There are various "black streak" removers marketed for RVs and they can be found wherever RV cleaning and polishing products are sold. Whether any of them will work on your stains is an open question, since these stains (streaks) are the result of whatever gunk has accumulated on the roof plus whatever minerals are in the rain water and dew. This cocktail varies with the area it originated in and sometimes one cleaner works and sometimes another. And sometimes it seems none of them work. In that case, it mostly takes a lot of elbow grease, i.e. repeated polishing with heavy duty boat or auto cleaner/polishes. The type that removes oxidation from fiberglass or metal.
Brown streaks sounds like iron or tree residue (often tannin) or decaying vegetation. I would try a couple of the available streak remover products (no particular brand recommended) and see if that helps. You can also try a vinegar and water solution, about 25-50% vinegar. That works on some kinds of stains. Then move onto stronger stuff. By the way - is it fiberglass or painted metal? Or maybe anodized aluminum?