If the roof is well shaded by the trees, it could be mold, mildew, or algae,
or a combination of the three. Increasing sunshine a bit and air circulation
would result from some tree pruning or removal, making for a more healthy
roof. Big box stores like Home Depot sell zinc compounds, such as Moss Out,
that will attack the stain. It is diluted with water, then applied with
hose-end sprayer or pump sprayer. Make sure that whatever you get, is not
going to damage the shingles.
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