# Betula papyrifera branch biomass, cross-sectional area at 0.3 m (NLS)

Branch biomass equation for Betula papyrifera, Canada, from Flade et al. 2021. 15 trees. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Flade et al. 2021 (Table 3, Eqs. 2-5):

> Betula papyrifera Branches NLS 12.7152 1.2921 0.905 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Cite: https://treeallometry.org/equations/flade-2021-bepa-branch-nls/#equation

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

```
Branch biomass = 12.7152 * (0.785398163397448 * D30^2)^1.2921 / 1000
```

Inputs: D30 = Stem diameter at 30 cm (cm).
The source's own form: 12.7152 * (0.785398163397448 * D30^2)^1.2921, with D30 in cm; output in g.
Cite: https://treeallometry.org/equations/flade-2021-bepa-branch-nls/#canonical

## What it covers

- Output: Branch biomass, kg
- Taxon: Betula papyrifera (species), family Betulaceae; broadleaf
- Where: Sporadic to discontinuous permafrost zone, Taiga Plains and Taiga Shield ecozones, northwestern Canada. Cite: https://treeallometry.org/equations/flade-2021-bepa-branch-nls/#where
- Biomes: boreal
- Stand: natural
- Trees measured: 15. Cite: https://treeallometry.org/equations/flade-2021-bepa-branch-nls/#n_trees
- R²: 0.905. Cite: https://treeallometry.org/equations/flade-2021-bepa-branch-nls/#r2
- Method: iterative nonlinear least squares power function, y = β x^α (unweighted), x = cross-sectional area. Cite: https://treeallometry.org/equations/flade-2021-bepa-branch-nls/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/flade-2021-bepa-branch-nls/#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

Flade, L., Hopkinson, C., & Chasmer, L. (2021). Aboveground Biomass Allocation of Boreal Shrubs and Short-Stature Trees in Northwestern Canada. Forests, 12(2), 234.

- DOI: https://doi.org/10.3390/f12020234
- Access: open access
- Copy we read: https://www.mdpi.com/1999-4907/12/2/234/htm
- Every equation from this source: https://treeallometry.org/sources/flade-2021/
- Cite: https://treeallometry.org/equations/flade-2021-bepa-branch-nls/#source

## The facts, in the source's words

**Equation** (Table 3, Eqs. 2-5):

> Betula papyrifera Branches NLS 12.7152 1.2921 0.905 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Cite: https://treeallometry.org/equations/flade-2021-bepa-branch-nls/#equation

**Trees measured** (Table 1, No. of Samples):

> Betula papyrifera 15

Cite: https://treeallometry.org/equations/flade-2021-bepa-branch-nls/#quote-fit-n-trees

**Our note:** Paper's predictor is cross-sectional area (cm2) of the stem(s) at 0.3 m; converted here to D30 as pi/4 * D30^2 (pi written as 0.785398163397448 * ...), so for multi-stemmed trees D30 is the equivalent diameter of the summed cross-sectional area. Paper output is in g dry mass; canonical form divides by 1000.  Fit range of the predictor is not stated, so none is given.

## 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 |
| --- | --- | --- | --- |
| D30 = 2 | 0.0558 | 0.0558 | Computed from the printed form: computed from the published form (coefficients as printed) |
| D30 = 5 | 0.596 | 0.596 | Computed from the printed form: computed from the published form (coefficients as printed) |
| D30 = 8 | 2.01 | 2.01 | Computed from the printed form: computed from the published form (coefficients as printed) |

Cite: https://treeallometry.org/equations/flade-2021-bepa-branch-nls/#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: Flade, L., Hopkinson, C., & Chasmer, L. (2021). Aboveground Biomass Allocation of Boreal Shrubs and Short-Stature Trees in Northwestern Canada. Forests, 12(2), 234. https://doi.org/10.3390/f12020234

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Betula papyrifera branch biomass, cross-sectional area at 0.3 m (NLS)", checked 2026-11-02, https://treeallometry.org/equations/flade-2021-bepa-branch-nls/. 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/flade-2021-bepa-branch-nls.json
Report a problem: email info@restorationscope.com with the equation id (flade-2021-bepa-branch-nls) and where the right value appears.