Modelagem e simulação do crescimento e produção de floresta tropical manejada na Amazônia Oriental

Orientador : Prof. Dr. Afonso Figueiredo FilhoCoorientadores : Prof. Dr. Jerome Klaas Vanclay, Prof. Dr. Sebastião do Amaral Machado, Prof. Dr. Ademir Roberto Ruschel e Prof. Dr. Lucas José Mazzei de FreitasTese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Agrárias, Programa de Pós-Graduação em Engenharia Florestal. Defesa: Curitiba, 19/09/2016Inclui referências : 140-157Área de concentração : Manejo FlorestalResumo: Este trabalho teve como objetivo estudar os aspectos ligados à classificação da produtividade, modelagem do crescimento, bem como a prognose e simulação da produção por meio de um modelo de árvore independente da distância. Os dados provieram da área experimental da Jari/EMBRAPA e da Unidade de Manejo Florestal nº 3 (UMF3) da Jari Florestal S.A., situadas, respectivamente, na localidade Morro do Felipe, município de Vitória do Jari, Estado do Amapá e na Região do Vale do Jari no Estado do Pará. O experimento tem sido monitorado pela Embrapa Amazônia Oriental e mantido pelo Grupo Jari desde 1983, sendo remedido em 8 ocasiões nos seguintes anos: 1984, 1986, 1988, 1990, 1994, 1996, 2004 e 2011. A área experimental é composta de 3 blocos, divididos em 12 parcelas distribuídas de forma aleatória, referentes a combinação de 3 intensidades de exploração e 4 de desbaste, somados a 4 parcelas controle, totalizando 40 parcelas permanentes de 1 hectare. O experimento foi idealizado em blocos ao acaso, entretanto, após aplicação de desbaste em 1994, o experimento foi analisado como parcelas subdivididas no tempo. Já a UMF3 é referente a uma unidade de produção explorada em 2006, com cerca de 3.786 ha de floresta nativa destinada a manejo florestal empresarial a partir do mesmo ano. Essa área propiciou um banco de dados de 16.099 árvores para a modelagem da relação hipsométrica de 25 espécies comerciais e de todas as espécies do experimento. Foram separados 10% dos dados para a validação da modelagem da relação hipsométrica, bem como 13 parcelas distribuídas em todos os tratamentos para a validação do simulador de crescimento desenvolvido. Para a classificação da produtividade foram testadas 9 técnicas diferentes que se baseiam em atributos populacionais como indicadores produtivos. As 337 espécies presentes, com DAP ? 5 cm, foram agrupadas a partir de critérios ecológicos, econômicos e de ritmo de crescimento, visando o melhor tratamento dos dados para a modelagem. O simulador de crescimento e produção foi desenvolvido a partir do ajuste de Modelos de Efeitos Mistos, técnica empregada principalmente nos submodelos de incremento diamétrico, sobrevivência e recrutamento. Foram feitas simulações de diferentes cenários produtivos por meio do programa de modelagem visual Simile®. A análise da dinâmica foi conduzida para os diferentes tratamentos do experimento. Foram aplicadas 5 técnicas de validação estatísticas dos submodelos propostos e do simulador desenvolvido. Para melhor apresentação da revisão teórica e dos resultados práticos, a tese foi dividida em 4 capítulos. O primeiro tratou da revisão bibliográfica dos métodos de avaliação da produtividade florestal em florestas tropicais. O segundo abordou a evolução histórica dos diferentes meios de modelagem do crescimento e produção aplicados no Brasil e no exterior. A relação hipsométrica de espécies tropicais foi o alvo do terceiro capítulo. O estudo do crescimento da floresta do Jari foi o tema