Sebastião do Amaral Machado

USING THE WEIBULL FUNCTION FOR PROGNOSIS OF YIELD BY DIAMETER CLASS IN Eucalyptus urophylla STANDS

This study aimed to fit the Weibull probability density function to stand data so as to represent the distribution of number of trees by diameter class, and also to fit models representing stand attributes so as to project growth and yield by diameter class and also yield of multiple wood products at the relevant rotation age (7 years). Data were collected from Eucalyptus urophylla stands owned by Anglo Americana plc (CODEMIM), a company situated in the municipality of Niquelândia, Goias state. Initially a 3P-Weibull probability function was fitted by the percentile method for the aggregate stand. Then models were fitted and selected of stand attributes using residuals plot, residual standard error (s yx ) and coefficient of determination (R²) as selection criteria. The hypsometric model of Trorey was then used to derive the average height of possible diameter classes, and the taper model of degree 5 and volumetric model of Takata were used to check compatibility of generated volumes. Prognosticated results were consistent with local productivity when compared to previous inventories complied by the same company of stands within the same age group. RESUMO: Nesta pesquisa, objetivou-se ajustar a funcao de densidade de probabilidade Weibull aos dados do povoamento, visando a representar a distribuicao do numero de arvores por classes de diâmetro bem como ajustar modelos que representem seus atributos para projetar o crescimento e a producao por classe diametrica e o rendimento dos multiplos produtos da madeira na idade da rotacao adotada pela empresa (sete anos). Os dados provieram de povoamentos de Eucalyptus urophylla da empresa Anglo Americana plc (CODEMIM), localizada no municipio de Niquelândia no estado de Goias. Inicialmente foi ajustada a funcao de probabilidade Weibull tres parâmetros pelo metodo dos percentis, para o povoamento como um todo. Posteriormente, foram ajustados e selecionados modelos dos atributos do povoamento, utilizando-se como criterios de selecao o Grafico de residuos, Erro Padrao Residual (s yx ) e o Coeficiente de Determinacao (R²). Em seguida, foi utilizado o modelo hipsometrico de Trorey para obtencao da altura media das possiveis classes diametricas e utilizado o modelo de afilamento de 5° grau e o modelo volumetrico de Takata, visando a compatibilidade dos volumes por eles gerados. Os resultados prognosticados foram coerentes com a producao do local, quando comparados com inventarios ja realizados na empresa em povoamento com essa faixa de idade.

Dinâmica da distribuição diamétrica de bracatingais na região metropolitana de Curitiba

O objetivo desta pesquisa foi estudar a dinâmica da distribuicao diametrica com relacao a idade, em povoamentos nativos de bracatinga (Mimosa scabrella Benth.) localizados nos municipios da regiao metropolitana de Curitiba. Os dados utilizados provieram de um experimento de densidades iniciais, delineado em blocos ao acaso, constituido de cinco blocos e quatro tratamentos, perfazendo um total de 20 parcelas de 325 m2, as quais foram remedidas as idades aproximadas de 4, 5, 6 e 7,5 anos. A densidade inicial sofreu reducao para 2.000, 4.000 e 8.000 arvores por hectare quando o povoamento tinha 1 ano de idade. Deixou-se tambem uma parcela-testemunha em cada bloco, as quais nao sofreram nenhum raleamento e tinham em media 25.000 arvores por hectare. Desses cinco blocos, um estava localizado na classe de sitio I, 2 na classe de sitio II e 2 blocos na classe de sitio III. Paralelamente, foram medidos os diâmetros e as alturas de todas as arvores em 124 parcelas temporarias distribuidas nos varios municipios da regiao metropolitana de Curitiba, representativos de povoamentos de bracatinga sob regime tradicional de cultivo e manejo, cobrindo idades de 3 a 18 anos, e as tres classes de sitio. Dentre as funcoes de densidade de probabilidade testadas por Bartoszeck (2000), a SB de Johnson foi a de melhor desempenho, sendo, portanto, utilizada para a estimativa do numero de arvores por classe diametrica e por hectare e consequente construcao das curvas de distribuicao diametrica para as inumeras combinacoes de idade, sitio e densidades disponiveis. Atraves da observacao visual das curvas sobrepostas, evidenciou-se que essas apresentaram assimetria para a direita e achatamento (curtose), com o aumento da idade. As curvas foram, entao, comparadas analiticamente entre si, pelo teste qui-quadrado, o qual revelou a existencia de diferencas significativas entre as curvas de distribuicao diametrica em diferentes idades.

