# Birch living branch biomass, young dense stands, N Sweden (Table 5)

Branch biomass equation for Betula, Sweden, from Repola & Ahnlund Ulvcrona 2014. 86 trees, DBH 1–11 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Repola & Ahnlund Ulvcrona 2014 (Table 5, p. 12):

> Living branches, kg, birch: Intercept −4.190; dbh/(dbh + n) 11.826; h/(h + m) −3.939; n 6; m 10; var(uk) 0.011; var(eki) 0.105

Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#equation

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

```
Branch biomass = exp(-4.190 + (0.011 + 0.105) / 2 + 11.826 * D / (D + 6) + (-3.939) * H / (H + 10))
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: exp(-4.190 + (0.011 + 0.105) / 2 + 11.826 * dbh / (dbh + 6) + (-3.939) * h / (h + 10)), with dbh in cm, h in m; output in kg.
Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#canonical

## What it covers

- Output: Branch biomass, kg
- Taxon: Betula (genus), family Betulaceae; broadleaf
- Where: Six young, dense, naturally regenerated stands in northern Sweden (63.26-65.69 N). Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#where
- Biomes: boreal
- Stand: natural
- Trees measured: 86. Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#n_trees
- DBH range: 1–11 cm. Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#dbh
- Height range: 1.8–8.6 m. Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#height
- Method: linear mixed model of ln(biomass) with random stand effect; ln(y) = Intercept + b1 dbh/(dbh + n) + b2 h/(h + m). Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#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

Repola, J., Ahnlund Ulvcrona, K. (2014). Modelling biomass of young and dense Scots pine (Pinus sylvestris L.) dominated mixed forests in northern Sweden. Silva Fennica, 48(5), 1190.

- DOI: https://doi.org/10.14214/sf.1190
- Access: open access
- Copy we read: https://silvafennica.fi/pdf/1190
- Every equation from this source: https://treeallometry.org/sources/repola-2014/
- Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#source

## The facts, in the source's words

**Equation** (Table 5, p. 12):

> Living branches, kg, birch: Intercept −4.190; dbh/(dbh + n) 11.826; h/(h + m) −3.939; n 6; m 10; var(uk) 0.011; var(eki) 0.105

Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#equation

**Equation** (Section 2.6, p. 10):

> a variance correction term, ((var(uk) + var(eki))/2) should be added to the intercept to correct for bias due to the logarithmic transformation

Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#quote-expression

**Trees measured** (Section 2.4, p. 6):

> In total, 280 trees were included in this destructive aboveground biomass study, of which 126 were pine, 68 spruce and 86 birch.

Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#quote-fit-n-trees

**Largest DBH** (Section 2.4, p. 6):

> The range of dbh was 1–22 cm, 1–21 cm and 1–11 cm for pine, spruce and birch, respectively

Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#quote-fit-dbh-max-cm

**h max m** (Section 2.4, p. 6):

> The range of heights was 1.7–11.7 m, 1.6–13.3 m and 1.8–8.6 m for pine, spruce and birch, respectively

Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#quote-fit-h-max-m

**Our note:** Fitted on pine-dominated mixed stands; fit n, DBH and height ranges are the species sample ranges. Expression applies the paper's stated additive correction (var(uk) + var(eki))/2 to the intercept. Variance values are as printed in Table 5; no other correction factor is stated. Living branches only (dead branches are modelled separately and not included). Birch coefficients are for Betula pendula and B. pubescens pooled. 

## 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 = 5, H = 5 | 0.933 | 0.933 | Computed from the printed form: hand-computed from the Table 5 coefficients with the (var(u) + var(e))/2 intercept correction |
| D = 10, H = 8 | 4.52 | 4.52 | Computed from the printed form: hand-computed from the Table 5 coefficients with the (var(u) + var(e))/2 intercept correction |

Cite: https://treeallometry.org/equations/repola-2014-branch-birch/#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: Repola, J., Ahnlund Ulvcrona, K. (2014). Modelling biomass of young and dense Scots pine (Pinus sylvestris L.) dominated mixed forests in northern Sweden. Silva Fennica, 48(5), 1190. https://doi.org/10.14214/sf.1190

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Birch living branch biomass, young dense stands, N Sweden (Table 5)", checked 2026-11-02, https://treeallometry.org/equations/repola-2014-branch-birch/. 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/repola-2014-branch-birch.json
Report a problem: email info@restorationscope.com with the equation id (repola-2014-branch-birch) and where the right value appears.