Correlation is causation

That is what Terry L. Root, Dena P MacMynowski, Michael D. Mastrandrea and Stephen H. Schneider appear to believe and the editors of the Proceedings of the National Academy of Sciences of the USA see fit to publish (open access). They find that recent changes in the dates of flowering and other seasonal activities of organisms are better correlated with temperature predictions of models that pose a human effect on climate than with those of models that do not include such effect. They then "assert that all these studies [theirs plus those that use the instrumental record of temperature] taken together demonstrate that recent (at least for the latter few decades of the 20th century) climatic changes seen at both the local and nine-grid-box scales, and observed changes in wild species, are highly likely to be forced to a considerable degree by human emissions of greenhouse gases and aerosols."

They go from correlation to causation (forcing). They explain how they estimated the Type I error (p < 0.05) of the statistical association. But how do they calculate the "likeliness" and the "degree" of the causal link?