The stains are normally algae or mildew. Mold would be uncommon on roofs. Zinc is toxic to all these organisms, so the best treatment is to spray with zinc sulfate (Moss Out) available in home and garden and home improvement stores. To remove the stains, I recommend you first treat with zinc and allow at least 2 weeks for organisms to die and lose their grip. Using a garden sprayer, apply bleach diluted 1:5 then use a pressure washer or hose with a good nozzle to flush off the stain. Be aware the bleach can be toxic to ornamental plants.
If you periodically apply zinc or attach zinc metal strips to the ridge line, this problem will not recur.