# Silver fir AGB, RIM, Dataset #4, D and H

Aboveground biomass equation for Abies alba, Romania, from Dutcă et al. 2020. 109 trees, DBH 5.1–64 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 #4, ln(D),ln(H) (Equation 3; back-transformed as Equation 5)):

> ln(D),ln(H): β0 = -2.7987, β1 = 1.8076, β2 = 0.804, RSE = 0.1548, CF = 1.0121

Cite: https://treeallometry.org/equations/dutca-2020-fir-rim4-dh/#equation

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

```
Aboveground biomass = 1.0121 * exp(-2.7987 + 1.8076 * ln(D) + 0.804 * ln(H))
```

Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m).
The source's own form: 1.0121 * exp(-2.7987 + 1.8076 * ln(D) + 0.804 * ln(H)), with D in cm, H in m; output in kg.
Cite: https://treeallometry.org/equations/dutca-2020-fir-rim4-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-rim4-dh/#where
- Biomes: temperate, montane
- Stand: natural
- Trees measured: 109. Cite: https://treeallometry.org/equations/dutca-2020-fir-rim4-dh/#n_trees
- DBH range: 5.1–64 cm. Cite: https://treeallometry.org/equations/dutca-2020-fir-rim4-dh/#dbh
- Height range: 3.5–28.9 m. Cite: https://treeallometry.org/equations/dutca-2020-fir-rim4-dh/#height
- Residual SE: 0.1548. Cite: https://treeallometry.org/equations/dutca-2020-fir-rim4-dh/#rse
- Correction factor: 1.0121 (applied). Cite: https://treeallometry.org/equations/dutca-2020-fir-rim4-dh/#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-rim4-dh/#method
- Verification: read in the original source
- Last checked: 2026-11-02. Cite: https://treeallometry.org/equations/dutca-2020-fir-rim4-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-rim4-dh/#source

## The facts, in the source's words

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

> ln(D),ln(H): β0 = -2.7987, β1 = 1.8076, β2 = 0.804, RSE = 0.1548, CF = 1.0121

Cite: https://treeallometry.org/equations/dutca-2020-fir-rim4-dh/#equation

**Smallest DBH** (Table 4, Dataset #4, silver fir):

> D range (cm) 5.1–64.0

Cite: https://treeallometry.org/equations/dutca-2020-fir-rim4-dh/#quote-fit-dbh-min-cm

**h min m** (Table 4, Dataset #4, silver fir):

> H range (m) 3.5–28.9

Cite: https://treeallometry.org/equations/dutca-2020-fir-rim4-dh/#quote-fit-h-min-m

**Trees measured** (Table 4, sample size):

> 151 (i.e., 144 + 7) / 109 (i.e., 102 + 7)

Cite: https://treeallometry.org/equations/dutca-2020-fir-rim4-dh/#quote-fit-n-trees

**Our note:** Fit on Dataset #4 (generic + reduced site sample of 7 trees). 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. Fit ranges are those of Dataset #4 (Table 4: generic trees plus the 7 smallest site 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 = 20, H = 16 | 129 | 129 | Computed from the printed form: computed from the published form (coefficients as printed) |
| D = 50, H = 30 | 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-rim4-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, RIM, Dataset #4, D and H", checked 2026-11-02, https://treeallometry.org/equations/dutca-2020-fir-rim4-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-rim4-dh.json
Report a problem: email info@restorationscope.com with the equation id (dutca-2020-fir-rim4-dh) and where the right value appears.