# Leaf biomass from diameter and height (Table III) Foliage biomass equation for Fagus sylvatica, Netherlands, from Bartelink 1997. 38 trees. Listed on Tree Allometrics, a free library of tree allometric equations, each quoted from the source that published it. ## Equation As printed in Bartelink 1997 (Table III, model below table and Leaves row, p. 43 (rendered page-06).): > Y = c₁*dbh^c₂*h^c₃; c₁ = 0.0167, c₂ = 2.951, c₃ = −1.101 Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#equation In this library's units, ready to compute (foliage biomass in kg): ``` Foliage biomass = 0.0167 * D^2.951 * H^(-1.101) ``` Inputs: D = Diameter at breast height (1.3 m) (cm); H = Total tree height (m). The source's own form: 0.0167 * dbh^2.951 * h^(-1.101), with dbh in cm, h in m; output in kg. Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#canonical ## What it covers - Output: Foliage biomass, kg - Taxon: Fagus sylvatica (species); broadleaf - Where: Forest area in the centre of the Netherlands. Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#where - Biomes: not stated - Stand: not stated - Trees measured: 38. Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#n_trees - R²: 0.923. Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#r2 - Method: nonlinear least squares. Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#method - Verification: read in the original source - Last checked: 2026-11-05. Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#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 Bartelink, H. H. (1997). Allometric relationships for biomass and leaf area of beech (Fagus sylvatica L). Annales des Sciences Forestières, 54(1), 39–50. - DOI: https://doi.org/10.1051/forest:19970104 - Peer review: A paper in a peer-reviewed journal. - Access: open access - Copy we read: https://hal.science/hal-00883130/document - Every equation from this source: https://treeallometry.org/sources/bartelink-1997/ - Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#source ## The facts, in the source's words **Equation** (Table III, model below table and Leaves row, p. 43 (rendered page-06).): > Y = c₁*dbh^c₂*h^c₃; c₁ = 0.0167, c₂ = 2.951, c₃ = −1.101 Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#equation **Equation** (Table III, p. 43 (rendered page)): > Leaves 0.0167 0.0097 2.951 0.283 −1.101 0.375 0.923 Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#quote-expression **Equation** (Table III, p. 43 (rendered page)): > The models are of the form Y = c₁*dbhᶜ²*hᶜ³. Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#quote-expression-2 **Output** (Results, p. 43): > leaf biomass Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#quote-output **Units** (Table III, p. 43 (rendered page)): > Nonlinear models between tree biomass amounts or leaf area (Y: in kg or m²) and dbh (in cm) and tree height (h: in m). Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#quote-published-units **Trees measured** (Table III, p. 43 (rendered page)): > The number of observations is 38. Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#quote-fit-n-trees **R²** (Table III, p. 43 (rendered page)): > Leaves 0.0167 0.0097 2.951 0.283 −1.101 0.375 0.923 Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#quote-fit-r2 **method** (Data analysis, p. 42): > In the case of nonlinear regression analysis the model was fitted directly by nonlinear least squares. Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#quote-fit-method **Taxon** (Title, p. 39): > beech (Fagus sylvatica L) Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#quote-taxon **Where** (Data collection, p. 40): > centre of the Netherlands. Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#quote-region **Our note:** DBH is measured at 1.30 m; h is measured tree height. The author reports that adding height increased R² and cautions against extrapolation, particularly for leaf and branch fits. R² is adjusted for degrees of freedom. ## 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 = 15, H = 14 | 2.7 | 2.7 | Computed from the printed form: Computed from Table III. | Cite: https://treeallometry.org/equations/bartelink-1997-iii-leaves/#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: Bartelink, H. H. (1997). Allometric relationships for biomass and leaf area of beech (Fagus sylvatica L). Annales des Sciences Forestières, 54(1), 39–50. https://doi.org/10.1051/forest:19970104 Cite this page for the record and checks: Tree Allometrics (Restoration Scope), "Leaf biomass from diameter and height (Table III)", checked 2026-11-05, https://treeallometry.org/equations/bartelink-1997-iii-leaves/. 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/bartelink-1997-iii-leaves.json Report a problem: email info@restorationscope.com with the equation id (bartelink-1997-iii-leaves) and where the right value appears.