## 4 Discussion  
As part of the conducted analyses, numerical calculations were performed to assess the impact of the ongoing mining exploration of the KWK Piast-Ziemowit mine in panels LW501 and LW502 on surface deformation. The calculations were carried out using a custom script based on Python, which allows for the automatic estimation of the values of parameters of the modelled rock layers located above the formed caving zone. To ensure the clarity of the results, the parameter values in the caving zone were assumed to be constant for all numerical models. This assumption does not align with observations of the behavior of caving zones resulting from mining activities. Previous studies unequivocally indicate that as mining progresses, the caving zone increases in height, causing various rock strata to collapse. Unfortunately, this assumption was necessary to ensure the clarity of the solution based on a program that automatically determines the mechanical parameters of individual rock layers. The program performed calculations according to the specified conditions and then compared the estimated deformation indicators with the measured values. The results are presented for a selected region of the underground coal mine. However, the methodology used allows for the determination of deformation indicators and rock mass parameters also for other regions of the mine. It is limited only by knowledge of mining conditions and having geodetic measurements and geological structure with preliminary \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **28 September 2021** & **25 November 2021** & **11 March 2022** & **12 May 2022** & **4 August 2022** \\ \hline ME [mm] & \(-0.5\) & 0.3 & \(-7.1\) & 3.1 & 5.7 \\ MAE [mm] & 0.9 & 2.0 & 18.0 & 23.7 & 27.4 \\ RMSE [mm] & 1.1 & 2.8 & 22.1 & 30.0 & 34.7 \\ \(\mu_{\text{s}_{\text{max}}}\) [\%] & 2.3 & 2.6 & 0.5 & \(-1.7\) & 0.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Modeling subsidence errors with the numerical method for subsequent face advances. Figure 9: Land surface subsidence (in meters) based on FEM analysis—4 August 2022.  
parameters. Based on these data, the program will adjust the values of \"real\" parameters to the measurement results using the method of similarity of geode measurement results described in this article. According to the procedure, calculations were conducted until the consistency of the selected deformation indicators was achieved, i.e., obtaining the global minimum of the specified objective function, which was the RMSE error. Subsequently, calculations were carried out for the next specified mining advance. The calculations showed a very high consistency of deformation indicators (see Table 7), meaning that for the assumed physical model, the actual values of the mechanical parameters of the rock layers were determined with high probability. Another way to assess accuracy of numerical modelling result is another deformation indicator. Based on the field observation data the tilts of subsidence trough profile were compared. The fitting errors of the modelled inclination \(T_{FEM}\) were determined in relation to the measured values \(T_{obs}\) similarly to those for subsidence, in accordance with Formulas (6)-(9). The results for individual operating states are presented in Table 8.  
Similarly to the subsidence, Figure 10 shows the tilts profiles of the subsidence trough after the end of operation of the LW 501 and LW502 walls. The obtained results indicate a good and very good match of the tilts of the subsidence trough. The increased fluctuations in relation to the subsidence result from the nature of the phenomenon, which was confirmed on the basis of research on the variability of deformation indicators and forecasting accuracy in numerous publications (e.g., [71]). The last period (4 August 2022) is characterized by increased values of error characteristics compared to the previous ones (see Table 8).