principal do capítulo 4, abrangendo a aplicação das diferentes técnicas de classificação da produtividade do sítio, agrupamento de espécies, técnicas de modelagem, simulações e meios de validação do modelo de árvore proposto. Palavras-chave: Modelo de árvore, Prognose da Produção, Classificação de sítio.Abstratc:: The objective of this work was to study the aspects related to the site productivity classification, growth modeling, as well as yield prediction and simulation by using a distance-independent tree model. The data came from Jari/EMBRAPA experimental area and the Forest Management Unit nº 3 (FMU3) of Jari Florestal SA, situated respectively in the locality of Morro do Felipe, municipality of Vitória do Jari, State of Amapá and in the Jari Valley Region in the State of Pará, Brazil. The experiment has been monitored by Embrapa Amazônia Oriental and maintained by the Jari Group since 1983, being remensured on 8 occasions in the following years: 1984, 1986, 1988, 1990, 1994, 1996, 2004 and 2011. The experimental area is composed of 3 blocks, divided into 12 randomly distributed plots, corresponding to the combination of 3 levels of exploitation intensities and 4 thinning levels, added to 4 control plots, totalizing 40 permanent plots of 1 hectare each. The experiment was designed in randomized blocks; however, after thinning procedures in 1994, the experiment was analyzed as split plot in time. The FMU3 refers to a production unit area exploited in 2006, with approximately 3,786 ha of native forest alocated for forest management from the same year. This area provided a 16,099 trees database for modeling the hypsometric relationship of 25 commercial species and all species in the experimental area. Ten percent of the data were separated for validation procedures of the hypsometric relationship model, as well as 13 plots were randomly selected in all treatments for validation of the developed growth simulator. For site productivity classification were tested 9 different techniques that are based on population attributes as productive indicators. The 337 species presented with DBH ? 5 cm were grouped according to ecological, economic and growth rate criteria, aiming the best treatment of the data for the modeling. The growth and yield simulator was developed based on the adjustment of Mixed Effects Models, a technique mainly employed in the diametric increment, survival and recruitment submodels. Simulations of different production scenarios were made by using the Simile® visual modeling software. The dynamics analysis was carried out for the different treatments of the experiment. Five statistical validation techniques were applied on the proposed submodels and the developed simulator. For a better presentation of the theoretical review and the practical results, the thesis was divided in 4 chapters. The first one dealt with the bibliographic review of assessing forest productivity methods in tropical forests. The second dealt with the historical evolution of the different modeling growth and yield techniques applied in Brazilian and exterior forests. The hypsometric relationship of tropical species was the subject of the third chapter. The study of the Jari forest growth was the main subject of chapter 4, covering the application of the different site classification, species grouping and modeling techniques, as well as simulations and validation procedures of the proposed tree model. Key-word: Tree model, Yield prognosis, Site classification

