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• W2068006972 abstract "AbstractAPPROXIMATION OF NUMERICAL INTEGRATION APPLIED TO Araucaria angustifólia STEM TAPER MODELSFunctions 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.Keywords: Taper; stem profile; individual volume. ResumoAproximação da integral numérica de modelos de forma do tronco para Araucaria angustifólia. Funções que descrevem a forma do tronco de árvores permitem determinar classes de dimensão e volume com aplicação direta no planejamento das atividades técnicas e econômicas na floresta. Neste sentido o presente estudo avaliou a acurácia da regra dos Trapézios e de Simpson 1/3 na aproximação da integral numérica aplicada aos modelos de Kozak, Lee et al. e Sharma e Zhang. Os dados avaliados incluem diâmetros e alturas relativas de sessenta árvores de Araucaria angustifolia (Bertol.) Kuntze provenientes de plantios florestais situados em Caçador, SC. A análise dos resultados mostrou alta eficiência dos dois métodos de determinação do volume e dos sortimentos quando comparados com o valor exato da integral numérica. Os modelos de Kozak e Lee et al. obtiveram resultados superiores quando confrontados com Sharma e Zhang, sendo estes, quando estimado o volume do tronco com casca, aplicando a regra do Trapézio, mostrou um erro inferior a 10-4 mediante a oito intervalos de integração equidistantes entre secções de comprimento relativo igual a 20% da altura total. A regra de Simpson 1/3 propiciou maior acurácia com erro inferior a 10-6, mas com estrutura matemática complexa utilizando seis intervalos de integração equidistantes.Palavras-chave: Afilamento; perfil do fuste; volume individual." @default.
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• W2068006972 date "2014-08-12" @default.
• W2068006972 modified "2023-10-16" @default.
• W2068006972 title "APPROXIMATION OF NUMERICAL INTEGRATION APPLIED TO Araucaria angustifólia STEM TAPER MODELS" @default.
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• W2068006972 doi "https://doi.org/10.5380/rf.v45i1.32686" @default.
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