Why does the atmosphere get colder with elevation?

[Hetware]

~50 years ago, Richard P. Feynman asserted that the reason the atmosphere is colder at higher elevation is because "The ground is heated by the sun, and the re-radiation of heat to the sky comes from water vapor high in the atmosphere; so at high altitudes the air is cold--very cold--whereas lower down it is warm" ~ FLP, Vol II, 9-4, paragraph 2.

I'm not even sure what that means, but I believe it is wrong.

Mind you, atmospherics was not Feynman's expertise, and the field has advanced considerably since he gave his lectures. He's quite clear that his lecture on electricity in the atmosphere was speculative. So, I'm not trying to take anything away from the worth of the FLP. I know of very little else in the FLP which has been superseded with the ensuing half a century. Besides, that chapter is what led me to hunger for an understanding of the dynamic of the atmosphere.

My understanding of what makes the atmosphere colder at higher elevations is that convection currents act as a "heat pump" drawing heat from higher elevations and "squeezing it out" as the pressure increases. I can't recall where I read that, but it was probably somewhere close to James F. Price of the Woods Hole Oceanography Institute.

 

[the_emi_guy]

Hetware,
Greetings.

Are you asking specifically about the troposphere? Above the troposphere the temperature zigzags back and forth between increasing and decreasing.
(increases in stratosphere, decreases in mesosphere, increases in thermosphere).

 

[Drakkith]

While convection does happen, it actually brings hot air from the surface to higher altitudes. The main reason the lower atmosphere is warmer is because most of the radiation from the Sun is absorbed at the surface and then transferred to the air from there through physical contact.

 

[Hetware]

Hetware,
Greetings.

Are you asking specifically about the troposphere? Above the troposphere the temperature zigzags back and forth between increasing and decreasing.
(increases in stratosphere, decreases in mesosphere, increases in thermosphere).

Yes.

 

[Hetware]

While convection does happen, it actually brings hot air from the surface to higher altitudes. The main reason the lower atmosphere is warmer is because most of the radiation from the Sun is absorbed at the surface and then transferred to the air from there through physical contact.

That's what Feynman specifically says doesn't happen. The temperature drop through adiabatic expansion is greater, according to his, un-demonstrated assertions, than the pressure differential. That is, warm air rising will cool faster than the ambient temperature differential, due to adiabatic expansion.

 

[sophiecentaur]

The atmosphere is very complicated. Two over-simplified models can be relied upon to yield conflicting predicted results for temperature at a given height. I don't think there's a lot of point in arguing, using anything but the most advanced and detailed model.

 

[Drakkith]

That's what Feynman specifically says doesn't happen. The temperature drop through adiabatic expansion is greater, according to his, un-demonstrated assertions, than the pressure differential. That is, warm air rising will cool faster than the ambient temperature differential, due to adiabatic expansion.

Is it not possible that both effects happen?

 

[jetwaterluffy]

No, convection has the opposite effect. To my knowledge convection never increases a thermal gradient, only decreases it. The main reason why is that energy from the sun is transferred into the ground, but not the air, because the air is transparent and the ground isn't. So an object further from the ground will be further from a heat source, so will be colder.

 

[mfb]

On the scale of our atmosphere, convection is more important than heat conduction - the equilibrium is indeed a temperature gradient. But if we would have that equilibrium, we would have nearly no convection. The sun heats the ground, increases the gradient and induces convection. So I think the answer is "both".
There are exceptions, where the gradient is too small to give convection.

 

[D H]

~50 years ago, Richard P. Feynman asserted that the reason the atmosphere is colder at higher elevation is because "The ground is heated by the sun, and the re-radiation of heat to the sky comes from water vapor high in the atmosphere; so at high altitudes the air is cold--very cold--whereas lower down it is warm" ~ FLP, Vol II, 9-4, paragraph 2.

I'm not even sure what that means, but I believe it is wrong.

It's correct. Feynman was essentially writing about the greenhouse effect.

Imagine things would look like if the atmosphere was completely transparent. This would result in a very different world than the one on which we live. Surface temperatures would fluctuate much more than does ours because of the surface would receive the full brunt of the Sun at day and radiate to the darkness of space at night. You can see this to some extent in the desert where humidity is very low. (However, even in the desert, other greenhouse gases such as CO₂ still mediate temperatures.)

In this world with a transparent atmosphere, there would be a rather thin layer just above the surface where atmospheric temperatures fluctuate over the course of a day. Beyond this layer, the atmosphere would be very close to isothermal up to the point where the atmosphere stops acting like a dense gas (that's the mesopause in our atmosphere).

