# US national species group: Soft maple/birch (Table 4)

Aboveground biomass equation for Soft maple/birch species group (hardwood), United States, from Jenkins et al. 2003. DBH 2.5–66 cm. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it.

## Equation

As printed in Jenkins et al. 2003 (Table 4 footnote, p. 20):

> bm = Exp(β0 + β1 ln dbh)

Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#equation

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

```
Aboveground biomass = exp(-1.9123 + 2.3651 * ln(D))
```

Inputs: D = Diameter at breast height (1.3 m) (cm).
The source's own form: exp(-1.9123 + 2.3651 * ln(dbh)), with dbh in cm; output in kg.
Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#canonical

## What it covers

- Output: Aboveground biomass, kg
- Taxon: Soft maple/birch species group (hardwood), United States (mixed species); broadleaf
- Where: Conterminous United States. Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#where
- Biomes: temperate, boreal
- Stand: mixed
- DBH range: 2.5–66 cm. Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#dbh
- R²: 0.958. Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#r2
- Residual SE: 0.491685. Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#rse
- Method: OLS on ln-transformed pseudodata (316 points, generally at 5 cm dbh intervals) generated from published equations; no back-transform correction applied. Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#method
- Verification: read in the original source
- Last checked: 2026-11-01. Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#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

Jenkins, J.C., Chojnacky, D.C., Heath, L.S., Birdsey, R.A. (2003). National-scale biomass estimators for United States tree species. Forest Science, 49(1), 12–35.

- DOI: https://doi.org/10.1093/forestscience/49.1.12
- Access: open access
- Copy we read: https://research.fs.usda.gov/download/treesearch/6996.pdf
- Every equation from this source: https://treeallometry.org/sources/jenkins-2003/
- Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#source

## The facts, in the source's words

**Equation** (Table 4 footnote, p. 20):

> bm = Exp(β0 + β1 ln dbh)

Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#equation

**Equation** (Table 4 row, p. 20):

> Soft maple/birch −1.9123 2.3651 316 66 0.491685 0.958

Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#quote-expression

**Smallest DBH** (Table 4 footnote, p. 20):

> bm = total aboveground biomass (kg) for trees 2.5cm dbh and larger

Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#quote-fit-dbh-min-cm

**Residual standard error** (Table 4 footnote §):

> Root mean squared error or estimate of the standard deviation of the regression error term in natural log units.

Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#quote-fit-rse

**Correction factor** (p. 19, Correction factors):

> we do not include CFs for the reader to use after back-transformation

Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#quote-fit-cf

**Our note:** Group membership: soft Acer species and Betula (Table 1). dbh_max_cm is the 'Max dbh of trees measured in published equations'; data points are pseudodata, not trees. Hardwood groups were extended to 230 cm dbh with Freedman (1984) pseudodata. No log-bias correction: the authors deliberately omit it; a user could multiply by exp(RMSE²/2) = 1.1285. Superseded for FIA reporting by NSVB (Westfall et al. 2024) but still widely used in carbon protocols.

## 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 | 460 | 460 | Computed from the printed form: computed from the published form at dbh = 30 cm |
| D = 10 | 34.2 | 34.2 | Computed from the printed form: computed from the published form at dbh = 10 cm |

Cite: https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/#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: Jenkins, J.C., Chojnacky, D.C., Heath, L.S., Birdsey, R.A. (2003). National-scale biomass estimators for United States tree species. Forest Science, 49(1), 12–35. https://doi.org/10.1093/forestscience/49.1.12

Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "US national species group: Soft maple/birch (Table 4)", checked 2026-11-01, https://treeallometry.org/equations/jenkins-2003-soft-maple-birch/. 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/jenkins-2003-soft-maple-birch.json
Report a problem: email info@restorationscope.com with the equation id (jenkins-2003-soft-maple-birch) and where the right value appears.