It has a name
The dark vertical streaking on asphalt shingle roofs across Middle Tennessee is a cyanobacteria called Gloeocapsa magma. It feeds on the powdered limestone that shingle manufacturers use as filler, and it protects itself with a dark pigmented sheath — which is the black you are looking at.
Why it runs downwards
Because rain moves it. Spores land on the ridge, colonise, and every rainfall washes some of the colony down the slope to start again lower. That is the whole reason the streaks are vertical and start at the top. Dirt would not do that, and neither would a gutter stain, which is the usual guess.
Why the north slope is worse
Same reason the north wall of the house is greener. Less direct sun means the surface stays damp longer after every rain, and damp is what the colony needs. Overhanging trees do the same thing to whichever slope they shade.
The part that costs money
The staining is cosmetic on day one. What follows is not: the colony holds moisture against the shingle, moss establishes in the damp, and shingles that stay wet shed their protective granules faster than they should. Granule loss is what actually ends a roof. Treating the algae is maintenance on the most expensive surface of the house.
Do not pressure wash it
This is the important part. A pressure washer will take the streaks off and take the granules with them, and a shingle stripped of granules is a shingle with years knocked off its life. Roofs are cleaned chemically at low pressure — the solution kills the organism and a gentle rinse carries it off. Anyone proposing to pressure wash your roof should be turned down.