[villagetinker]

Not sure what a 'barrel' lock is, but I have found that making sure the latch is properly adjusted makes a real big difference in keeping the screen doors closed in high wind. I would probably go with a simple hook-eye in stainless steel (if I could find one) to avoid rusting and locate it in the vicinity of the door handle. Also remember, if you install these types of additional locks and you are on the wrong side of the locked door you will not be able to get in or out.