locator":"Table 4, Trembling aspen"},{"field":"expression","quote":"bbark1 0.0063","locator":"Table 4, Trembling aspen"},{"field":"expression","quote":"bbark2 2.0819","locator":"Table 4, Trembling aspen"},{"field":"expression","quote":"bbark3 0.6617","locator":"Table 4, Trembling aspen"},{"field":"fit.n_trees","quote":"Trembling aspen        773     17.7±0.4     15.8±0.2     161.7±7.2","locator":"Table 2 (No. of trees)"},{"field":"fit.dbh_min_cm","quote":"(0.7;47.2)   (1.8;28.3)    (0.1;1081.5)","locator":"Table 2, Trembling aspen (ranges of dbh, height, total biomass)"},{"field":"fit.r2","quote":"Stem 0.0092 0.95 37.6 3.74 0.0003 0.98 25.3 4.67","locator":"Table 5, Trembling aspen (AdjRSq in the dbh- and height-based set, second block)"}],"check":[{"inputs":{"D":20,"H":15},"expected":102.1634,"origin":"computed","note":"computed from the published form at dbh = 20 cm, H = 15 m"}],"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."}