Open pit mining leads to irreversible changes in topographical relief, which makes a return to the original morphology virtually impossible. This is important for quarries that were part of former mining areas. This research presents an innovative approach to the reconstruction of the relief of anthropogenically transformed land on the example of Liban Quarry in Cracow, where operations began before 1873 to 1986. The basis for the reconstructed area was a Topographic Map of Poland with a scale 1:10,000 from 1997, from which a set of data was obtained to perform spatial analyses. The estimation was conducted using the ordinary kriging method, enabling a reconstruction of the morphology of the studied area and presenting it in the form of a hypsometric map and a digital elevation model. The correctness of the modelling was verified by cross-validation and a kriging standard deviation map (SDOK). These revealed low values of estimation errors in the places without contour lines on the base map. The comparison of the obtained maps and model with a Tactical Map of Poland with a scale 1:100,000 from 1934 indicated great similarities. The highest interpolation error value was recorded in the part of the pit where the difference between the actual and reconstructed elevation was about 30 m on average. In the exploited part, the SDOK did not exceed 0.52 m, and in the entire studied area, it reached a maximum of 0.56 m. The proposed approach fulfilled the assumptions of reconstruction, as the analysis revealed elements matching the historic relief in both forms of presentation of the topography of the quarry, on the obtained hypsometric map and on the tactical map. Our study is among the very few in the world concerning the application of geostatistics in the restoration of the relief of land transformed by open pit mining activities.

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Based on the analysis and interpretation of maps, remote sensing data published in the literature, and environmental reconnaissance, this article discusses environmental transformations in the Wojkowice area in southern Poland (up to the year 2020). A comprehensive analysis was carried out concerning spatial development, mining activity, hydrogeological conditions and the biotic environment. The current state of the hydrogeological conditions was also characterized. Mining activity in the vicinity of the studied town caused significant changes in its relief, which contributed to its area dropping by about 5 m. In fact, these terrain forms are overgrown by various forms of vegetation that colonized these areas both naturally and as a result of forest reclamation. The contemporary vegetation of Wojkowice differs from the potential natural vegetation, which is an indicator of the complete anthropogenization of the natural environment. Over 100 years of industrial activity in Wojkowice has also contributed to a strong transformation of the groundwater. There has been a quantitative depletion of usable groundwater in the Triassic and Carboniferous formations. With inflows to the ore mines of up to 17 m3/min, the groundwater table has dropped by more than 60 m. The aquifer of Muschelkalk has been practically drained. At present, wells extract the waters from the Röth aquifer. There has been a major transformation of groundwater chemistry. The waters of the Triassic carbonate complex are anthropogenically transformated and are characterized by increased mineralization, multi-ionic types and usually with a quality class III and IV, and, therefore, they require some treatment.

The paper presents four stages of acquiring the knowledge about kriging. The second stage has been focused on application of the free software E{Z}-Kriging, which allows to learn the empiric basis of ordinary kriging.

This article describes two methods of showing the distribution of temperature on the surface and inside a spoil tip (coal mine waste dump) located in Wojkowice (in the Silesian Voivodeship). Two deterministic estimation methods were tested, i.e., Inverse Distance Weighting (IDW) and Radial Basis Functions (RBF). According to isotherm maps the highest temperature on the surface of the “Wojkowice” spoil tip was in the NE area, while inside the heap the highest temperature noted was in the SW area. Better results were obtained from the application of the RBF method. A three-dimensional model (3D model) was generated by the method, which visualized the temperature distribution within the “Wojkowice” spoil tip. According to the 3D model of the temperature distribution the greatest heat centre inside the heap in Wojkowice was located in the SW part with a temperature of around 300°C. As a result, it can be concluded that the material of the “Wojkowice” spoil tip is burning out in a NW direction. On the basis of the model obtained it is possible to determine the location of potentially dangerous places which are exposed to possible deformations caused by the material burning under the surface. The results of the research presented make it possible to assess the thermal state of the spoil heap located in Wojkowice, Poland.