Here is an interesting story from AZCentral that describes how one Arizona farmer is growing wheat and other crops in the desert by careful use of water combined with regenerative agriculture, a process of rebuilding soil organic matter and restoring degraded soil biodiversity through cover crops and other conservative methods. By growing his crop organically, he has increased the market value at the same time that he is using much less water and releasing less carbon to the atmosphere than when he grew conventional crops. The health of the soil has also improved and organic matter has increased. You can read more about his methods here.

Source: David Monniaux, Commons Wikimedia