# Short-stature boreal trees (<=4.5 m), AGB from stem diameter at 0.3 m (NLS)

Aboveground biomass equation for Multispecies short-stature trees (Betula papyrifera, Picea spp., Populus balsamifera, Populus tremuloides), Canada, from Flade et al. 2020. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

Fitted on Betula papyrifera, Populus balsamifera, Populus tremuloides, and other species the source does not name here.

## Equation

As printed in Flade et al. 2020 (Table 5 and Eq. 7):

> Multispecies trees, Diameter at 0.3 m: NLS β 59.072, NLS α 2.479; y = β x^α

Cite: https://treeallometry.org/equations/flade-2020-trees-d30-nls/#equation

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

```
Aboveground biomass = 59.072 * D30^2.479 / 1000
```

Inputs: D30 = Stem diameter at 30 cm (cm).
The source's own form: 59.072 * D30^2.479, with D30 in cm; output in g.
Cite: https://treeallometry.org/equations/flade-2020-trees-d30-nls/#canonical

## What it covers

- Output: Aboveground biomass, kg
- Taxon: Multispecies short-stature trees (Betula papyrifera, Picea spp., Populus balsamifera, Populus tremuloides) (mixed species); mixed
- Where: Fort Liard area, Taiga Plains, Northwest Territories. Cite: https://treeallometry.org/equations/flade-2020-trees-d30-nls/#where
- Biomes: boreal
- Stand: natural
- Height range: up to 4.5 m. Cite: https://treeallometry.org/equations/flade-2020-trees-d30-nls/#height
- R²: 0.988. Cite: https://treeallometry.org/equations/flade-2020-trees-d30-nls/#r2
- Method: nonlinear least squares power function, y = beta * x^alpha (unweighted). Cite: https://treeallometry.org/equations/flade-2020-trees-d30-nls/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/flade-2020-trees-d30-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. (2020). Allometric Equations for Shrub and Short-Stature Tree Aboveground Biomass within Boreal Ecosystems of Northwestern Canada. Forests, 11(11), 1207.

- DOI: https://doi.org/10.3390/f11111207
- Access: open access
- Copy we read: https://www.mdpi.com/1999-4907/11/11/1207/htm
- Every equation from this source: https://treeallometry.org/sources/flade-2020/
- Cite: https://treeallometry.org/equations/flade-2020-trees-d30-nls/#source

## The facts, in the source's words

**Equation** (Table 5 and Eq. 7):

> Multispecies trees, Diameter at 0.3 m: NLS β 59.072, NLS α 2.479; y = β x^α

Cite: https://treeallometry.org/equations/flade-2020-trees-d30-nls/#equation

**R²** (Table 4):

> NLS, Diameter at 0.3 m, R2 0.988

Cite: https://treeallometry.org/equations/flade-2020-trees-d30-nls/#quote-fit-r2

**h max m** (Section 2.3):

> Live trees were chosen from the understory and open areas across different height ranges determined in intervals of 0.5 m up to ≤4.5 m

Cite: https://treeallometry.org/equations/flade-2020-trees-d30-nls/#quote-fit-h-max-m

**Our note:** Total aboveground dry biomass (stem, branches, leaves) in grams; canonical form divides by 1000 for kg. Stem diameter measured 0.3 m along the stem from the ground. Paper gives the NLS and LLRC forms; the LLRC correction factor (epsilon = e^(MSE/2)) value is in Supplementary Table S4, which was not read, so LLRC is not added. n_trees omitted: text says 106 trees, Table 1 says 105 tree samples. Shrub volume/basal-diameter models and the cross-sectional-area models, the stem-length model and species-specific models not added (no canonical variable, or coefficients only in the supplement).

## 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 | 0.329 | 0.329 | Computed from the printed form: computed from the published form (coefficients as printed) |
| D30 = 5 | 3.19 | 3.19 | Computed from the printed form: computed from the published form (coefficients as printed) |
| D30 = 10 | 17.8 | 17.8 | Computed from the printed form: computed from the published form (coefficients as printed) |

Cite: https://treeallometry.org/equations/flade-2020-trees-d30-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. (2020). Allometric Equations for Shrub and Short-Stature Tree Aboveground Biomass within Boreal Ecosystems of Northwestern Canada. Forests, 11(11), 1207. https://doi.org/10.3390/f11111207

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Short-stature boreal trees (<=4.5 m), AGB from stem diameter at 0.3 m (NLS)", checked 2026-11-02, https://treeallometry.org/equations/flade-2020-trees-d30-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-2020-trees-d30-nls.json
Report a problem: email info@restorationscope.com with the equation id (flade-2020-trees-d30-nls) and where the right value appears.