Can you be more specific when you say "more dirt"?
I've noticed fairly large specks of dirt and bits and pieces appearing and I guess they are things just falling out of the air. They look bigger and more dramatic than they really are because the water forms a meniscus around them and this acts like a lens to focus the light.
(See the rather hastily-drawn and not-to-scale diagram below.)
By the time the roof is dry, the bits are still there, but much less noticeable - and are quite unavoidable as they just fall out of the sky!
(This is the same stuff that falls on your patio. Have you noticed how you can sweep it clean one day and there's loads of dust and bits there the next day?)
Or do you mean something different?