First time chicken owner, have some questions about run design - Pic added

[Liz Birdlover]

Open top run wouldn't work for hungry hawks & falcons or raccoons adept at climbing.

My runs must be predator proof, dug down 2 feet, too. On my property daily, chicken and/or egg lovers...fox, coyote, raccoon, hawk or falcon, Bald Eagle, snake, opossum, skunk, etc. If you really want your flock safe, you need enclosed run, only free range when you're out there with them or have a great guard dog supervising.

 

[KyCoop]

My coop and run are also on a hill. You will want to dig a drainage trench right outside your apron so the rain water does not run down the hill and straight into your run.
I personally would do HW cloth on the top just for peace of mind knowing the hawks and racoons could not get in for sure. You can still do it with the tree there, just a little tricky is all.