{"id":"lambert-2005-trembling-aspen-dbh-h-branches","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 (branches; Table 4)","output":{"quantity":"branch_biomass"},"expression":"0.0137 * D^2.927 * H^(-0.6221)","published":{"expression":"0.0137 * dbh^2.927 * H^(-0.6221)","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":0.76,"method":"Nonlinear seemingly unrelated regression with weight functions; additivity constrained so compartments sum to total"},"evidence":[{"field":"expression","quote":"y branches = β branches1D βbranches2Hβbranches3 + e branches","locator":"Eq. 3"},{"field":"expression","quote":"bbranches1 0.0137","locator":"Table 4, Trembling aspen"},{"field":"expression","quote":"bbranches2 2.9270","locator":"Table 4, Trembling aspen"},{"field":"expression","quote":"bbranches3 –0.6221","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":"Branches 0.0001 0.76 12.6 4.49 0.0003 0.76 12.4 4.05","locator":"Table 5, Trembling aspen (AdjRSq in the dbh- and height-based set, second block)"}],"check":[{"inputs":{"D":20,"H":15},"expected":16.3376,"origin":"computed","note":"computed from the published form at dbh = 20 cm, H = 15 m"}],"verification":"original_read","checked_at":"2026-11-03","notes":"All branches, cut at the stem base (live branches; dead branches excluded). 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."}