Even in desert conditions, there exists some level of humidity that, with the right material, can be soaked up and squeezed out to produce clean drinking water. In recent years, scientists have developed a host of promising sponge-like materials for this “atmospheric water harvesting.”
The number returned by Google (for what that's worth) is:
The Sahara Desert has an average relative humidity of 25 percent.
In the part of the world with driest air and least rainfall ... you could always melt the ice underfoot.