We don't have a transparent atmosphere thanks to those greenhouse gases that absorb in the infrared, and also to ozone that reacts chemically with ultraviolet radiation. It's those greenhouse gases coupled with daytime heating / nighttime cooling at the surface that steer conditions away from isothermal. In the lower atmosphere, water is by far the most potent greenhouse gas. What Feynman wrote was essentially correct, at least with regard to the troposphere.

 

[sophiecentaur]

If you look at the maximum height that clouds can be found is round about the tropopause. If I am right that the max height of clouds indicates the maximum height that convection can work the it would seem to me that the temperature lapse rate must be affected by convection. If energy were not being transferred to this height by convection, wouldn't that increase the lapse rate?
I know it's a dodgy subject so I could be falling into a pitfall here. Am I?

 

[D H]

If you look at the maximum height that clouds can be found is round about the tropopause.

That's because there's a temperature inversion at the tropopause. The ozone layer is above the tropopause. The ozone-oxygen cycle absorbs energy from incoming ultraviolet sunlight, heating up the stratosphere. Temperature increases with increasing height in the stratosphere. Temperature inversions create an absolutely stable atmosphere. There is little if any convection in an absolutely stable atmosphere.

 

[Hetware]

I should qualify what I said about Feynman regarding the consequence of adiabatic expansion not sufficing to cause a continual updraft. He states that such an updraft can be sustained if there is sufficient water vapor because as the rising air cools, the water vapor condenses releasing latent heat, thus warming the air, which in turn causes it to expand and rise still more.

Kerry Emanuel, in Divine Wind: The Science and History of Hurricanes, gives a decent account of atmospheric heat. He doesn't make the claim Feynman makes regarding the behavior of dry air, but he does agree that water plays an important role in the process of cooling Earth's surface through the same mechanism Feynman described.

Emanuel asserts "A detailed calculation of the radiative balance of the Earth's surface and atmosphere yields an average surface temperature of 135°F, much warmer than observed." That is ignoring convective effects.

He also observes that:

"the atmosphere is nearly opaque to infrared radiation. The radiation absorbed by gases in the atmosphere is re-emitted, both upward and downward. In consequence, the Earth's surface receives both infrared radiation emitted downward from the atmosphere and solar radiation. In is a remarkable fact that, on average, the surface receives more radiation from the atmosphere than directly from the sun."​

 

[haruspex]

"the atmosphere is nearly opaque to infrared radiation. The radiation absorbed by gases in the atmosphere is re-emitted, both upward and downward. In consequence, the Earth's surface receives both infrared radiation emitted downward from the atmosphere and solar radiation. In is a remarkable fact that, on average, the surface receives more radiation from the atmosphere than directly from the sun."​

Maybe, but the surface gets both the re-radiated IR and the direct visible light, so gets more in total than does the atmosphere. The ground becomes hotter than the atmosphere, and the proof is the existence of large scale convection. Convection (up to the tropopause) acts to flatten the gradient, but adiabatic expansion limits the ability of convection to do so.
I liken it to sand dunes on a beach. The wind and waves pile up the sand; gravity acts to level it out; sand particle interactions limit the flattening out.

 

[sophiecentaur]

That's because there's a temperature inversion at the tropopause. The ozone layer is above the tropopause. The ozone-oxygen cycle absorbs energy from incoming ultraviolet sunlight, heating up the stratosphere. Temperature increases with increasing height in the stratosphere. Temperature inversions create an absolutely stable atmosphere. There is little if any convection in an absolutely stable atmosphere.

I now appreciate the Ozone effect but I'm not sure whether that answers all of the 'why' question. It may just be stating a situation. I think that I am, in effect, asking how much the convection effects the position of the tropopause. I would imagine it's a matter of where one effect runs out and the other takes over.
The height that turbulence reaches is governed by the a mount of heat energy at ground level, I think. I seem to remember calculating and equating the change in mgh for a given amount of thermal energy and that gives an indication of the height that a bubble of hot air can reach. Afair, that corresponded to the max height that you find clouds.

I wonder what temperature distribution you would get if you could suppress convection (by a series of vertical baffles, for instance). I suggest that the tropopause would end up quite a bit lower. Someone is bound to have studied a model like that.

 

[D H]

That's what Feynman specifically says doesn't happen. The temperature drop through adiabatic expansion is greater, according to his, un-demonstrated assertions, than the pressure differential. That is, warm air rising will cool faster than the ambient temperature differential, due to adiabatic expansion.

