# Flade et al. 2021: Aboveground Biomass Allocation of Boreal Shrubs and Short-Stature Trees in Northwestern Canada

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
- Status: no retraction or correction notice recorded (Crossref is asked weekly); last checked 2026-11-02
- Page: https://treeallometry.org/sources/flade-2021/

## Equations from this source (35)

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

Branch biomass for Betula papyrifera, Canada. Inputs: D30. 15 trees.

As printed (Table 3, Eqs. 2-5):

> Betula papyrifera Branches LLRC 2.634 13.9294 1.144 1.0542 0.9 (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)

Page: https://treeallometry.org/equations/flade-2021-bepa-branch-llrc/

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

Branch biomass for Betula papyrifera, Canada. Inputs: D30. 15 trees.

As printed (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)

Page: https://treeallometry.org/equations/flade-2021-bepa-branch-nls/

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

Foliage biomass for Betula papyrifera, Canada. Inputs: D30. 15 trees.

As printed (Table 3, Eqs. 2-5):

> Betula papyrifera Leaves NLS 7.8627 1.2143 0.853 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-bepa-leaf-nls/

### Betula papyrifera stem biomass, cross-sectional area at 0.3 m (LLRC)

Stem biomass for Betula papyrifera, Canada. Inputs: D30. 15 trees.

As printed (Table 3, Eqs. 2-5):

> Betula papyrifera Stems LLRC 3.970 52.9845 1.237 1.066 0.898 (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)

Page: https://treeallometry.org/equations/flade-2021-bepa-stem-llrc/

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

Stem biomass for Betula papyrifera, Canada. Inputs: D30. 15 trees.

As printed (Table 3, Eqs. 2-5):

> Betula papyrifera Stems NLS 41.4994 1.5494 0.913 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-bepa-stem-nls/

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

Branch biomass for Multi-species short-stature trees (all tree genera/species sampled), Canada. Inputs: D30. 105 trees.

As printed (Table 3, Eqs. 2-5):

> Multi-species short-stature trees Branches LLRC 2.336 10.3398 1.269 1.6568 0.919 (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)

Page: https://treeallometry.org/equations/flade-2021-multi-branch-llrc/

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

Branch biomass for Multi-species short-stature trees (all tree genera/species sampled), Canada. Inputs: D30. 105 trees.

As printed (Table 3, Eqs. 2-5):

> Multi-species short-stature trees Branches NLS 12.792 1.4315 0.923 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-multi-branch-nls/

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

Foliage biomass for Multi-species short-stature trees (all tree genera/species sampled), Canada. Inputs: D30. 105 trees.

As printed (Table 3, Eqs. 2-5):

> Multi-species short-stature trees Leaves LLRC 2.584 13.25 1.107 1.5055 0.768 (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)

Page: https://treeallometry.org/equations/flade-2021-multi-leaf-llrc/

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

Foliage biomass for Multi-species short-stature trees (all tree genera/species sampled), Canada. Inputs: D30. 105 trees.

As printed (Table 3, Eqs. 2-5):

> Multi-species short-stature trees Leaves NLS 20.2891 1.1807 0.767 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-multi-leaf-nls/

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

Stem biomass for Multi-species short-stature trees (all tree genera/species sampled), Canada. Inputs: D30. 105 trees.

As printed (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)

Page: https://treeallometry.org/equations/flade-2021-multi-stem-llrc/

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

Stem biomass for Multi-species short-stature trees (all tree genera/species sampled), Canada. Inputs: D30. 105 trees.

As printed (Table 3, Eqs. 2-5):

> Multi-species short-stature trees Stems NLS 49.179 1.1712 0.94 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-multi-stem-nls/

### Picea spp. branch biomass, cross-sectional area at 0.3 m (LLRC)

Branch biomass for Picea spp., Canada. Inputs: D30.

As printed (Table 3, Eqs. 2-5):

> Picea spp. Branches LLRC 3.430 30.8766 1.023 1.1129 0.892 (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)

Page: https://treeallometry.org/equations/flade-2021-picea-branch-llrc/

### Picea spp. branch biomass, cross-sectional area at 0.3 m (NLS)

Branch biomass for Picea spp., Canada. Inputs: D30.

As printed (Table 3, Eqs. 2-5):

> Picea spp. Branches NLS 19.1842 1.2866 0.904 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-picea-branch-nls/

### Picea spp. leaf biomass, cross-sectional area at 0.3 m (LLRC)

Foliage biomass for Picea spp., Canada. Inputs: D30.