Modelagem e prognose da produção de uma floresta tropical úmida densa de terra-firme na Amazônia Central

Orientador: Prof. Sebastião do Amaral MachadoCo-orientadores: Prof. Afonso Figueiredo Filho e prof. Niro HiguchiDissertação (mestrado) - Universidade Federal do Paraná, Setor de Ciências Agrárias, Programa de Pós-Graduação em Engenharia Florestal. Defesa: Curitiba, 16/02/2012Inclui bibliografiasÁrea de concentração: Manejo FlorestalResumoResumo: Este trabalho teve como objetivo estudar os aspectos da dinâmica, tais como crescimento e produção de uma amostra representativa de Floresta Tropical Úmida Densa de Terra-Firme, manejada experimentalmente ao longo de 30 anos, visando à modelagem matemática do experimento por meio de um Modelo de Crescimento e Produção por Distribuição Diamétrica. A área de estudo está situada na Estação Experimental de Silvicultura Tropical, do Instituto Nacional de Pesquisa da Amazônia (EEST/INPA), distante aproximadamente 90 km do centro urbano de Manaus - AM. Os dados são provenientes do Projeto BIONTE (Biomassa e Nutrientes Florestais) iniciado em 1980, tendo como base 12 parcelas permanentes de 1 ha, com medições anuais de todos os indivíduos com DAP 10 cm, entre os anos de 1990 e 2008. A área foi explorada em 1987 e 1988 sob diferentes intensidades de corte, sendo demarcada experimentalmente em blocos ao acaso, com parcelas subdivididas em tratos silviculturais, com 6 tratamentos e 3 repetições. Desses tratamentos, 4 foram utilizados nesta pesquisa: T0 = Testemunha ou controle; T1 = 25% da área basal explorada entre agosto e setembro de 1987; T2 = 50% da área basal explorada entre outubro e novembro de 1987; T3 = 75% da área basal explorada entre setembro e novembro de 1988. Para aplicar a modelagem à floresta, todas as espécies do experimento foram classificadas em dois grupos, pioneiras e não pioneiras, de acordo com suas características ecológicas, bem como foram aplicados modelos biomatemáticos para expressar a dinâmica da sobrevivência (recrutamento e mortalidade), área basal, somatório dos diâmetros, e a capacidade produtiva de cada tratamento e grupo ecológico do experimento. A função densidade de probabilidade de Weibull foi utilizada como base para modelagem da distribuição diamétrica, bem como outros modelos já desenvolvidos que estimam o volume comercial e a biomassa fresca foram utilizados na prognose da produção dessas variáveis e do estoque de carbono por unidade de área para cada tratamento. Visando melhor entendimento de cada processo aplicado nesse trabalho, bem como seus resultados, a dissertação foi dividida em capítulos. O primeiro discorre sobre o embasamento teórico e suas influências sobre o manuscrito. O segundo apresenta um novo método de classificação da produtividade a partir do Índice de Variação das Espécies Pioneira. O terceiro vislumbra a modelagem da sobrevivência, recrutamento e mortalidade, das espécies pioneiras e de todas as espécies por hectare. O quarto e último trata da modelagem da dinâmica da área basal e do somatório dos diâmetros bem como do modelo de crescimento e produção para a floresta sob análise, verificando sua eficiência na projeção do crescimento para o ano de 2009. Os resultados obtidos e a eficiência do método são apresentados em seus respectivos capítulos.Abstract: The objective of this work was to study aspects of the dynamics, such as growth and yield of a representative sample of upland Tropical rainforest, experimentally managed over 30 years, aimed mathematical modeling of the experiment using a Model of Growth and Yield by Diameter Distribution. The study area is situated in the Tropical Forest Experimental Station, from National Institute of Amazon Research (EEST / INPA), about 90 km distant from the urban center of Manaus - AM, Brazil. The data came from Project BIONTE (Forest Biomass and Nutrients) started in 1980, based on 12 permanent plots of 1 ha, annually measured of all individuals with DBH ? 10 cm, between the years 1990 and 2008. The area was explored in 1987 and 1988 under different intensities of cutting, being demarcated experimentally at random block design with sub-plots in which silvicultural treatments, were applied with 6 treatments and 3 repetitions. Of these treatments, four were used: T0 = Witness or control, T1 = 25% of basal area explored between august and september 1987, T2 = 50% of basal area explored between october and november 1987, T3 = 75% of basal area explored between september and november 1988. To apply the model to the forest, all species of the experiment were classified into two groups, pioneers and non-pioneer species, according to their ecological characteristics, as well as biomathematics models were employed to express the dynamics of survival (recruitment and mortality), basal area, sum of diameters, and the productive capacity of each treatment and ecological group. The probability density function of Weibull was used as the basis for modeling the diameter distribution, as well as other already developed models that estimate the volume of trade and fresh biomass was used in the prognosis of these variables and the production of carbon stock per unit area for each treatment. The dissertation was divided into chapters aimed better understanding of each process applied in this work and its results. The first bleach on the theoretical background and its influence on the manuscript. The second presents a new method of productivity classification from the Pioneer Species Diametric Variation. The third model shows the survival, recruitment and mortality of pioneer species and all species per hectare. The fourth, and last, present the modelling of basal area dynamics and the sum of the diameters, as well as the model of growth and yield for the forest under analysis, and its efficiency in growth projection for the year 2009. The results and efficiency of the method are in their respective chapters

