Resumo As funções de afilamento são ferramentas úteis para estimar diâmetros de toras e volumes comerciais de madeira a quaisquer alturas, sendo de grande importância para os empreendimentos florestais que buscam a otimização do uso de suas florestas. Este trabalho teve como objetivo avaliar modelos de afilamento segmentados, não segmentados e modelos de forma variável para estudo do afilamento do tronco de árvores de Eucalyptus sp. Com uma base de dados proveniente de um plantio de Eucalyptus sp. localizado no sul do estado de São Paulo aos 6,3 anos de idade, os modelos de afilamento testados foram: os modelos não segmentados de Ormerod (1973) e de Schöepfer (1966), o modelo segmentado de Max e Burkhart (1976), e os modelos de forma variável de Muhairwe (1999), Methol (2001) apud Rachid et al. (2014) e de Kozak (2004). Os volumes reais foram calculados utilizando-se o método de Smalian. O modelo de Kozak (2004) obteve as melhores medidas de precisão para estimativa dos diâmetros, já a equação de Muhairwe (1999) demonstrou os melhores resultados gráficos de dispersão de resíduos para a mesma estimativa. Para a estimativa volumétrica, a equação que obteve os melhores resultados foi a proposta por Methol (2001) apud Rachid et al. (2014), com as melhores medidas de precisão e melhor comportamento gráfico, com menores tendências e dispersão mais concentrada dos resíduos.

Abstract Taper functions are useful tools for estimating log diameters and commercial wood volumes at any height, being of great importance to forestry enterprises that aim to optimize the use of their forests. Thus, the aim of this work was to evaluate segmented, non-segmented and variable-exponent taper models for studying the trunk taper of Eucalyptus sp. With a database from a 6.3-year-old Eucalyptus sp. planted forest, in the south of the state of São Paulo, the taper models tested were: the non-segmented models of Schöepfer (1966) and Ormerod (1973) the segmented model of Max and Burkhart (1976), and the variable-exponent models of Muhairwe (1999), Methol (2001) apud Rachid et al. (2014) and Kozak (2004). Real volumes were calculated using the Smalian formula. The equation proposed by Kozak (2004) obtained the best accuracy to estimate the diameters, whereas the Muhairwe (1999) equation showed the best graphic dispersion results for the same estimate. For volume estimation, the equation that obtained the best results was that proposed by Methol (2001) apudRachid et al. (2014), with the best measures of precision and better graphical behavior, with smaller trends and more concentrated dispersion of the residues.

Resumen La agricultura sustentable de plantaciones forestales exige la estimación permanente de la cantidad o volumen de madera que se está produciendo en un momento dado, lo que es difícil en extensas áreas de bosque, si solo se utilizan procedimientos manuales en campo. En la presente investigación se modelaron redes neuronales artificiales (ANNs, su sigla en inglés) de perceptrón multicapa para la estimación espacial de volúmenes de madera en una plantación de Eucalyptus sp. localizada en el estado de Mato Grosso del Sur, región Centro-oeste de Brasil. Para el efecto se emplearon como variables de predicción bandas espectrales, texturas de las bandas obtenidos con matriz de coocurrencia de niveles de grises e índice de vegetación, que fueron derivados de imagen digital de satélite Spot 6. La ANN resultante con mejor desempeño presentó una precisión de 93.32% y un coeficiente de determinación de 0.9761, con respecto a valores obtenidos con medidas de campo; no obstante, presentó un error cuadrático medio relativo de 16.32% (RMSE de 7.85 m3/ha), pero la distribución de los residuos no fue tendenciosa, por tanto, el modelo fue promisorio para mapear los volúmenes de madera en extensas áreas sin sobreestimar o subestimar la predicción. La red construida mostró mayor precisión y exactitud cuándo se comparó con otros métodos que usaron variables similares de estimación, inclusive en comparación con modelos neuronales que utilizaron solo bandas espectrales e índices de vegetación.

