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The recent release of worldwide SRTM 1 DEM and AW3D30 adds new members to the open global medium resolution (90-30 m ground spacing) digital elevation models. Together with the previously existing SRTM 3 and ASTER GDEM, their quality is of great interest to various scientific applications. This paper uses 1:50,000 DEM in Hubei Province of China as a reference to assess their vertical accuracy in terms of terrain types, slopes, and land cover. For ASTER GDEM and AW3D30, we further evaluate their accuracy in terms of the stack number, i.e., the number of scenes used to generate the DEM. It is found out that: (1) all of the DEMs have nearly the same horizontal offset due to the adoption of different datums; (2) the vertical accuracy varies in terms of terrain complexity, from ~5 m for plains, ~10 m for hills to ~20 m for mountains; (3) the vertical accuracy is negatively related to the tangent of terrain slope exponentially in forest areas and linearly in cultivated lands; (4) forest areas have the lowest vertical accuracy, comparing to built-up areas, wetland, and cultivate land areas while SRTM 1 and AW3D30 have the highest accuracy in all land cover classes; (5) the large elevation differences over forest areas are likely due to canopy coverage; and (6) for ASTER GDEM and AW3D30, their accuracy is in general positively related to the stack number. This study provides a practically useful quality specification and comprehensive understanding for these four global DEMs, especially the recently released worldwide SRTM 1 DEM and AW3D30.