Read again. Feynman specifically says exactly the opposite. If an isolated packet of rising warm air cools faster than the environmental lapse rate that isolated packet will fall back to earth. This happens for example, when wind forces air upward over a mountain on a clear day. For a rising packet of air to continue rising, the air in that packet must cool at less than the environmental lapse rate. When this happens, the rising packet will be warmer, and thus less dense, than the surrounding air. It will continue rising. This is exactly what Feynman says, sans the term "lapse rate".

In fact, he goes on to say that the observed lapse rate inside clouds is less than would be predicted by assuming isolated packets of rising air. This is because of entrainment (a term that Feynman does use). The rising packets are not quite isolated; they eventually do mix with the surrounding air. That surrounding air cools the rising air, or alternatively, the rising air warms the surrounding air.

Another way to look at it: Convection, when it occurs, transfers heat from the surface to the atmosphere. Convection can only occur when the lapse rates are conducive to convection.

Emanuel asserts "A detailed calculation of the radiative balance of the Earth's surface and atmosphere yields an average surface temperature of 135°F, much warmer than observed." That is ignoring convective effects.

And evaporation. Evaporation has a much greater cooling effect on the surface than does simple convection (e.g., thermals).

He also observes that:

"the atmosphere is nearly opaque to infrared radiation. The radiation absorbed by gases in the atmosphere is re-emitted, both upward and downward. In consequence, the Earth's surface receives both infrared radiation emitted downward from the atmosphere and solar radiation. In is a remarkable fact that, on average, the surface receives more radiation from the atmosphere than directly from the sun."​

Maybe, but the surface gets both the re-radiated IR and the direct visible light, so gets more in total than does the atmosphere. The ground becomes hotter than the atmosphere, and the proof is the existence of large scale convection.

That convection would not exist were it not for greenhouse gases. The ground would be a whole lot warmer than the atmosphere if the atmosphere was transparent in both the visible and infrared portions of the spectrum -- and there would be no large scale convection.

 

[sophiecentaur]

That convection would not exist were it not for greenhouse gases. The ground would be a whole lot warmer than the atmosphere if the atmosphere was transparent in both the visible and infrared portions of the spectrum -- and there would be no large scale convection.

This is interesting. Are you saying that it is not actual 'contact with the ground' by the air that causes the heat transfer and that it is absorption of IR by the air above the ground (and most of the transfer would need to be quite close to the ground, too)? Is this totally reasonable? I say this because, unless it works that way, it doesn't seem likely that you could get significant, thermals over small areas of ground (ploughed fields etc) as used by gliders and birds - the heat transfer being much more general and diffuse into the higher regions of the atmosphere. If it is true, then it would be difficult to explain the blanketing effect of quite high layers of cloud at night.
Maybe there are two mechanisms, one which explains the heating effect close to the ground and another that explains the effect over thousands of metres.
This is all fiendishly complicated and it's hard to get a measure of the significance of all the mechanisms involved.

 

[Hetware]

This is interesting. Are you saying that it is not actual 'contact with the ground' by the air that causes the heat transfer and that it is absorption of IR by the air above the ground (and most of the transfer would need to be quite close to the ground, too)? Is this totally reasonable? I say this because, unless it works that way, it doesn't seem likely that you could get significant, thermals over small areas of ground (ploughed fields etc) as used by gliders and birds - the heat transfer being much more general and diffuse into the higher regions of the atmosphere. If it is true, then it would be difficult to explain the blanketing effect of quite high layers of cloud at night.
Maybe there are two mechanisms, one which explains the heating effect close to the ground and another that explains the effect over thousands of metres.
This is all fiendishly complicated and it's hard to get a measure of the significance of all the mechanisms involved.

Air is not a very good conductor of heat. But according to what I posted above from Kerry Emanuel, air does absorb IR radiation very effectively. It would make sense to me that most of the surface to air transfer is radiative as opposed to conductive. Radiative absorption certainly allows for a larger volume in which the transfer will take place.

As for thermals, I don't see the disconnect. If air readily absorbs IR, then it would make sense that air over a warm radiator near the surface would be heated significantly more than nearby air over a colder surface.

 

[sophiecentaur]

Air is not a very good conductor of heat. But according to what I posted above from Kerry Emanuel, air does absorb IR radiation very effectively. It would make sense to me that most of the surface to air transfer is radiative as opposed to conductive. Radiative absorption certainly allows for a larger volume in which the transfer will take place.

As for thermals, I don't see the disconnect. If air readily absorbs IR, then it would make sense that air over a warm radiator near the surface would be heated significantly more than nearby air over a colder surface.

