I see from various online sources (including GIS.SE's own How to download the entire ASTER GDEMv2 dataset?) that the ASTER GDEM has 22'000 tiles, each 1°×1° and 3601×3601 pixels (each pixel being 16-bit integer), with both elevation and quality rasters.
A handy napkin says the uncompressed data would be
22000 * 3601 * 3601 * 2 * 2 / 1024**3, or ~1063 GB. But how big is the compressed data that you download from the official providers?