An arroyo is a dry creek bed, usually found in mountainous desert regions. Two elements are necessary for the formation of arroyos. There must be significant elevation change over the length of the arroyo, and the water table must be low enough that the arroyo is only fed by rain water.
Physical Characteristics
For those who have never seen an arroyo, a dry creek bed is an adequate analogy. However, a creek is immediately distinguishable from an arroyo due to the fact that is has a more regular water flow. The main difference is the size and location of the watershed involved.
For desert rivers such as the Rio Grande, a large watershed must exist in a wetter region, typically in the mountains where more rain and snow fall. By contrast, a large arroyo may have a very large watershed, but in a drier area that can not provide continuous flow. It is not unusual to see greater flow in an arroyo than a nearby creek during a heavy storm.
Arroyos can vary in width and depth quite a bit, but they change quickly when the rains come. Due to the sandy desert soil, erosion occurs quickly and unpredictably. Larger arroyos have steep banks and are filled with sand, providing an excellent recreation area free of cacti and other prickly desert flora. Just remember to keep out when it rains!
American Southwest
The American Southwest is the only place in the English-speaking world where arroyos are numerous and prominent. The word arroyo is borrowed directly from the spanish who first settled the area. Other parts of the world use different terminology for similar topographical features, such as the word wadi in the middle-east.
If you drive anywhere in New Mexico or Arizona you will cross countless arroyos. Arroyos are seen as amenities by local residents and are natural places for parks. Depending on the frequency of rainfall they may be flanked by slightly more or greener vegetation than the surrounding areas, especially in the high desert.
Illegal dumping is a major problem in New Mexican arroyos, because they are numerous and well hidden. It's perfectly legal to dump certain types of rock and gravel in an arroyo, but people dump all kinds of things. In Santa Fe I've seen everything from shopping carts to washing machines. And even minor refuse does not decompose in the desert.
Urbanization
Arroyos function as storm sewers in the desert. Other regions with more rain typically have more vegetation and wetlands to absorb moderate precipitation, however in the desert flash floods are the normal result of rain. The same thing happens in paved areas without storm sewers. When you build a city in the desert, you can have pretty decent flood control simply by maintaining the arroyos.
Arroyo maintenance comes mostly in the form of erosion control. Permeable walls can be made out of large stones wrapped in chain link fence to slow erosion. Concrete embankments can be created to prevent erosion where it encroaches on development. As an extreme measure, the entire arroyo can be paved. This maximizes human control and allows more water to be claimed for human use, but increases the rate of runoff and the danger of catastrophic flooding. A natural arroyo adapts to changes in the amount of rainfall, but a fully paved arroyo can not erode or change direction. Sufficient rain will simply overflow into city streets.
The Beauty
Arroyos are one of the most beautiful parts of the desert. If you are nearby when a storm hits, you can watch the sand turn into a rushing rivulet, sometimes gradually, sometimes as torrent appearing suddenly. Often the flow will crest after the storm has passed, amidst a backdrop of gorgeous desert rainbows. Soon the water ebbs, leaving behind the wet sand of a beach at low tide. Sometimes if you are in the right place, the water will be just enough to reach you before melting away quietly.