Moss on a roof is quaint but makes it deteriorate sooner.
Updated: Sep 20, 2019
So will pressure washing your asphalt shingles! Round -up will not kill moss...something to do with being the first land plant. A bleach solution will but may ruin your favorite knock-around clothes. If you don't want to use bleach, try this, but read the label carefully about danger to pets and such... Also, bleach and Wet & Forget will also kill lichen and take care of those black streaks, which are blue-green algae. Click on image for link.
Or call a professional roof cleaning service like Smart Wash.