How can I account for rainfall effects on air pollution?
Sounds like you want a dataset that is unadjusted for rainfall.  I'm not sure what you have to gain from that, but there are ways to do it.  One way to do this would be to find the inverse correlation between rain and black carbon concentrations, and extrapolate to zero rainfall.  Or, if you have any months that have zero rainfall, you could use that for other months where temperature is similar (thus the mixing layer should be similar).  This would all need to be done for each location separately, so that source contributions weren't mixed up.