This kind of structure looks a little like a greenhouse made from tubes and wire mesh. The roof is a gentle arch of metal, often covered with mesh and sometimes with extra metal or waterproof fabric on top. I like this style because it gives my birds space to flap their wings and even hop to catch bugs that fly inside.
When you add a stronger metal roof layer on top of the arch, rain slides off the curve instead of sitting on the surface. Snow tends to fall away too, which is friendly for people in colder areas.
This looks like mine