Why does the stratosphere cool under GW?

How about this:

GHG's are emitted at or near ground level. They absorb heat radiated from the ground. The more they absorb, the less remains to heat the higher layers of atmosphere.

It's the first law of thermodynamics in action.

Nice. Let me try.

Question: All else being equal, the upper why does the upper atmosphere (the stratosphere) cool during "Global Warming"?

START TIMER

Answer: Increased Carbon Dioxide in the atmosphere makes both the lower atmosphere (troposphere) and the upper atmosphere (stratosphere) better able to both absorb AND dispel heat, but to different degrees. It turns out that the lower atmosphere gets MORE better at absorbing heat and the upper atmosphere gets MORE better at dispelling heat.

On balance, the whole atmosphere gets warmer, but the upper atmosphere ironically cools. Funny that.

STOP TIMER

16 seconds. And I don't feel that using the phrase "it turns out that" because, after all, you did not supply the calculus either!

Here's an even simpler explanation which will be easily understood by all but is probably fundamentally wrong and should be avoided (unless it's right, but I don't think it is):

Why does the top of the atmosphere cool when the total atmosphere heats up under global warming? It's a greenhouse effect! If you want your greenhouse to be WARMER, replace single pane glass with triple pane glass. Then, hold your hand on the outside of the greenhouse. It will be cooler to the touch!

[No; your explanation doesn't work. Because (a) "the upper atmosphere gets MORE better at dispelling heat" is just hand waving, if you don't mention ozone; and (b) your explanation would predict that a simple atmosphere with no stratosphere would cool at the top, and it doesn't -W]

I don't feel that using "It turns out" is bad (I shouldda said ... sorry, it's very windy here, some of the words get blown around as I type)

Indeed we have gone over this before - and just like last time, the UV absorption by ozone is irrelevant. To demonstrate that one only needs to see that the mesosphere (no UV absorption by ozone, decreasing temperature with altitude) is also cooling. The reason why is because the atmosphere is not grey - spectral absorption is the key.

Greg's explanation is half right. In the important CO2 bands absorptivity and emissivity increase with increasing CO2 (of course). But absorption in these bands depends very much on what is emitted from the troposphere in these bands and as CO2 increases, this goes down. Hence the increase in emissivity dominates the increase in absorptivity and the stratosphere (and mesosphere) cools.

Why is the important factor the spectral absorption? Because the net LW (at equilibrium) at the tropopause in a higher CO2 world doesn't change - and if the stratosphere absorbed at all wavelengths the increase in emissivity and absorptivity would mostly cancel out (though actually the increase in absorptivity would win).

So here is my elevator explanation:

The stratosphere is very dry and so the main long-wave absorber is CO2 (with some help from ozone). Increasing CO2 leads to increasing emissivity from the stratosphere and also the possibility of increased absorption in CO2 wavelengths coming from the troposphere. However, in the troposphere as CO2 increases, more of the radiation in CO2 bands is blocked (it is compensated for by an increase in LW radiation in other bands, very little of which is absorbed by the stratosphere). So in the key band - there is less coming up from below, and there is more being emitted, leading, inevitably, to a cooling.

=====

32 seconds (could be better I suppose....)

PS. I speak as someone who has publicly got this wrong more times than most

I gather other planets also have stratospheres (I see Venus, Jupiter and Saturn mentioned, browsing Scholar). Why?

[I don't know. Guessing, you end up with a layer higher up that absorbs some of the incident solar so is warmer than below, so is stratified. Wikipedia doesn't know, I see -W]

I struggled with this on a skeptical science thread on the topic, and came up with the following easy explanation, which I guess, as it's easy, is fundamentally wrong in some way.

START TIMER

In the stratosphere, radiative heat transfer dominates over convective.

UV absorption by O2 and O3 significantly heats the stratosphere

The stratosphere is cooled by radiative thermal emission, which CO2 takes a major role in.

More CO2 does NOT increase UV absorption, but DOES increase thermal emission.

Ergo, more CO2 = cooler stratosphere.

END TIMER

There is probably a grave error in this somewhere as far better qualified folk come up with more complicated answers.

