One of the things I like to ponder is how to decide whether something is science or not. An attempt to come up with a clear demarcation criterion is Karl Popper's, which gets more widely distributed as being "If it isn't falsifiable, it isn't science." I'm not sure what he said himself, but philosophers tend to write books on these topics, rather than short sentences, so I'll guess that some details are lost in this version.
The question arises here because a recent question at the question place (yes, Robert, that's exactly what it's for) mentioned Popper. I'll give a different response and discussion here. (Same conclusion*).
For some cases, Popper's falsifiability criterion works well. Religion is not science. There is no observation, experiment, or test that will tell someone that their religion is wrong. No matter what you observe, the religion can accommodate it. Same thing for mathematics, actually, as it isn't necessarily concerned with observations. Unfortunately, those (theology and mathematics) are the only two areas which can lay claim to absolute Truth (of a sort -- mathematical truth is only about mathematical things). Science is left with only approximate truth -- the theory seems to work pretty well, the observations are pretty reliable. But not absolutely reliable, and not absolutely perfectly.
For others, though, it's more difficult. In the later 1800s, astronomers observed that the planet Mercury wasn't where it was supposed to be according to Newton's laws. Its point of closest approach to the sun (perihelion) was moving by 43 seconds of arc per century too much$. If Popper's criterion were correct, astronomers and physicists should have immediately thrown out Newton's laws and gone looking for something else. Instead, some patches were suggested -- like a planet 'Vulcan', orbiting even closer to the Sun than Mercury, in just such a way to cause Mercury to behave as observed. But it was never observed. Eventually, Einstein proposed his theories of relativity to expand on Newton's laws. Among other things, they explained why Mercury wasn't where Newton expected it to be.
For climatology, Popper is not so much relevant, or at least doesn't pose very much difficulty.
2 hours ago