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A lot if you want the raw data. The 10-meter (also knows as 1/3 arcsecond) national elevation dataset is somewhere around 330GB in an unprojected form. There's also the 3-meter tiles for limited areas which take up 9 times as much storage.

However, it doesn't stop there. As part of the 3DEP (3D Elevation Program)[1], Lidar/IfSAR data is being collected across CONUS. One of the products that will be available (hopefully next year) is a 1-meter DEM, which should roughly be around 35TB (100 times as much data compared to 10-meter).

[1] http://pubs.usgs.gov/circ/1399/pdf/circ1399.pdf



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