As the article & comments say: dilute bleach and water;
wait a week or two for algae, moss, etc to die;
rinse off detritus, and add zinc strips to the roof
to inhibit future growth. Vary to protect nearby shrubs,
fish. etc. Never use more than low pressure. Move carefully, have adequate health insurance, or both.
Gloeocapsa magma is the species that blackens roofs. I have it and it's ugly and annoying.