NSVB paper birch, Warm Continental Division (210): branch biomass (wood and bark), Schumacher-Hall model (Eq. 1)

Branch biomassBetula papyrifera · BetulaceaeUnited StatesRead from the original paper

Equation

As printed (Table S7a (Table S7a_branch_biomass_coefs_spcd.csv, WO-GTR-104-Supp1), columns SPCD,DIVISION,STDORGCD,model,a,b,b1,c)

375,210,,1,21.60137175,3.225808314,,-1.344948117

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

Branch biomass = 0.45359237 * 21.60137175 * (D/2.54)^3.225808314 * (H/0.3048)^(-1.344948117)

D: Diameter at breast height (1.3 m), cm
H: Total tree height, m

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 BRT_WDBK_DW_TOT in 210 (table S19).

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:10.2737/WO-GTR-104 · Open access · copy we read

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

375,paper birch,N,Betula,papyrifera,,,Betula papyrifera

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

total branch wood and bark biomass

Output · Methods, Model development, p. 4

"Branches","BRT_WDBK_DW_TOT","375","210","WARM_CONTINENTAL_DIVISION",83,6.3421686746988,1.3,13.6

Fit · Table S19_component_division_spcd_scorecard.csv (WO-GTR-104-Supp1), columns VAR2,VAR3,SPCD,DIVISION,DIVISION_DESCRIPTION,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

Trees measured: 83
DBH range: 3.3–34.54 cm
Method: NSVB Schumacher-Hall model (Eq. 1), coefficients for SPCD 375 in DIVISION 210 from table S7a; fitted with weighted regression to destructively sampled trees
Where: FIA ecodivision Warm Continental Division (210), mapped in GTR fig. 1
Last checked: 2026-11-03

Calculate

DBH (cm)Height (m)

Height from

97.9

Branch biomass (kg)

Carbon (kg), ×0.47

169

CO₂e (kg), ×44/12

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%.

Inputs	Expected	We get	From
D = 30.5, H = 21.3	97.9	97.9	Computed from the printed form computed from the published form at D = 12 in, H = 70 ft, converted to cm, m and kg

Report a problem with this equation · JSON

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Compare these curves

NSVB paper birch, Warm Continental Division (210): branch biomass (wood and bark), Schumacher-Hall model (Eq. 1)

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