As printed (Table 3, Eqs. 2-5):

> Picea spp. Leaves LLRC 3.821 45.6498 0.8059 1.1088 0.702 (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)

Page: https://treeallometry.org/equations/flade-2021-picea-leaf-llrc/

### Picea spp. leaf biomass, cross-sectional area at 0.3 m (NLS)

Foliage biomass for Picea spp., Canada. Inputs: D30.

As printed (Table 3, Eqs. 2-5):

> Picea spp. Leaves NLS 42.2998 0.9148 0.704 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-picea-leaf-nls/

### Picea spp. stem biomass, cross-sectional area at 0.3 m (LLRC)

Stem biomass for Picea spp., Canada. Inputs: D30.

As printed (Table 3, Eqs. 2-5):

> Picea spp. Stems LLRC 3.894 49.1069 1.067 1.0782 0.928 (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)

Page: https://treeallometry.org/equations/flade-2021-picea-stem-llrc/

### Picea spp. stem biomass, cross-sectional area at 0.3 m (NLS)

Stem biomass for Picea spp., Canada. Inputs: D30.

As printed (Table 3, Eqs. 2-5):

> Picea spp. Stems NLS 42.8437 1.2201 0.929 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-picea-stem-nls/

### Populus balsamifera branch biomass, cross-sectional area at 0.3 m (LLRC)

Branch biomass for Populus balsamifera, Canada. Inputs: D30. 31 trees.

As printed (Table 3, Eqs. 2-5):

> Populus balsamifera Branches LLRC 1.773 5.8885 1.114 1.4758 0.736 (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)

Page: https://treeallometry.org/equations/flade-2021-pobal-branch-llrc/

### Populus balsamifera branch biomass, cross-sectional area at 0.3 m (NLS)

Branch biomass for Populus balsamifera, Canada. Inputs: D30. 31 trees.

As printed (Table 3, Eqs. 2-5):

> Populus balsamifera Branches NLS 7.6872 1.234 0.737 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-pobal-branch-nls/

### Populus balsamifera leaf biomass, cross-sectional area at 0.3 m (LLRC)

Foliage biomass for Populus balsamifera, Canada. Inputs: D30. 31 trees.

As printed (Table 3, Eqs. 2-5):

> Populus balsamifera Leaves LLRC 2.028 7.5989 1.037 1.4577 0.832 (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)

Page: https://treeallometry.org/equations/flade-2021-pobal-leaf-llrc/

### Populus balsamifera leaf biomass, cross-sectional area at 0.3 m (NLS)

Foliage biomass for Populus balsamifera, Canada. Inputs: D30. 31 trees.

As printed (Table 3, Eqs. 2-5):

> Populus balsamifera Leaves ILS 8.31954 1.1007 0.834 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-pobal-leaf-nls/

### Populus balsamifera stem biomass, cross-sectional area at 0.3 m (LLRC)

Stem biomass for Populus balsamifera, Canada. Inputs: D30. 31 trees.

As printed (Table 3, Eqs. 2-5):

> Populus balsamifera Stems LLRC 3.805 44.9253 1.132 1.1648 0.919 (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)

Page: https://treeallometry.org/equations/flade-2021-pobal-stem-llrc/

### Populus balsamifera stem biomass, cross-sectional area at 0.3 m (NLS)

Stem biomass for Populus balsamifera, Canada. Inputs: D30. 31 trees.

As printed (Table 3, Eqs. 2-5):

> Populus balsamifera Stems NLS 47.3512 1.3235 0.924 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-pobal-stem-nls/

### Populus tremuloides branch biomass, cross-sectional area at 0.3 m (LLRC)

Branch biomass for Populus tremuloides, Canada. Inputs: D30. 30 trees.

As printed (Table 3, Eqs. 2-5):

> Populus tremuloides Branches LLRC 1.682 5.3763 1.091 1.538 0.816 (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)

Page: https://treeallometry.org/equations/flade-2021-potre-branch-llrc/

### Populus tremuloides branch biomass, cross-sectional area at 0.3 m (NLS)

Branch biomass for Populus tremuloides, Canada. Inputs: D30. 30 trees.

