When little rivulets of running water gather together and cut small channels in the soil, the process is called

When many tiny running streams join and carve small channels in the soil, the wearing away is called rill erosion.

Gully erosion is a more advanced stage where those channels deepen into large gullies.

Sheet erosion removes a thin uniform layer of topsoil without forming channels.

Channel erosion refers to scouring within an established river or stream bed.

The small incipient channels described here mark the rill stage.

Untreated rills can widen and merge into gullies, causing severe loss of farmland.