Dinâmica da relação hipsométrica em função da idade, do sítio e da densidade inicial de povoamentos de bracatinga da Região Metropolitana de Curitiba, PR

The objective of this research was to analyse the behavior and the dynamics of hypsometric curves for age, site and initial density in native stands of bracatinga ( Mimosa scabrella Benth), growing in the Curitiba Metropolitan Region. The data came from DBH and total height measurements of each tree in 20 permanent sample plots, remeasured 4 times from 4 to 7,5 years old, covering 3 different site classes and the initial densities of 2,000, 4,000, 8,000 and the control plots, with average 25,000 plants/ha. Basing on the same set of data Bartoszeck (2000) carried out an intensive research on modeling the height-diameter relation. Then the Curtis model, resulting in an equation for each combination of factors, was used to proceed

Distribution of total height, transverse area and individual volume for Araucaria angustifolia (Bert.) O. Kuntze.

This study aimed to test probability density functions for the distribution of variables total height, transverse area and individual volume, considering three different class intervals. Data were obtained from the measurement of diameter (DBH) and total height and from estimation of the individual volume of 338 pine trees in a fragment of Mixed Ombrophylous Forest with an area of 15.24 ha, which is located in Jardim Botânico campus of UFPR, Curitiba-PR. Ten functions were fitted, including commonly used models for diameter distribution as well as other recently developed models applied to forest science. Selection criteria included Kolmogorov-Smirnov adherence test, standard error of estimate in percentage and adjusted coefficient of determination. Three class intervals were used as obtained by Sturges, Dixon & Kronmal, and Velleman criteria. The Normal function for variable height, and the Weber function for distribution of transverse area and individual volume, provided the best fit, considering the three class intervals adopted. The models fitted better for larger size class intervals as obtained by Sturges rule.

Comparação de métodos e processos de amostragem para estimar a área basal para grupos de espécies em uma floresta ecotonal da região norte matogrossense

O objetivo do presente estudo foi o de comparar a acuracidade e a precisao das estimativas de area basal obtidas de processos, intensidades e metodos amostrais com valores obtidos pelo censo, numa floresta ecotonal de 120 hectares na regiao norte matogrossense, para oito grupos de especies e para especies individuais para arvores com DAP ≥ 30 centimetros. Aplicaram-se os processos: aleatorio e o sistematico, com uma intensidade amostral de 5 e 10% para 22 tamanhos e formas de parcelas variando de 400 m2 a 10000 m2. A area basal media por hectare foi de 11,08 m2. As parcelas de 2500 m2 (125 m x 20 m) apresentaram erros reais e de amostragem sempre inferiores a 10% na estimativa de area basal para os grupos de todas as especies e para as 15 de maiores valores de importância (VI). Para os demais grupos os erros aumentam na medida em que decresce a quantidade de arvores por hectare. Para as especies, individualmente, os erros variaram de 28,7% (Vochysia sp.) a 250,59 (Hymenaeae courbaril), respectivamente, para a mais e a menos frequente, mostrando inviabilidade na aplicacao de processos estimativos tradicionalmente empregados nos inventarios florestais, notadamente para estimar parâmetros especificos de especies raras (baixa frequencia por hectare).

Uso de análise exploratória de dados e de regressão robusta na avaliação do crescimento de espécies comerciais de terra firme da Amazônia

This research originated from a data base of two forest inventories at 100%, carried out in 1984 and 2000 on an area of 576 hectares of an upland primary forest, located in the National Forest of Tapajos, in Belterra, Para, Brazil. The objective of the research was to use exploratory data analysis and robust regression for modeling diameter and basal area growths. In the two inventories, circumference breast height (CBH)-cm, was measured with a common tape; the commercial heights were measured with a Weise hypsometer in 1984 and, estimated with the use of sticks in 2000. The minimum DBH was 55 cm in 1984 and 35 cm in 2000, for all species. The statistical analyses were preceded by exploratory data analysis (EDA), where the box plot was used for outliers detection, and the stem-and-leaf graph to filter the extreme observations. Robust regression was used to adjust the models in the outliers presence. This research showed that, in spite of the intra and inter specific variations the six species together presented an observed and expected growth rate in diameter and basal area of 4,56 and 4.28 mm/year and 13.00 and 13.09 cm2/ha/year, respectively. It was also shown that the use of exploratory data analysis and robust regression made possible the analysis and determination of periodic increments in diameter and basal area in a consistent way. The methodology used for the available data and variable types was found to be more efficient when using robust regression for the method Least Trimmed Square than for the ordinary minimum square method.

