Studies funded by the National Science Foundation, a major source of the funding you're talking about, explicitly require that you note the grant number in your published papers. From that you should have no problem auditing where the money went.
More money may be spent in climate research but how much of that goes into designing, building, launching and downloading data from satellites? How much of it goes into supercomputers and other hardware? How much goes in to funding expeditions to remote sites? Very little gets spent on that sort of thing by the other side.