Behavior of the hypsometric relationship of Araucaria angustifolia in the forest copse of the faculty of forest - Federal University of Paraná, Brazil

Abstract

The objective of this research was to test and select mathematics models for estimating total heigh (ht) and bole high (hb), as a function of DBH, as well as, to establish the dendrometric relationship  between ht/hb. The data came from measurements of diameters (DBH), total height and bole height of all Araucaria angustifolia trees from an Ombrophylous Mix Forest fragment of 15,24 ha situated in the Botanical Garden Campus of the UFPR, Curitiba-PR, Brazil. Thirteen  models were tested, including arithmetic, logarithmic and nonlinear  models, such as Chapman-Richards and Mitschertich or monomolecular adapted; the nonlinear models were fitted by the Levenberg-Marquart algorithm. The statistic criteria for selecting the best models were the graphic analysis of residuals, Standard error of estimate in percentage (Syx%) and adjusted determination coefficient (R2 aj). The R2 aj were very low for all fitted models, characterizing an advanced and asymptotic stage of the species under study. The best equation for estimating ht was that one proposed by Stoffels & Van Soest, and for hf the Curtis equation in its logarithmic form, chosen due to its statistics values and easy utilization. The adjusted linear equation to estimate total height as a function of bole height presented R2 aj = 0.88 and Syx% = 5 %, characterizing a strong relationship between these two variables.