The mean square approximation of average course of mining area subsidence with the use of a flat spline as a approximating function was conducted to determine an approximate course of curvatures observed on a measuring line set over exploitation run by “Chwałowice” coalmine. The assumed minimising criterion of loss function was referred to the forecast values of vertical ground displacements calculated via Knothe’s formulas. The average courses of inclinations and curvatures of mining area were obtained via the calculation of their values by means of empirical formulas taking into consideration the obtained approximate values of measured subsidence.

The article presents the results of numerical calculations conducted with the use of a computer programme EDN – OPN for forecasting permanent deformations of a mining area being the result of the underground exploitation of coal deposits. The theoretical values of basic deformation indicators (decreases, inclinations, curvatures, displacements and horizontal strains) were determined with the use of Bialek`s formulas. They were subsequently juxtaposed with the practical values obtained thanks to the geodetic measurements conducted in the years 2001-2011 on the established observation line. The evaluation of the effectiveness of the conducted forecast of effects of the mining exploitation was carried out on this basis.

The article demonstrates the comparison of prognosed values of deformation indicators with their values obtained from geodetic measurements. The value of correlation coefficient R between its theoretical and practical values was calculated for each indicator. Following the measured values as basic ones, the evaluation of efficiency of prognosis via the use of Knothe`s theory (a mathematical model, in which lowering of point is calculated as a double integral from Gauss error function with adequate parameters).

In this paper we address the problem of water basins surface measurements. This problem is important in regions where coal extraction took place because of it significant impact on the landscape. We propose method based on usage of quadrotor equipped with non-metrical camera. Presented concept include discussion about quadrotor path planning, image tracing, quadrotor state estimation and altitude stabilization.

The article presents the way of determining an average course of subsidences of mining area measured after the termination of the subsequent mining stages run in the south of Poland by “Chwałowice” coalmine. The mean square approximation was conducted via smooth spline with the use of R – project programme. The problem of ambiguity of parameter value of smoothing of approximation function spar (in case when the function illustrating dependence among parameter values of smoothing and values obtained by generalised cross validation reaches its minimum value in a certain range of its values) was solved with the use of mean square minimalisation criterion of loss function between approximated and forecast subsidence values of Bialek’s formulas and the Budryk-Knothe theory. The efficiency of both forecasts was verified as well as their accuracy was estimated based on average course of measured subsidences.

The article presents the original results of the study concerning the way of approximation of average course of measured curvatures of mining area. The mean square approximation of average course of mining area subsidence with the use of a flat spline as a approximating function was conducted to determine an approximate course of curvatures observed on a measuring line set over exploitation run by “Chwałowice” coalmine. The assumed minimising criterion of loss function was referred to the forecast values of vertical ground displacements calculated via Bialek’s formulas. The average courses of inclinations and curvatures of mining area were obtained via the calculation of their values by means of empirical formulas taking into consideration the obtained approximate values of measured subsidence. Subsequently, they were compared with the forecast values by Bialek’s formulas and theoretical values obtained on the basis of empirical formulas including subsidence values forecast by Bialek’s formulas. Due to that the determination of errors of the forecast and theoretical distributions of curvatures and estimation of usefulness of the conducted analyses was possible.