Dirty wheel rims

It turns out that it basically doesn’t rain in California in the summer (or so I am assured by the people at work), so now that the weather is nice again I have been riding to work at lot more. I am suffering from a problem I hadn’t considered though, mainly because I normally only ride on paved surfaces.

About 10% of my work commute is across a car park with dirt roads, and they are producing a lot of dust. Apart from making the bike dirty (which isn’t so bad), the wheel rims are being coated in enough dust for there to be noticeable abrasion noises when I brake after the dirt road stretch of my ride.

This must be a common problem for mountain bikes, so, what should I do about it? I imagine that at worst it’s shortening the life of my rims marginally, but I’m not massively concerned as my current rims are cheap ones anyway. Apart from wiping the rims down each evening, is there anything else I can and should be doing?