Modelagem do crescimento e da produção de Pinus taeda L. por meio de função probabilística e processo de difusão

Abstract

Resumo: O presente trabalho teve como objetivo testar duas metodologias distintas de estimativa do crescimento e da produção, comparando os resultados obtidos em cada uma delas. Para isso, foram utilizados dados de 325 parcelas permanentes de Pinus taeda L. sem desbaste, provenientes da empresa International Paper do Brasil. Dessas, 172 parcelas possuíam 2 medições e 153 possuíam 3 medições, localizadas em diferentes sítios, com idades variando de 4 a 24 anos. Para a função probabilística, uma das metodologias de simulação utilizada, foram ajustados os modelos de altura dominante, sítio, sobrevivência, área basal, variância dos diâmetros e foi escolhida a distribuição Weibull para estimativa das distribuições diamétricas a partir do método dos momentos. Para o processo de difusão, a outra metodologia de simulação, foi ajustado o modelo de crescimento, a partir de um banco de dados pareado árvore a árvore, e um modelo de mortalidade, seguindo a metodologia desse processo. Foram sorteadas 70 parcelas para fazer a comparação entre os dados reais com os estimados pelas duas metodologias. De modo geral, tanto o processo de difusão quanto a função probabilística geraram resultados satisfatórios para estimativa da freqüência por classe de diâmetro, número de árvores e área basal. Para o volume o erro obtido na estimativa foi de 3,4% na função probabilística e 3,1% no processo de difusão. A função probabilística é a metodologia de simulação mais conhecida e estudada atualmente, devido à eficiência de suas estimativas, comprovada em diversos trabalhos. Para Pinus taeda essa metodologia é empregada no sistema SISPINUS que é amplamente difundido pelo Sul do Brasil. O processo de difusão ainda é pouco utilizado no Brasil e pode gerar estimativas comparáveis à funçã6 probabilística, com resultados satisfatórios para simulação do crescimento e da produção.

Abstract: The objective of this research was to test and compare two different methodologies for growth and yield modeling. The data carne from 325 permanent samples established in unthinned Pinus taeda L. (loblolly pine) stands owned by the International Paper of Brazil Co. A total of 172 samples were measured at three occasions and 153 were measured at two times. The plots were located in different sites, with ages varying from 4 to 24 years. The methodology called "probability function", one of two utilized in the study, used functions for dominant height, site, mortality, basal area and variance of the diameters. The Weibull probability distribution chosen to be used was fitted to data by the moments' method. The methodology called "diffusion process", the other to be tested, consisted in connecting growth increment and mortality models in the so-called "forward equation". Seventy sample plots were randomly chosen in order to make the comparison among the observed and predicted values from both modeling methodologies. In general, the diffusion process as well as the probability function provided satisfactory estimates of tree diameter class frequencies, number of trees and basal area per hectare. The errors obtained for the stem volume per hectare were 3.4% by using the probabilistic function and 3.1% for the diffusion process. The probability function approach is the most known methodology for growth and yield modeling of Pinus taeda in Brazil, because of this efficiency and of its estimates, as proved by several works. This methodology has been widely used in Pinus taeda simulations though the so-called SISPINUS software developed for the southern Brazilian conditions. The diffusion process is not widely used 1h Brazil yet, but it can provide predictions comparable to those of the probability function approach. Therefore, the diffusion process can give results so reliable as those obtained from the probability function modeling in order to simulate growth and yield of this species.

ABSTRACT The objective of this research was to test and compare two different methodologies for growth and yield modeling. The data came from 325 permanent samples established in unthinned Pinus taeda L. (loblolly pine) stands owned by the International Paper of Brazil Co. A total of 172 samples were measured at three occasions and 153 were measured at two times. The plots were located in different sites, with ages varying from 4 to 24 years. The methodology called "probability function", one of two utilized in the study, used functions for dominant height, site, mortality, basal area and variance of the diameters. The Weibull probability distribution chosen to be used was fitted to data by the moments' method. The methodology called "diffusion process", the other to be tested, consisted in connecting growth increment and mortality models in the so-called "forward equation". Seventy sample plots were randomly chosen in order to make the comparison among the observed and predicted values from both modeling methodologies. In general, the diffusion process as well as the probability function provided satisfactory estimates of tree diameter class frequencies, number of trees and basal area per hectare. The errors obtained for the stem volume per hectare were 3.4% by using the probabilistic function and 3.1% for the diffusion process. The probability function approach is the most known methodology for growth and yield modeling of Pinus taeda in Brazil, because of this efficiency and of its estimates, as proved by several works. This methodology has been widely used in Pinus taeda simulations though the so-called SISPINUS software developed for the southern Brazilian conditions. The diffusion process is not widely used in Brazil yet, but it can provide predictions comparable to those of the probability function approach. Therefore, the diffusion process can give results so reliable as those obtained from the probability function modeling in order to simulate growth and yield of this species. Key - words: simulation, growth and yield, probability function, diffusion process, Pinus taeda.