Why does the atmosphere get colder with elevation?

[Andre]

no?

No, you really need to have a good look at convection. Let's try another example, let's take the moon. Daytime temperature at the equator reaching up to 390K and nighttime only 100K. Now imagine hypothetically, that we give the moon an atmosphere of N2 and O2 only, which are almost transparant for both visible light and infrared.

So looking at a certain part on the equator, as the sun rises it starts heating the moon surface only from 100K slowly to 390K at zenith, the surface infrared radiation increases - counteracting the radiation inbalance, but that does nothing with our hypothetically transparent atmosphere. The radiation disappears into space.

But the heated surface also agitate the N2 and O2 molecules directly in contact with the surface, conduction of heat. This hot boundary layer gets less dense and the buoyancy causes it to rise. A hot air balloon without a balloon. As it rises into less dense pressure heights, it expands, which cools it adiabatically, but the surrounding atmosphere is also cooling with altitude, so as long as the rising air remains warmer than the environment, it continues to rise. On the Earths equator deep convection in the Hadley cell may continue to the tropopause.

Obviously, in this process, the molecules at the surface boundary layer are replaced with others which heat up at their turn and because of that start to rise too, etc etc. creating a vertical heat circulation system in the hypothetical atmosphere.

When the sun sets, the moon surface cools rapidly, due to out radiation of infra red. This still doesn't change anything in the inert transparent atmosphere. But as the surface cools so does the boundary layer of the atmosphere at the surface due to conduction, the molecules slow down hence it gets more dense, hence less buoyant and therefore it stays put*. There is no negative convection. Consequently, lacking radiative properties, the higher parts of the hypothetical atmosphere have no other means to cool down by conduction by contact with the lower boundary layer and obviously that is very ineffective.

So as the daily cycle repeats, the one way heat transport into the atmosphere continues until equilibrium, when the rising cooling air is equal in temperature with the environment, so that even at the highest surface temperature, there is no more convection.

Note also that this doesn't change the heating-cooling sequence of the moon surface a lot, the exchange of heat energy merely slows down the heating and cooling rate a little bit. Bottom line is that if the atmosphere can't radiate heat out, it continues to accumulate heat by means of convection until equilibrium with the highest temperature is reached, not the 'grey' body temperature.

* (we see that on Earth too, it's called ground inversion).

 

[D H]

That wouldn't be a realistic scenario. Everything radiates and absorbs EM.

No, everything doesn't. You're talking about black bodies. A black body has zero reflectivity and zero transmissivity at all frequencies. A black body absorbs 100% of incoming light. Black bodies are idealizations; their is no substance that acts like a perfect black body. A real body will reflect some incoming light, and some of the non-reflected light will pass right through the body. Moreover, that reflectivity and absorptivity often depends on frequency. (This is certainly the case for greenhouse gases.) The vast majority of the atmosphere consists of nitrogen and oxygen. Nitrogen and oxygen don't act anything like black bodies. They are pretty much transparent to visible and infrared light.

This is not an unrealistic scenario. It is pretty much what our atmosphere will look like a billion years or so from now. The oceans will be gone, evaporated, thanks to the Sun's increased intensity. Water vapor that reaches the upper atmosphere will be dissociated and the hydrogen will escape. The Earth's surface and its atmosphere will eventually be bone dry. Weathering of rock will have removed most of the CO₂ from the atmosphere. The Earth will have a greenhouse gas-free atmosphere in the far distant future.

If only those gases were present then the mean surface temperature of the Earth, based only on radiation balance, would be about -18C.

This ignores both that there is an atmosphere, that there is a sun, a point that radiates all the energy and that the planet rotates, causing equators to heat up via Stefan Boltzman when under zenith and it ignores energy transport via convection.

It obviously doesn't ignore that there is a sun. The Earth's surface would be a nice balmy 2.73 K if the Sun wasn't there. It does ignore rotation. Accounting for rotation would make that temperature even lower. Just look to the Moon. It's effective temperature is 270.6 K, which results from assuming an albedo of 0.11. It's mean temperature: 220 K. The difference between those two figures results from the Moon's rotation.

It does not ignore transport via convection. What convection? There would essentially be no convection in a greenhouse gas-free atmosphere. Except for a very thin layer near the surface, the Earth's atmosphere would be close to isothermal were it not for those greenhouse gases. An isothermal atmosphere is the maximum entropy state. The greenhouse gases coupled with incoming energy steer the atmosphere away from this maximum entropy state.

What this -18° C figure does ignore, quite intentionally, are the effects of the greenhouse gases on the temperature of the Earth's surface. This figure results from ignoring the effects of rotation and from assuming an albedo of 0.30, the same value as the Earth's current albedo. That latter assumption is not quite valid; clouds, ice, and snow make the Earth's albedo fairly high. This figure nonetheless illustrates the importance of greenhouse gases.

 

[Andre]

What convection? There would essentially be no convection in a greenhouse gas-free atmosphere. Except for a very thin layer near the surface, the Earth's .

With a solar constant of about 1360 w/m2 and an albedo of 30%, the square meter directly under the sun has an equilibrium temperature of 360K when using Stefan Boltzmann. This is comparable with the max temp of the moon.

If the ambient temperature is -18°C, 255K and the surface boundary layer of the atmosphere under the zenith is heated via conduction approaching 360K, what would stop the convection?

 

[sophiecentaur]

@DH
I'm not talking black bodies. I talking about every real thing. Since when did gases not absorb and emit EM? I never implied broad band behaviour

 

[haruspex]

No, you really need to have a good look at convection.

I couldn't find anything in that post which contradicted what I last wrote.
The "no?" you appeared to be replying to was in this context:

"The upper atmosphere would settle at the same average, no? "​

I.e. the average atmospheric temperature would be the same as the ground's. Why would it be otherwise? The only heat exchange available to such an atmosphere would be with the ground surface. Perhaps I was wrong to say "upper" though. It might average warmer aloft.

 

[D H]

With a solar constant of about 1360 w/m2 and an albedo of 30%, the square meter directly under the sun has an equilibrium temperature of 360K when using Stefan Boltzmann. This is comparable with the max temp of the moon.

If the ambient temperature is -18°C, 255K and the surface boundary layer of the atmosphere under the zenith is heated via conduction approaching 360K, what would stop the convection?

You're assuming a lot here. You are assuming a significant heat transfer rate from the surface to the surface boundary layer, and you assuming an ambient temperature of -18°C.

I thought I had read articles on a greenhouse gas free atmosphere, but the closest I can find in the scientific literature are articles snowball Earth. Those studies however still had CO₂ and other greenhouse gases in the atmosphere.

We're both speculating, so the best thing to do is to stop with this particular line of discussion.

@DH
I'm not talking black bodies. I talking about every real thing. Since when did gases not absorb and emit EM? I never implied broad band behaviour

Oxygen and nitrogen don't, or at least not very much. Those simple diatomic gases don't absorb much in the IR, so they don't emit in that band. Absorption and emissivity go hand-in-hand. That O₂ and N₂ are not thermally active is key to remote sensing. We wouldn't be able to use those satellite-based water vapor channels to "see" water vapor in the atmosphere if oxygen and nitrogen absorbed and emitted thermal radiation.

Addendum
An even better example are the noble gases. These gases are even more immune from thermal radiation than are the diatomic gases. This is why expensive double pane windows are filled with argon, and even more expensive ones are filled with krypton. Cheap ones are filled with nitrogen, and even cheaper ones are filled with dry air.

 

[Andre]

We're both speculating, so the best thing to do is to stop with this particular line of discussion.

Fair enough. I'm intending send you a pm tomorrow.