Yes but, if it absorbed it so easily, there would be no IR left for high cloud cover to make any difference to night temperatures. Do you see the conflict here? it probably needs figures in the explanation.

 

[haruspex]

It would make sense to me that most of the surface to air transfer is radiative as opposed to conductive.

Here's a very good illustration of all the heat flows: http://www.windows2universe.org/ear...earth_rad_budget_kiehl_trenberth_1997_big.gif

 

[Andre]

Imagine things would look like if the atmosphere was completely transparent. This would result in a very different world than the one on which we live. Surface temperatures would fluctuate much more than does ours because of the surface would receive the full brunt of the Sun at day and radiate to the darkness of space at night.

That's a very important -vital- observation; what if the atmosphere was unable to absorb and radiate electromagnetic energy?

Indeed the world would be very different, because these conditions would not inhibit convection at all, the hottest air in contact with the surface rising at daytime, heating the rest of the atmosphere, but it would inhibit atmosphere cooling down again at night since it cannot reradiate the convected energy at night.

The only way the atmosphere could lose it's added energy due to day time convection is by contact/conduction at the Earth surface, but that's only the boundary layer. The hotter air would stay aloft, since it's less dense.

 

[sophiecentaur]

That's a very important -vital- observation; what if the atmosphere was unable to absorb and radiate electromagnetic energy?

That wouldn't be a realistic scenario. Everything radiates and absorbs EM. Any object in space can be expected to reach equilibrium if its external conditions don't change (e.g. the nearest star is not blowing up or contracting). Its 'surface' temperature (or at least, its' effective, mean' surface temperature will be reached when the power gained is the power lost.

The nearest thing to your scenario would be 'no atmosphere', which is what you get on small objects like the moon. A much simpler system to analyse.

 

[the_emi_guy]

Want another layer of complexity?

According to recent research from the KamLAND antineutrino detector, about half of the Earth's heat is not absorbed from the Sun but self generated by radioactive decay.

 

[sophiecentaur]

Wow. As much as that?

 

[the_emi_guy]

Apparently we radiate 44terawatts into space, half of which is due to nuclear decay, the other half due to heat left over from Earth's formation. (still way less than what we absorb from the Sun, sorry my previous post was misleading).

http://newscenter.lbl.gov/news-releases/2011/07/17/kamland-geoneutrinos/

 

[haruspex]

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

Absorption and emission of EM is a very complicated subject. It always involves net accelerations of charge, but that can happen in many ways, imposing different constraints. Quantum mechanical considerations restrict many of these mechanisms to narrow bands of frequency, but which then are blurred e.g. by Doppler effects.
In the specific case of visible light and IR through N₂ and O₂, at atmospheric temperatures, the energy levels don't match up. That's why air is almost transparent. If only those gases were present then the mean surface temperature of the Earth, based only on radiation balance, would be about -18C.
CO₂ and H₂O have extra modes of vibration which allow for absorption and emission in the IR band. Even then, each only acts in specific ranges, so you can't just add up (in a weighted manner) the CO₂ and H₂O concentrations.

 

[sophiecentaur]

Apparently we radiate 44terawatts into space, half of which is due to nuclear decay, the other half due to heat left over from Earth's formation. (still way less than what we absorb from the Sun, sorry my previous post was misleading).

http://newscenter.lbl.gov/news-releases/2011/07/17/kamland-geoneutrinos/

Underfloor heating?? Haha I did wonder.

 

[Andre]

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

True, but it's not about realistic scenarios, it's about the null hypothesis, what if not...etc And I did not set it up, I merely reproduced it.

But what if some hypothetical planet had an atmosphere of non-radiative gasses only; or at least not in the EM spectrum of visible light and in the IR band that is consistent with the temperature range of the goldilocks zone like O2 and N2, then you might want to think about the one way temperature/energy transport only. Up by convection at day time, but not down or out during night time.

 

[Andre]

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

That's pretty much the result of Stefan Boltzmann only, assuming a grey body absorption in the case of a steady state uniformly distributed radiation balance.

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.

 

[haruspex]

it ignores energy transport via convection.

What would the temperature distribution be in the atmosphere if the gases neither absorbed nor emitted radiation?
Seems to me that the only convection that would arise would be from uneven distribution of radiation on the surface (latitudinal and temporal). The latitudinal component would help even out the surface temperature, thereby making the average -18C a slightly better approximation, and the diurnal component would be quite minimal, again tending to reduce the error in the approximation.
The upper atmosphere would settle at the same average, no?

 

[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.