Runoff generated on cropland during storms or long winter rains concentrates in the thalweg where it can lead to rill or gully erosion.   
Rills and gullies further concentrate runoff and speed up its transfer, which can worsen damage occurring downstream. This can result in a muddy flood. 
In this context, a grassed waterway allows increasing soil cohesion and roughness. It also prevents the formation of rills and gullies. Furthermore, it can slow down runoff and allow its re-infiltration during long winter rains. In contrast, its infiltration capacity is generally not sufficient to reinfiltrate runoff produced by heavy spring and summer storms. It can therefore be useful to combine it with extra measures, like the installation of earthen dams across the grassed waterway, in order to buffer runoff temporarily.