Tree Allometrics

Quercus rubra / Foliage biomass

NSVB northern red oak, Warm Continental Division (210): foliage biomass, Schumacher-Hall model (Eq. 1)

Foliage biomassQuercus rubra · FagaceaeUnited StatesRead from the original paper
Photo of Quercus rubra
© Sandy Wolkenberg · CC BY · iNaturalist
Equation

As printed (Table S9a (Table S9a_foliage_coefs_spcd.csv, WO-GTR-104-Supp1), columns SPCD,DIVISION,STDORGCD,model,a,a1,b,b1,c,c1)

833,210,,1,0.044051316,,1.89179929,,0.326716181,

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

Foliage biomass = 0.45359237 * 0.044051316 * (D/2.54)^1.89179929 * (H/0.3048)^0.326716181
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 FOL_DW in 210 (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
833,northern red oak,N,Quercus,rubra,,,Quercus rubra
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
"Foliage","FOL_DW","833","210","WARM_CONTINENTAL_DIVISION",102,9.23039215686275,1.9,30.2
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
102
DBH range
4.83–76.71 cm
Method
NSVB Schumacher-Hall model (Eq. 1), coefficients for SPCD 833 in DIVISION 210 from table S9a; 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
Height from
8.81
Foliage biomass (kg)
4.14
Carbon (kg), ×0.47
15.2
CO₂e (kg), ×44/12
Fitted DBH range05101520253035102030405060DBH (cm)Foliage biomass (kg)Foliage 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 = 21.38.818.81Computed 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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