Originally Posted by WindowsonWashington
If you don't vent it, SPF is best and easiest. If you do vent it, consider furring down the framing as you mentioned to get additional rafter total depths so that you can properly insulate while still leaving a 2" ventable space.
Rigid foam works well in these cases.
Alabama is warm with high humidity.
I imagine you want to keep the heat out?
Keep in mind that the heat of the sun is mainly transferred by conduction.
You will want the rafters and the roof isolated from the air inside.
Leaving a two inch gap between the roof and the insulation, in most cases will provide a gap for air movement, to dry off any rain that may seep through. In this case you will encourage hot air into the room.
You want to totally enclose the roof and rafters to stop the transfer of heat, (as much as you can) through the roof. Keep in mind that 13 inches of polystyrene will stop most conduction, but you have to be practical and probably settle for less. Filling the gaps between the rafters, then covering the rafters with three inches of polystyrene, then adding more rafters and more polystyrene will make a real difference.
Then you need to think about the walls facing the sun.