Water for Deserts - The Solar Fridge
Why not use a solar powered fridge? An ammonia/hydrogen cycle fridge with the sun light as the heater and shadow as the heat sink.
I also suggest the use of a solar powered fridge as a cooler for desert air (in a cooling tower - See diagram) to cool the hot desert air to extract water for drinking and irrigation.
The idea is that a mirror separated the sunlit side of a plate and the cool underside. On the hot side the hydrogen is separated from the ammonia. The Hydrogen and ammonia (Liquid) is passed into the shadow to cool in separate pipes then the two are allowed to mix in an adsobant in the cooling tower and the cold liquid passes through tubes in the tower. The tower is open to the air which is cooled and falls down the tower and the water content condenses to be collected at the bottom. This is pure water that can be used for drinking and irrigation (in covered closhes to prevent evaporation).
The enthalpy of solution of hydrogen gas in liquid ammonia is negative so the solution is cold. The solar heating separates the fluids again to be recycled. The gas and liquid motion in continued by convection, so no mechanical moving parts are required.
The diagram attached as a GIF file is not very well drawn, it is only an indication.
I don't know much about the hydrogen-ammonia fridge but the right hand shaded box separates the hydrogen from the ammonia and the left hand box is where the hydrogen is re-absorbed by the ammonia. Efficiency would be low but there is plenty of sunshine in a hot desert.