Tree Allometrics

Quercus alba / Branch biomass

NSVB white oak, Hot Continental Mountains (M220): total branch biomass (wood and bark), Schumacher-Hall model (Eq. 1)

Branch biomassQuercus alba · FagaceaeUnited StatesRead from the original paper
Photo of Quercus alba
© Douglas Goldman · CC BY-SA · iNaturalist
Equation

As printed (Example 4, p. 24)

Wbranch = 0.003795934624 × 18.1^2.337549205679 × 65^1.30586951288 = 770.251512414918

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

Branch biomass = 0.45359237 * 0.003795934624 * (D/2.54)^2.337549205679 * (H/0.3048)^1.30586951288
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

Output is dry weight of all branch wood and bark (Wbranch) before NSVB's harmonization with total AGB; the harmonized branch weight differs. Coefficients for white oak in the Hot Continental Mountains (M220) only; other ecodivisions use other coefficients. 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 M220 (table S19). DBH is measured at 4.5 ft (1.37 m).

Source
a live white oak (Quercus alba; SPCD = 802) tree having D = 18.1 inches, H = 65 feet
Taxon · Example 4, p. 21
growing in the Hot Continental Mountains (DIVISION = M220)
Where · Example 4, p. 21
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
total branch wood and bark biomass
Output · Methods, Model development, p. 4
"Branches","BRT_WDBK_DW_TOT","802","M220","HOT_CONTINENTAL_REGIME_MOUNTAINS",98,12.4326530612245,1,42
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
98
DBH range
2.54–106.68 cm
Method
NSVB Schumacher-Hall model (Eq. 1), coefficients for SPCD 802 in DIVISION M220 from table S7a (the total branch biomass (wood and bark) table used in Example 4); fitted with weighted regression to destructively sampled trees
Where
FIA ecodivision M220, Hot Continental Mountains (mapped in GTR fig. 1)
Last checked
2026-11-03
Calculate
Height from
349
Branch biomass (kg)
164
Carbon (kg), ×0.47
602
CO₂e (kg), ×44/12
Fitted DBH range05001,0001,5002,00020406080DBH (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 = 46, H = 19.8349349Value printed in the paper
Example 4 (p. 24) prints 770.251512414918 lb for D = 18.1 in, H = 65 ft; inputs and expected converted to cm, m, kg

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