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I guess the movies about being buried by sandstorms are no joke. One researcher found a 30 mph wind to blow 6,000 lbs of sand across a 100 foot line in one hour. http://www.nps.gov/archive/whsa/Sand%20Dune%20Geology.htmIn scientific terms, that’s 2 lb•ft–1•mph–1•hr–1 Whoa!!! One reseacher defined sand as between .02 mm and 1.0 mm in diameter, while another used the range of .1 mm to 1.6 mm. Averaging the two methods, we obtain 0.68 mm per grain. Then dig a smallish vertical shaft, one grain in diameter, down through the dune until you reach "non-dune". You'll need to keep count of the grains you remove. Then multiply the total grains removed by 0.68 mm per grain, convert to the English system if desired, and you have your answer.  I recommend using a hand tally counter for improved accuracy.
The depth to bedrock varies greatly. As sand can be blown by the wind, it forms drifts (d'oh) and tends to level out the landscape. The sand fills in the deeper part of the landscape, burying river valleys and all other features. Imagine filling up the Alps so that only mountain tops remain, then the mountain tops are worn down by sand "blasting' the exposed rocks. This is what has happened in some of the older deserts. The process of sand filling in areas can be seen on Google Earth in northern and northwestern China. There are several areas. Two I found are located at 43° 07' 58" N 112° 12' 55.76" EAND39° 50' 12.2" N 102° 29' 36 EThe last one has a lots of pictures and shows how sand - not deserts - encroach on formerly fertile areas.
There is a little grass left for you to feed on in the last area at least.