# NSVB black willow, species-level (all ecodivisions): total aboveground biomass (without foliage), Schumacher-Hall model (Eq. 1) Aboveground biomass equation (without leaves) for Salix nigra, United States, from Westfall et al. 2024. 6 trees, DBH 37.08–63.75 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it. ## Equation As printed in Westfall et al. 2024 (Table S8a (Table S8a_total_biomass_coefs_spcd.csv, WO-GTR-104-Supp1), columns SPCD,DIVISION,STDORGCD,model,a,a1,b,b1,c,c1): > 922,,,1,0.183406635,,1.928925794,,0.776309008, Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#equation In this library's units, ready to compute (aboveground biomass, without leaves in kg): ``` Aboveground biomass, without leaves = 0.45359237 * 0.183406635 * (D/2.54)^1.928925794 * (H/0.3048)^0.776309008 ``` Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m). The source's own form: 0.183406635 * DBH^1.928925794 * HT^0.776309008, with DBH in in, HT in ft; output in lb. Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#canonical This total leaves out leaves (foliage), as the source defines it. ## What it covers - Output: Aboveground biomass, without leaves, kg - Taxon: Salix nigra (species), family Salicaceae; broadleaf - Where: United States, species-level fit (NSVB uses it wherever table S8a has no row for the tree's ecodivision). Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#where - Biomes: subtropical - Stand: not stated - Trees measured: 6. Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#n_trees - DBH range: 37.08–63.75 cm. Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#dbh - Method: NSVB Schumacher-Hall model (Eq. 1), coefficients for SPCD 922 (species-level row, no DIVISION) from table S8a; fitted with weighted regression to destructively sampled trees. Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#method - Verification: read in the original source - Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#checked_at A missing fit statistic is one the source doesn't state, or that we haven't recorded; it is never estimated. Outside the stated DBH range or region, the equation is an extrapolation. ## Source Westfall, J.A., Coulston, J.W., Gray, A.N., Shaw, J.D., Radtke, P.J., Walker, D.M., Weiskittel, A.R., et al. (2024). A national-scale tree volume, biomass, and carbon modeling system for the United States. Gen. Tech. Rep. WO-104. Washington, DC: USDA Forest Service. 37 p. - DOI: https://doi.org/10.2737/WO-GTR-104 - Access: open access - Copy we read: https://research.fs.usda.gov/download/treesearch/66998.pdf - Every equation from this source: https://treeallometry.org/sources/westfall-2024/ - Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#source ## The facts, in the source's words **Equation** (Table S8a (Table S8a_total_biomass_coefs_spcd.csv, WO-GTR-104-Supp1), columns SPCD,DIVISION,STDORGCD,model,a,a1,b,b1,c,c1): > 922,,,1,0.183406635,,1.928925794,,0.776309008, Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#equation **Equation** (Eq. 1, p. 2): > yi = a × Di^b × Hi^c + εi Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#quote-expression **Units** (Methods, Model development, p. 2): > Di is diameter (inches) at breast height (4.5 feet), Hi is total tree height (feet) Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#quote-published-units **published.output unit** (Examples of tree-level calculations, p. 8): > units for volume and biomass predictions are cubic feet and pounds, respectively Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#quote-published-output-unit **Taxon** (FIADB REF_SPECIES.csv (FIA DataMart), columns SPCD,COMMON_NAME,SHARED_COMMON_NAME_IND,GENUS,SPECIES,VARIETY,SUBSPECIES,SCIENTIFIC_NAME: the species codes the NSVB tables use): > 922,black willow,N,Salix,nigra,,,Salix nigra Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#quote-taxon **output.excludes** (Methods, Model development, p. 4): > total aboveground biomass (without foliage) Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#quote-output-excludes **Where** (Results, p. 6): > If a species occurs in an ecodivision not explicitly listed, the entry having no ecodivision noted is used. Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#quote-region **Fit** (Table S13_component_spcd_scorecard.csv (WO-GTR-104-Supp1), columns VAR2,VAR3,SPCD,N,Avg_DBH,Min_DBH,Max_DBH): > "Total Tree Wood+Bark","TT_WDBK_DW_ADJ","922",6,19.6,14.6,25.1 Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#quote-fit **Fit** (Methods, Model development, p. 6): > key modeling statistics such as sample sizes (n), tree diameter distributions (minimum, mean, and maximum) Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#quote-fit-2 **Our note:** Output is gross AGB without foliage (AGBPredicted), before NSVB's cull and broken-top reductions and harmonization with components. DBH is measured at 4.5 ft (1.37 m). Paper units: in, ft, lb; expression converts D cm→in (/2.54), H m→ft (/0.3048) and lb→kg (×0.45359237). n and the DBH range are from the scorecard for TT_WDBK_DW_ADJ across ecodivisions (table S13). For AGB the scorecard rates NSVB's harmonized total (TT_WDBK_DW_ADJ), not this model alone; only its n and DBH range are used. Species-level row: NSVB applies it in every ecodivision that has no row of its own for this species in this table. ## Checks this equation passes On every build, the library's form and the source's own form (in its units) must both give these values within 1%. | Inputs | Expected | We get | From | | --- | --- | --- | --- | | D = 50.292, H = 21.336 | 714 | 714 | Computed from the printed form: computed from the published form at D = 19.8 in, H = 70 ft, converted to cm, m and kg | Cite: https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/#checks The calculator on the page shows carbon as biomass × 0.47 (IPCC 2006 Guidelines, Vol. 4, Ch. 4, Table 4.3) and CO₂e as carbon × 44/12. ## How to cite Cite the source for the equation: Westfall, J.A., Coulston, J.W., Gray, A.N., Shaw, J.D., Radtke, P.J., Walker, D.M., Weiskittel, A.R., et al. (2024). A national-scale tree volume, biomass, and carbon modeling system for the United States. Gen. Tech. Rep. WO-104. Washington, DC: USDA Forest Service. 37 p. https://doi.org/10.2737/WO-GTR-104 Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "NSVB black willow, species-level (all ecodivisions): total aboveground biomass (without foliage), Schumacher-Hall model (Eq. 1)", checked 2026-11-03, https://treeallometry.org/equations/westfall-2024-salix-nigra-agb/. Data CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Quotes are the authors' words. Data for this equation: https://treeallometry.org/data/equations/westfall-2024-salix-nigra-agb.json Report a problem: email info@restorationscope.com with the equation id (westfall-2024-salix-nigra-agb) and where the right value appears.