# Gray alder, Arkhangelsk: branch biomass from D (Table 2)

Branch biomass equation for Alnus incana, Russia, from Karaban et al. 2023. 50 trees, DBH 3.6–16.9 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Karaban et al. 2023 (Table 2, ln Pb row):

> ln Pb (1) –4,4668 2,4038 – – 0,729 0,469 50 (ln Pi = a0 + a1 ln D)

Cite: https://treeallometry.org/equations/karaban-2023-branch-d/#equation

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

```
Branch biomass = exp(-4.4668 + 2.4038 * ln(D))
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: exp(-4.4668 + 2.4038 * ln(D)), with D in cm; output in kg.
Cite: https://treeallometry.org/equations/karaban-2023-branch-d/#canonical

## What it covers

- Output: Branch biomass, kg
- Taxon: Alnus incana (species), family Betulaceae; broadleaf
- Where: Arkhangelsk region, northern taiga (Primorsky, Krasnoborsky and Kargopolsky districts). Cite: https://treeallometry.org/equations/karaban-2023-branch-d/#where
- Biomes: boreal
- Stand: mixed
- Trees measured: 50. Cite: https://treeallometry.org/equations/karaban-2023-branch-d/#n_trees
- DBH range: 3.6–16.9 cm. Cite: https://treeallometry.org/equations/karaban-2023-branch-d/#dbh
- Residual SE: 0.469. Cite: https://treeallometry.org/equations/karaban-2023-branch-d/#rse
- Method: OLS regression on natural logarithms; free term corrected for log transformation (Baskerville 1972). Cite: https://treeallometry.org/equations/karaban-2023-branch-d/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/karaban-2023-branch-d/#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

Karaban, A. A., Usoltsev, V. A., Tretyakov, S. V., Koptev, S. V., Paramonov, A. A., Tsvetkov, I. V., Davydov, A. V., & Tsepordey, I. S. (2023). Biomass of gray alder trees and its allometric models in the conditions of the Arkhangelsk region. Forests of Russia and economy in them, 2(85), 42–50.

- DOI: https://doi.org/10.51318/fret.2023.36.20.005
- Access: open access
- Copy we read: https://usfeu.ru/media/filer_public/31/1c/311c8894-375c-49bb-9c23-860c9d9a5c51/5_karaban_usoltsev_dr_biomassa_derevev_olkhi.pdf
- Every equation from this source: https://treeallometry.org/sources/karaban-2023/
- Cite: https://treeallometry.org/equations/karaban-2023-branch-d/#source

## The facts, in the source's words

**Equation** (Table 2, ln Pb row):

> ln Pb (1) –4,4668 2,4038 – – 0,729 0,469 50 (ln Pi = a0 + a1 ln D)

Cite: https://treeallometry.org/equations/karaban-2023-branch-d/#equation

**Trees measured** (Methods, p. 44):

> Полная характеристика полученных данных о 50 модельных деревьях ольхи серой дана в табл. 1.

Cite: https://treeallometry.org/equations/karaban-2023-branch-d/#quote-fit-n-trees

**Smallest DBH** (Table 1, tree No. 25 (smallest D, 3.6 cm); largest D is tree No. 15, 16.9 cm):

> 25 20 3,6 5,10 12,22 6,48 0,004 0,001 2,596 0,121 0,230 0,049 2,875 4,250

Cite: https://treeallometry.org/equations/karaban-2023-branch-d/#quote-fit-dbh-min-cm

**Our note:** The note to Table 2 says the free term includes the correction for logarithmic transformation (Baskerville 1972), so no separate factor is applied. Natural log (ln) as printed. The paper reports adjusted R2 (not R2); adjR2 = 0.729. Stand origin not stated (pure stands or with admixture of other species). DBH range is the min and max of column D in Table 1 over the 50 trees.

## 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 | 0.55 | 0.55 | Computed from the printed form: computed from the published form (coefficients as printed; free term already includes the Baskerville log correction per the Table 2 note) |
| D = 10 | 2.91 | 2.91 | Computed from the printed form: computed from the published form (coefficients as printed; free term already includes the Baskerville log correction per the Table 2 note) |
| D = 15 | 7.71 | 7.71 | Computed from the printed form: computed from the published form (coefficients as printed; free term already includes the Baskerville log correction per the Table 2 note) |

Cite: https://treeallometry.org/equations/karaban-2023-branch-d/#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: Karaban, A. A., Usoltsev, V. A., Tretyakov, S. V., Koptev, S. V., Paramonov, A. A., Tsvetkov, I. V., Davydov, A. V., & Tsepordey, I. S. (2023). Biomass of gray alder trees and its allometric models in the conditions of the Arkhangelsk region. Forests of Russia and economy in them, 2(85), 42–50. https://doi.org/10.51318/fret.2023.36.20.005

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Gray alder, Arkhangelsk: branch biomass from D (Table 2)", checked 2026-11-02, https://treeallometry.org/equations/karaban-2023-branch-d/. 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/karaban-2023-branch-d.json
Report a problem: email info@restorationscope.com with the equation id (karaban-2023-branch-d) and where the right value appears.