Saturday, January 21, 2017

Gravity in the Greenhouse

Gravity is the cause of the greenhouse effect.


Well if a Rabett thinks long enough and hard enough about it, the greenhouse effect is a consequence of three things, two of which are the result of gravity and the other of quantum mechanics.  The quantum mechanics part is that there are gases in the atmosphere that absorb and emit infrared radiation (for  such as CO2 and H2O, let's stick with radiation, there are folks who object to calling IR photons light and Eli does not have enough money to buy the beers needed to settle that one).

The first is the lapse rate, the decline of temperature with altitude in the troposphere.  There are plenty of detailed derivations of the dry lapse rate on the net and a bunny can even throw in some water vapor, but the basic principle is that the atmosphere is for all thermodynamic purposes an ideal gas, and the temperature decreases with pressure, and pressure decreases with altitude because of gravity. 

The second is the decrease in density with altitude, again because pressure decreases with altitude because of gravity.  The higher you go the less stuff.

Both of these effects explain why radiative energy transfer from the ground to space slows, the higher greenhouse gas concentrations are. 

Absorption of IR radiation by greenhouse gases is strong enough that any IR photon doesn't get very
far before being absorbed.  A good rule of thumb is that it will get about 3 m at ground level on an absorption line before being absorbed and maybe about 30 m in the space between the lines.

Because density falls with altitude, at some point the density is so low that IR radiation emitted from greenhouse gases can escape to space rather than being absorbed by another greenhouse gas molecule.  The higher the percentage (or mixing ratio if a bunny prefers) the higher this level will be and because of the lapse rate the colder it will be.

Emission from colder things is slower than from hotter things, thus raising the level at which the atmosphere can emit to space, that is increasing the concentration of greenhouse gases, slows the rate at which the Earth can shed the energy absorbed from the Sun.  If you heat something at a constant rate, and you limit the rate at which it can get rid of that heat, the something will warm. 

The greenhouse effect is a consequence of gravity.  Everything else is detail.


CapitalistImperialistPig said...

"Everything should be made as simple as possible, but no simpler."...Einstein

A couple of crucial details, also due to QM: The lapse rate has a lot to do with the convective instability of the atmosphere which in turn is due to radiative transport being less effective than convective in the Troposphere; and the atmosphere is much more transparent to visible than IR.

Nick Stokes said...

"The greenhouse effect is a consequence of gravity."
Well, yes, because without gravity there would be no atmosphere, GHG or no. But really, the GHE is a consequence of obstructing outward heat flux. There is always going to be some mechanism that will raise temperature as a consequence.

I find it useful to think about the Rosseland limit of radiative heat transfer (OD>3 or so). That photon free path essentially means diffusion. And the Rosseland limit is a diffusion equation, with the conductivity proportional to the path length.

EliRabett said...

Nick, one can have an atmosphere with gravity and no greenhouse gases and while the Rosseland limit is useful it is complex.

Anonymous said...

The the greenhouse effect and global warming are the long sought after unifications of general relativity and quantum mechanics I have been searching for. Eli, you are a genius. There is nothing global warming can't do! My time on Earth has not been wasted.

Pedro J: said...

Actually dT/dz = -g/Cp and Cp depends on the molecular degrees of freedom, a quantum property. So the lapse rate is quantum gravity in full action :)

Anonymous said...

It's a pretty simple model that applies well at many levels in a scale invariant universe. Therefore ... quarks and gluons. I can't wait until we can start using dark matter axions for attitude control and propulsion. That's Trump et al.'s approach. Who cares about this planet when there are all those other planets out there. Who cares if they are all dead. That's a feature, not a bug. We have an infinite supply of babies, easily indoctrinated by the mass media.

Oops, was I supposed to keep that a secret?

David Appell said...

A planet needs gravity to retain an atmosphere. But other than that, if that atmosphere stores heat, the planet has a greenhouse effect.

Anonymous said...

Right, David, but a gravitational gradient establishes up and down and inwards and outwards. Convection handles sideways. Plus there is night and day. I'm pretty sure astronomers have this all worked out by now.

But then again, analytic geometry might be wrong. It's only a theory.

David Appell said...

I don't understand why all that's necessary.

If you have an atmosphere that stores heat, it radiates. Some of that radiation will warm the surface and lower atmosphere.

Anonymous said...

