DIGITALNA ARHIVA ŠUMARSKOG LISTA

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ŠUMARSKI LIST 11-12/2009 str. 29 <-- 29 --> PDF |

S.Andrašev, M. Bobinac, S. Orlović: DIAMETER STRUCTURE MODELS OF BLACK POPLAR SELECTED ... Šumarski list br. 11–12, CXXXIII (2009), 589-603 response to environmental conditions (primarily soil conditions and tree competition) of each genotype. The sample of trees used for the construction of the diameter structure model (total 168 samples) comprised the measured diameters at breast height (mean value of two cross measurements) in each row (4 repetition),for each clone (6 clones) and measurement year (7 years). Basal area, as the sum of basal areas of all trees, and the stand quadratic mean diameter were calculated for each tree samples. Table 1 Number of trees of studied clones by repetitions after planting and after 20 years. Tablica 1.Broj stabala istraživanih klonova po ponavljanjima pri osnivanju nasada i nakon 20 godina. Clone Klon Number of trees after planting per repetitions Broj stabala nakon sadnje po ponavljanjima Number of trees after 20 years per repetitions Broj stabala nakon 20 godina po ponavljanjima I II III IV I II III IV S 6-36 25 25 25 25 23 24 24 24 NS 1.3 22 22 22 22 21 20 21 20 NS 11-8 25 25 25 25 23 23 24 23 Pannonia 25 25 25 25 22 24 22 24 PE19/66 20 20 20 20 19 17 19 19 S 6-7 25 25 25 25 24 23 22 23 The selected model was the Weibull distribution with three parameters.The mathematical model of the Weibull distribution is defined as follows: (1) where:a– location parameter;b– scale parameter; c – shape parameter. The mathematical model of the Weibull cumulative distribution is expressed as: (2) Location parameter (a) defines the location distribution in the coordinate system, i.e. its distribution along the abscissa. Scale parameter (b) is equal to 63% of the distribution of unknown value (x) in the increasing order, i.e. about 63%of the trees have diameter at breast height lower than the sum of parameters “a”and “b”. Shape parameter (c) defines the distribution skewness: forc<1 the distribution decreases, and forc>1 it has bell shape. In the interval 1 and for c=3.6 it approximates the normal probability density function (PDF). If the location parameter (a) is equal to zero the mathematical model turns into the so-called two-parameter model of theWeibull distribution, defined by the expression: The parameters of the Weibull probability density function can be estimated in several ways (from sample trees), depending on the desired estimation of two (b, c) or all three parameters (a,b,c).The unidentified parameters of the Weibull distribution were estimated using the so-called “hybrid system”, i.e. the method of moments estimation in combination with the percentile method (Knoebel, et al, 1986). Location parameter (a)in diameter structure modelling is directly related to minimal diameter and can vary from 0 (zero) todmin. So the parameter “a” was calculated by the percentile method, with the following percentiles of the minimal diameter: 0.00; 0.01; 0.05; 0.10; 0.15; 0.20; 0.25; 0.30; 0.35; 0.40; 0.45; 0.50; 0.55; 0.60; 0.65; 0.70; 0.75; 0.80; 0.85; 0.90; 0.95; 0.99; 1.00. Scale parameter (b) and shape parameter (c) were estimated by the moments method.They were estimated by subtracting the measured values (diameters at breast height) from the previously defined parameter “a”.This method is based on the following equations – - 2 of the first (x) and the second (x) common moment of theWeibull two-parameter distribution: (5) (6) where.(·) – gamma function. The assessed variance () of theWeibull distribution is expressed as: (3) (7) and the coefficient of variation (): and the cumulative model: (8) (4) |