Corrections would be most welcome

[That is essentially equivalent to mine. Unfortunately Gavin doesn't like it. Alas, I have to admit that Gavin normally knows what he is talking about and can often prove it. I'd advise a careful reading of his comment -W]

[Posted by me, during the Great Registration Failure]

I agree with Gavin that the spectrum is important, but I think SW heating by ozone is important too - or at least that it contributes something. You could get some cooling with either, depending on where ozone heating is relative to the effective skin layer for the grey gas case.

Time not determined:

1. In a grey (LW) gas, except in convecting portions, a net upward LW flux is required to balance the net downward SW flux, and this requires a temperature gradient *on the scale of the photon paths for LW radiation* that decreases with height (in global average effect)(temperature gradients can be locally reversed due to concentrations of SW radiative heating or cooling. Convection of course also requires a decrease in temperature with height of sufficient magnitude (ozone layers are not necessary to have a stratosphere; a stratosphere in a general sense can have a small positive lapse rate).

2. Increasing optical thickness shortens the photon paths and thus requires an increased temperature gradient. Due to heat capacity, particularly such as that of an ocean convectively coupled to a troposphere, a radiative disequilium at TOA can remain even after the upper atmosphere has equilibrated - thus, the upper atmopshere can approach a lower skin temperature than before (the temperature of a skin layer as determined by the OLR at equilibrium - in this case a 'transient equilibrium', pardon the oxymoron). So there can be trasient cooling in the uppermost atmosphere; at full equilbrium the OLR must be restored to balance solar heating, and so this transient cooling must disappear - so the temperature at TOA is the same as before, but the gradient below has increased (except for in the troposphere, and with regional/seasonal variations), and so at all other levels (generally) the temperature has increased.

3. If there is direct solar heating of the skin layer, then the equilibrium temperature is higher; increasing the optical thickness in LW decreases the thickness of the skin layer, effectively reducing the concentration of solar heating, allowing the skin layer to approach the skin temperature that it would have without direct solar heating.

4a. If the gas has constant optical thickness in a portion (an absorption band) of the LW spectrum and transparent outside it, then increasing the concentration of that gas will still result in warming at the surface and in the troposphere (they respond together because convective heating and cooling reacts to vertical distributions of radiative heating and cooling with a tendency to smooth the temperature response and keep the troposphere near a neutrally-stable lapse rate (generally), so long as pure radiative equilibrium would otherwise make it unstable; the whole convectively-coupled system responds to changes in fluxes at it's boundaries; geothermal and tidal heating, etc, being unimportant on Earth, for many purposes we only need the top boundary - the tropopause - and hence, references to tropopause-level radiative forcing).

4b. However, there is also the stratospheric cooling (or cooling somewhere near TOA)

There will be a transient cooling as the radiative flux from below has decreased, thus lowering the effective skin temperature (note that the skin temperature is now a function of the spectra of greenhouse gases, because of the way the Planck function varies over both wavelength and temperature).

However, as the surface and troposphere warm up, the surface, or any gases or clouds able to emit outside the LW absorption band of the forcing, can increase emission to space. So the OLR within the absorption band remains lower even in full equilibrium (some has been displaced to other parts of the spectrum), and so the temperature near TOA, while it may recover a bit, remains lower than before.

(PS as best I can recall, I think I saw this explanation given by Andy Lacis.)

4c.
But if a new absorption band is added, this can now absorb radiation at other wavelengths where the OLR brightness temperature is higher, and thus increase the skin temperature. The effect will increase up to a point, but then cooling will ensue again as more and more OLR is displaced from this new absorption band to other parts of the spectrum. Will the temperature at TOA be the same once the new band is as optically thick as the old band is? Actually it should be warmer (at least unless the old band was sufficiently saturated in the stratosphere), because some portion of the OLR that is being displaced from the new band may be filtering through the old one. However, it could be either warmer or cooler due to where the bands are in the spectrum - see part 5 - and note that, for the same OLR brightness temperature, the skin temperature determined by a band at shorter wavelengths will higher than it would be for a band at longer wavelengths - at vary long wavlengths I think would be be about half the OLR brightness temperature, while at sufficiently short wavelengths it may be close to the OLR brightness temperature - for a grey gas it's the OLR brightness temperature divided by the fourth root of 2. For well-mixed gases (at least up to heights sufficient to be effectively at TOA for the OLR for the optical thicknesses involved), the band with greatest optical thickness will have the greatest effect on skin temperature, other things (band width, spectral location) being equal.

