# Oak dead branch biomass, Eq. 2

Branch biomass equation for Quercus (Q. robur and Q. petraea), Czechia, from Cienciala et al. 2008. 51 trees, DBH 6–59 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

**Not fully checked:** Table 4 prints the multiplicative coefficient as 0.004, only one significant digit; obtain more precise coefficients before relying on precise dead-branch estimates. The stored height range follows the abstract's 6–32 m, but Table 1 reports conflicting site height ranges; confirm the fitted height limits before treating them as firm applicability bounds.

Fitted on Quercus robur, Quercus petraea.

## Equation

As printed in Cienciala et al. 2008 (Table 4, Eq. 2, p. 116 (rendered page)):

> Y = p₀ × D^{p₁} × H^{p₂}

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#equation

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

```
Branch biomass = 0.004 * D^5.712 * H^(-4.186)
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 0.004 * D^5.712 * H^(-4.186), with D in cm, H in m; output in kg.
Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#canonical

## What it covers

- Output: Branch biomass, kg
- Taxon: Quercus (Q. robur and Q. petraea) (genus); broadleaf
- Where: Six sites in the Czech Republic. Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#where
- Biomes: temperate
- Stand: not stated
- Trees measured: 51. Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#n_trees
- DBH range: 6–59 cm. Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#dbh
- Height range: 6–32 m. Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#height
- Method: Nonlinear regression. Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#method
- Verification: read in the original source
- Last checked: 2026-11-05. Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#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

Cienciala, E., Apltauer, J., Exnerová, Z., and Tatarinov, F. (2008). Biomass functions applicable to oak trees grown in Central-European forestry. Journal of Forest Science, 54(3), 109–120.

- DOI: https://doi.org/10.17221/2906-jfs
- Peer review: A paper in a peer-reviewed journal.
- Access: open access
- Copy we read: https://www.agriculturejournals.cz/publicFiles/01003.pdf
- Every equation from this source: https://treeallometry.org/sources/cienciala-2008/
- Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#source

## The facts, in the source's words

**Equation** (Table 4, Eq. 2, p. 116 (rendered page)):

> Y = p₀ × D^{p₁} × H^{p₂}

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#equation

**Equation** (Table 4, Eq. 2, p0, p. 116):

> 0.004

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-expression

**Equation** (Table 4, Eq. 2, p1, p. 116):

> 5.712

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-expression-2

**Equation** (Table 4, Eq. 2, p2, p. 116):

> –4.186

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-expression-3

**Output** (Table 4 caption, p. 116):

> The component of dead branches

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-output

**Units** (Fig. 2, p. 111):

> D (cm)

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-published-units

**Units** (Fig. 2, p. 111):

> Tree height (m)

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-published-units-2

**Units** (Fig. 7, p. 118):

> BB (kg/tree)

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-published-units-3

**taxon.members** (Keywords, p. 109):

> Quercus robur; Quercus petraea

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-taxon-members

**Where** (Abstract, p. 109):

> different regions of the Czech Republic

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-region

**Where** (Keywords, p. 109):

> temperate region

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-region-2

**Trees measured** (Abstract, p. 109):

> 51 grown trees sampled from 6 sites

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-fit-n-trees

**Trees measured** (Methods, p. 111):

> The pooled dataset of all trees and their compo-

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-fit-n-trees-2

**Smallest DBH** (Abstract, p. 109):

> breast height diameter (D) ranging from 6 to 59 cm

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-fit-dbh-min-cm

**Largest DBH** (Abstract, p. 109):

> breast height diameter (D) ranging from 6 to 59 cm

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-fit-dbh-max-cm

**h min m** (Abstract, p. 109):

> tree height (H) from 6 to 32 m

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-fit-h-min-m

**h max m** (Abstract, p. 109):

> tree height (H) from 6 to 32 m

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-fit-h-max-m

**method** (Table 4 caption, p. 116):

> non-linear regression analysis applied to Eqs. (1) and (2)

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#quote-fit-method

**Our note:** This predicts dead branches only. The authors fitted this model by nonlinear regression, including zero observations; the log-model correction factor is not applied. Their mean prediction error excludes zero observations. Adjusted R² is not stored as unadjusted R².

## 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 = 30, H = 20 | 3.92 | 3.92 | Computed from the printed form: Computed from Table 4's printed coefficients. |

Cite: https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/#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: Cienciala, E., Apltauer, J., Exnerová, Z., and Tatarinov, F. (2008). Biomass functions applicable to oak trees grown in Central-European forestry. Journal of Forest Science, 54(3), 109–120. https://doi.org/10.17221/2906-jfs

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Oak dead branch biomass, Eq. 2", checked 2026-11-05, https://treeallometry.org/equations/cienciala-2008-dead-branch-dh/. 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/cienciala-2008-dead-branch-dh.json
Report a problem: email info@restorationscope.com with the equation id (cienciala-2008-dead-branch-dh) and where the right value appears.