Elevation correction ASTER GDEM2 (+10m)

This is a job for the Raster Calculator, it's under the Raster menu (don't confuse this with RasterCalc!). The expression:

snowdon_dem.tif@1 + 10

will do this, where 'snowdon_dem.tif@1' is the name of the original DEM. You can also find additional informations here.

i think this is a normal elevation error. if you check any validation report of GDEM2, you always see that it is reported Standart Deviation (SD) is to 12.7 m. whereas version 1 is 15.4 meter.

The ASTER GDEM version 1 was released in July 2009 and the version 2, now under processing, will be released in the October 2011. The GDEM version 2 is reproduced using the updated algorithm. Validation study of the GDEM version 2 confirmed that elevation offset and horizontal resolution will be greatly improved in GDEM version 2 and the enhanced horizontal resolution will serve to reduce the standard deviation of elevation and horizontal error.

Likely you will have set your GPS device to WGS84 ellipsoid, while the ASTER GDEM data are referenced to the EGM96 geoid:

See: "The data are posted on a 1 arc-second (approximately 30–m at the equator) grid and referenced to the 1984 World Geodetic System (WGS84)/ 1996 Earth Gravitational Model (EGM96) geoid." https://lpdaac.usgs.gov/content/view/full/11033