4d.
For the important (in Earthly conditions) CO2 LW band, the optical thickness roughly halves per some spectral interval from the peak, so doubling CO2 effectively widens the band by that amount while increasing optical thickness at the peak.

Adding CO2 effectively adds new absorption bands while increasing optical thickness at existing absorption bands, so it's a mixed case; however, it can also be viewed as shifting existing bands a little over the spectrum (not much effect, except for the shape of the Planck function) and then inserting a new band that is more optically thick than the rest - bringint it up to such optical thickness, first we have some warming of the stratosphere as it is now absorbing OLR originating from the troposphere or surface, then some cooling as less radiation reaches up into the stratosphere from warmer levels below and more OLR is displaced to other parts of the spectrum - but some of that displaced OLR is found in the wings of the CO2 band - see 4c. above, but note that this new band will end up with greater opacity than the prior band of greatest opacity, and the absorptivity of the wings was already there, and the increased radiative heating from the increase in upward radiation from below is limited to where the the optical thickness is small enough to allow increased radiation from below to reach, and thus where the fraction absorbed will not be large. If warming occured due to increased LW heating in the CO2 wings, this would tend to be stronger in the lower stratosphere, and concievably there could still be cooling in the upper stratosphere from the additon of the most opaque band, which is the band that tends to shape skin temperature.

It is helpful to consider the shape of the absorption spectrum:

CO2 is, or is nearly, saturated near the band center at the tropopause. IF the OLR valley in the CO2 absorption band had a flat bottom, we could say the same at TOA. The depth of the valley in net LW flux at the tropopause is greater than the depth of the valley in OLR at TOA because the stratosphere is otherwise transparent in that part of the spectrum, so the OLR at TOA is the same as the net upward flux at the tropopause in the absence of CO2; meanwhile, CO2 can bring the net flux down to zero at the tropopause but can never cause such a complete elimination of OLR at TOA.

So the forcing from widenning the band (approximately equal to band widenning * depth of the valley being widenned) will be larger at the tropopause than at TOA - and the difference is a negative forcing on the stratosphere - causing a net cooling of the stratosphere (the stratosphere cools so that it emits that much less radiation to space or downward at the tropopause).

A portion of that stratospheric forcing may (depending on stratospheric optical thickness and where the cooling occurs) be transfered to the tropopause level forcing upon stratospheric cooling, thus reducing the warming of the troposphere and surface required for restoring balance - but there is still a positive tropopause level forcing to cause warming, and upon that warming (including effects of water vapor, clouds, lapse rate, snow and sea ice, etc, feedbacks), the stratosphere recieves more LW radiation from below and can warm up, but this is limited by the fraction of the increased LW flux from below that the stratosphere absorbs; if it is smaller than the initial stratospheric forcing then some overall stratospheric cooling will remain.

Given solar heating of the ozone layer, OLR actually has a little peak in the bottom of the valley which can grow with more CO2 (at least transiently, which is the forcing), so the forcing at TOA will be less and the stratospheric cooling greater. In the absence of direct solar heating of the upper atmosphere, the OLR valley would/might (potential complexities lurk) not be flat (because temperature would continue to decrease upward until effective TOA), and so the forcing at TOA could be more than it would be just from the band-widenning effect - but the OLR won't go to zero even after the increased CO2, so TOA forcing must still initially be less than tropopause-level forcing, so there is still stratospheric cooling, and some stratospheric cooling at full equilibrium could remain because of OLR displacement to where the stratosphere is transparent or nearly so.

Note that stratospheric cooling would be reduced more if positive feedbacks include increased solar heating of the surface or troposphere, but only according to the fraction of the necessary increase in OLR that must be emitted from the stratosphere (much will be emitted from below the stratosphere). Can water vapor feedback increase stratospheric cooling (and likewise reduce stratospheric warming from solar forcing)? The spectrum is a bit different and there's the issue of vertical distribution to consider.