I agree, David, but where did those surfaces come from? How did they arise? Maybe these are the fundamental mysteries of space the Donald was talking about. N-dimensional hypersurfaces and spheres are a part of the fundamental topology of the universe, and our universe is dimensionally reduce to the minimum necessary to have particle=energy mass-flux with an arrow of time. Hold a 0.1 meV dark matter axion in front of these people and that's all the crackpot physics they need in order to blow off the more immediate and near term existential threat to the more imaginary and delusional ones, like for instance, 4000 Gt of stored carbon reserves, two ice sheets, a global ocean and many continents being a threat to jobs for seven billion religious nutjobs.

I mean, there are only so many things a pristine, life and water bearing terrestrial with an active hydrogeological cycle, a stable star and a wonderful climate can do for people desperate for work.

Paradise just ain't what it used to be.

David Appell said...

OK, I thought you were being serious about this. My mistake.

Anonymous said...

Eli and Pedro already explained the general idea, and they are right of course. Nobody thinks about these things rationally anymore, they just take it for granted, up is up and down is down, and that is that.

But now we live in an America where up is down and war is peace, and therefore it's legitimate to ask just what the hell is going on.

Axions and standard model particles in a locally curved gravitational field is going on David, where mass and energy and particles evolve pushed along by an arrow of time, another half a dimension so to speak.

What's wrong with just saying that? It can't be said enough in a nation where now the lower half of the IQ spread have absolute power. Say it so often those low IQ voter puke or cringe or run away in fear. Otherwise some day they'll be knocking on your door at night.

David Appell said...

You're way off topic, and riffing for who knows why. But what you're writing is not relevant to the GHE.

Anonymous said...

David, the greenhouse effect of greenhouse gases is so well understood that I don't see the need to discuss it AT ALL, unless something new come up or some new perspective arises in its discussion. Here the topic is quantum gravity as far as I can see, or if you prefer, quantum mechanics and general relativity. So as far as I see it, axions and gravitons are particularly germane to that subject.

Yes, I am biased and I do have a few axes that need grinding.

I like the term 'forward'. It suits me.


It's 3-d, 8c -- gravity gradiometers readily measure ocen tides and can do gravity waves in the atmosphere as well

But Nick takes the gong by invoking ballistic thermal transport :

" the Rosseland limit is a diffusion equation, with the conductivity proportional to the path length."

Works fine for phonons in monoisotopic perfect crystals at cryogenic temperatures - what could possibly go wrong in a wet mixture of gases ?

Anonymous said...

All your particle are belong to us.

Bernard J. said...

I've waited years for this post Eli. There were moments previously when I thought that it would come, but better delayed than never emitted...

And nary a SCUBA tank or balloon in sight.

Nick Stokes said...

But Nick takes the gong by invoking ballistic thermal transport "

Nothing to do with ballistics. The path length is the path of the photon. Eli's 3-30 m. Nothing to do with moisture. It simply describes what happens when there is a temperature gradient in an active gas and small parcels of heat are transferred (by emission and absorption) up and down the gradient. There is a diffusive flux, following Fourier's law. Rosseland developed it for star interiors, but it's main terrestrial application (as in the link) is to smoky gases.

Mike Dombroski said...

Is the Wabbett offering a welcome to Doug Co##on?

Fernando Leanme said...

We must remember that CO2 causes a negative greenhouse effect if the surface is colder than the atmosphere. The effect of co2 isn't linear, therefore at current co2 concentrations we are probably seeing close to the maximum negative co2 greenhouse effect over those areas where the atmosphere is warmer than the surface. This happens over the South Pole, and explains in part why Antarctica has been cooling over the last 30 years.

BBD said...

This happens over the South Pole, and explains in part why Antarctica has been cooling over the last 30 years.

More bollocks from Fernando. No overall trend for Antarctica. Regional warming and some regional cooling (very slight). Ozone hole most likely responsible for central Antarctic cooling (if it really exists at all).


Nick, path length - proportional thermal conductivity implies lossless ballistic transport, as in ballistic electrons or phonons- the thermal conductivity of perfect crystals in the low temperature regime ( well below theta Debye) is indeed proportional to their size.

dlen said...

Imagine an atmosphere on a planet without gravitation with a glass ceiling at the top with no radiation effects, that is put there in order to prevent the escape of the gas into the vacuum.
In this case, we would still get a greenhouse effect and a temperature decrease with height. At each absorbtion lenght step, temperature would drop a certain amount. The temperature drop would actually increase with each step - otherwise, there wouldn't be a continuity of the energy flow. The outermost layer would radiate into vacuum. This atmosphere would have a kind of overall thermal resistivity, which would be rising with rising absorbtivity.
But of course you know that as well!

David Appell said...

dlen: Oh come on. Without gravity the distribution of gas molecules would clearly be a constant per unit volume, at equilibrium, and the temperature would be the same throughout that volume.