Equations / Height

Height from DBH, Michaelis-Menten model, terra-firme

HeightMixed Amazonian forest trees (367 species in terra-firme, 65 in várzea)BrazilnaturalRead from the original paper

Many species, no single photo

Equation

As printed (Table 1 (form) and Table 2, Terra-firme block)

H = a × DBH/(b + DBH) + ε ; Table 2: Michaelis-Menten a 51.09644 0.988 4.021 0.87 6,501.9 | b 25.11112 0.99

In this library's units, ready to compute (m)

Height = 51.09644 * D / (25.11112 + D)

D: Diameter at breast height (1.3 m), cm

Predicts total tree height from DBH. RSE printed in Table 2 is 4.021 (height scale, m), so fit.rse is not stored. Ranges are those printed for the trees sampled in this forest type. No correction factor is applied; the paper reports local models deviate 0.1% from measured heights.

Source

Baia, A.L.P., Nascimento, H.E.M., Guedes, M., Hilário, R., Toledo, J.J. (2025). Tree height-diameter allometry and implications for biomass estimates in Northeastern Amazonian forests. PeerJ, 13, e18974.

doi:10.7717/peerj.18974 · Open access · copy we read

We sampled 1,156 trees of 367 species ... in the terra-firme sites, and 806 trees of 65 species ... in várzea

Trees measured · Abstract

In the terra-firme sites, trees ranged from 1 to 109.1 cm DBH and 1.2 to 51.9 m in total height. In várzea sites, trees ranged from 5 to 139.5 cm DBH and 2.3 to 38.8 m in total height.

Smallest DBH · Results, first paragraph

Adj. pseudo R2 0.87

R² · Table 2, Terra-firme block

Trees measured: 1,156
DBH range: 1–109.1 cm
Height range: 1.2–51.9 m
R²: 0.87
Method: nonlinear least squares height-diameter model; R2 is the adjusted pseudo R2
Where: Non-flooded terra-firme forest, National Forest of Amapá (NFA), Brazil
Last checked: 2026-11-02

Calculate

DBH (cm)

14.6

Height (m)

Shaded: the DBH range the model was fitted on. Other inputs held at the values above.

Checks this equation passes

On every build, the library's form and the paper's own form (in its units) must both give these values within 1%.

Inputs	Expected	We get	From
D = 10	14.6	14.6	Computed from the printed form computed from the published form (coefficients as printed)
D = 30	27.8	27.8	Computed from the printed form computed from the published form (coefficients as printed)
D = 60	36	36	Computed from the printed form computed from the published form (coefficients as printed)

Report a problem with this equation · JSON

Height from DBH, Michaelis-Menten model, both forests pooled · Baia et al. 2025 · DBH
Height from DBH, Quadratic model, both forests pooled · Baia et al. 2025 · DBH
Height from DBH, Weibull model, both forests pooled · Baia et al. 2025 · DBH
Height from DBH, Quadratic model, terra-firme · Baia et al. 2025 · DBH
Height from DBH, Michaelis-Menten model, várzea · Baia et al. 2025 · DBH
Height from DBH, Quadratic model, várzea · Baia et al. 2025 · DBH
Height from DBH, Michaelis-Menten model, both forests pooled · same paper · Height
Height from DBH, Quadratic model, both forests pooled · same paper · Height
Height from DBH, Weibull model, both forests pooled · same paper · Height
Height from DBH, Quadratic model, terra-firme · same paper · Height
Height from DBH, Michaelis-Menten model, várzea · same paper · Height
Height from DBH, Quadratic model, várzea · same paper · Height

Compare these curves

Height from DBH, Michaelis-Menten model, terra-firme

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