In semi arid south west (Phoenix), the drainage is managed by creating incised channels. Typically, the dirt channel can erode with even very low velocities of moving water. To reduce erosion therefore vegetation needs to be established. This is difficult due to lack of adequate and consistent rain runoff. Any suggestion on what kind of vegetation ( ground cover, grass etc) could be used so that gradually it establishes (with minimum infrequent rain) a strong root structure causing a stable environment for handling rain runoff.
Grasses would be your best bet for erosion control since their extensive fibrous root systems do a good job of holding the soil. Here is a list of grasses that are native to Arizona and will withstand dry conditions. To get them established you may have to do some minimal watering at first, but then they should be able to handle dry conditions and hold the soil when it rains.
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