# NSVB red maple, species-level: total branch biomass (wood and bark), Schumacher-Hall model (Eq. 1) Branch biomass equation for Acer rubrum, United States, from Westfall et al. 2024. 469 trees, DBH 2.54–85.6 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 (Example 2, p. 15): > Wbranch = 0.011144618401 × 11.1^3.269520661293 × 38^0.421304343724 = 135.001927997271 Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#equation In this library's units, ready to compute (branch biomass in kg): ``` Branch biomass = 0.45359237 * 0.011144618401 * (D/2.54)^3.269520661293 * (H/0.3048)^0.421304343724 ``` Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m). The source's own form: 0.011144618401 * DBH^3.269520661293 * HT^0.421304343724, with DBH in in, HT in ft; output in lb. Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#canonical ## What it covers - Output: Branch biomass, kg - Taxon: Acer rubrum (species), family Sapindaceae; broadleaf - Where: United States, species-level fit (NSVB uses it wherever table S7a has no row for the tree's ecodivision). Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#where - Biomes: subtropical, temperate, montane - Stand: not stated - Trees measured: 469. Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#n_trees - DBH range: 2.54–85.6 cm. Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#dbh - Method: NSVB Schumacher-Hall model (Eq. 1), coefficients for SPCD 316 species-level row (no DIVISION) from table S7a (the total branch biomass (wood and bark) table used in Example 2); fitted with weighted regression to destructively sampled trees. Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#method - Verification: read in the original source - Last checked: 2026-11-03. Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#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-acer-rubrum-branch/#source ## The facts, in the source's words **Equation** (Example 2, p. 15): > Wbranch = 0.011144618401 × 11.1^3.269520661293 × 38^0.421304343724 = 135.001927997271 Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#equation **Taxon** (Example 2, p. 12): > Assume a red maple (Acer rubrum; SPCD = 316) Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#quote-taxon **check** (Example 2, p. 12): > growing in the Warm Continental Mountains (DIVISION = M210) Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#quote-check **Equation** (Eq. 1, p. 2): > yi = a × Di^b × Hi^c + εi Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#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-acer-rubrum-branch/#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-acer-rubrum-branch/#quote-published-output-unit **Output** (Methods, Model development, p. 4): > total branch wood and bark biomass Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#quote-output **Fit** (Table S13_component_spcd_scorecard.csv (WO-GTR-104-Supp1), columns VAR2,VAR3,SPCD,N,Avg_DBH,Min_DBH,Max_DBH): > "Branches","BRT_WDBK_DW_TOT","316",469,6.58379530916844,1,33.7 Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#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-acer-rubrum-branch/#quote-fit-2 **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-acer-rubrum-branch/#quote-region **Our note:** Output is dry weight of all branch wood and bark (Wbranch) before NSVB's harmonization with total AGB; the harmonized branch weight differs. Species-level coefficients (no ecodivision): table S7a in the supplement has no red maple row for M210, the division of the tree in Example 2, so the example uses the species-level row; NSVB uses division-specific coefficients where table S7a has a row for the tree's division. These are the coefficients NSVB applies to red maple in the Warm Continental Mountains (M210). 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 BRT_WDBK_DW_TOT across ecodivisions (table S13). DBH is measured at 4.5 ft (1.37 m). ## 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 = 28.194, H = 11.5824 | 61.2 | 61.2 | Value printed in the paper: Example 2 (p. 15) prints 135.001927997271 lb for D = 11.1 in, H = 38 ft; inputs and expected converted to cm, m, kg | Cite: https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/#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 red maple, species-level: total branch biomass (wood and bark), Schumacher-Hall model (Eq. 1)", checked 2026-11-03, https://treeallometry.org/equations/westfall-2024-acer-rubrum-branch/. 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-acer-rubrum-branch.json Report a problem: email info@restorationscope.com with the equation id (westfall-2024-acer-rubrum-branch) and where the right value appears.