99% of these stains are caused by Gloeocapsa magma, an airborne form of algae.
It only seems to take one wet night with a warm morning. My neighbors recommended that we install a zinc or copper bar at the top to counteract the algae formation but spraying a bleach and water mixture up there did the trick and got rid of all the stains. Its been 9 months and I have not had any more growth and roof was not damaged in the process. Its an easy fix.