5. Because of the shape of the Planck function, in a grey gas, in pure radiative equilibrium, there will be net radiant heating and cooling at different parts of the spectrum which balance. Adding optical thickness at particular parts of the spectrum may increase heating or cooling due to the Planck function's properties. PS while there is so little water vapor in the stratosphere that it would be transparent near the CO2 band were it not for CO2, there remains some optical thickness from water vapor elsewhere in the spectrum, and there is some from ozone as well.

Where there is already sufficient optical thickness in some parts of the spectrum, adding optical thickness where there is none will tend to warm the upper atmosphere by intercepting OLR - unless solar heating is sufficiently large, in which case there may be a cooling effect. Adding optical thickness where there is none will tend to warm the cooler layers and cool the warmer layers - if any are warmer than the brightness temperature of the average of the upward and downward fluxes at that point. Adding optical thickness where there is already a lot will tend to warm regions where the laspe rate decreases with height sufficiently rapidly with height (so that the optical thickness is not already too large over the spatial scales involved), and would tend to cool layers where the laspe rate increases sufficiently rapidly with height. The optical properties at different parts of the spectrum may be tugging on the temperature in different directions.

That's probably way longer than you wanted - if anyone can shorten it up and make it clearer, go ahead.

Had a contemplate of this overnight.

My summary of Gavinâs analysis is that in the troposphere under a higher CO2 concentration, the intensity of emission between CO2 bands is dependent on surface temperature, which rises. The intensity of emission in the CO2 bands must therefore fall (and the effective temperature falls and height of emission rises). The total energy radiated (at equilibrium at least) of course stays the same. The net effect is to reduce the potential for absorption of upwelling radiation in the stratosphere, as more of it is between CO2 bands. This causes the stratosphere to cool correspondingly.

So far, so good.

However, here is a thought experiment. What if Co2 in the troposphere stayed the same, but in the stratosphere alone rose. Under these conditions, upwelling radiation would be unchanged, but surely the stratosphere would still cool as itâs higher temperature would still mean net additional emissions in the CO2 bands.

So I reckon itâs a combination of both less upwelling radiation in the CO2 bands from the troposphere and more emission from the stratosphere â and further that the two are largely independent of each other.

Does this hold water?

My understanding (from reading "Principles of Planetary Climate" by Pierrehumbert) is that the troposphere is that part of the atmosphere where there is heat transported up by convection, and where the (normal) lapse rate is defined by radiative/convective equilibrium, and the stratosphere starts where you have a purely radiative equilibrium.

Chapters 3 and 4 go into more detail.

I understand that you still get a stratosphere in a uniformly grey atmosphere.

[I can see you'd get a stratosphere in a uniformly grey atmosphere, given a suitable incident solar forcing (or would you? Actually it seems a bit dubious. Don't you require nearly-100% absorption of UV high up? Where did you get that from?). I don't see why you'g get a stratosphere in an atmosphere grey in the LW but transparent in SW -W]

Couldn't it be because of water vapor? Higher temperatures in the troposphere would cause more evaporation, and water is a powerful greenhouse gas. But water vapor condenses out before it gets to the stratosphere (mostly).

William says: I can see you'd get a stratosphere in a uniformly grey atmosphere, given a suitable incident solar forcing (or would you? Actually it seems a bit dubious. Don't you require nearly-100% absorption of UV high up? Where did you get that from?). I don't see why you'g get a stratosphere in an atmosphere grey in the LW but transparent in SW.

Actually, I shouldn't have said uniformly grey. I actually do mean an atmosphere grey in LW and transparent in the SW.

Easiest case is the optically thin case. First, assume only radiative heat transfers. In this case, the atmosphere is heating from below by LW (because it is transparent in the SW). However, being optically thin means that very little of the LW is actually stopped. At equilibrium, the atmosphere receives the same energy as it emits. But it absorbs only from below, and emits both up and down. It therefore has an equilibrium temperature of 2^0.25 times less than the surface temperature. This is cooler than the surface. Hence, there will be heat flow by convection from the surface (contrary to the initial assumption), and a lapse rate with falling temperatures with altitude is established, from the warm surface up to the level where the "skin" temperature is reached (2^0.25 times less than the surface). That marks the end of the troposphere (and the end of convection) and the start of a stratified atmosphere (no convection) called the stratosphere.

