# Root system dry biomass from DBH and height (Table 4, form 5)

Root biomass equation for Androstachys johnsonii, Mozambique, from Magalhães 2015. 93 trees, DBH 5–32 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Magalhães 2015 (Table 4, Root system rows, and Eq. (5; Ŷ = b0 × DBH^b1 × TH^b2)):

> Root system 2 1/0.000008 × DBH1.7645 0.0185 (±0.0064)** 2.1990 (±0.0793)*** 0.4699 (±0.1898)*

Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#equation

In this library's units, ready to compute (root biomass in kg):

```
Root biomass = 0.0185 * D^2.199 * H^0.4699
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 0.0185 * DBH^2.199 * TH^0.4699, with DBH in cm, TH in m; output in kg.
Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#canonical

## What it covers

- Output: Root biomass, kg
- Taxon: Androstachys johnsonii (species), family Picrodendraceae; broadleaf
- Where: Mabote, Funhalouro, Panda, Mandlakaze and Chibuto districts, Inhambane and Gaza provinces. Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#where
- Biomes: tropical, dryland
- Stand: natural
- Trees measured: 93. Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#n_trees
- DBH range: 5–32 cm. Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#dbh
- Height range: 5.69–16 m. Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#height
- R²: 0.9978. Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#r2
- Method: Weighted nonlinear least squares (nls, Gauss-Newton); r2 is the adjusted R² in Table 5; CVr = 23.406%. Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#checked_at

A missing fit statistic is one the source doesn't state, or that we haven't recorded; it is never estimated. Outside the stated DBH range or region, the equation is an extrapolation.

## Source

Magalhães, T.M. (2015). Allometric equations for estimating belowground biomass of Androstachys johnsonii Prain. Carbon Balance and Management, 10, 16.

- DOI: https://doi.org/10.1186/s13021-015-0027-4
- Access: open access
- Copy we read: https://cbmjournal.biomedcentral.com/track/pdf/10.1186/s13021-015-0027-4
- Every equation from this source: https://treeallometry.org/sources/magalhaes-2015/
- Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#source

## The facts, in the source's words

**Equation** (Table 4, Root system rows, and Eq. (5; Ŷ = b0 × DBH^b1 × TH^b2)):

> Root system 2 1/0.000008 × DBH1.7645 0.0185 (±0.0064)** 2.1990 (±0.0793)*** 0.4699 (±0.1898)*

Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#equation

**Trees measured** (Methods, Data acquisition):

> 93 trees (DBH range 5–32 cm; TH range 5.69–16 m)

Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#quote-fit-n-trees

**Smallest DBH** (Methods, Data acquisition):

> DBH range 5–32 cm

Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#quote-fit-dbh-min-cm

**R²** (Table 5, Root system):

> Root system 2 99.78 23.4060

Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#quote-fit-r2

**Output** (Methods, Data acquisition):

> The dry weight of the root system was obtained by summing the dry weights of taproot and lateral roots (fine and coarse ones).

Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#quote-output

**Our note:** Ranked below the D²H form (form 6) by CVr but the author notes height improved fit only negligibly and prefers DBH-only or RCD-only models. Weight function 1/(0.000008 × DBH^1.7645). Root system = taproot (including root collar) + lateral roots, excavated to full depth, fine roots included, dry mass at 105 C; stump above 20 cm is not part of it. Independent (not WNSUR additive) model, which the author recommends over the simultaneous ones. One of four independent root-system models in Table 4; all performed almost equally.

## Checks this equation passes

On every build, the library's form and the source's own form (in its units) must both give these values within 1%.

| Inputs | Expected | We get | From |
| --- | --- | --- | --- |
| D = 8, H = 7 | 4.47 | 4.47 | Computed from the printed form: hand-computed from the Table 4 coefficients |
| D = 15, H = 10 | 21.1 | 21.1 | Computed from the printed form: hand-computed from the Table 4 coefficients |
| D = 25, H = 13 | 73.2 | 73.2 | Computed from the printed form: hand-computed from the Table 4 coefficients |

Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/#checks

The calculator on the page shows carbon as biomass × 0.47 (IPCC 2006 Guidelines, Vol. 4, Ch. 4, Table 4.3) and CO₂e as carbon × 44/12.

## How to cite

Cite the source for the equation: Magalhães, T.M. (2015). Allometric equations for estimating belowground biomass of Androstachys johnsonii Prain. Carbon Balance and Management, 10, 16. https://doi.org/10.1186/s13021-015-0027-4

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Root system dry biomass from DBH and height (Table 4, form 5)", checked 2026-11-02, https://treeallometry.org/equations/magalhaes-2015-root-system-dbh-th/. Data CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Quotes are the authors' words.

Data for this equation: https://treeallometry.org/data/equations/magalhaes-2015-root-system-dbh-th.json
Report a problem: email info@restorationscope.com with the equation id (magalhaes-2015-root-system-dbh-th) and where the right value appears.