GROWTH ESTIMATE OF Eucalyptus STANDS BASED ON NONLINEAR MULTILEVEL MIXEDEFFECTS MODEL THEORY

O presente estudo foi baseado na utiliza\ue7\ue3o da teoria dos modelos n\ue3o-lineares de efeito misto em multin\uedveis para a modelagem do crescimento em altura de povoamentos clonais de Eucalyptus. A base de dados utilizada representa medi\ue7\uf5es de \ue1rvores individuais, tomadas em diferentes locais e no tempo, sendo a mesma classificada de longidudinal, irregularmente espa\ue7ada, n\ue3o-balanceada, com autocorrela\ue7\ue3o e com a presen\ue7a de heterogeneidade de vari\ue2ncia. O modelo log\uedstico de tr\ueas par\ue2metros foi utilizado para a estimativa do crescimento em altura. Os par\ue2metros do modelo foram estimados como de efeitos fixos e aleat\uf3rios em dois n\uedveis: unidade amostral (n\uedvel 1) e \ue1rvore individual dentro das unidades amostrais (n\uedvel 2). A inclus\ue3o de tais n\uedveis reduziu sensivelmente o erro padr\ue3o da estimativa para o modelo. As estimativas tamb\ue9m foram melhoradas com a modelagem da heterogeneidade da vari\ue2ncia, utilizando estruturas diagonais, e da autocorrela\ue7\ue3o, com a estrutura ARMA(2,1).This study was based on the application of the nonlinear multilevel mixed-effects theory in modeling the height growth of Eucalyptus plantation. The database was from individual tree measurements, taken from different sites and over time. This type of database is considered as longitudinal, irregularly spaced, unbalanced, with autocorrelation and heteroscedasticity. The tree-parameter logistic model was used to estimate the height growth with fixed and random effects in two levels: sample units (level 1) and trees inside sample units (level 2). By including both levels, the standard error of estimate was reduced significantly. Also, the estimates were improved by modeling the variance heterogeneity and the autocorrelation, using the ARMA(2,1) structure

Estimativa do crescimento de povoamentos de Eucalyptus baseada na teoria dos modelos não lineares em multinível de efeito misto.

This study was based on the application of the nonlinear multilevel mixed-effects theory in modeling the height growth of Eucalyptus plantation. The database was from individual tree measurements, taken from different sites and over time. This type of database is considered as longitudinal, irregularly spaced, unbalanced, with autocorrelation and  heteroscedasticity. The tree-parameter logistic model was used to estimate the height growth with fixed and random effects in two levels: sample units (level 1) and trees inside sample units (level 2). By including both levels, the standard error of estimate was reduced significantly. Also, the estimates were improved by modeling the variance heterogeneity and the autocorrelation, using the ARMA(2,1) structure.O presente estudo foi baseado na utilização da teoria dos modelos não-lineares de efeito misto em multiníveis para a modelagem do crescimento em altura de povoamentos clonais de Eucalyptus. A base de dados utilizada representa medições de árvores individuais, tomadas em diferentes locais e no tempo, sendo a mesma classificada de longidudinal, irregularmente espaçada, não-balanceada, com autocorrelação e com a presença de heterogeneidade de variância. O modelo logístico de três parâmetros foi utilizado para a estimativa do crescimento em altura. Os parâmetros do modelo foram estimados como de efeitos fixos e aleatórios em dois níveis: unidade amostral (nível 1) e árvore individual dentro das unidades amostrais (nível 2). A inclusão de tais níveis reduziu sensivelmente o erro padrão da estimativa para o modelo. As estimativas também foram melhoradas com a modelagem da heterogeneidade da variância, utilizando estruturas diagonais, e da autocorrelação, com a estrutura ARMA(2,1)

Análise de algumas alternativas para obter o coeficiente angular da reta no método da altura relativa.

The relative height method allows the characterization of stem profile without meeding sample trees to upper diameter measurements. The analytical geometry is applied on the diameter taken on 0,3 meters and on hr = (h-2)/2, as well as dbh and total height (h), making possible the measurement of these variables, simultaneously, with others measured on the permanent sampling in forest inventory. This study evaluated some alternatives in characterizing the stem profile by using analytical geometry, comparing it to the original method according Andrade (2001). It was concluded that the use of relative diameters to dbh showed better results in regression analysis to generate straight line angular coefficient. Also, to obtain better accuracy, it is more adequate to implement the relative height method using all trees inside the inventory sample unit.O método da altura relativa permite caracterizar o perfil do tronco sem precisar do abate de árvores-amostra para cubagem. Emprega-se geometria analítica nas variáveis obtidas partindo de diâmetros tomados a 0,3 metros do terreno e em hr = (h-2)/2, além de d1,3 e h, o que viabiliza a medição destas, simultaneamente, com as demais variáveis mensuradas nas parcelas de inventário florestal. Neste trabalho, foram avaliadas algumas opções para caracterização do perfil do tronco empregando geometria analítica, comparando-se com o seu uso original conforme Andrade (2001). Concluiu-se que o uso de diâmetros relativos ao dap apresentaram melhores resultados para empregar a análise de regressão, a fim de se gerar coeficientes angulares da reta. Também, na expectativa de melhor acurácia, é mais adequado empregar o método da altura relativa utilizando todas as árvores delimitadas pelas parcelas do inventário

