# Multi-species short-stature trees stem biomass, cross-sectional area at 0.3 m (LLRC)

Stem biomass equation for Multi-species short-stature trees (all tree genera/species sampled), Canada, from Flade et al. 2021. 105 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):

> Multi-species short-stature trees Stems LLRC 3.833 46.2009 1.109 1.1296 0.939 (columns: ln(β), β, α, CF, RMSE, R2); y = βx^α + ε (Eq. 2); y = βx^α × ε (Eq. 4), ε = e^(MSE/2) (Eq. 5)

Cite: https://treeallometry.org/equations/flade-2021-multi-stem-llrc/#equation

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

```
Stem biomass = 46.2009 * 1.1296 * (0.785398163397448 * D30^2)^1.109 / 1000
```

Inputs: D30 = Stem diameter at 30 cm (cm).
The source's own form: 46.2009 * 1.1296 * (0.785398163397448 * D30^2)^1.109, with D30 in cm; output in g.
Cite: https://treeallometry.org/equations/flade-2021-multi-stem-llrc/#canonical

## What it covers

- Output: Stem biomass, kg
- Taxon: Multi-species short-stature trees (all tree genera/species sampled) (mixed species); mixed
- Where: Sporadic to discontinuous permafrost zone, Taiga Plains and Taiga Shield ecozones, northwestern Canada. Cite: https://treeallometry.org/equations/flade-2021-multi-stem-llrc/#where
- Biomes: boreal
- Stand: natural
- Trees measured: 105. Cite: https://treeallometry.org/equations/flade-2021-multi-stem-llrc/#n_trees
- R²: 0.939. Cite: https://treeallometry.org/equations/flade-2021-multi-stem-llrc/#r2
- Correction factor: 1.1296 (applied). Cite: https://treeallometry.org/equations/flade-2021-multi-stem-llrc/#cf
- Method: linear log regression with correction factor (LLRC), y = β x^α × CF, x = cross-sectional area. Cite: https://treeallometry.org/equations/flade-2021-multi-stem-llrc/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/flade-2021-multi-stem-llrc/#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-multi-stem-llrc/#source

## The facts, in the source's words

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

> Multi-species short-stature trees Stems LLRC 3.833 46.2009 1.109 1.1296 0.939 (columns: ln(β), β, α, CF, RMSE, R2); y = βx^α + ε (Eq. 2); y = βx^α × ε (Eq. 4), ε = e^(MSE/2) (Eq. 5)

Cite: https://treeallometry.org/equations/flade-2021-multi-stem-llrc/#equation

**Trees measured** (Section 2.2):

> A total of 206 shrub and 105 tree individuals were measured and destructively sampled at 65 different peatland and forest sites.

Cite: https://treeallometry.org/equations/flade-2021-multi-stem-llrc/#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. LLRC correction factor applied as printed in the CF column. 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 | 0.186 | 0.186 | Computed from the printed form: computed from the published form (coefficients as printed) |
| D30 = 5 | 1.42 | 1.42 | Computed from the printed form: computed from the published form (coefficients as printed) |
| D30 = 8 | 4.02 | 4.02 | Computed from the printed form: computed from the published form (coefficients as printed) |

Cite: https://treeallometry.org/equations/flade-2021-multi-stem-llrc/#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), "Multi-species short-stature trees stem biomass, cross-sectional area at 0.3 m (LLRC)", checked 2026-11-02, https://treeallometry.org/equations/flade-2021-multi-stem-llrc/. 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-multi-stem-llrc.json
Report a problem: email info@restorationscope.com with the equation id (flade-2021-multi-stem-llrc) and where the right value appears.