[OK, yes, I think I believe this and I think my earlier picture was therefore wrong. Hmmm -W]

In the case where you have an optically thick atmosphere grey in LW and transparent in SW, you still have an atmosphere heated from below, and hence with temperature falling with altitude; but without convection it will still be a cooler atmosphere than the surface; and so there must be convection up from the surface UNTIL the point where the atmospheric profile defined by lapse rate intersects the weaker lapse rate for the purely radiative case. The intersection point, as before, is the tropopause; the boundary between a troposphere heated in part by convection, and a stratosphere where convention is negligible. This tends to be a sharp boundary.

The effects of oxygen and ozone are to allow some SW absorption, which alters the profiles of temperature; but that is an added complication; not a definition of what causes a stratosphere.

A stratosphere is simply the point where heat flow by convection ceases. Reference "Principle of Planetary Climate" as before. This is not a transcription, but my attempt to summarize. Errors are thus my own.

I have little useful to add, except:

(1) Any and all thought experiment arguments above are testable with an idealized 1-d radiative transfer model (not that I have the time to do so); and

(2) I think the phrase in paragraph 4 ("a though experiment") is absolutely marvelous and superior to the intended phrase. "This would happen" "Though if this other process dominates..." "Though if you change this aspect..."

correction to my comment # 6 (PS thanks for posting it)- at the end of the second-to-last paragraph in section 4d., refering to the increase in upward radiation at the tropopause that balances the forcing, to the fraction of that which is absorbed by the stratosphere:
if it is smaller than the initial stratospheric forcing then some overall stratospheric cooling will remain. - actually true for absorbed fraction of the final amount of increased upward radiation, the later being a bit larger due to feedback between that and the increased downward radiation from the stratospheric warming - some of which can be in water vapor and ozone bands.

Re 7 VeryTallGuy - If CO2 in the stratosphere is increased, that would not reduce the upward flux at the tropopause (a part of radiative forcing there) but it would increased the downward flux at the tropopause, which will have a warming effect on the surface and troposphere. It would also decrease the upward flux at TOA by blocking some radiation from below - depending on whether or not and how much and where solar heating occurs. It's less obvious that the TOA forcing would be less than the tropopause-level forcing.

The tropopause forcing is reduced relative to the same increase in CO2 everywhere, because the upward flux is unchanged; a portion of that difference filters through the wings of the CO2 band in the stratosphere and reaches space, so the TOA forcing is also reduced in some proportionate way (but what proportion?).

Anyway, the end result should tend toward some warming of the surface and troposphere and the OLR redistribution must result in some cooling of the stratosphere, or if not the whole stratosphere, the upper part of it (I think some lower portion could warm as the stratospheric CO2 band now juts outside the tropospheric band and can intercept greater fluxes from below).

Gavin's explanation is missing something, two things to be exact. First, the upper troposphere is also very dry, so the argument works as well for the upper troposphere as well as the stratosphere.

Second, the reason emission is high from the stratosphere is that the temperature is high (relatively) because of the ozone absorption.

So here is a go. Clock on
-------------------------
Greenhouse gas emission from the stratosphere is high because a. the temperature is high because of ozone UV absorption and b. because the atmosphere is thin, emitted IR light is not reabsorbed, but either exits to space or goes down into the troposphere.

The net result is if you increase the amount of CO2, cooling will be faster.
---------------------------

Clock off.

Caveat: increase it enough so that reabsorption is important and you have a different ballgame, but we will be too busy at the bottom to worry about that.

I don't know if the climate models allow for increasing methane concentrations, but in the real atmosphere some of the increased methane goes into the stratosphere where it is converted into water vapor, etc. Increased stratospheric water vapor should result in coling there.

neutrino

[The GCMs include methane but not usually methane chemistry (subject to correction on that). OTOH they tend not to have brilliant stratospheres, either -W]

So, hm -- does a stratosphere exist _because_ some component of the atmosphere can no longer remain liquid, so condenses, at that altitude? Water for Earth.

Scholar finds articles on stratospheres for Venus and the gas giants, and for Titan.

[I don't think so. Having been converted to the CHS way of thinking, I'd got for "stratospheres exist because the lapse rate means the convection line will eventually get below radiative equilibrium" -W]

Hurried observations by an amateur (probably equivalent to some others).

