You don't really need a compute terrain to do something like this, but you need to start with a fairly smooth terrain, find a place where the waterfall can be, add a plane, displace it the same way as the terrain, but sink it a little, then mask out the stream/torrent by simple shape that follows the direction of that stream. Then use that mask to deepen the streambed in the terrain, and your waterplane will be visible in the gully.
Then use the same mask, but inverted, for additional finer displacement of the terrain after the line goes off to the plane, so to speak, so the gully remains open and the water visible. If you want rocks in your stream, you can use the mask for just those streamrocks, e.g.
That's one way of tackling this.