Tree Allometrics

Equations / Aboveground biomass, without leaves

NSVB willow spp., species-level (all ecodivisions): total aboveground biomass (without foliage), Schumacher-Hall model (Eq. 1)

Aboveground biomass, without leavesSalix · SalicaceaeUnited StatesRead from the original paper
Covers the whole genus
Equation

As printed (Table S8a (Table S8a_total_biomass_coefs_spcd.csv, WO-GTR-104-Supp1), columns SPCD,DIVISION,STDORGCD,model,a,a1,b,b1,c,c1)

920,,,1,0.183406635,,1.934937524,,0.776309008,

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

Aboveground biomass, without leaves = 0.45359237 * 0.183406635 * (D/2.54)^1.934937524 * (H/0.3048)^0.776309008
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. Output is gross AGB without foliage (AGBPredicted), before NSVB's cull and broken-top reductions and harmonization with components. 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 TT_WDBK_DW_ADJ across ecodivisions (table S13). For AGB the scorecard rates NSVB's harmonized total (TT_WDBK_DW_ADJ), not this model alone; only its n and DBH range are used. 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 aboveground biomass (without foliage)
output.excludes · 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
"Total Tree Wood+Bark","TT_WDBK_DW_ADJ","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 S8a; fitted with weighted regression to destructively sampled trees
Where
United States, species-level fit (NSVB uses it wherever table S8a has no row for the tree's ecodivision)
Last checked
2026-11-03
Calculate
Height from
65.3
Aboveground biomass, without leaves (kg)
30.7
Carbon (kg), ×0.47
113
CO₂e (kg), ×44/12
Fitted DBH range0100200300400500510152025303540DBH (cm)Aboveground biomass, without leaves (kg)Aboveground biomass, without leaves

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 = 21.365.365.3Computed 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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