Raypierre's tiny explanation included e.g. here in his inline reply to this comment is the one which originally pleased me because it is easy to understand.

http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy…

The one in his book has become a bit more elaborate.

What interests me is why this argument is simpler than the one for the troposphere. Its because you can imagine a thin slice of the stratosphere to be partially isolated because of its internal heat source. You could imagine it to be surrounded by a 'one-way' substance which allows outgoing but not incoming infra-red.

Discussions of incoming infra-red are more or less irrelevant, because all we need to know is that changes in it are going to be swamped by changes in outgoing infra-red. The only significant way that this slice is connected to the outer world is via the incoming U.V. and the outgoing I.R. But if you start discussing feedbacks, would you have to add some words about the change in U.V. reflected from changing cloud tops or melting snow below the slice?

A thin slice of the troposphere cannot be understood by analagous local arguments because its source of heating is external I.R.

Correction: It should have ended with "external I.R. and convection".

The earth has a stratosphere because it has oxygen.

The chemistry of the Chapman cycle is

O2 + UV light (below 200 nm) --> O + O
O + O2 --> O3
O3 + UV light (below 300 nm) --> O + O2

In the last step the O3 dissociation heats up the middle stratosphere, leading to an inversion of temperature (why the O3 lands @ 25 km or so is also interesting) When there is an inversion (higher is hotter), there is no convection so the stratosphere is stratified with no rising or lowering flow.

Second thought about my #17.

The introduction of an imaginary one way substance, was unnecessary, which is good, because it would probably have yielded unphysical results if the internal heat source were to vanish.

Could someone apply their theoretical framework to explain the observed behaviour of stratospheric temperatures?

Clearly the most striking features are the two huge spikes caused by the El Chichon 1982 and Pinatubo 1991 eruptions. However it's also clear that the trend post-Pinatubo (1993-present) is effectively zero.

While looking for answers elsewhere I found this interesting paper, Forster 2011: http://folk.uio.no/gunnarmy/paper/forster_jgr_2011.pdf. It probably won't answer your 'why' question but it does demonstrate how well the theory (represented by climate models) matches observations. Quite well overall, with a few minor discrepancies.

In astronomy, we'd look at the problem like this. If there is only radiative transport (no convection), and absorption is independent of frequency (gray), and you have to carry a fixed flux of energy, then you must satisfy

flux ~ (temperature gradient) / (opacity)

If the opacity goes up (which implies that light is more likely to be absorbed), the temperature difference between the top and bottom of the atmosphere has to get larger.

This at minimum means that the difference in temperature between the bottom and top of the atmosphere must go up.

You actually have to solve the equations to know how much the bottom heats up and the top cools, but the basic reason why they respond differently is pretty straightforward.

If the person standing with you in the elevator is a climate scientist, these are GREAT explanations, each pointing out a subtle feature of the dynamics of the system, or an interesting way in which our thinking about this sort of thing has to be fine tuned. And, if I was on the elevator I'd never want to the elevator to stop, it is so fascinating.

However, I'm thinking of being on the elevator with, say, my brother-in-law the investment banker who hears that the stratosphere is cool, figures the stratosphere is a layer of the atmosphere rather than a kind of guitar (he does have a good college education, after all) and says "So, if global warming is real, how come the upper atmosphere is cool? That makes no sense!"

The explanation must not use any words that he hast look up. For example, IV, flux, emission, absorption and so on can't be used.

I know that is not the point of this conversation, but if we can't do that than this conversation is moot. In a very very bad way. Remember, my BIL is an investment banker. He and his ilk run this planet. The rest of us and our silly science are here at his pleasure.

[Your BIL may just be doomed. There are questions that can't be explained in an elevator, or without special words; and I think this is likely to be one -W]

Since Mars can be considered to have a stratosphere, O2 is not the answer. I'll have to go back over pages (approx.) 201--216 of Ray Pierrehumbert's "Principles of Planetary Climate"
http://geosci.uchicago.edu/~rtp1/PrinciplesPlanetaryClimate/index.html
again. [And no, I'm not taken with Gavin's expostion.]

