Farm puzzle

I flew from D.C. to Philadelphia yesterday on my way home to Vegas. This leg of the flight is short, just 25 minutes, and they never climb above 11,000 feet, so I had a nice view of the ground all the way.

I was curious about something I saw in the farms. As you can see in the photo (click to view it at full size), most farms have "arms" of greenery snaking through them. These are clearly not streams, because they end rather than going all the way across (at least mostly). I thought of irrigation ditches, but it seems unlikely that farms in this part of the country need irrigation ditches, and, besides, these are strangely irregular for irrigation ditches; at least the ones I've seen in the western U.S. are perfectly uniform and evenly spaced.

Whatever these things are, they always start at an edge of a field and end within the field; that is, there seems never to be one that has both ends within the field, and only a few that go all the way across. Some branch, some don't. Some are straight, some curved. Some are long, some short.

I can't figure out what these things are and/or what their purpose is (which I suppose is really the same question). I suppose they could be just ordinary, naturally occurring ditches draining into streams, but there seem to be a lot more of them than I would expect. Of course, my experience is based on growing up in Illinois, where things are a lot flatter, so maybe this is just how farms in more contoured regions are, with drainage ditches.

Enlighten me, readers!