As printed (Table 3, Eqs. 2-5):

> Populus tremuloides Branches NLS 4.591 1.8127 0.888 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-potre-branch-nls/

### Populus tremuloides leaf biomass, cross-sectional area at 0.3 m (LLRC)

Foliage biomass for Populus tremuloides, Canada. Inputs: D30. 30 trees.

As printed (Table 3, Eqs. 2-5):

> Populus tremuloides Leaves LLRC 2.255 9.5353 0.8919 1.1365 0.854 (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)

Page: https://treeallometry.org/equations/flade-2021-potre-leaf-llrc/

### Populus tremuloides leaf biomass, cross-sectional area at 0.3 m (NLS)

Foliage biomass for Populus tremuloides, Canada. Inputs: D30. 30 trees.

As printed (Table 3, Eqs. 2-5):

> Populus tremuloides Leaves NLS 8.07253 1.4362 0.917 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-potre-leaf-nls/

### Populus tremuloides stem biomass, cross-sectional area at 0.3 m (LLRC)

Stem biomass for Populus tremuloides, Canada. Inputs: D30. 30 trees.

As printed (Table 3, Eqs. 2-5):

> Populus tremuloides Stems LLRC 3.770 43.3801 1.067 1.1627 0.95 (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)

Page: https://treeallometry.org/equations/flade-2021-potre-stem-llrc/

### Populus tremuloides stem biomass, cross-sectional area at 0.3 m (NLS)

Stem biomass for Populus tremuloides, Canada. Inputs: D30. 30 trees.

As printed (Table 3, Eqs. 2-5):

> Populus tremuloides Stems NLS 41.7058 1.2658 0.96 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-potre-stem-nls/

### Short-stature hardwood trees branch biomass, cross-sectional area at 0.3 m (LLRC)

Branch biomass for Short-stature hardwood trees (deciduous species excluding Picea spp.), Canada. Inputs: D30.

As printed (Table 3, Eqs. 2-5):

> Short-stature hardwood trees Branches LLRC 1.927 6.8689 1.127 1.4893 0.76 (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)

Page: https://treeallometry.org/equations/flade-2021-hardwood-branch-llrc/

### Short-stature hardwood trees branch biomass, cross-sectional area at 0.3 m (NLS)

Branch biomass for Short-stature hardwood trees (deciduous species excluding Picea spp.), Canada. Inputs: D30.

As printed (Table 3, Eqs. 2-5):

> Short-stature hardwood trees Branches NLS 6.4825 1.5966 0.789 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-hardwood-branch-nls/

### Short-stature hardwood trees leaf biomass, cross-sectional area at 0.3 m (LLRC)

Foliage biomass for Short-stature hardwood trees (deciduous species excluding Picea spp.), Canada. Inputs: D30.

As printed (Table 3, Eqs. 2-5):

> Short-stature hardwood trees Leaves LLRC 2.138 8.4825 0.9655 1.2434 0.826 (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)

Page: https://treeallometry.org/equations/flade-2021-hardwood-leaf-llrc/

### Short-stature hardwood trees leaf biomass, cross-sectional area at 0.3 m (NLS)

Foliage biomass for Short-stature hardwood trees (deciduous species excluding Picea spp.), Canada. Inputs: D30.

As printed (Table 3, Eqs. 2-5):

> Short-stature hardwood trees Leaves NLS 8.28683 1.2225 0.841 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-hardwood-leaf-nls/

### Short-stature hardwood trees stem biomass, cross-sectional area at 0.3 m (LLRC)

Stem biomass for Short-stature hardwood trees (deciduous species excluding Picea spp.), Canada. Inputs: D30.

As printed (Table 3, Eqs. 2-5):

> Short-stature hardwood trees Stems LLRC 3.830 46.0625 1.122 1.1482 0.887 (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)

Page: https://treeallometry.org/equations/flade-2021-hardwood-stem-llrc/

### Short-stature hardwood trees stem biomass, cross-sectional area at 0.3 m (NLS)

Stem biomass for Short-stature hardwood trees (deciduous species excluding Picea spp.), Canada. Inputs: D30.

As printed (Table 3, Eqs. 2-5):

> Short-stature hardwood trees Stems NLS 41.4212 1.4431 0.904 (columns: β, SE(β), α, SE(α), RMSE, R2); y = βx^α + ε (Eq. 2)

Page: https://treeallometry.org/equations/flade-2021-hardwood-stem-nls/