## 5 Results and Discussion. ### Structural Analysis and Spatial Modeling  
Geostatistical models work in general by considering the probabilistic nature of the underlined variable but also account for the spatial dependency of observations. According to the above assertion, these algorithms adopt a certain spatial correlation of the natural variables, which, in all other ways, are considered as random processes. This assumption allows a certain degree of interdependence between model values at different spatial locations [28]. As stated above, the spatial inhomogeneity and local absence of information in the dataset prompts to the adoption of auxiliary variables for mapping LCV values. The choice of the proper quality characteristics to be employed as auxiliary variables is done by considering the correlation of LCV to the other available attributes. The results of this test indicate a significant correlation between ash, CO\({}_{2}\), and LCV. On the other hand, moisture is poorly correlated to LCV (Figure 7). In order to study the spatial dependencies of LCV values, the experimental variogram was calculated with a lag size of 1 m on the vertical direction and 330 m on the horizontal plane (Figure 8). A model with two spherical structures was adjusted to the data. Moreover, to investigate the cross-correlation between the quality parameters in space, it was necessary to study the individual variograms and the cross variograms of the above variables (Figures 9 and 10). A coregionalization model consisting of two spherical structures was adjusted on the experimental variograms, which were calculated with a lag size of 10 m on the vertical direction and 250 m on the horizontal plane. Sill matrixes were adjusted through conditional fitting of the experimental variograms. Experimental variograms show a range of about 20 m in vertical and 1300 m in horizontal direction. Figure 7: Scatter plots of LCV versus CO\({}_{2}\), moisture, and ash. Figure 8: Experimental and fitted anisotropic variogram models for LCV. Dashed polylines (blue color) represent experimental variograms; thin dashed lines (black color) represent variance; continuous lines (red color) represent variogram models. Figure 9: Experimental and model cross variograms for LCV, ash, and CO\({}_{2}\) in the horizontal directions. Experimental structure is modeled by an isotropic spherical variogram. Dashed polygonal lines (blue color) symbolize experimental variograms; thin dashed lines (black color) symbolize variance and covariance; continuous lines (red color) symbolize variogram models. Principal Component Analysis was applied to reduce the dimensionality of the dataset and to synthesize the necessary information by using independent components. This way, cokriging could be avoided. As seen in Figure 11, the significance of each factor, as revealed by the weight of its eigenvalue, is expressed by its percentage of the total variance. Due to the overabundance of information due to inter-correlations among the quality parameters, the first two PCA factors explain almost 92% of the total variance. Figure 11: Projection of the quality parameters on the plane spanned by the first two factors of the Principal Component Analysis (PCA). Figure 10: Experimental and model cross variograms for LCV, ash, and CO\({}_{2}\) in the vertical direction. Experimental structure is modeled by an isotropic spherical variogram. Dashed polygonal lines (blue color) symbolize experimental variograms; thin dashed lines (black color) symbolize variance and covariance; continuous lines (red color) symbolize variogram models. The variogram models for Factors 1 and 2 (Figures 12 and 13) were fitted as double spherical structures with a lag size of 1 m on the vertical direction and 330 m on the horizontal plane. Variogram model ranges are 700 and 1400 m in the horizontal plane and 25 m in the vertical direction.