Modelos não lineares com erro de medidas em estimativas volumétricas de Eucalyptus spp no pólo gesseiro do araripe

Abstract

The estimation of forest volume with more precision has been the target of several researches focusing on sustainable forest management. For this reason, the objective of this work was to elaborate a mathematical model that takes into account the non-systematic error associating one of the independent variable, height, since this is one of the sources of input in the estimation of the volume of the trees. The experiment was carried out in Araripina, Pernambuco, at the Institute of Agricultural Research (IPA), composed of 60 plots, with 49 trees in each plot in a spacing of 3 m x 2 m. For the composition of the database, using the systematic sampling procedure, 300 trees wereselected to estimate the heights using the hypsometer. After the volume determination by Smalian methodology, information diameter at breast height (DBH), height and form factor of each tree were obtained. Five volumetric models were compared using: (1) volume determined by strict cubing; (2) the mean value of the form factor, the DDH and the height estimated by the hypsometer; (3) the mean value of the form factor, the DBH and height; (4) model of Schumacher and Hall; (5) model of Schumacher and Hall with measurement error; (6) Spurr model and (7) Spurr model with measurement error. The models were compared using analysis of variance (ANOVA) and multiple comparisons using the Tukey test, both with 5% significance. Since all models presented no significant differences among them, simulations were performed, varying the size of the sample in the expectation that the model with error measure could capture the error of the values of the estimated heights in small sample sizes. After modeling with the five models with samples of sizes of 30, 50, 100, 150 and 200 trees, the statistical analysis procedure previously adopted was repeated. The results of the comparisons favored the Schumacher and Hall model, due to its simplicity of application and because it is one of the most used in forest mensuration, since the model estimates did not show a significant difference among them.