You need a threshold that is slightly raised and water tight to the ground and to the door. You need to prevent any running water from spilling down into the stairwell from the surrounding area. You need to make the floor at the bottom of the stairs pitch away from the door and put in a large drywell that will allow the water to drain away. You shouldn't get all that much water falling into that stairwell. If this still isn't enough, then you could put a roof over this area to stop rain from directly falling into it.