Classic erosion caused by clearing.
The mechanics of erosion involves the speed of the water.
If it gets above about 3-4 feet a second it will cause the soil grains to move.
Speed of course is a function of volume and size of the gully.
The best anti erosion systems invoke stopping the water from getting up to erodible speeds.
Dams, flood retention basins all work, but the best systems involve keeping the water as static as possible, so that it creeps along and does not rush away.
Of course it means some of the pasture you have created will need to change, but if you don't change it,
In Australia we have a few different systems developed.
Keyline which you may know about and another one, its name slips me at the moment which involves vegetation to slow water down.
In the UK, some shires have adopted similar plans and they tend to not have the big floods that we see from time to time. Their rivers and creeks are tangled messes that prevent a quick escape, thus ensuring the lower towns are not flooded.
Keyline involves ploughing along the contour and having small connected dames to hold water and encourage it to soak in .