# Silver fir AGB, RIM, Dataset #3, D only

Aboveground biomass equation for Abies alba, Romania, from Dutcă et al. 2020. 116 trees, DBH 5.1–92.6 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, RIM, Dataset #3, ln(D) (Equation 2; back-transformed as Equation 4)):

> ln(D): β0 = -2.4756, β1 = 2.4219, RSE = 0.2033, CF = 1.0209

Cite: https://treeallometry.org/equations/dutca-2020-fir-rim3-d/#equation

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

```
Aboveground biomass = 1.0209 * exp(-2.4756 + 2.4219 * ln(D))
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: 1.0209 * exp(-2.4756 + 2.4219 * ln(D)), with D in cm; output in kg.
Cite: https://treeallometry.org/equations/dutca-2020-fir-rim3-d/#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-rim3-d/#where
- Biomes: temperate, montane
- Stand: natural
- Trees measured: 116. Cite: https://treeallometry.org/equations/dutca-2020-fir-rim3-d/#n_trees
- DBH range: 5.1–92.6 cm. Cite: https://treeallometry.org/equations/dutca-2020-fir-rim3-d/#dbh
- Residual SE: 0.2033. Cite: https://treeallometry.org/equations/dutca-2020-fir-rim3-d/#rse
- Correction factor: 1.0209 (applied). Cite: https://treeallometry.org/equations/dutca-2020-fir-rim3-d/#cf
- Method: random intercept mixed model on log-log data (generic plus site-specific trees); estimates for the Șinca site. Cite: https://treeallometry.org/equations/dutca-2020-fir-rim3-d/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/dutca-2020-fir-rim3-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

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-rim3-d/#source

## The facts, in the source's words

**Equation** (Table 5, silver fir, RIM, Dataset #3, ln(D) (Equation 2; back-transformed as Equation 4)):

> ln(D): β0 = -2.4756, β1 = 2.4219, RSE = 0.2033, CF = 1.0209

Cite: https://treeallometry.org/equations/dutca-2020-fir-rim3-d/#equation

**Trees measured** (Table 3, Dataset #3 sample size):

> 159 / 116

Cite: https://treeallometry.org/equations/dutca-2020-fir-rim3-d/#quote-fit-n-trees

**Our note:** Fit on Dataset #3 (generic + full site sample). 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). For RIM models the parameters printed are those retained for the Șinca site.

## 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 | 122 | 122 | Computed from the printed form: computed from the published form (coefficients as printed) |
| D = 50 | 1,118 | 1,118 | Computed from the printed form: computed from the published form (coefficients as printed) |

Cite: https://treeallometry.org/equations/dutca-2020-fir-rim3-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: 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, RIM, Dataset #3, D only", checked 2026-11-02, https://treeallometry.org/equations/dutca-2020-fir-rim3-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/dutca-2020-fir-rim3-d.json
Report a problem: email info@restorationscope.com with the equation id (dutca-2020-fir-rim3-d) and where the right value appears.