# Analysis of Mining Waste Dump Site Stability Based on Multiple Remote Sensing Technologies
## 4 Discussion of Experimental Results
### SBAS Results
For convenience, the cumulative deformation from SBAS was resampled according to the time lines of the ground measurements. As shown in Figure 11, the cumulative displacements from SBAS and ground measurements have been consistent over all the points, especially from May to the end of July. Figure 11: Comparison between SBAS time series and ground measurements. Figure 10: Cumulative deformation of the thirteen total station measurements. In August and September, SBAS underestimated the displacements of B2 and B3, highlighted with a green box in Figure 11c,d. This is probably because SBAS was only able to measure displacements correctly within the wrapped phase (\(-\pi\),\(\pi\)), which was approximately 31.2 mm in the LOS direction according to the wavelength of the X-band SAR sensors. By translating the measurement extent of the LOS to the slope direction, according to the specific locations of Points B2 and B3, a measurement extent of 43.33 mm was obtained. However, the cumulative deformation of Points B2 and B3 were far beyond the measurement limits of the X-band SAR, which are 130.81 m and 137.94 mm, respectively. Therefore, the cumulative displacements for Points B2 and B3 were underestimated in August and September. On the other hand, fortunately, there was no underestimation for Point A3 due to its smaller cumulative displacement. The authors also plotted the weather from 6 May to 15 September in Figure 12, where the yellow bars represent a sunny day, the green bars represent cloud, the cyan bars represent light rain or showers, and the red bars represent moderate rain or heavy rain. As is clearly shown in Figure 12, moderate continuous and heavy rainfall happened in August, which explains the dramatic increase in displacements in the ground measurements. The continuous rain may be another reason for the underestimates of SBAS in August, because of the short wavelengths of the X-band SAR sensors. For the purpose of quantitatively assessing the performance of SBAS, the relative error and root mean square error (RMSE) of SBAS measurements, with reference to the ground measurements of the same time, were calculated. Let us take Point A in Figure 4 as an example, the relative error, \(error^{\prime}\), and RMSE of Point A can be expressed with the following equations:  
\[error^{\prime}=\frac{\Sigma(d_{A\_SBAS}(t_{i})-d_{A\_Total\_Sati_{i}}(t_{i}))}{N} \tag{12}\] \[RMSE=\sqrt{\frac{\sum_{i=1}^{N}(d_{A\_SBAS}(t_{i})-d_{A\_Total\_Sati_{i }}(t_{i}))^{2}}{N}}\]  
where \(d_{A\_SBAS}(t_{i})\) is the displacement along slope direction estimated by SBAS at moment \(t_{i}\), \(d_{A\_Total\_Sati_{i}}(t_{i})\) represents the displacement of ground measurements at moment \(t_{i}\), and \(N\) is the number of observations conducted during the temporal span. RMSE is a measure of accuracy, which is the square root of the average squared relative errors. In general, a lower RMSE indicates that the SBAS result is more consistent with the terrestrial measurements. The estimated relative error and RMSE of the four points over the whole period is shown in Table 1. Generally speaking, the accuracy of the SBAS result for Point A3 was the highest according to the relative error index, whereas the worst was for Point B3. If all the measurements from May to September are taken into consideration, the relative errors and standard deviations of Points B2 and B3 are even higher than that of Point B1. However, if the obviously erroneous estimates in August and September are neglected, the relative errors and standard deviations of Points B2 and B3 are much smaller. By comparing the RMSE index, it is obvious that Point B1 has the smallest residual error, whereas Point B3 has the largest. If the  
Figure 12: Weather information from 6 May to 15 September (yellow: sun; green: cloud; cyan: light rain or shower; red: moderate rain or heavy rain) [65]. clearly biased estimations in August and September are discarded, the RMSE of Point B2 can be significantly improved.