I am doing the same! The best of both worlds.If you want both rain protection and light, you could use clear polycarbonate roofing panels - like these:
https://www.homedepot.com/p/Suntuf-26-in-x-6-ft-Polycarbonate-Roof-Panel-in-Clear-155030/206166246
That's what I'm planning on using for my run. I've seen lots of people use them and like them.