Modeling height-diameter relationship in pinus pinaster ait. in the forest intervention zone of Lomba, NE-Portugal. Msaouak, K. Master's thesis, School of Agriculture of Bragança, July, 2016.
Modeling height-diameter relationship in pinus pinaster ait. in the forest intervention zone of Lomba, NE-Portugal [link]Paper  abstract   bibtex   
In this work, the relationship between diameter at breast height (d) and total height (h) of individual-tree was modeled with the aim to establish provisory height-diameter (h-d) equations for maritime pine (Pinus pinaster Ait.) stands in the Lomba ZIF, Northeast Portugal. Using data collected locally, several local and generalized h-d equations from the literature were tested and adaptations were also considered. Model fitting was conducted by using usual nonlinear least squares (nls) methods. The best local and generalized models selected, were also tested as mixed models applying a first-order conditional expectation (FOCE) approximation procedure and maximum likelihood methods to estimate fixed and random effects. For the calibration of the mixed models and in order to be consistent with the fitting procedure, the FOCE method was also used to test different sampling designs. The results showed that the local h-d equations with two parameters performed better than the analogous models with three parameters. However a unique set of parameter values for the local model can not be used to all maritime pine stands in Lomba ZIF and thus, a generalized model including covariates from the stand, in addition to d, was necessary to obtain an adequate predictive performance. No evident superiority of the generalized mixed model in comparison to the generalized model with nonlinear least squares parameters estimates was observed. On the other hand, in the case of the local model, the predictive performance greatly improved when random effects were included. The results showed that the mixed model based in the local h-d equation selected is a viable alternative for estimating h if variables from the stand are not available. Moreover, it was observed that it is possible to obtain an adequate calibrated response using only 2 to 5 additional h-d measurements in quantile (or random) trees from the distribution of d in the plot (stand). Balancing sampling effort, accuracy and straightforwardness in practical applications, the generalized model from nls fit is recommended. Examples of applications of the selected generalized equation to the forest management are presented, namely how to use it to complete missing information from forest inventory and also showing how such an equation can be incorporated in a stand-level decision support system that aims to optimize the forest management for the maximization of wood volume production in Lomba ZIF maritime pine stands. [In Portuguese] Neste trabalho modelou-se a relação entre o di\^ametro à altura do peito (d) e a altura total da árvore individual com vista ao estabelecimento de equações hipsométricas provisórias para povoamentos de pinheiro bravo (Pinus pinaster Ait.) na ZIF da Lomba, Nordeste de Portugal. Com dados recolhidos localmente, testaram-se várias equações locais e generalizadas apresentadas na literatura, tendo-se considerado igualmente algumas adaptações. No ajustamento das equações utilizou-se o método dos mínimos quadrados não lineares (MQNL). Os modelos selecionados, local e generalizado, foram testados na forma de modelos mistos, tendo-se utilizado um método de estimação condicional de primeira ordem e estimadores de máxima verosimilhança para estimar os efeitos fixos e aleatórios. Para a calibração dos modelos mistos usou-se o mesmo método de aproximação linear para testar diferentes tipologias de amostragem. Os resultados revelaram melhores performances das equações hipsométricas locais com dois par\^ametros relativamente às análogas com tr\^es par\^ametros. Contudo, o mesmo conjunto de valores dos par\^ametros não pode ser usado em todos os povoamentos de pinheiro bravo da ZIF da Lomba e, portanto, uma equação hipsométrica generalizada com inclusão de variáveis do povoamento para além de d torna-se necessária para uma capacidade preditiva adequada. Não se observaram evid\^encias de superioridade do modelo misto generalizado relativamente ao obtido por MQNL. Por outro lado, no caso da equação local, a performance preditiva melhorou claramente após a inclusão de efeitos aleatórios. Os resultados mostraram que o modelo misto baseado na equação local selecionada é uma alternativa viável para a estimação de h na aus\^encia de informação sobre variáveis do povoamento. Além disso, observou-se que é possível obter uma calibração adequada com medições adicionais de apenas 2 a 5 pares h-d em árvores correspondentes a quantis (ou ao acaso) da distribuição de d na parcela (povoamento). Ponderando o esforço de amostragem, exatidão e facilidade de uso em aplicações práticas, o modelo generalizado resultante do ajustamento por MQNL é recomendado. São apresentados exemplos de aplicação da equação generalizada selecionada em gestão florestal, nomeadamente como usar a equação para completar informação em falta num contexto de inventário e também para mostrar como uma equação deste tipo pode ser incorporada num sistema de suporte à decisão ao nível do povoamento com o objetivo de otimizar a gestão para a maximização do volume lenhoso produzido em povoamentos de pinheiro bravo da ZIF da Lomba.
@mastersthesis{citeulike:14134053,
    abstract = {In this work, the relationship between diameter at breast height (d) and total height (h) of individual-tree was modeled with the aim to establish provisory height-diameter (h-d) equations for maritime pine (Pinus pinaster Ait.) stands in the Lomba {ZIF}, Northeast Portugal. Using data collected locally, several local and generalized h-d equations from the literature were tested and adaptations were also considered. Model fitting was conducted by using usual nonlinear least squares (nls) methods. The best local and generalized models selected, were also tested as mixed models applying a first-order conditional expectation ({FOCE}) approximation procedure and maximum likelihood methods to estimate fixed and random effects. For the calibration of the mixed models and in order to be consistent with the fitting procedure, the {FOCE} method was also used to test different sampling designs. The results showed that the local h-d equations with two parameters performed better than the analogous models with three parameters. However a unique set of parameter values for the local model can not be used to all maritime pine stands in Lomba {ZIF} and thus, a generalized model including covariates from the stand, in addition to d, was necessary to obtain an adequate predictive performance. No evident superiority of the generalized mixed model in comparison to the generalized model with nonlinear least squares parameters estimates was observed. On the other hand, in the case of the local model, the predictive performance greatly improved when random effects were included. The results showed that the mixed model based in the local h-d equation selected is a viable alternative for estimating h if variables from the stand are not available. Moreover, it was observed that it is possible to obtain an adequate calibrated response using only 2 to 5 additional h-d measurements in quantile (or random) trees from the distribution of d in the plot (stand). Balancing sampling effort, accuracy and straightforwardness in practical applications, the generalized model from nls fit is recommended. Examples of applications of the selected generalized equation to the forest management are presented, namely how to use it to complete missing information from forest inventory and also showing how such an equation can be incorporated in a stand-level decision support system that aims to optimize the forest management for the maximization of wood volume production in Lomba {ZIF} maritime pine stands.

