# Modelling of Evenness of Runways as an Element of Sustainable Airport Maintenance
## 5 Discussion  
The obtained results show the comparability of all described methods for modelling the evenness of runways. Different models, already presented, were used based on the same measurements. The results are presented in the form of longitudinal and cross sections of the analyzed runway and can be seen in the following graphs. The comparison of modelling of longitudinal cross sections P1, P2, and P3 is presented in Figure 8 and  
Figure 6: Results of TIN interpolation. Figure 7: Modelling of the longitudinal section P3 using TIN interpolation methods. the comparison of modelling of cross sections P4 and P5 is presented in Figure 9. The modelling methods used are those that have proven useful in research. Figure 8: Runway modelling in longitudinal cross-section P1, P2, and P3 by selected models. The cross sections presented in Figures 8 and 9 were created using the above modelling methods. In the intermediate area, where no measurements were made, the elevation values were estimated. Figure 8 clearly shows the influence of the different interpolation methods, especially in the area where no measurements were made (from the edge of the runway to the area where measurements were made). While the regression plane approximation yields a continuous plane that is clearly and demonstrably valid over the entire bounded area of the analyzed runway (line marked with an orange lock (RR) in Figure 8), the accuracy of the IDW methods outside the measurement area is questionable. The accuracy of the IDW methods within the considered cross sections (lines marked in red and green in Figure 9) (IDW1 and IDW3) depends on the distance to the measured points. TIN1 (the line marked in blue in Figure 9) is determined only within the area where measurements were performed. From the presented longitudinal and cross sections, it can be seen that among the presented methods for modelling the evenness of airport runways, the methods of modelling with linear interpolation based on the triangulated irregular network (TIN1) and approximation with the regression plane (RR) have a useful value. It should be emphasized that modelling is a process of converting the results of individual measurements into a plane shape. The resulting planes are a better or worse representation of the actual condition of the runway. To claim that one method of modelling is better than another is not professionally correct. Modelling results can only be more or less useful. To answer the question of the similarity of the results obtained by each method, we compared the results obtained with the average linear slope of each cross section considered. The average linear slope was determined by the average of the modelled values (according to the considered models) at the beginning and at the end of the considered cross-section. The descriptive statistics of the absolute deviation of the modelling results from the average linear slope are presented in Tables 4 and 5. The largest detected values are highlighted in \"**bold**\". Figure 9: Runway modelling in cross section P4 and P5 by selected models. Descriptive statistic (shown in Table 5) taken into consideration only the part of cross-sections where all models were defined (from 11 to 34 m). With the descriptive statistics for all considered cross-sections, we can confirm that all considered methods of pavement evenness modelling are similar to each other and a greater utility can be attributed to the interpolation methods based on the linear triangular irregular network (TIN) and the regression plane approximation (RR). A substantial comparison of the two proposed methods shows that:  
* regression plane approximation (RR): The method allows for the calculation of the elevation of each selected point of the regression plane. Since the regression plane is continuous, the alignments of the measured runway irregularities are likely to be large.