Abstract The sustainable agriculture of forest plantations demands the permanent monitoring of the quantity of processed wood, thus becoming difficult to monitor large planted areas by using only manual procedures. Therefore, in this research artificial neural networks (RNA) of multilayer perceptrons, were modeled to estimate the spatial of wood volume in a Eucalyptus-sp plantation located in the state of Mato Grosso del Sur in the Central-West region of Brazil. As input variables in the RNA spectral bands, the textures of the bands obtained with Gray Level Co-occurrence Matrices and vegetation index were used, which were derived from digital satellite image Spot 6. The resulting RNA with the best performance presented accuracy of 93.32% and coefficient of determination of 0.9761. However, this network presented a mean square error of 16.32% (RMSE de 7.85 m3ha-1), but with a unbiased distribution of the residuals. So, the model showed to be suitable to monitor the amount of wood in large areas without overestimating or underestimating the prediction. Compared with different machine learning methods using the same variables, the built network seems to have a higher precision and accuracy. Even in the neuronal models using only spectral bands and vegetation indexes, a better performance was evidenced, showing that the textures contribute in the improvement of predictions.

ABSTRACT The aim of this study was to apply geostatistics to predict the spatial pattern of variations in moisture content of eucalyptus wood chip piles to generate subsidies for adequate sampling and material handling. Wood chip piles were installed in three different storage cycles using newly cut material for 7, 30, and 60 days. Sampling was performed in axial (top, middle, and base) and lateral positions, so that all samples were georeferenced in relation to the distance from the ground and the center of the pile. Moisture values were submitted to geostatistical analysis and kriging. The results confirmed the spatial dependence of moisture content over the piles stored at 7 and 30 days; however, the effect of rainfall was crucial to reduce the spatial dependence of moisture content. The results showed that geostatistics is a useful tool for the creation of reliable sampling protocols.

RESUMO Neste trabalho, está sendo proposta uma abordagem bayesiana para resolver o problema de inferência com restrições nos parâmetros, em modelos não lineares que representam a relação hipsométrica em clones de Eucalyptus sp. As estimativas Bayesianas são calculadas com a técnica de simulação de Monte Carlo em Cadeia de Markov (MCMC). O método proposto foi aplicado a diferentes conjuntos de dados reais, dos quais foram selecionados dois para mostrar os resultados obtidos. Estes foram comparados aos obtidos pelo método de mínimos quadrados, destacando-se a superioridade da abordagem Bayesiana empírica proposta, uma vez que esta abordagem sempre gera resultados coerentes biologicamente para a relação hipsométrica.

ABSTRACT In this paper we propose a Bayesian approach to solve the inference problem with restriction on parameters, regarding to nonlinear models used to represent the hypsometric relationship in clones of Eucalyptus sp. The Bayesian estimates are calculated using Monte Carlo Markov Chain (MCMC) method. The proposed method was applied to different groups of actual data from which two were selected to show the results. These results were compared to the results achieved by the minimum square method, highlighting the superiority of the Bayesian approach, since this approach always generate the biologically consistent results for hipsometric relationship.

Neste trabalho foi considerado o modelo de Curtis para a relação hipsométrica em clones de Eucalyptus sp. com os parâmetros sujeitos a restrições. Para fazer a inferência dos parâmetros do modelo com restrições, utilizou-se uma abordagem bayesiana com densidade a priori construída empiricamente. As estimativas bayesianas são calculadas com a técnica de simulação de Monte Carlo em Cadeia de Markov (MCMC). O método proposto foi aplicado a diferentes conjuntos de dados reais, dos quais foram selecionados cinco para exemplificar os resultados. Estes foram comparados com os resultados obtidos pelo método de mínimos quadrados, destacando-se a superioridade da abordagem bayesiana proposta.

The model of Curtis was considered in this work for the hypsometric relationship in Eucalyptus sp. clones with parameters submitted to restrictions. A Bayesian a priori density was empirically constructed to infer the parameters of the models with restrictions. The Bayesian estimates are calculated using Monte Carlo Markov Chain (MCMC) Method. The proposed method was applied to different groups of real data from which five were selected to show the results. Those were compared to the achieved results by the minimum square method and the superiority of the Bayesian approach is highlighted.