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median line to the nearest forest road. The mean SDs of the study area is given by the sum of weighted SDs of each buffer strip area. The following formula was used:
where: SDs_buffer – shortest mean extraction distance of the study area, computed with the buffer method, in m; i – current buffer strip number; n – total number of buffer strips used in computations; Wbs width of the buffer strip, in m; Ai area covered by buffer strip i, in ha;  At total surface of the study area, in ha.
Computing correction factors – Izračun faktora korekcije
The extraction correction factor (ks) was calculated as the ratio between SDe determined with raster method and SDs computed with the spatial methods. The road network correction factor (kn) was computed separately for the assumptions of one sided and two sided timber extraction to forest roads. The following formulas were used:
where:  – is the SDe computed with the raster method, in m; – is the SDs computed with the grid point methods, in m; – is the SDs computed with CGR method, in m; – is the SDs computed with the buffer method, in m; SD0– is the theoretical mean extraction distance, computed with the analytical method, in m.
The total correction factor (kt) was computed with the following formula:
Statistical and empiric analyses of the computation methods – Statistička i empirijska analiza metoda izračuna srednje udaljenosti privlačenja
For testing the possible differences between infrastructure scenarios in respect of SDs values computed with the grid point methods, Student’s t-test (Bühl 2010) was performed. The standard error (SE) for computing SDs was determined and then compared to the preferred SE (which was set at 5%) in order to identify the accurate grid point methods. The minimum number of points required for a statistically sound determination of the SDs was computed for a confidence interval (CI) of ±10% and precision of 5%, with the following formula:
where: sx – standard deviation of the SDs; – standard error of the SDs; CI – confidence interval of the determination of SDs; t – t-value distribution for α=5%.
Post-hoc analyses were performed in order to test if there were any significant differences between SDs values computed with these methods. For homogenous variances Bonferroni’s and Duncan’s tests were carried out, while for non-homogenous variance the Tamhane-T2 test was performed (Backhaus et al.2011; Bühl 2010). For all tests, the significance level was set to 5%. Empiric analyses were performed between the grid point methods, the centre of gravity method and the buffer strips method. The necessary computation time for running the models was also determined. In this way the reliable computation methods were identified.
3 Research results
Rezultati istraživanja
Analytic methods – Analitičke metode
Table 1 reveals the structure indices computed with classical methods. A considerable reduction of the theoretical and real mean extraction distances as well as of the maximum extraction distance was reported in scenarios proposing new roads (FR1-FR3) compared to scenario ZERO.
GIS based methods – Metode izračuna utemeljene na GIS-u
The SDs values are presented in Table 2 by computation method and analyzed scenario. The paired samples Student’s t-tests revealed that SDs in scenario Zero is significantly higher than scenarios FR1-FR3 due to the low road density (Table 3). Significant differences were reported between SDs values in scenarios FR1 and FR3, respectively between scenarios FR2 and FR3. The extraction distance is one of the factors which influence the efficiency of forest operations. The economic, the environmental and the social aspects of timber harvesting depend on the extraction distance. Longer extraction distances generally lead to lower productivity, higher costs, higher energy input and higher strain on the machine operators (e.g. exposure to vibrations; Rottensteiner 2014).
Methods G100, G50 and G10 reported the highest accuracy in computing SDs (Figure 4). Table 4 shows the minimum required number of points for computing SDs varies between 151 and 245 (SE of 5%), respectively between 38 and 61 (SE of 10%), depending on scenario and grid point.