In Arizona, Nevada, New Mexico and inland California the enemy is evaporation. A pile that would be perfect in Ohio will be bone dry in a fortnight here, and a dry pile is as inactive as a frozen one. Below: how desert composting works in practice, what it demands of you, and who it actually suits.
Desert composting.
The constraint: water leaves faster than you add it
Low humidity, intense sun and wind strip moisture continuously. Most failed desert piles are not unbalanced. They are simply dehydrated.
What works
Site it in shade. Full sun is not survivable for a pile here. North side of a building, under a tree, or under shade cloth.
Enclose it. A contained bin loses far less moisture than an open heap. Some desert composters use a lidded bin specifically to trap humidity.
Water it deliberately, as a scheduled task, mixing as you go rather than pouring on top.
Go deeper, not wider. Less surface area exposed to drying air.
Pit and trench methods shine here
Below-ground composting is dramatically more moisture-stable in an arid climate, and it is the traditional approach in dry regions for exactly that reason. See trench composting.
Where water is scarce, running a compost pile that needs regular watering is a genuine trade-off. Trenching, or a sealed worm bin indoors, uses far less.