# Silver fir AGB, Bayesian, Dataset #1, D and H

Aboveground biomass equation for Abies alba, Romania, from Dutcă et al. 2020. 14 trees, DBH 6.3–92.6 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Dutcă et al. 2020 (Table 5, silver fir, Bayesian, Dataset #1, ln(D),ln(H) (Equation 3; back-transformed as Equation 5)):

> ln(D),ln(H): β0 = -2.7679, β1 = 1.9264, β2 = 0.6847, RSE = 0.2788, CF = 1.0396

Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-dh/#equation

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

```
Aboveground biomass = 1.0396 * exp(-2.7679 + 1.9264 * ln(D) + 0.6847 * ln(H))
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 1.0396 * exp(-2.7679 + 1.9264 * ln(D) + 0.6847 * ln(H)), with D in cm, H in m; output in kg.
Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-dh/#canonical

## What it covers

- Output: Aboveground biomass, kg
- Taxon: Abies alba (species), family Pinaceae; conifer
- Where: Șinca virgin forest, Romania. Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-dh/#where
- Biomes: temperate, montane
- Stand: natural
- Trees measured: 14. Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-dh/#n_trees
- DBH range: 6.3–92.6 cm. Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-dh/#dbh
- Height range: 3.5–43.5 m. Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-dh/#height
- Residual SE: 0.2788. Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-dh/#rse
- Correction factor: 1.0396 (applied). Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-dh/#cf
- Method: Bayesian log-log model with informative priors from the generic sample. Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-dh/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-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

Dutcă, I., Zianis, D., Petrițan, I. C., Bragă, C. I., Ștefan, G., Yuste, J. C., & Petrițan, A. M. (2020). Allometric Biomass Models for European Beech and Silver Fir: Testing Approaches to Minimize the Demand for Site-Specific Biomass Observations. Forests, 11(11), 1136.

- DOI: https://doi.org/10.3390/f11111136
- Access: open access
- Copy we read: https://bucks.repository.guildhe.ac.uk/id/eprint/18110/1/forests-11-01136.pdf
- Every equation from this source: https://treeallometry.org/sources/dutca-2020/
- Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-dh/#source

## The facts, in the source's words

**Equation** (Table 5, silver fir, Bayesian, Dataset #1, ln(D),ln(H) (Equation 3; back-transformed as Equation 5)):

> ln(D),ln(H): β0 = -2.7679, β1 = 1.9264, β2 = 0.6847, RSE = 0.2788, CF = 1.0396

Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-dh/#equation

**Trees measured** (Section 2.1.2, p. 3):

> 15 European beech and 14 silver fir trees

Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-dh/#quote-fit-n-trees

**Our note:** Fit on Dataset #1 (full site sample, Bayesian priors from generic data). Whole-tree dry AGB including foliage (stem and branches with leaves/needles weighed and dried). Equation form AGB = exp(β0)·D^β1·(H^β2)·CF with CF = exp(σ²/2) printed in Table 5 and applied here. D in cm, H in m, output kg (units not restated beside Table 5; stated in Table 1 for D, H, AGB).

## 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 = 16 | 140 | 140 | Computed from the printed form: computed from the published form (coefficients as printed) |
| D = 50, H = 30 | 1,256 | 1,256 | Computed from the printed form: computed from the published form (coefficients as printed) |

Cite: https://treeallometry.org/equations/dutca-2020-fir-bay1-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: Dutcă, I., Zianis, D., Petrițan, I. C., Bragă, C. I., Ștefan, G., Yuste, J. C., & Petrițan, A. M. (2020). Allometric Biomass Models for European Beech and Silver Fir: Testing Approaches to Minimize the Demand for Site-Specific Biomass Observations. Forests, 11(11), 1136. https://doi.org/10.3390/f11111136

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Silver fir AGB, Bayesian, Dataset #1, D and H", checked 2026-11-02, https://treeallometry.org/equations/dutca-2020-fir-bay1-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/dutca-2020-fir-bay1-dh.json
Report a problem: email info@restorationscope.com with the equation id (dutca-2020-fir-bay1-dh) and where the right value appears.