Current hydroelectric systems rely on building a dam, say 50m high, and generating electricity from a large mass of water falling that 50m.
Might another approach be to build a tower as high as possible, say 500m, and catch rain up there. You might catch less rain, but you'd have a lot more height.
Obviously the challenge with this is getting a large catchment area very high up. I guess you'd need some kind of aerodynamic design like a kite to allow a massive square meter-age to stay aloft during storms.