Yes, but I'm pretty sure none of our food is farmed in desert regions. And regardless it's still a renewable resource; it's not used up, just moved around and mixed with different things
There's a bunch of farming done in the desert in (for instance) Arizona.
Cotton isn't food, but it still uses huge amounts of water to grow it in the desert.
Getting plants to grow in the Sonoran Desert is made possible by importing billions of gallons of water each year. Cotton is one of the thirstiest crops in existence, and each acre cultivated here demands six times as much water as lettuce, 60 percent more than wheat. That precious liquid is pulled from a nearby federal reservoir, siphoned from beleaguered underground aquifers and pumped in from the Colorado River hundreds of miles away. Greg Wuertz has been farming cotton on these fields since 1981, and before him, his father and grandfather did the same. His family is part of Arizona’s agricultural royalty. His father was a board member of the Central Arizona Water Conservation District for nearly two decades. Wuertz has served as president of several of the most important cotton organizations in the state.
But what was once a breathtaking accomplishment — raising cotton in a desert — has become something that Wuertz pursues with a twinge of doubt chipping at his conscience. Demand and prices for cotton have plummeted, and he knows no one really needs what he supplies. More importantly, he understands that cotton comes at enormous environmental expense, a price the American West may no longer be able to afford.
Basically he, and the other cotton farmers in arizona and california, are only still growing cotton because of government subsidies which make it almost impossible to lose money on it.
Rather than paying direct subsidies to cotton farmers, starting this year the USDA will use taxpayer dollars to buy farmers additional crop insurance. Policies that once covered up to around 70 percent of farmers’ losses can now be supplemented with new coverage covering up to 90 percent, cushioning the shallowest of losses. The lucrative marketing loan program that serves as a sort of price guarantee also remains in place.
Right now, though, the stubbornly low price of cotton is making Wuertz nervous that the new, enhanced insurance program won’t deliver the same revenues as the old direct subsidies. He’s temporarily cut back, then, planting less cotton this year and only the most valuable strains.
Still, the more than 161,000 acres of cotton that were planted in Arizona in 2013 accounted for almost one out of every five acres of the state’s irrigated farmland. Many believe the insurance program is likely to keep the practice going because it limits most — if not all — downsides, encouraging farmers to take big chances with limited resources.
“If I knew my 401k was guaranteed to not fall below 85 percent of its current level and there was no limit on the upside,” said Craig Cox a senior vice president at the Environmental Working Group, who was a former staff member for the Senate committee on Agriculture, Nutrition and Forestry, “my portfolio would be a lot riskier than it is.”
California and Arizona are able to produce more than twice as much cotton on each acre they plant as can cotton powerhouses like Texas and Georgia because they irrigate their fields more often. But that also means that they use two to four times as much water per acre.
From almost the beginning, Arizona’s cotton farmers understood they were withdrawing from a finite account. “There was a sense the water would run out,” said Wuertz’s father, Howard, now 89. “You could tell there was going to be an end to it, even in the 1950s.”
They’ve made it last, in large part, because as the aquifers beneath their feet were depleted, the state brought in new supplies, mainly from the Colorado River.
The water taken from the Colorado for cotton is water that could have gone to other crops (which would admittedly still be in a desert), or to cities with people in them - and it's experiencing a severe drought (which the article, and IIRC the other articles in that series, talk about. This one is just chiefly about cotton).