I live in the Seattle area. Below is a picture my roof. What are the green traces on the roof.
Is this algae or moss? What is the easiest way to remove it without damaging the shingles and the paint?
It's algae now & will become moss later & it will come back until you properly pitch the gutters &/or clean the gutters. Any wetness that continues long after everything else has dried, like you have, indicates a drainage problem. However, a tablespoon of bleach to a cup of water with a gentle & light brushing (don't scrub the shingle granules off the shingles) will remove it. Bad gutter installer, as indicated by lower gutter.
Malarkey and Atlas have Scotchguard lifetime algae resistant shingles. If your shingles are either of those brands you may have a warranty claim. Other manufacturers have 10-15 yr algae resistant warranties where they might cover a cleaning. They recommend TSP, Bleach and Water mix. Atlas