rill

n. any of many long trenches on the surface of the moon (also rille); small brook, stream

A rill is a narrow and shallow incision into soil resulting from erosion by overland flow that has been focused into a thin thread by soil surface roughness. Rilling, the process of rill formation, is common on agricultural land and unvegetated ground.Some rills will continue to grow, as they are widened and/or deepened by the runoff which flows through them. Other rills may decline in importance as sediment is deposited within them. Eventually, a hydrologically efficient rill network will be formed. The development of such a network is an example of self-organisation.
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Noun
1. a small stream
(synonym) rivulet, run, runnel, streamlet
(hypernym) stream, watercourse
2. a small channel (as one formed by soil erosion)
(hypernym) channel

(v. i.)
To run a small stream.
  

(n.)
See Rille.
  

(n.)
A very small brook; a streamlet.
  

A small channel eroded into the soil by surface runoff; can be easily smoothed out or obliterated by normal tillage.