Equations / Total volume

Nothofagus obliqua (roble) total volume, ln v from ln(d²h) (Cuadro 5, Grupo 3)

Total volumeNothofagus obliqua · NothofagaceaeChilenaturalRead from the original paper

Equation

As printed (Cuadro 5 (Ecuaciones de volumen total de las especies de Rucamanque), Roble row; model form is modelo 9 of Cuadro 1, Ln(v) = b0 + b1 Ln d²h (Kawas 1978))

Roble: Ln v = b0 + b1 Ln d²h; b0 = −9,918535; b1 = 0,95733

In this library's units, ready to compute (m³)

Total volume = exp(-9.918535 + 0.95733 * ln(D^2 * H))

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

Table values are images on SciELO. Ln is the natural log (paper defines Ln as base neperiana). No back-transformation correction factor is printed, so none is applied. v is total over-bark volume obtained by non-destructive relascope cubing. Other groups (laurel-lingue-tepa, ulmo, tineo) need the diameter at 6 m (d6), which is not a canonical variable, and are not included. The reported R2a (0,985, Cuadro 5) is adjusted, so not entered as r2. Cuadro 2 is the covariance-analysis species matrix; the descriptive statistics by group are in Cuadro 3 and the recommended equations in Cuadro 5.

Source

Salas Eljatib, C. (2002). Ajuste y validación de ecuaciones de volumen para un relicto del bosque de Roble-Laurel-Lingue. Bosque, 23(2), 81-92.

doi:10.4067/s0717-92002002000200009 · Open access · copy we read

Grupo 3 Roble (n = 107)

Trees measured · Cuadro 3

d [cm] mínimo 11,5; máximo 121,0; h [m] mínimo 9,8; máximo 53,5

Smallest DBH · Cuadro 3, Grupo 3

Trees measured: 107
DBH range: 11.5–121 cm
Height range: 9.8–53.5 m
Method: ordinary least squares, ln(v) = b0 + b1 ln(d²h)
Where: Predio Rucamanque, Temuco, Araucanía (38°39'S 72°35'W)
Last checked: 2026-11-02

Calculate

DBH (cm)Height (m)

Height from

0.204

Total volume (m³)

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 = 20, H = 15	0.204	0.204	Computed from the printed form computed from the published form (coefficients as printed, natural log, no correction factor)
D = 45, H = 27	1.69	1.69	Computed from the printed form computed from the published form (coefficients as printed, natural log, no correction factor)
D = 90, H = 40	9.29	9.29	Computed from the printed form computed from the published form (coefficients as printed, natural log, no correction factor)

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Nothofagus antarctica total over-bark volume from D and H (Schumacher-Hall, Cuadro 4) · Lencinas et al. 2002 · DBH + Height

Compare these curves

Nothofagus obliqua (roble) total volume, ln v from ln(d²h) (Cuadro 5, Grupo 3)

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