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

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. (4; Ŷ = b0 × DBH^b1)):

> Root system 1 1/0.00007 × DBH4.3051 0.0405 (±0.0064)*** 2.3402 (±0.0545)***

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

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

```
Root biomass = 0.0405 * D^2.3402
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: 0.0405 * DBH^2.3402, with DBH in cm; output in kg.
Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh/#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/#where
- Biomes: tropical, dryland
- Stand: natural
- Trees measured: 93. Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh/#n_trees
- DBH range: 5–32 cm. Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh/#dbh
- R²: 0.9973. Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh/#r2
- Method: Weighted nonlinear least squares (nls, Gauss-Newton); r2 is the adjusted R² in Table 5; CVr = 24.6597%. Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh/#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/#source

## The facts, in the source's words

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

> Root system 1 1/0.00007 × DBH4.3051 0.0405 (±0.0064)*** 2.3402 (±0.0545)***

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

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

> DBH range 5–32 cm

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

**R²** (Table 5, Root system):

> Root system 1 99.73 24.6597

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

**Our note:** Recommended by the author as the preferred model when only DBH is available ("models using either DBH or RCD only should be preferred"). Weight function 1/(0.00007 × DBH^4.3051). 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 | 5.26 | 5.26 | Computed from the printed form: hand-computed from the Table 4 coefficients |
| D = 15 | 22.9 | 22.9 | Computed from the printed form: hand-computed from the Table 4 coefficients |
| D = 25 | 75.7 | 75.7 | Computed from the printed form: hand-computed from the Table 4 coefficients |

Cite: https://treeallometry.org/equations/magalhaes-2015-root-system-dbh/#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 (Table 4, form 4)", checked 2026-11-02, https://treeallometry.org/equations/magalhaes-2015-root-system-dbh/. 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.json
Report a problem: email info@restorationscope.com with the equation id (magalhaes-2015-root-system-dbh) and where the right value appears.