Basically, without any calculations that allow us to predict how the climate is likely to change (other than extrapolations of existing trends) they claim that because the climate change in the last twenty years is unprecedented, it must be man-made.

I don't doubt that the climate is undergoing unprecedented changes. I seriously doubt that it is something we have caused. Which means that is is not likely something we can do anything about, either. In short: "Live with it".

Batten down those hatches! Get the hurricane lantern supply ready! We're in for a hot time.