Preussner functions for volume estimation of Pinus taeda L. in Southern Brazil

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Flavio Roberto Stefanello
Sylvio Péllico Netto
Alexandre Behling
Allan Libanio Pelissari
Gabriel Agostini Orso


modelling, taper, volume estimation, Preussner, Schöpfer’s 5th-degree polynomial, Kozak’s taper model, Burkhard’s taper model


Background: Taper modelling and volume estimation are key procedures in the management and planning of planted
forests. The objective of this work was to evaluate the taper and volume behaviour of Pinus taeda L. species, along the stem
in different ages, using the Preussner taper functions, compared to Schöpfer’s 5th-polynomial, Kozak’s and Max-Burkhart’s
models. This work focused on plantations of Pinus taeda L., due to its wide use as a source of raw material in the forest
industry of southern Brazil.

Methods: The data were collected in the last 22 years from the Midwest region of Santa Catarina, of trees ranging in age
from 3.5 to 18 years. This dataset consisted of a collection of volume sections, with relative diameter measurements along
the stem, used in conventional forest inventory. The total volume of the trees, obtained by integrating the Preussner taper
functions, was equated by dividing the stem into four parts, in which parabolas were fitted, and compared with the total
and merchantable volume estimated by Schöpfer’s 5th-degree polynomial, Kozak’s and Max-Burkhart’s functions.

Results: Bias, RMSE and r were generally better with the application of Kozak’s model, and AIC and BIC for the Preussner’s

Conclusions: Kozak functions were better to provide the merchantable volume. In terms of total volume both functions,
Kozak and Preussner, provided reliable estimates. The advantage of the procedure proposed by Preussner is the flexibility
of the fitted taper functions, the simplicity of volume calculations by integration, and the feasibility for interpreting their

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