Tree Allometrics

Equations / Branch biomass

NSVB willow spp., species-level (all ecodivisions): branch biomass (wood and bark), Schumacher-Hall model (Eq. 1)

Branch biomassSalix · SalicaceaeUnited StatesRead from the original paper
Covers the whole genus
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)

920,,,1,1.010223097,3.008140626,,-0.589318704

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

Branch biomass = 0.45359237 * 1.010223097 * (D/2.54)^3.008140626 * (H/0.3048)^(-0.589318704)
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

FIA's SPCD 920 (Salix spp.) is for trees recorded only to genus, so this is a genus record. 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 across ecodivisions (table S13). Species-level row: NSVB applies it in every ecodivision that has no row of its own for this species in this table.

Source
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
920,willow spp.,N,Salix,spp.,,,Salix spp.
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
If a species occurs in an ecodivision not explicitly listed, the entry having no ecodivision noted is used.
Where · Results, p. 6
"Branches","BRT_WDBK_DW_TOT","920",7,4.07142857142857,1.3,10.1
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
Trees measured
7
DBH range
3.3–25.65 cm
Method
NSVB Schumacher-Hall model (Eq. 1), coefficients for SPCD 920 (species-level row, no DIVISION) from table S7a; 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
7.04
Branch biomass (kg)
3.31
Carbon (kg), ×0.47
12.1
CO₂e (kg), ×44/12
Fitted DBH range020406080100120140160510152025303540DBH (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 = 14.5, H = 21.37.047.04Computed from the printed form
computed from the published form at D = 5.7 in, H = 70 ft, converted to cm, m and kg

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