Elevated deck drainage

Just moved in to this new house. We have an elevated deck outside our dining room. It has a newly poured patio beneath it. Sounds cool but when it rains, the water from above drains right down onto the patio below, bringing leaves, seeds and whatever else has accumulated up there through the floorboard gaps down onto the cement below.
It seems to me that maybe I could suspend some fiberglass sheets angled down from the back side into a gutter with a down spout.
Are there any simpler solutions?
I appreciate any advice.
Thanks!