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|Summary: By applying modified Brink’s function, this paper presents the unique generalized taper model of Norway spruce tree, developed for the area of Bosnia and west Serbia. The objective of this research is adapt generalized taper models (Models 1 and 2) for trees presented in the paper Matović, et al. (2007), for practical use in forestry.|
The significant quality of the modified Brink’s function is the correlation of the characteristics of individual trees and stands and the function parameters, so in this way generalized taper models can be calculated for the use in a definite geographic region.
The study of Norway spruce taper is based on the data collected from 86 even-aged stands in the region of Bosnia and west Serbia, which is adjacent to Bosnia. The total number of model trees is 156, and the number of data pairs (diameter-height) is 2028.
The original parameters i, p and q of the modified Brink’s function were first calculated for all model trees by the optimisation method - equations (1). By applying the multiple regression method, a link has been established between original values of parameters i, p and q, and characteristics of individual trees (diameter at breast height and tree height), i.e. Model 3 has been obtained.
Model 3 is consisted of three functions used for determining the parameters of generalized taper model i, p and q. Unknown parameters of the three functions a1, a2, a3,...,.a15 are determined on the basis of available data, by applying multiple regression – equations (2), (3) and (4).
In order to test the estimation of taper volume, on the material used for the development of generalized taper models of spruce trees by applying multiple regression, dual input volume tables were created. For that purpose Näslund and Schumacher-Hall functions were used – equations (6) and (7).
This research confirms that Model 3 shows less accuracy in estimating the diameter along the taper and volume than Models 1 and 2, which besides using the diameter at breast height and tree height, also require using the stand quadratic mean diameter. However, such difference, from the aspect of practical use, is not important, so Model 3 that applies only the diameter at breast height and tree height (in fact, reduced to the level of dual input volume tables) can be successfully used in forestry practice.
Obtained Model 3 is the superior substitute for conventional dual input volume tables, because besides the total volume it enables the volume estimation for particular parts of the standing tree, and also estimation of the diameter along the taper. Model 3 indirectly enables the calculation of tree heights with some diameters characteristic for forestry practice.
Model 3, with all above mentioned practical possibilities, can be very simply used by applying one EXCEL application. Because of the dimensions of trees used for Model 3 design, it can be reliably used in practice for Norway spruce trees with diameters at breast height of 10 to 60 cm and height of 6 to 37 m.
Key words: generalized model; modified Brink’s function; taper