21 January 2010

Theory of Climate -- Examples

Now let's move from philosphy of what a Theory of Climate would look like, to some of the components.  To repeat yesterday's list:
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
But notice that, as fits a  complex theory, that none of these immediately tell you that, say, the mean surface temperature of the earth should be 287 K, or how much it should change if you add a certain amount of a greenhouse gas.  Let's see, though, how these can be important to understanding climate.  This would be what our book titled 'Theory of Climate' would provide detail on.

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.

Quantum theory:
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.

Tectonic 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.


Bruce Princeton said...

I am a physics student and was looking for some info on different laws. It woulld be nice if you post Law of Entropy as well.

carrot eater said...

I'd give the First Law of thermodynamics top billing because it's the most basic piece: if more energy is coming from the sun to the earth/atmsophere than is leaving the earth/atmosphere to space, the climate system must warm up. All the rest is working out the details.

jg said...

Is albedo part of quantum theory?


Tracy P. Hamilton said...

What about stellar evolution?

Penguindreams said...

The list isn't actually in order

If we got hard core about it, albedo would be derived out of quantum, I suppose. But, unlike the absorption bands of gases where we (meaning people other than me, but scientists somewhere) do try to compute it directly from quantum theory, for albedo, we do it by observing. So I'll definitely go with a free-standing 'thing you have to know about' for albedo.

Good one. As with plate tectonics, if we want to get climate right over long periods (hundreds of millions of years and up), we have to pay attention to how the sun evolves.

Michael Hauber said...

Peano axioms?

If you can't count you can't add up. If you can't add up you can't subtract, multiply or divide. If you can't do any of these you can't calculate anything.

Or can you? Just because our definitions of mathematical operations are built from counting and then addition, does that mean they necessarily must be built from this base?

quasarpulse said...

Yes, I think one of the underlying assumptions for any physical science theory needs to be that "math works as advertised." What exactly in mathematical theory is required for math to work as advertised is a question that can probably be left to the mathematicians.

From chemistry, you probably want to include atomic theory and Le Chatelier's Principle, at least. Transition state theory is probably applicable, but I don't know if it's necessary since you can use empirical observations for your reaction rates.

Penguindreams said...

While, as quasarpulse mentions, we do assume that mathematics works as advertised, I can't think of a time that someone referred to 'thanks to the Peano axioms we know X' and X was something about climate.

In a sense, that mathematics works (and Peano axioms certainly help us understand foundations of mathematics), is a metaphysical assumption we make in doing any science. Another, for instance, would be that there aren't invisible pink unicorns running around changing the readings on our thermometers. We do make these assumptions, and they're probably correct. But they're not really amenable to testing.

In contrast, we do assume the Ideal Gas Law applies to the atmosphere. But we can go ahead and test how closely the atmosphere is represented by that law.

That said, I think I'll at least mention the mathematics when I do the longer write up.

Thanks for the additions. Good to see you back.

carrot eater said...

In my view, math isn't a theory or philosophy used by physical language, but the language. Maybe that isn't a meaningful distinction, but if somebody invented a radically different framework for doing math, the knowledge we have about physics would still apply. It'd just be written in a different language, just as a book can be written in Chinese or Spanish yet hold the same information.

Horatio Algeranon said...

These days, everyone seems to have a "Theory of Climate"