Approximation of numerical integration applied to Araucaria angustifolia stem taper models

Abstract

Functions describing stem shape allow to determine dimension and volume class, with direct application in technical and economic activities in the forest. The aim of this study was to evaluate the accuracy of the Trapezoidal and Simpson 1/3 rules in the approximation of numerical integration applied to Kozak, Lee et al. and Sharma and Zhang models. The evaluated data were diameter and height of sixty Araucaria angustifolia (Bertol.) Kuntze individuals from a planted forest located in Caçador, State of Santa Catarina, Brazil. Analysis of results showed the high efficiency of the two volume and assortments determination methods compared to the exact value of the numerical integration. Kozak and Lee et al. models showed better results compared to Sharma and Zhang models. The first, when estimating volume of trunk with bark, applying the Trapezoidal rule, showed an error smaller than 10 -4, through eight integration intervals, equidistant between sections with relative length equal to 20% of the total height. The Simpson 1/3 rule resulted in greater accuracy with an error smaller than 10 -6, though with complex mathematical structure using six equidistant integration intervals.