Tree Allometrics

Equations / Root biomass

Oak root biomass (compatible total-biomass system)

Root biomassQuercus · FagaceaeChinamixedRead from the original paper
Covers the whole genus
Equation

As printed (Table 10, Eq. 35-37)

Broot = 0.018969 (D 2 H) 0.89162 (37)

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

Root biomass = 0.018969 * (D^2 * H)^0.89162
D
Diameter at breast height (1.3 m), cm
H
Total tree height, m

Final root model of the compatible system, fitted on trees with root samples (n from Table 1). Compatible total-biomass system (aboveground fitted independently, total and root fitted jointly by simultaneous estimation; weighted nonlinear least squares). Total = aboveground + root. The paper lists the sample as stratified random felled trees across eight diameter classes (4-32 cm) from 2022-2023; the reported minimum and maximum DBH and height are for all sampled trees of the species (Table 1). Root biomass was measured on a subset only (whole-root excavation: root collar, coarse roots, fine roots), so root and total fit ranges are not given beyond the full sample. No back-transform factor (nonlinear fit). The paper also gives aboveground-component (stem, crown, wood, bark, branch, foliage) systems (Tables 17-39), not added here. Eq. 37 and Table 10 print the same parameters. R² is the evaluation row marked * (the 50 trees with measured roots, matching n_trees; the paper's Discussion cites these starred values as the root-model R²); the unstarred row (0.8592) is evaluated over all sampled trees, most of which have no measured roots.

Source
Oak 157 (50) (Total Samples (Root Samples))
Trees measured · Table 1
(28) * 0.7778 23.78 −0.80 14.34 47.64 85.29
R² · Table 13, row (28) * (root model evaluated on the trees with measured root samples)
Trees measured
50
R²
0.7778
Method
weighted nonlinear least squares
Where
Hunan Province (14 prefecture-level cities and autonomous prefectures)
Last checked
2026-11-02
Calculate
Height from
8.17
Root biomass (kg)
3.84
Carbon (kg), ×0.47
14.1
CO₂e (kg), ×44/12
020406080100510152025303540DBH (cm)Root biomass (kg)Root 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 = 10, H = 98.178.17Computed from the printed form
hand-computed from the published form
D = 30, H = 20118118Computed from the printed form
hand-computed from the published form

Report a problem with this equation · JSON

Related

Compare these curves