# Norway spruce total above-ground biomass, Model 1c (Eq. 17)

Aboveground biomass equation for Picea abies, Finland, from Repola 2009. 166 trees. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Repola 2009 (Eq. 17, p. 633):

> ln(yki) = b0 + b1 dSki/(dSki + 20) + b2 ln(hki) + uk + eki

Cite: https://treeallometry.org/equations/repola-2009-picea-abies-total/#equation

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

```
Aboveground biomass = exp(-1.808 + 9.482 * (2 + 1.25*D)/((2 + 1.25*D) + 20) + 0.469 * ln(H) + (0.006 + 0.013)/2)
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: exp(-1.808 + 9.482 * (2 + 1.25*d)/((2 + 1.25*d) + 20) + 0.469 * ln(h) + (0.006 + 0.013)/2), with d in cm, h in m; output in kg.
Cite: https://treeallometry.org/equations/repola-2009-picea-abies-total/#canonical

## What it covers

- Output: Aboveground biomass, kg
- Taxon: Picea abies (species), family Pinaceae; conifer
- Where: Finland, mineral-soil stands (mostly southern and central Finland). Cite: https://treeallometry.org/equations/repola-2009-picea-abies-total/#where
- Biomes: boreal
- Stand: mixed
- Trees measured: 166. Cite: https://treeallometry.org/equations/repola-2009-picea-abies-total/#n_trees
- Correction factor: 1.00955 (applied). Cite: https://treeallometry.org/equations/repola-2009-picea-abies-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-2009-picea-abies-total/#method
- Verification: read in the original source
- Last checked: 2026-11-01. Cite: https://treeallometry.org/equations/repola-2009-picea-abies-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. (2009). Biomass equations for Scots pine and Norway spruce in Finland. Silva Fennica, 43(4), 625–647.

- DOI: https://doi.org/10.14214/sf.184
- Access: open access
- Copy we read: https://silvafennica.fi/pdf/184
- Every equation from this source: https://treeallometry.org/sources/repola-2009/
- Cite: https://treeallometry.org/equations/repola-2009-picea-abies-total/#source

## The facts, in the source's words

**Equation** (Eq. 17, p. 633):

> ln(yki) = b0 + b1 dSki/(dSki + 20) + b2 ln(hki) + uk + eki

Cite: https://treeallometry.org/equations/repola-2009-picea-abies-total/#equation

**Equation** (Table 7, p. 634):

> Total Eq. 17 N = 166 b0 –1.808 b1 9.482 b2 0.469 var(uk) 0.006 var(eki) 0.013

Cite: https://treeallometry.org/equations/repola-2009-picea-abies-total/#quote-expression

**Equation** (variable definitions):

> dSki = 2 + 1.25 dki

Cite: https://treeallometry.org/equations/repola-2009-picea-abies-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-2009-picea-abies-total/#quote-fit-cf

**Our note:** Total above-ground biomass of the stem wood, bark, living and dead branches and needles. dS = 2 + 1.25d. Variance correction (0.006+0.013)/2 = 0.0095 added to the intercept in both forms. Sample trees spanned d 1.7–41.7 cm and h 2.1–35.0 m (Table 3, all 613 trees); the total equation used 166 trees, so no fit range is stated. Mineral-soil stands, Finland.

## 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 | 149 | 149 | 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-2009-picea-abies-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. (2009). Biomass equations for Scots pine and Norway spruce in Finland. Silva Fennica, 43(4), 625–647. https://doi.org/10.14214/sf.184

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Norway spruce total above-ground biomass, Model 1c (Eq. 17)", checked 2026-11-01, https://treeallometry.org/equations/repola-2009-picea-abies-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-2009-picea-abies-total.json
Report a problem: email info@restorationscope.com with the equation id (repola-2009-picea-abies-total) and where the right value appears.