# Birch total root biomass, disaggregated model (Eq. 24), Liaoning site

Root biomass equation for Betula platyphylla, China, from Pan & Wang 2022. 493 trees, DBH 3.4–11.9 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Pan & Wang 2022 (Eq. 24, Section 3.3):

> ft(D, H; βt) = exp[Bt1 + βt2 ln DBH + βt3 ln HT + βts2S2 + βts3S3]

Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#equation

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

```
Root biomass = exp(-1.0113 + 2.2706 * ln(D) - 0.8676 * ln(H) - 0.0108)
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: exp(-1.0113 + 2.2706 * ln(DBH) - 0.8676 * ln(HT) - 0.0108 * 1 - 0.6541 * 0), with DBH in cm, HT in m; output in kg.
Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#canonical

## What it covers

- Output: Root biomass, kg
- Taxon: Betula platyphylla (species), family Betulaceae; broadleaf
- Where: Liaoning Province, Northeast China. Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#where
- Biomes: temperate
- Stand: plantation
- Trees measured: 493. Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#n_trees
- DBH range: 3.4–11.9 cm. Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#dbh
- Height range: 4.5–14 m. Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#height
- Method: log-transformed (multiplicative error) nonlinear system with site dummies. Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#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

Pan, L., & Wang, X. (2022). Additive Root Biomass Equations for Betula platyphylla Suk. Plantations in Northeast China. Forests, 13(5), 661.

- DOI: https://doi.org/10.3390/f13050661
- Access: open access
- Copy we read: https://www.mdpi.com/1999-4907/13/5/661/pdf?version=1650953273
- Every equation from this source: https://treeallometry.org/sources/pan-2022/
- Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#source

## The facts, in the source's words

**Trees measured** (Section 2.1):

> with a total of 493 sample trees

Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#quote-fit-n-trees

**Smallest DBH** (Table 2 (DBH 3.4 cm, HT 4.5 m minimum)):

> Min 3.40 4.50 0.10 0.02 0.02 0.14

Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#quote-fit-dbh-min-cm

**Largest DBH** (Table 2 (DBH 11.9 cm, HT 14.0 m maximum)):

> Max 11.90 14.00 9.29 10.19 3.98 20.27

Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#quote-fit-dbh-max-cm

**Equation** (Eq. 24, Section 3.3):

> ft(D, H; βt) = exp[Bt1 + βt2 ln DBH + βt3 ln HT + βts2S2 + βts3S3]

Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#equation

**Equation** (Table 6):

> ft βt1 −1.0113 0.1807 0.0000; βt2 2.2706 0.1251 0.0000; βt3 −0.8676 0.12 0.0000; βts2 −0.0108 0.0946 0.9088; βts3 −0.6541 0.0682 0.0000

Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#quote-expression

**Our note:** Total root biomass function ft of the disaggregated system. Site: Liaoning, S2 = 1 and S3 = 0. The paper fits one model with site dummies (Liaoning when S2 = 1 and S3 = 0, Jilin when S2 = 0 and S3 = 1, Heilongjiang when S2 = 0 and S3 = 0); this file sets the dummies for one site. It is fitted on all 493 trees from the three sites (Heilongjiang 333, Jilin 26, Liaoning 134 per Table 1), so the site term is a shift on common slopes. The paper reports no back-transform correction factor for the log-normal error and none is applied. The paper reports only ten-fold cross-validation R2, not a fit R2, so none is given here. Roots were excavated and sieved into coarse (>5 mm), medium (2-5 mm) and fine (<2 mm) classes; the total includes all three.

## 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 = 9.4 | 5.79 | 5.79 | Computed from the printed form: hand-computed from the published form |
| D = 11, H = 13 | 9 | 9 | Computed from the printed form: hand-computed from the published form |

Cite: https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/#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: Pan, L., & Wang, X. (2022). Additive Root Biomass Equations for Betula platyphylla Suk. Plantations in Northeast China. Forests, 13(5), 661. https://doi.org/10.3390/f13050661

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Birch total root biomass, disaggregated model (Eq. 24), Liaoning site", checked 2026-11-02, https://treeallometry.org/equations/pan-2022-bgb-total-disagg-liaoning/. 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/pan-2022-bgb-total-disagg-liaoning.json
Report a problem: email info@restorationscope.com with the equation id (pan-2022-bgb-total-disagg-liaoning) and where the right value appears.