## 4 DEM Validation Based on ICESat-2 Data  
### DEM Error Assessment  
Besides the five free global DEMs, TDX30 resampled from the 90 m resolution TanDEM-X DEM by the bicubic interpolation method was also used for the error assessment. The histogram of the height differences between these DEMs and the high-precision ICESat-2 altimetry points are displayed in Figure 2. The ME values vary from \(-\)3.4 m to \(-\)4.7 m, indicating that all these DEMs provide the elevations higher than those of reference points. Furthermore, these negative ME values can be partly attributed to the impact of dense vegetation canopy, in which the short wavelength SAR or optical satellite sensors cannot'see' the sub-canopy topography. In addition, we found that the errors of all DEMs are normally distributed with small negative biases and negative skewness values (see Figure 2). The RMSE values range from 8.0 m to 10.1 m. For the entire area, SRTM1 DEM shows the highest accuracy with the mean value of \(-\)4.1 m and the lowest RMSE of 8.0 m, and ASTER GDEM has the lowest quality with the highest mean value (\(-\)3.4 m) and the highest RMSE (10.1 m).  
For the DEMs with the resolution of \(-\)90 m, TDX90 DEM shows better quality than SRTM3 DEM. However, due to the stronger penetrability of C-band than that of X-band, the phase centers of SRTM DEM should be closer to the earth surface than that of TDX90 DEM. In theory, SRTM3 DEM has higher quality than TDX90 DEM, but the result is opposite in this study. This result can be partly explained by that the combination of multi-baselines or ascending and descending viewing geometry can improve the DEM quality [13]. Of course, we cannot exclude the influence of vegetation change in height over a period of more than a decade on the results obtained. For example, the natural growth or deforestation of the vegetation can result in the variation of DEM elevation, which will impact the analysis results. Future studies and analysis should answer this question.  
Among the DEMs with the resolution of \(\sim\)30 m, SRTM1 DEM has the best quality with ME of \(-\)4.1 m and RMSE of 8.0 m. ASTERGDEM2, AW3D30 DEM and TDX30 DEM even show lower qualities than the SRTM3 and TDX90 DEMs. This result could be partly attributed to the advantages of InSAR technology over vegetation coverage areas. In addition, the SRTM3 DEM has lower quality than SRTM1 DEM, indicating that down-sampling SRTM does reduce DEM quality, especially for mountainous topography. This also demonstrates the advantages of higher resolution DEM in depicting terrain details. TDX30 DEM has lower quality than TDX90 DEM. This result could have resulted from many reasons: (1) up-sampling TDX90 DEM may change the spatial feature information of the original DEM product. (2) the up-sampling (from TDX90 to TDX30) and IDW interpolation (from TDX30 to ICESat-2 footprint) operations were performed to assess the TDX30 DEM accuracy respectively, which will lead to the accumulation of DEM errors. Therefore, the spatial interpolation technique has no ability to improve the DEM accuracy, especially in the mountain area, as it cannot add any more topographic detail information.  
TanDEM-X DEM is expected to be a new standard in global DEMs, regarding the geometric resolution, accuracy and ability to depict complex topography [11; 13]. However, the TDX90 DEM is not accurate enough due to its low resolution. This conclusion is in agreement with the results of [21].