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.
Popper's criterion is mostly concerned with theories, not observations. And climatology has few theories of its own. It borrows theories from other areas of science -- the laws of conservation of mass, energy (first law of thermodynamics), and momentum (Newton's laws), the second law of thermodynamics, Planck's law for blackbody radiation, quantum mechanics (to get emission and absorption of radiation by gases), and a few more subtle matters. Climatology also makes some use of observations -- where are the absorption lines of CO2 and how strong are they, what is the saturation vapor pressure of H2O, what is the freezing point of water, and so on.
To the extent that people complain about climatology, and climate models, the theory (theories) that have to be wrong are from somewhere else (usually physics). The climate models are just trying to carry out the laws and theories from physics.
Popper's criterion, to come back to it, doesn't have much to say about observations. I am 6'1" (185 cm) tall. At least I claim that this is true. Suppose you come to my house and measure my height and see that I'm, instead, 184 cm tall. Maybe you've 'falsified' my claim. But what has changed in the world of science? Nothing. No portion of science relied on me being 185 cm tall rather than 184 cm tall. Certainly far less depended on that than depended on Mercury's orbit, and that didn't, on its own, cause the downfall of Newton's mechanics and gravity.
But the law(?), theory of conservation of energy is something to falsify. It _could_ be falsified. If you observed the amount of energy in a system at one time, and then some time later saw that it had less (or more), you'd be on your way to a Nobel prize. Or at least a new revolution in science. One of the major importances of Einstein's E = mc^2 was that it showed there was a new place to find energy in the universe. Odds are good, given the 100+ years that people have been at it, that you've just made an error in your observation process. Still ... maybe you've got something.
Rather than drive on to a firmer conclusion, I'll stop here and invite discussion. What theory or theories do you think climatology has that couldn't be falsified? Which ones do you think have already been falsified? If you think climatology is making claims which could not, even in principle, be falsified, what are they? Is Popper's criterion even a good one to use? And so on.
* There's an old story that goes: A student who was not doing very well in a class discovered that their professor always gave the same test every year. Even better, it was multiple choice. So they tracked down an old, corrected, copy of the test and memorized the answers. Come the day of the final, they checked off all the previously-memorized answers. Then was extremely surprised to have gotten an F (failing grade). After some internal debate, the student went to the professor and said what they had done. The professor answered "Yes, I give the same questions every year. But I change which answers are correct!"
$ 43 seconds of arc is a seriously small number. A circle has 360 degrees. Each degree has 60 minutes of arc. Each minute of arc has 60 seconds of arc. The difference was 43 / (360*60*60) of a circle -- 0.00003318 of a circle (about 33 parts per million, far less than the fraction of the atmosphere that is CO2, and small enough that the thickness of the line when you draw a circle is much larger than this).