Growth and yield models for eucalyptus stands obtained by differential equations

The main purpose of this study was to assess nonlinear models generated by integrating the basal area growth rate to estimate the growth and yield of forest stands. The database was collected from permanent sample units, in Paraopeba county, in the state of Minas Gerais, Brazil. The stands were represented by Eucalyptus camaldulensis × Eucalyptus urophylla hybrid trees, with 3 × 3 meters of spacing. The data were divided into two groups: fitting and validating databases. Two nonlinear models (Strategy A and Strategy B) were developed using differential equations to estimate the basal area growth and yield of the sample units. The logistic model was fitted to estimate the volumetric yield as a function of age, site index and basal area. The efficiency of the systems generated by logistic model and models obtained by differential equations (Strategy A and Strategy B) was also compared to the efficiency of the system estimated by the Clutter model (Strategy C). The projection models used to estimate basal area obtained by differential equations were compatible with forest growth and yield, and the logistic model with covariates was compatible with volumetric growth and yield. Strategy A and Strategy B generated different thinning and harvesting options for different site indices, which is biologically consistent

ANALYSIS OF SOME ALTERNATIVES TO CHARACTERIZE THE TREE PROFILE OF EUCALYPT USING ANALITICAL GEOMETRY

The relative height method allows the characterization of stem profile without meeding sample trees to upper diameter measurements. The analytical geometry is applied on the diameter taken on 0,3 meters and on hr = (h-2)/2, as well as dbh and total height (h), making possible the measurement of these variables, simultaneously, with others measured on the permanent sampling in forest inventory. This study evaluated some alternatives in characterizing the stem profile by using analytical geometry, comparing it to the original method according Andrade (2001). It was concluded that the use of relative diameters to dbh showed better results in regression analysis to generate straight line angular coefficient. Also, to obtain better accuracy, it is more adequate to implement the relative height method using all trees inside the inventory sample unit.</p

ANALYSIS OF SOME ALTERNATIVES TO CHARACTERIZE THE TREE PROFILE OF EUCALYPT USING ANALITICAL GEOMETRY

O m\ue9todo da altura relativa permite caracterizar o perfil do tronco sem precisar do abate de \ue1rvores-amostra para cubagem. Emprega-se geometria anal\uedtica nas vari\ue1veis obtidas partindo de di\ue2metros tomados a 0,3 metros do terreno e em hr = (h-2)/2, al\ue9m de d1,3 e h, o que viabiliza a medi\ue7\ue3o destas, simultaneamente, com as demais vari\ue1veis mensuradas nas parcelas de invent\ue1rio florestal. Neste trabalho, foram avaliadas algumas op\ue7\uf5es para caracteriza\ue7\ue3o do perfil do tronco empregando geometria anal\uedtica, comparando-se com o seu uso original conforme Andrade (2001). Concluiu-se que o uso de di\ue2metros relativos ao dap apresentaram melhores resultados para empregar a an\ue1lise de regress\ue3o, a fim de se gerar coeficientes angulares da reta. Tamb\ue9m, na expectativa de melhor acur\ue1cia, \ue9 mais adequado empregar o m\ue9todo da altura relativa utilizando todas as \ue1rvores delimitadas pelas parcelas do invent\ue1rio.The relative height method allows the characterization of stem profile without meeding sample trees to upper diameter measurements. The analytical geometry is applied on the diameter taken on 0,3 meters and on hr = (h-2)/2, as well as dbh and total height (h), making possible the measurement of these variables, simultaneously, with others measured on the permanent sampling in forest inventory. This study evaluated some alternatives in characterizing the stem profile by using analytical geometry, comparing it to the original method according Andrade (2001). It was concluded that the use of relative diameters to dbh showed better results in regression analysis to generate straight line angular coefficient. Also, to obtain better accuracy, it is more adequate to implement the relative height method using all trees inside the inventory sample unit

Changing the calculated surface area of wood samples to define drying schedules for Eucalyptus clones

The aim of this study was to determine how varying the inputted surface area value of wood samples would affect the determination of kiln-drying schedules using the drastic drying test. For this purpose, eight individuals of two Eucalyptus clones were selected. Specimens were obtained for drastic drying tests at 100 °C, to measure the basic density and to determine the initial moisture content. The initial and final temperatures and the drying potential were calculated in 100 mm × 50 mm × 10 mm samples, considering the surface area to be 130 cm² (Updated Method), in contrast to the surface area of 100 cm² that is commonly used in the method known as the Standard Method. Based on these findings, kiln-drying schedules were set for the lumber from each clone. Although the significant differences aforementioned, it was observed that the drying schedules developed by Standard Method and Updated Method are similar