Tree Allometrics

Acer rubrum / Branch biomass

NSVB red maple, species-level: total branch biomass (wood and bark), Schumacher-Hall model (Eq. 1)

Branch biomassAcer rubrum · SapindaceaeUnited StatesRead from the original paper
Photo of Acer rubrum
mefisher · CC0 · iNaturalist
Equation

As printed (Example 2, p. 15)

Wbranch = 0.011144618401 × 11.1^3.269520661293 × 38^0.421304343724 = 135.001927997271

In this library's units, ready to compute (kg)

Branch biomass = 0.45359237 * 0.011144618401 * (D/2.54)^3.269520661293 * (H/0.3048)^0.421304343724
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

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).

Source
Assume a red maple (Acer rubrum; SPCD = 316)
Taxon · Example 2, p. 12
growing in the Warm Continental Mountains (DIVISION = M210)
check · Example 2, p. 12
yi = a × Di^b × Hi^c + εi
Equation · Eq. 1, p. 2
Di is diameter (inches) at breast height (4.5 feet), Hi is total tree height (feet)
Units · Methods, Model development, p. 2
units for volume and biomass predictions are cubic feet and pounds, respectively
published.output unit · Examples of tree-level calculations, p. 8
total branch wood and bark biomass
Output · Methods, Model development, p. 4
"Branches","BRT_WDBK_DW_TOT","316",469,6.58379530916844,1,33.7
Fit · Table S13_component_spcd_scorecard.csv (WO-GTR-104-Supp1), columns VAR2,VAR3,SPCD,N,Avg_DBH,Min_DBH,Max_DBH
key modeling statistics such as sample sizes (n), tree diameter distributions (minimum, mean, and maximum)
Fit · Methods, Model development, p. 6
If a species occurs in an ecodivision not explicitly listed, the entry having no ecodivision noted is used.
Where · Results, p. 6
Trees measured
469
DBH range
2.54–85.6 cm
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
Where
United States, species-level fit (NSVB uses it wherever table S7a has no row for the tree's ecodivision)
Last checked
2026-11-03
Calculate
Height from
61.2
Branch biomass (kg)
28.8
Carbon (kg), ×0.47
106
CO₂e (kg), ×44/12
Fitted DBH range01002003004005006001020304050DBH (cm)Branch biomass (kg)Branch biomass

Shaded: the DBH range the model was fitted on. Other inputs held at the values above.

Checks this equation passes

On every build, the library's form and the paper's own form (in its units) must both give these values within 1%.

InputsExpectedWe getFrom
D = 28.2, H = 11.661.261.2Value 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

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