Forest activity in rural properties of the region of Otacílio Costa SC, Brazil

O município de Otacílio Costa (SC) vem se destacando no cenário catarinense devido a sua grande participação no setor florestal, evidenciada pela ocupação florestal de sua área territorial. Com vistas a analisar as interações dessa atividade na propriedade rural e na região, este estudo teve como objetivo levantar informações dos proprietários rurais com relação à atividade florestal, avaliando a visão deles frente ao conhecimento que possuem da prática florestal, bem como de sua importância na manutenção, adequação, benefícios percebidos e das variáveis econômicas e ambientais associadas à propriedade rural. Os dados foram obtidos através da aplicação de questionários em entrevistas aos produtores rurais no município de Otacílio Costa. As características dos proprietários e das propriedades indicam uma tendência de concentração de terras. Os produtores de florestas, com pouco conhecimento técnico das práticas silviculturais e falta de assistência técnica, implantam florestas com recursos próprios, gerando um plantio florestal de baixa produtividade e tecnologia, reduzindo a capacidade econômica dos povoamentos. Para a difusão do conhecimento técnico e da legislação florestal, torna-se necessário o desenvolvimento de políticas públicas por órgãos competentes e de programas empresariais, tais como os de fomento florestal e de extensão rural, na região.Palavras-chave: Fomento florestal; extensão rural; produtor rural. AbstractForest activity in rural properties of the region of Otacílio Costa SC, Brazil. The municipality of Otacílio Costa shows up in Santa Catarina State scenario because of its increasing participation in the forestry sector, which is evidenced by the enlargement of forest land area. In order to analyze interactions of such activity on rural property as on the region, this study aimed to collect data of the rural proprietors regarding to forestry activity, for evaluation of their knowledge towards forestry practice, as well as its importance, maintenance, adequacy, perceived benefits, and economic and environmental variables associated to rural property. The collected data is result of application forms used in interviews with rural producers in Otacílio Costa - SC, Brazil. Characteristics of proprietors and properties indicate a trend of land concentration. Forest producers, with little technical knowledge of forestry and lack of technical assistance, implant forests by their own, having as result a reforestation of low productivity and technology, which reduce the economic potential of the stands. In order to improve dissemination of technical knowledge and forest law it is necessary to develop public policies by relevant bodies and programs of companies, such as forest promotion and rural extension in the region.Keywords: Forest promotion; rural extension; rural producer.The municipality of Otacílio Costa shows up in Santa Catarina State scenario because of its increasing participation in the forestry sector, which is evidenced by the enlargement of forest land area. In order to analyze interactions of such activity on rural property as on the region, this study aimed to collect data of the rural proprietors regarding to forestry activity, for evaluation of their knowledge towards forestry practice, as well as its importance, maintenance, adequacy, perceived benefits, and economic and environmental variables associated to rural property. The collected data is result of application forms used in interviews with rural producers in Otacílio Costa - SC, Brazil. Characteristics of proprietors and properties indicate a trend of land concentration. Forest producers, with little technical knowledge of forestry and lack of technical assistance, implant forests by their own, having as result a reforestation of low productivity and technology, which reduce the economic potential of the stands. In order to improve dissemination of technical knowledge and forest law it is necessary to develop public policies by relevant bodies and programs of companies, such as forest promotion and rural extension in the region

USING DIAMETER VARIATION INDEX OF PIONEER SPECIES FOR CLASSIFICATION AND MODELING TROPICAL FOREST YIELD

This study sought to classify the productivity of a representative area of tropical forest, as well as to analyze the relationship between the structural variability of pioneer species and the yield of three management regimes. The study area is located at the Tropical Forestry Experimental Station belonging to INPA (National Institute for Amazon Research), approximately 90 km from downtown Manaus, in the State of Amazonas, Brazil. Data were collected from twelve 1 ha sample plots. Diameter was measured annually for all individuals with DBH  10 cm between the years 1990 and 2008. Pioneer species served as the basis for calculating the Diameter Variability Index VI% over time. Three classes of variability were established according to the guide curve technique used for site classification by the dominant height. Biological and probabilistic functions were used to model VI% as a function of time of exploitation, as well as the volumetric yield over time as a function of VI%. There is an inverse relationship between VI% and yield, which allows classification of site yield and conception of global yield models to which present good statistics of precision and adjustment, allowing the prediction of productivity and their dynamics throughout the time

Modelagem da sobrevivência, mortalidade e recrutamento de uma floresta na Amazônia Central

The objective of this research was to test and to select models for description of survival, ingrowth and mortality of all species and for group of pioneer species present in a tropical rainforest in center of the Amazon. The study area is located in the Tropical Forest Experiment Station, 90 km far from the urban center of Manaus - AM, Brazil. The data came from 12 permanent 1 ha plots with annual measurements of all individuals with a DBH equal or greater than 10 cm, between years 1990 and 2008. Probabilistic and biological growth functions adapted for modeling cumulative recruitment and mortality were used, as well as current survival per unit of area for all species; and for pioneer species of the forest. The statistical criteria of fitting the Schlaegel Index, standard error of estimate and graphical analysis of residuals, indicate that: i) the pdf of the Weibull model as being the most appropriate function for modeling the cumulative recruitment of the group of pioneers and the total of species; ii) Sloboda and Weibull models in modeling the cumulative mortality of the group of pioneers and the total of species; iii) Logistic and Levakovik I functions to model the survival of the group of pioneers and the total of species per hectare

