BORROW STRENGTH APPROACH APPLIED TO A GEOSTATISTICAL MODEL TO ESTIMATE VOLUME

Abstract

O presente estudo teve como objetivo utilizar o compartilhamento de par\ue2metros de modelos geoestat\uedsticos aplicado aos estimadores de m\ue1xima verossimilhan\ue7a para predizer os volumes por hectare em tr\ueas fragmentos de Floresta Estacional Subtropical localizados em Santa Teresa - RS empregando a abordagem Borrow strenght. Os dados foram coletados em 56 unidades amostrais (U.A) de tamanho vari\ue1vel com aproximadamente 250 m2 em um total de 9 ha, distribu\ueddas em um grid sistem\ue1tico de 40 x 40 m, sendo medidas as vari\ue1veis dendrom\ue9tricas dos indiv\uedduos com DAP 65 10 cm pr\uf3ximas ao centro das unidades. Foram elaboradas duas abordagens para o conjunto de dados, sendo que a primeira considerou as \ue1reas totalmente independentes entre si, subdivididas em dois tipos: ajuste ao modelo n\ue3o espacial (NSM) e ajuste pelo m\ue9todo de m\ue1xima verossimilhan\ue7a (MV) n\ue3o compartilhado (ajuste individual). A segunda abordagem descreveu os ajustes dos modelos de m\ue1xima verossimilhan\ue7a compartilhados em fun\ue7\ue3o do erro aleat\uf3rio ou nugget, sendo: modelos sem nugget fixo (variabilidade entre as U.A) e com nugget fixo (variabilidade dentro das U.A), utilizando como correla\ue7\ue3o a fun\ue7\ue3o exponencial da fam\uedlia Mat\ue8rn. Em seguida, os modelos foram comparados pelo crit\ue9rio de informa\ue7\ue3o de Akaike (AIC) e grau de depend\ueancia espacial para posterior krigagem e elabora\ue7\ue3o das superf\uedcies de predi\ue7\ue3o dos modelos selecionados. Foi observado que os modelos combinados para estimativa do volume foram superiores para os valores de AIC e grau de depend\ueancia espacial em rela\ue7\ue3o aos ajustes para as \ue1reas individuais. Entre os modelos compartilhados, observou-se que houve um ganho nas estimativas dos par\ue2metros utilizando o nugget fixo, que resultaram em uma correla\ue7\ue3o das amostras e grau de depend\ueancia espacial maior (AP = 88 m), em rela\ue7\ue3o aos modelos compartilhado sem nugget fixo (AP = 75 e 66 m). O AIC mostrou-se eficiente, uma vez que comparou os diferentes n\uedveis de ajustes propostos na metodologia do trabalho, selecionando um modelo com parcim\uf4nia e compat\uedvel com os padr\uf5es de distribui\ue7\ue3o espacial encontrados nas \ue1reas. Sugere-se o uso de modelos compartilhados para dados de amostragem em diferentes \ue1reas, com introdu\ue7\ue3o da estimativa do erro intraparcela (nugget fixo) nas equa\ue7\uf5es de MV, para aumentar a correla\ue7\ue3o entre as U.A, com avalia\ue7\ue3o conjunta do AIC somado ao grau de depend\ueancia espacial na estimativa de vari\ue1veis dendrom\ue9tricas.This study aimed to use the share parameters of the geo-statistical models applied to maximum likelihood estimators to predict the volumes per hectare in three fragments of a Deciduous Forest located in Santa Teresa, RS state, employing the \u2018Borrow Strength\u2019 approach. Data were collected in 56 sampling units (S.U) of variable sizes with approximately 250 m2 for a total of nine ha, distributed in a systematic grid of 40 x 40 m. Dendrometric variables from individuals with DBH 65 10 cm near the center of the S.U. were measured. Two approaches to the data set were prepared, the first of which considering both areas entirely independent themselves, subdivided into two types: a fit to non-spatial model (NSM) and a fit to the maximum likelihood (ML) not shared (individual adjustment) model. The second approach described the adjustment of the shared as a function of random error or nugget, comprising models: a shared model without fixed nugget (variability between S.U) and a shared model with fixed nugget (variability within S.U) models, using a logarithmic function of M.L applied to the Mat\ue8rn family of exponential correlation model. Then, the models were compared using Akaike information criterion (AIC) and by degree of spatial dependence for subsequent preparation of both kriging and prediction surfaces of the selected models. It was observed that the combined volume models to estimate values were higher for the AIC values and spatial dependence with respect to the adjustments for the individual areas. Among the shared models, it was observed that there was a gain in the parameter estimates using the fixed nugget, which resulted in a higher correlation of samples and spatial dependence (AP = 88 m), than the shared models without the fixed nugget (AP = 75 and 66 m). The AIC was efficient because it compared the different levels of proposed adjustments to the methodology of the study, selecting a model with parsimony and compatible with the spatial distribution patterns found in the areas. The use of combined models for data sampling in different areas with the introduction of the error estimate intra-plot (fixed nugget) in the equations of MV can be suggested to increase the correlation between the S.U and combined evaluation of the AIC plus the degree of spatial dependence in estimating dendrometric variables