What Dogfish said...

Power washing and scraping removes material from composition tiles and is counter productive if you want it to last longer. The best time to treat moss is when it is actively growing during Fall or Spring weather.

If the moss is really bad and clumpy, you can broom it off gently, use a blower to clear it off and then chemically treat the roof.
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In the legend of King Arthur, the Fisher King was a renowned angler whose errant ways caused him to be struck dumb in the presence of the sacred chalice. I am no great fisherman, and a steelhead is not the covenant of Christ, but with each of these fish I am rendered speechless.