COMPARISON OF DIFFERENT METHODS OF MEASURING TREE VOLUMES IN THE MUNICIPALITY OF ANAPU, PARÁ, BRAZIL

The objective of this study was to compare three methods of measuring the volume of individual trees used extensively as a basis for adjusting volumetric functions in areas under forest management in the Brazilian Amazon, and verify the influence of species and diameter classes in obtaining the volume of individual trees.   A total of 53 sample trees belonging to five species were analyzed and separated into three diametric classes.  The real volume (VR) was obtained using Smalian’s method on fixed sections of 2 meters intervals along the stem; the geometric volume (VG) was also obtained by Smalian’s method, but with the lengths of the various sections along the stem.  Volume loss (VP) was subtracted from the VR to obtain the usable volume (VA).  An ANOVA in a factorial design (5 x 3 x 3) was performed to verify the effect of 5 species, 3 diameter classes, and 3 volume measurement methods (VR, VG, and VA) on the different volumes obtained.  The 3 factors did affect the outcome of the analysis, but there were no interactions found between these variables.  The volumes obtained by cubic scaling with different lengths (VG) presented a lower mean volume than VR.  Although there was no difference between the means of VA and VR, wood loss was 6.5% of the total volume. There is a relationship between section length and volume loss, according to the presence of hollows, twists and cracks in the logs in the largest diameter classes

Effect of age and site on the height distribution of Mimosa scabrella

 Este trabalho teve como objetivo avaliar o efeito do sítio e da idade na distribuição de alturas de bracatingais nativos da Região Metropolitana de Curitiba, bem como selecionar uma Função Densidade de Probabilidade (FDP), dentre seis, que melhor represente o histograma da variável altura desses povoamentos. Foram utilizados dados de altura provenientes de 88 parcelas de área variável de 100 a 400 m², em três classes de sítio, nas idades de 5, 8, 9 e 13 anos, nos quais se efetuaram o ajuste das funções probabilísticas. O ajuste dos modelos foi realizado com auxílio do aplicativo Solver do Microsoft Excel 2007, pelo método dos mínimos quadrados. As FDPs testadas foram Beta, Gamma, Log Normal, Normal, Sb de Jonhson e Weibull, sendo selecionada a de melhor ajuste pelo teste de Kolmogorov-Smirnov, Índice de Schlaegel e Erro Padrão da Estimativa Percentual. O sítio e a idade afetam a amplitude, a forma e a dinâmica da distribuição de alturas, sendo o sítio a variável relacionada à curtose e a idade à assimetria da distribuição. A FDP que melhor descreveu a distribuição de alturas dos bracatingais foi a função Beta, seguida pela Sb de Johnson e Normal.Palavras-chave: Bracatinga; distribuição hipsométrica; mínimos quadrados. AbstractEffect of age and site on the height distribution of Mimosa scabrella. This study aimed to evaluate the effect of site and age on the height distribution in native stands of “bracatinga” (Mimosa scabrella Benth) on the Metropolitan Region of Curitiba, PR, Brazil, as well as to select a Probability Density Function (pdf), between six, that represents the histogram of the variable height of these stands. It was used height data from 88 plots with variable area from 100 to 400 m², classified into three site classes. The ages 5, 8, 9 and 13 years were selected for fitting probability density functions by each site. The adjustment of the models was performed using the Solver application of Microsoft Excel 2007, by the least squares method. The pdfs tested were Beta, Gamma, Log Normal, Normal, Weibull and Sb Johnson, being selected the best by Kolmogorov-Smirnov test, Schlaegel Index and Percentage Standard Error of Estimate. The site and age affect the amplitude, shape and dynamics of the height distribution, with the site related to the kutosis and age to skewness of the distribution. The pdf that best described height distribution of the native stands of “bracatinga” was Beta function, followed by Sb Johnson and Normal.Keywords: Bracatinga; hypsometric distribution; least squares.AbstractThis study aimed to evaluate the effect of site and age on the height distribution in native stands of “bracatinga” (Mimosa scabrella Benth) on the Metropolitan Region of Curitiba, PR, Brazil, as well as to select a Probability Density Function (pdf), between six, that represents the histogram of the variable height of these stands. It was used height data from 88 plots with variable area from 100 to 400 m², classified into three site classes. The ages 5, 8, 9 and 13 years were selected for fitting probability density functions by each site. The adjustment of the models was performed using the Solver application of Microsoft Excel 2007, by the least squares method. The pdfs tested were Beta, Gamma, Log Normal, Normal, Weibull and Sb Johnson, being selected the best by Kolmogorov-Smirnov test, Schlaegel Index and Percentage Standard Error of Estimate. The site and age affect the amplitude, shape and dynamics of the height distribution, with the site related to the kutosis and age to skewness of the distribution. The pdf that best described height distribution of the native stands of “bracatinga” was Beta function, followed by Sb Johnson and Normal.Keywords: Bracatinga; hypsometric distribution; least squares