Modelagem do volume do povoamento para Mimosa scabrella Benth. na regição metropolitana de Curitiba

2. Em cada parcela, mensurou-se o diâmetro a altura do peito, bem como a altura total de todas as arvores, em bracatingais de 3 a 18 anos de idade. Para a estimativa do volume total com casca, testaram-se varios modelos de regressao selecionados da literatura, o que gerou uma matriz com 58 variaveis independentes, visando construir modelos por meio do metodo Stepwise. As equacoes de melhor ajuste foram validadas utilizando-se o teste Qui-quadrado, a analise grafica de residuos e o erro-padrao da estimativa. Varias equacoes tiveram bom desempenho, apresentaram valores de coeficiente de determinacao ajustados superiores a 0,995, erro-padrao da estimativa inferior a 3% e adequada distribuicao de residuos. As duas equacoes de melhor desempenho foram validadas, apresentando erro-padrao da estimativa de 2,37% e 2,13%, valor nao-significativo para o teste do Qui-quadrado e equilibrada distribuicao dos residuos.

Distribuição espacial de um fragmento de Floresta Ombrófila Mista Montana

The objective of this research was to analyze the spatial distribution of a Mixed Ombrophylus Forest fragment, as well as of three species pertaining to distinct successional groups belonging to the same, by the Ripleys K function. The data came from a census carried out in a fragment located in the Campus Botanical Garden, UFPR, Curitiba - PR, Brazil, where all trees with DBH above 10cm were georeferenced. One plot with 4 ha was used for the analysis of the spatial distribution of the forest and individually for the species of Araucaria angustifolia (Bertol.) O. Kuntze, Casearia Sylvestris Sw. and Cedrela fissilis Vell. The spatial relationship between species, as well as the spatial relationship between diameter classes of the same were also analyzed. The forest showed a random spatial distribution, however, the three selected species showed an aggregate spatial distribution when analyzed individually. The Casearia Sylvestris presented an attraction relationship with Araucaria angustifolia and Cedrela fissilis, and these trees in turn, were related to repulsion between them. The spatial relationship between DBH classes of Araucaria angustifolia was attraction between individuals of smaller classes with larger individuals. This result reflects the form of seed dispersal of species, where regeneration occurs in the proximity to the parental trees. For the Casearia Sylvestris and Cedrela fissilis, aggregation occurred only between the smaller individuals.

Simulação de estratégias de manejo florestal na Amazônia com o uso do modelo SYMFOR

The SYMFOR model was used to simulate the ecological processes of tree growth, mortality and recruitment, and the forest management processes, in the terra firme forests of the eastern Amazon. The simulation utilized all the trees that have a diameter greater than 5 cm, from 40 permanent sample plots of 1 ha each (36 logged and 4 unlogged). The stand was measured in 1984, logged in 1985 and remeasured in 1986, 1988, 1990, 1994, 1996 and 2004. Ten species groups are used to describe the natural processes affecting tree behavior. Model performance compares the simulation results with real data describing the forest recovery for 19 years following logging. The treatments, combinations of logging intensities (15%, 25% and 35% of the total volume of the trees higher than 60 cm of DBH had been tested) and thinning intensities (0%, 30%, 50% and 70% of the original basal area) were analyzed as management strategies. The model was applied to simulate current forest management practice in the Brazilian Amazon, with 30 m3 ha−1 of timber extracted with a cutting cycle of 30 years. Results show that the similarity among observed and simulated data for SYMFOR validated the model to represent the dynamics of the unlogged forest. In the simulation of the current management practice applied in the Amazon forest, it is suggested that the financial benefits decrease with successive harvests and, consequently, the timber volume cannot be sustained.

Comparação dos valores estimados por amostragem na caracterização da estrutura de uma área de floresta na Amazônia com as informações registradas no censo florestal

The aim of this work was to compare the estimated values obtained by sampling with the actual values recorded in the Forest Census (inventory 100%) of a forest area in the Amazon. A systematic sampling was simulated, attending the requirements of IBAMA, with 2-ha sample units and sampling intensity of 14% in a 1,000-ha area, which was subjected to a forestry census. The census and simulation of forest inventory considered only the population with DBH > 40 cm and a list of 60 species which were identified as the population of trees considered of commercial value. It was evaluated the deviations of abundance, basal area and volume per hectare of sampling in relation to population. Deviations were evaluated with respect to individual species and species grouped according to the classification of price used by the Brazilian Forest Service. Deviations were also evaluated by diameter class, by group, and the total population. Even with sampling intensity of 14%, six species (10%) were not recorded in the sample, resulting in deviations from more than 614% to more and 100% to less in relation to abundance, basal area and volume.