# Birch total above-ground biomass excluding foliage, Model 1a (Eq. 11)

Aboveground biomass equation (without leaves) for Betula, Finland, from Repola 2008. 127 trees, DBH 2.5–38 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 2008 (Eq. 11, p. 612):

> ln(yki) = b0 + b1 dSki/(dSki + 12) + b2 hki/(hki + 22) + u5k + e5ki

Cite: https://treeallometry.org/equations/repola-2008-betula-total/#equation

In this library's units, ready to compute (aboveground biomass, without leaves in kg):

```
Aboveground biomass, without leaves = exp(-3.654 + 10.582 * (2 + 1.25*D)/((2 + 1.25*D) + 12) + 3.018 * H/(H + 22) + (0.00068 + 0.00727)/2)
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: exp(-3.654 + 10.582 * (2 + 1.25*d)/((2 + 1.25*d) + 12) + 3.018 * h/(h + 22) + (0.00068 + 0.00727)/2), with d in cm, h in m; output in kg.
Cite: https://treeallometry.org/equations/repola-2008-betula-total/#canonical

This total leaves out leaves (foliage), as the source defines it.

## What it covers

- Output: Aboveground biomass, without leaves, kg
- Taxon: Betula (genus), family Betulaceae; broadleaf
- Where: Finland, mineral-soil stands (mostly southern and central Finland). Cite: https://treeallometry.org/equations/repola-2008-betula-total/#where
- Biomes: boreal, temperate
- Stand: mixed
- Trees measured: 127. Cite: https://treeallometry.org/equations/repola-2008-betula-total/#n_trees
- DBH range: 2.5–38 cm. Cite: https://treeallometry.org/equations/repola-2008-betula-total/#dbh
- Correction factor: 1.00398 (applied). Cite: https://treeallometry.org/equations/repola-2008-betula-total/#cf
- Method: Multivariate linear mixed model on ln(biomass) with stand random effects (fitted jointly with component equations); fixed part shown, with variance correction (var(u)+var(e))/2 added to the intercept. Cite: https://treeallometry.org/equations/repola-2008-betula-total/#method
- Verification: read in the original source
- Last checked: 2026-11-01. Cite: https://treeallometry.org/equations/repola-2008-betula-total/#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. (2008). Biomass equations for birch in Finland. Silva Fennica, 42(4), 605–624.

- DOI: https://doi.org/10.14214/sf.236
- Access: open access
- Copy we read: https://silvafennica.fi/pdf/236
- Every equation from this source: https://treeallometry.org/sources/repola-2008/
- Cite: https://treeallometry.org/equations/repola-2008-betula-total/#source

## The facts, in the source's words

**Equation** (Eq. 11, p. 612):

> ln(yki) = b0 + b1 dSki/(dSki + 12) + b2 hki/(hki + 22) + u5k + e5ki

Cite: https://treeallometry.org/equations/repola-2008-betula-total/#equation

**Equation** (Table 4, p. 613):

> Total above-ground Eq. (11) N = 127 b0 –3.654 b1 10.582 b2 3.018; u5k 0.00068; e5ki 0.00727

Cite: https://treeallometry.org/equations/repola-2008-betula-total/#quote-expression

**Equation** (variable definitions):

> dSki = 2 + 1.25 dki

Cite: https://treeallometry.org/equations/repola-2008-betula-total/#quote-expression-2

**Correction factor** (Section 2.4 (2009) / Section 3 (2008)):

> a variance correction term, (σu² + σe²)/2 … should be added to the intercept

Cite: https://treeallometry.org/equations/repola-2008-betula-total/#quote-fit-cf

**Our note:** B. pendula (66% of sample trees) and B. pubescens (34%) pooled. The paper states foliage biomass was not included in the total above-ground biomass, so this is AGB of stem, bark and living + dead branches without leaves. Variance correction (0.00068+0.00727)/2 added to the intercept in both forms. Sanity check: the uncorrected fixed part averaged over the four plot 4_11 trees of Table 7 gives 94.5 kg, matching Predfixed in Table 8.

## 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 = 20, H = 18 | 154 | 154 | Computed from the printed form: computed from the published form (with variance correction) at d = 20 cm, h = 18 m |

Cite: https://treeallometry.org/equations/repola-2008-betula-total/#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. (2008). Biomass equations for birch in Finland. Silva Fennica, 42(4), 605–624. https://doi.org/10.14214/sf.236

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Birch total above-ground biomass excluding foliage, Model 1a (Eq. 11)", checked 2026-11-01, https://treeallometry.org/equations/repola-2008-betula-total/. 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-2008-betula-total.json
Report a problem: email info@restorationscope.com with the equation id (repola-2008-betula-total) and where the right value appears.