Comparison of methods for estimating heights from complete stem analysis data for Pinus taeda.

The objective of this research was to compare actual heights at known ages with those estimated by the methods proposed by Graves (1906), Carmean (1972), Lenhart (1972), Newberry (1978), and the Ratio and Graphic methods, in order to identify the most accurate one for Pinus taeda from Southern Brazil. That way, six trees aged at least 11 years were used. Cross-sections with 5 cm thickness were collected at heights of 0.10 meters, 0.70 meters, 1.30 meters and so on at every 1 meter along the bole. True height growth for a given age was measured on the section itself by dividing it in two parts along the pith and looking for the exact point where the true annual height growth took place. The accuracy analyses were based on residuals between true heights and those estimated by the tested methods for each age. For this analysis, the relative mean deviation (D%), relative mean absolute deviation (AbsD%), standard deviation of differences (Sd) and sum of squared relative residuals (SSRR) were calculated. These 4 statistics evaluated together, allowed for the identification of the most accurate method for every age. Complementarily, the non paired t0.05 test for data was applied to evaluate whether the residuals from each method were significant or not. The results of the analysis indicated that Carmean (1972) and Lenhart (1972) were identical owing to the fact that they estimated the same height value for sections where there was only one growth ring finishing in the same section. This situation occurred for most of the results in this current study. It was concluded that Carmean (1972) and Lenhart (1972) were the best methods for estimating height growth because both produced non-significant residuals for the majority of the trees studied.The objective of this research was to compare actual heights at known ages with those estimated by the methods proposed by Graves (1906), Carmean (1972), Lenhart (1972), Newberry (1978), and the Ratio and Graphic methods, in order to identify the most accurate one for Pinus taeda from Southern Brazil. That way, six trees aged at least 11 years were used. Cross-sections with 5 cm thickness were collected at heights of 0.10 meters, 0.70 meters, 1.30 meters and so on at every 1 meter along the bole. True height growth for a given age was measured on the section itself by dividing it in two parts along the pith and looking for the exact point where the true annual height growth took place. The accuracy analyses were based on residuals between true heights and those estimated by the tested methods for each age. For this analysis, the relative mean deviation (D%), relative mean absolute deviation (AbsD%), standard deviation of differences (Sd) and sum of squared relative residuals (SSRR) were calculated. These 4 statistics evaluated together, allowed for the identification of the most accurate method for every age. Complementarily, the non paired t0.05 test for data was applied to evaluate whether the residuals from each method were significant or not. The results of the analysis indicated that Carmean (1972) and Lenhart (1972) were identical owing to the fact that they estimated the same height value for sections where there was only one growth ring finishing in the same section. This situation occurred for most of the results in this current study. It was concluded that Carmean (1972) and Lenhart (1972) were the best methods for estimating height growth because both produced non-significant residuals for the majority of the trees studied

Modelagem da distribuição diamétrica de quatro espécies de Lauraceae em um fragmento de Floresta Ombrófila Mista.

