Answer: Based on your description I am not certain if you have moss, algae or lichen growing on your roof and/or in your yard. I would suggest you work with your local county extension to identify specifically what it is and based on knowing that, decide how to proceed.
Since you have a new roof, you may also want to contact the roofer and roofing supplier and manufacturer for advice, especially if there is a warranty involved. In the meantime, here is a quick overview of handling this type of roof problem. You may need to cut and paste the complete url into your browser to make it work correctly.
I am sorry I can't be more specific for you long distance.
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