Tree Allometrics

Equations / Branch biomass

NSVB ash spp., Subtropical Division (230): branch biomass (wood and bark), Schumacher-Hall model (Eq. 1)

Branch biomassFraxinus · OleaceaeUnited 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)

540,230,,1,1.479473428,2.802762416,,-0.550722765

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

Branch biomass = 0.45359237 * 1.479473428 * (D/2.54)^2.802762416 * (H/0.3048)^(-0.550722765)
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

FIA's SPCD 540 (Fraxinus 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 in 230 (table S19).

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
540,ash spp.,N,Fraxinus,spp.,,,Fraxinus 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
"Branches","BRT_WDBK_DW_TOT","540","230","SUBTROPICAL_DIVISION",235,3.46297872340426,1,23.5
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
235
DBH range
2.54–59.69 cm
Method
NSVB Schumacher-Hall model (Eq. 1), coefficients for SPCD 540 in DIVISION 230 from table S7a; fitted with weighted regression to destructively sampled trees
Where
FIA ecodivision Subtropical Division (230), mapped in GTR fig. 1
Last checked
2026-11-03
Calculate
Height from
68.4
Branch biomass (kg)
32.2
Carbon (kg), ×0.47
118
CO₂e (kg), ×44/12
Fitted DBH range0100200300400500102030405060DBH (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 = 30.5, H = 21.368.468.4Computed from the printed form
computed from the published form at D = 12 in, H = 70 ft, converted to cm, m and kg

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