hmmm. I suppose if you detonated a container of "heavy water", the resultant vaporisation could result in normal water, and the cloud falling out of the sky.
Normal shells would have a dispersive effect, but they'd only blow the could apart & higher, which would mean it was only a matter of time before it came back, and more grey the next time.
A plane will chew up the clouds pretty easily, so long as it's jet propelled, but that'll prove expensive to say the least.
Sorry, just proving I'm a geek still