[In Portuguese] Neste trabalho modelou-se a rela\c{c}\~{a}o entre o di\^{a}metro \`{a} altura do peito (d) e a altura total da \'{a}rvore individual com vista ao estabelecimento de equa\c{c}\~{o}es hipsom\'{e}tricas provis\'{o}rias para povoamentos de pinheiro bravo (Pinus pinaster Ait.) na {ZIF} da Lomba, Nordeste de Portugal. Com dados recolhidos localmente, testaram-se v\'{a}rias equa\c{c}\~{o}es locais e generalizadas apresentadas na literatura, tendo-se considerado igualmente algumas adapta\c{c}\~{o}es. No ajustamento das equa\c{c}\~{o}es utilizou-se o m\'{e}todo dos m\'{\i}nimos quadrados n\~{a}o lineares ({MQNL}). Os modelos selecionados, local e generalizado, foram testados na forma de modelos mistos, tendo-se utilizado um m\'{e}todo de estima\c{c}\~{a}o condicional de primeira ordem e estimadores de m\'{a}xima verosimilhan\c{c}a para estimar os efeitos fixos e aleat\'{o}rios. Para a calibra\c{c}\~{a}o dos modelos mistos usou-se o mesmo m\'{e}todo de aproxima\c{c}\~{a}o linear para testar diferentes tipologias de amostragem. Os resultados revelaram melhores performances das equa\c{c}\~{o}es hipsom\'{e}tricas locais com dois par\^{a}metros relativamente \`{a}s an\'{a}logas com tr\^{e}s par\^{a}metros. Contudo, o mesmo conjunto de valores dos par\^{a}metros n\~{a}o pode ser usado em todos os povoamentos de pinheiro bravo da {ZIF} da Lomba e, portanto, uma equa\c{c}\~{a}o hipsom\'{e}trica generalizada com inclus\~{a}o de vari\'{a}veis do povoamento para al\'{e}m de d torna-se necess\'{a}ria para uma capacidade preditiva adequada. N\~{a}o se observaram evid\^{e}ncias de superioridade do modelo misto generalizado relativamente ao obtido por {MQNL}. Por outro lado, no caso da equa\c{c}\~{a}o local, a performance preditiva melhorou claramente ap\'{o}s a inclus\~{a}o de efeitos aleat\'{o}rios. Os resultados mostraram que o modelo misto baseado na equa\c{c}\~{a}o local selecionada \'{e} uma alternativa vi\'{a}vel para a estima\c{c}\~{a}o de h na aus\^{e}ncia de informa\c{c}\~{a}o sobre vari\'{a}veis do povoamento. Al\'{e}m disso, observou-se que \'{e} poss\'{\i}vel obter uma calibra\c{c}\~{a}o adequada com medi\c{c}\~{o}es adicionais de apenas 2 a 5 pares h-d em \'{a}rvores correspondentes a quantis (ou ao acaso) da distribui\c{c}\~{a}o de d na parcela (povoamento). Ponderando o esfor\c{c}o de amostragem, exatid\~{a}o e facilidade de uso em aplica\c{c}\~{o}es pr\'{a}ticas, o modelo generalizado resultante do ajustamento por {MQNL} \'{e} recomendado. S\~{a}o apresentados exemplos de aplica\c{c}\~{a}o da equa\c{c}\~{a}o generalizada selecionada em gest\~{a}o florestal, nomeadamente como usar a equa\c{c}\~{a}o para completar informa\c{c}\~{a}o em falta num contexto de invent\'{a}rio e tamb\'{e}m para mostrar como uma equa\c{c}\~{a}o deste tipo pode ser incorporada num sistema de suporte \`{a} decis\~{a}o ao n\'{\i}vel do povoamento com o objetivo de otimizar a gest\~{a}o para a maximiza\c{c}\~{a}o do volume lenhoso produzido em povoamentos de pinheiro bravo da {ZIF} da Lomba.},
    author = {Msaouak, Khaoula},
    citeulike-article-id = {14134053},
    citeulike-linkout-0 = {http://mfkp.org/INRMM/article/14134053},
    citeulike-linkout-1 = {http://hdl.handle.net/10198/13144},
    comment = {== References ==

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    editor = {Nunes, Lu\'{\i}s and P\'{e}rez-Rodr\'{\i}guez, Fernando and Mhammed, Bouhaloua},
    keywords = {empirical-equation, forest-resources, pinus-pinaster, portugal, regression},
    month = jul,
    pages = {68},
    posted-at = {2016-09-09 15:28:44},
    priority = {2},
    school = {School of Agriculture of Bragan\c{c}a},
    title = {{Modeling height-diameter relationship in pinus pinaster ait. in the forest intervention zone of Lomba, NE-Portugal}},
    url = {http://mfkp.org/INRMM/article/14134053},
    year = {2016}
}
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