## 4 DEM Validation Based on ICESat-2 Data
### Impact of Slope and Aspect on the DEM Error  
Slope and aspect are the two main factors affecting the DEM error, since they induce geometric distortion in the imaging processing associated with optical photogrammetry and InSAR, which prohibits us from extracting true topography [51; 52]. The slope and aspect at each ICESat point were calculated from the AW3D30 DEM. As Figure 4 shows, the DEM errors of all datasets decrease significantly with the increasing slope, suggesting that the terrain slope has stronger effect on the DEM errors of both InSAR and optical photogrammetry technology. Furthermore, this result provides a possibility for us to correct DEM errors related to ground slope, as demonstrated in [53].  
Figure 4: Scatter density plots between DEM error and slope for (**a**) SRTM1; (**b**) SRTM3; (**c**) ASTER; (**d**) AW3D30; (**e**) TDX30 and (**f**) TDX90.  
Figure 3: Mean Error (ME), Root Mean Square Error (RMSE) and Standard Deviation (STD) of the DEM errors.  
To quantify the impact of slope on DEM error, all the DEM errors were divided into four groups according to the terrain slope, which are the flat (slope angle \(<\)2\({}^{\circ}\)), hilly (2-6\({}^{\circ}\)), mountain (6-25\({}^{\circ}\)) and high mountain areas (\(>\)25\({}^{\circ}\)) [54]. The ME, RMSE and STD were then calculated and are shown in Figure 5. The MEs exhibit obvious increasing trends with the increasing terrain slope. In the areas with the slope angle smaller than 2\({}^{\circ}\), the MEs of InSAR DEM (except for TDX30) are close to 0. The maximum of the MEs appear at the slope angles of \(>\)25\({}^{\circ}\). In the middle and bottom panels, the RMSEs and STDs linearly increase with the slopes. In addition, the RMSE values of all datasets except for ASTER GDEM2 are less than 5 m in the region where the slope angle is under 2\({}^{\circ}\). The values peak (15 m) in the areas where the slope angles are larger than 25\({}^{\circ}\). These demonstrate that the terrain slope has a serious effect on the DEM errors of both InSAR and optical photogrammetry technology. Such change pattern can be explained by the influence of slope on image acquisition. In addition, when the slope is small (\(<\)25\({}^{\circ}\)), the RMSEs of SRTM1 and SRTM3 are similar, but when the terrain slope is \(>\)25\({}^{\circ}\), the difference of their RMSEs are remarkable. This confirms that the DEMs with high resolution can depict the terrain slope. The comparison between TDX30 and TDX90 shows that the spatial interpolation cannot reduce the DEM error significantly. Thus, for flat terrains, all the DEMs excepting the ASTER GDEM2 can be used as high precision DEMs. However, for high mountain areas, SRTM1 is a better choice than other DEMs, due to its high resolution, though TDX90 shows an equal vertical accuracy with it. No clear relationship has been found between the elevation residuals and terrain aspect (Figure 6). However, some relevant researches indicate that there is an obvious cosine relationship between the DEM errors and terrain aspect [28; 55], which can be attributed to the horizontal shifts between different datasets rather than the effect of terrain aspect on DEM accuracy. In order to solve this problem, co-registration of different datasets is an effective and applicable method [55; 56].