O presente estudo teve como objetivo ajustar e selecionar funções de densidade de probabilidade que descrevam a distribuição diamétrica de quatro espécies de Lauraceae existentes em um fragmento de Floresta Ombrófila Mista. Os dados usados no ajuste das funções provêem do censo realizado em um fragmento de 15,24 ha, conhecido como “Capão da Engenharia Florestal”, localizado no Campus Jardim Botânico da UFPR, Curitiba-PR, em que foram medidas, marcadas, identificadas e georreferenciadas todas as árvores com DAP acima de 10 cm. Foram então ajustadas as funções probabilísticas de Weibull 2 e 3 parâmetros, Gamma, Gamma (adaptada), Sb de Johnson, Beta, Weber, Péllico, e as Exponenciais de Meyer tipo I, e tipo II. As funções foram ajustadas pelo método dos mínimos quadrados, utilizando um intervalo de classe de 5 cm. Os critérios de seleção utilizados foram o teste de Kolmogorov-Smirnov e a soma de quadrados dos resíduos. De acordo com estes critérios, a função de Weber foi a que melhor descreveu a distribuição diamétrica de Ocotea bicolor Vattimo e Nectandra lanceolata Ness. Para Ocotea nutans (Nees) Mez e Ocotea puberula (Reich.) Ness, os modelos que melhor representaram sua distribuição foram as funções Weibull 3 parâmetros e Sb de Johnson, respectivamente

Comparison Of Methods For Estimating Heights From Complete Stem Analysis Data For Pinus taeda

O objetivo do presente trabalho foi comparar os valores reais das alturas dos an\ue9is de crescimento anual com os estimados por meio da t\ue9cnica de an\ue1lise de tronco pelos m\ue9todos de Graves (1906), Carmean (1972), Lenhart (1972), Newberry (1978), Propor\ue7\uf5es e Gr\ue1fico e identificar o mais acurado para \ue1rvores de Pinus taeda do sul do Brasil. Para isso, foram usadas seis \ue1rvores de regenera\ue7\ue3o natural com idade m\uednima de 11 anos. Coletaram-se discos de 5 cm de espessura nas alturas 0,1m, 0,7m, 1,30m e a cada 1 m at\ue9 o fim do tronco. Os valores reais das alturas em cada ano foram medidos diretamente nos troncos, rachando-se as se\ue7\uf5es entre discos ao longo da medula e procurando pelo ponto exato em que cada idade terminava. As an\ue1lises de precis\ue3o foram baseadas nos res\uedduos entre os valores reais das alturas em cada ano e os valores estimados para cada m\ue9todo. Para esse fim, foram calculados o desvio m\ue9dio relativo (D%), desvio m\ue9dio relativo dos valores em m\uf3dulo (AbsD%), desvio-padr\ue3o (Sd) e soma de quadrado dos desvios relativos (SSRR). Essas quatro estat\uedsticas avaliadas em conjunto, permitiram identificar o m\ue9todo mais preciso para cada ano. Complementarmente foi aplicado o teste de t0.05 para dados n\ue3o pareados, para avaliar se, no geral, os desvios foram significantes ou n\ue3o. Os resultados das an\ue1lises indicaram que os m\ue9todos de Carmean (1972) e Lenhart (1972) tiveram desempenho id\ueantico, em fun\ue7\ue3o de estimarem a mesma altura quando h\ue1 apenas um anel de crescimento terminando numa mesma se\ue7\ue3o. Isso ocorreu na maioria das vezes. Concluiu-se que esses dois m\ue9todos foram os melhores por terem gerado desvios n\ue3o significativos para a maioria das \ue1rvores estudadas.The objective of this research was to compare actual heights at known ages with those estimated by the methods proposed by Graves (1906), Carmean (1972), Lenhart (1972), Newberry (1978), and the Ratio and Graphic methods, in order to identify the most accurate one for Pinus taeda from Southern Brazil. That way, six trees aged at least 11 years were used. Cross-sections with 5 cm thickness were collected at heights of 0.10 meters, 0.70 meters, 1.30 meters and so on at every 1 meter along the bole. True height growth for a given age was measured on the section itself by dividing it in two parts along the pith and looking for the exact point where the true annual height growth took place. The accuracy analyses were based on residuals between true heights and those estimated by the tested methods for each age. For this analysis, the relative mean deviation (D%), relative mean absolute deviation (AbsD%), standard deviation of differences (Sd) and sum of squared relative residuals (SSRR) were calculated. These 4 statistics evaluated together, allowed for the identification of the most accurate method for every age. Complementarily, the non paired t0.05 test for data was applied to evaluate whether the residuals from each method were significant or not. The results of the analysis indicated that Carmean (1972) and Lenhart (1972) were identical owing to the fact that they estimated the same height value for sections where there was only one growth ring finishing in the same section. This situation occurred for most of the results in this current study. It was concluded that Carmean (1972) and Lenhart (1972) were the best methods for estimating height growth because both produced nonsignificant residuals for the majority of the trees studied