In climate, some of our principles, or statements of theory, would include:
- Conservation of mass applies to the climate system
- Conservation of momentum applies
- The laws of thermodynamics apply
- The general theory of relativity applies
- Quantum theory applies
- Tectonic theory
Conservation of mass:
The water cycle is one of the climate expressions of conservation of mass. If you evaporate water from somewhere, there is less water there. If you condense water from vapor into cloud droplets or ice crystals (make a cloud) then there is less water vapor in that part of the atmosphere. If those cloud droplets or ice crystals fall to earth, then there is less liquid or solid water in the cloud, but more in the patch of ground or ocean that the precipitation fell on. This extends another step -- if some patch of ground experiences more evaporation than precipitation, it will dry out. Or, if it is a lake or inland sea (like the Aral Sea) it will shrink.
Conservation of momentum:
This leads us to learning that winds are largely driven by pressure differences. If something in the climate system changes the pressure differences -- say by warming the poles faster than the equator -- we expect changes to the winds. Getting detailed about this requires paying attention to all the other effects.
Laws of thermodynamics:
This includes both conservation of energy and the entropy law. Conservation of energy tells us that when water condenses from vapor to liquid or solid, it will release energy. It can be quite a lot of energy -- which is what drives hurricanes and typhoons -- if you get enough water to condense. The entropy tells us, for instance, that cloud droplets will form more readily on a nucleus of some kind -- dust or salt particle, for instance -- and something about how much.
General theory of relativity:
I don't need to worry about this in the day job, but it does apply to thinking about climate on periods longer than a few hundred thousand years. On the few thousand to few million year time scale, the earth's orientation and orbit change (Milankovitch theory here). Once you get past a certain point, you need to include general relativity to get an accurate orbit.
The absorption of radiation by the atmosphere depends intimately on quantum mechanics (quantum theory). We can pretty much get away with a simple rule for emission from the surface (Stefan-Boltzmann law -- black body emission and absorption). But the atmosphere is nowhere near a black body. It is extremely selective about what colors of light it will absorb, and equally selective about what it will emit. That's why we can largely ignore the major gases in the atmosphere -- nitrogen, oxygen, and argon -- and focus our attention on the rare gases water vapor, carbon dioxide, ozone, methane, and such. Understanding the selectivity is a problem in quantum theory.
Continents move over time, and plate tectonics is our theory for the hows, whys, and how fast. Application of the other components of climate theory tells us that the motion of continents also changes climate. So this is another part of a full climate theory.
Additional theories, laws, principles, ... that would be part of a full Theory of Climate are welcome.