AlanB,
The Madison is formed by the confluence of two rivers at Madison Junction in Yellowstone Park.
It flows out and into Hebgen Lake and then through Quake Lake (formed by a 1959 earthquake) and then on for over 150 miles to eventually meet up with two other great rivers at Three Forks where they become the Missouri River.
The area in the photo might be considered high plains which the beautiful river traverses until reaching Enis Lake and then beyond, to Three Forks.