I have trees all over my dam, but not willows.(trying to manage as I can, Katrina helped some) Willows are in shallow end. With a willows root system that grows so rapidly, I would cut the tree, paint the stump with Ortho brush killer full strength(trichlopir). The willows roots will probably not die, but will grow much more slowly. You can always dig it up and repair later if water level drops excessively.