[I'm already convinced by for example #10 which provides a clear explanation of why you end up with a stratosphere, even with no special absorption higher up -W]

My brother in law is not doomed! He just hears no explanation forthcoming and assume he was correct, that global warming is a hoax, because the stratosphere is cooling. Makes no difference to him!

[But that isn't what you said before. What you said before was that he heard an explanation, but he didn't understand it, or even some of the words in it.

Your unspoken continuation is (sorry): "and he is so arrogant that he assumes that if he can't understand it, it must be gobbledegook. He doesn't have the humility (being a high-pressure banker and all) to realise that there are difficult problems he won't immeadiately be able to understand, let alone solve" -W]

If the point is to understand the science, that is one thing. If the point is to make the science understood, then that is another thing. The requirement that in order for a concept like this to be explained to a lay person's satisfaction is that the lay person must become a specialist, the I assure you, it is the science that is doomed, not the investment banker.

Fox news says "Stratosphere is cooling, global warming therefore isn't real"

Investment banker turns to you and says "Aha! I knew it! Now I don't have to worry about global warming any more!"

And you're in an elevator. There has to be an answer. So far, I'm going with the triple glazed glass answer because I know it will work, and I'll feel a little bad about that because it is not scientifically perfect and only works at a metaphorical level (which it does). But I am a little surprised that this can't be improved on.

Greg, if that was the situation, why get into radiative transfer at all?

Stratospheric cooling at the same time as surface warming was predicted with the first 1-dimensional model published over 40 years ago - decades before the data came in and any trends could have been discerned. This is precisely how science gains credibility - observe, theorise, predict, confirm.

Metaphors, errors and approximations.

Re: #1, #24 and my #17 and #20

When the banker in the economic stratosphere says that there is less wealth in the economy so everyone lower down has to become poorer while he has to become richer he is using a metaphor for global cooling.*

When I took the smaller of two heating terms **, the external one, and set it equal to zero, I was making an approximation to the behaviour of an internally heated gas.

When you made the opposite assumption of neglecting the bigger term (as I did myself when I was even more of a beginner) you were describing a different mechanism not creating a metaphor.
--------------------
* Produced e.g. by Dyson's fiction of the carbon eating trees,
** Smaller because of the initial energy balance condition, in the presence of an internal heater.

Re my previous comment.

* A volcano; no need for trees.
http://www.nature.com/nature/journal/v301/n5899/abs/301406a0.html

Gavin: Stratospheric cooling at the same time as surface warming was predicted with the first 1-dimensional model published over 40 years ago

That is obviously not a description, but it is an excellent elevator answer!

Geoff: Now we are on to something.

"Think of the stratosphere as the top 10% of wealth and the troposphere as everyone else. Now consider the following adjustment in Capital Gains tax ...."

Yes, comment #10 by Chris Ho-Stuart is quite good.

Is this too simplistic or does it still grasp the essentials:

A stronger greenhouse effect causes more IR to be absorbed (below the stratosphere), so less reaches the stratosphere, which cools as a result.

[I think this might be true, but it isn't first-order obvious. Because "A stronger greenhouse effect causes more IR to be emitted" is also true, point by point. You can only find out which effect dominates by working it out, so that sentence alone is at best a clue to the right answer, not the answer itself -W]

See also http://climate-change.suite101.com/article.cfm/climate_change_basics:

âSince the heat gets trapped here [presumably the troposphere â red.] by greenhouse gases that absorb it, less heat travels outward to the stratosphere. Itâs as if radiated heat on the Earth is a dense collection of balloonsâif there are more balloons near the surface, there will be fewer balloons for higher up.â

[But "Since the heat gets trapped here [presumably the troposphere â red.] by greenhouse gases that absorb it, less heat travels outward to the stratosphere." is just wrong. Obviously, no? -W]

Article on upper atmospheric trends:
http://www.ann-geophys.net/26/1255/2008/angeo-26-1255-2008.pdf:

âIn the upper atmosphere, the radiative effects of greenhouse gases, particularly CO2, become more pronounced and produce a cooling, rather than a warming effect. At these altitudes, CO2 is optically thin and is unable to contain outgoing infrared radiation; thermal energy is transferred by collisions with ambient gas to the excited states of CO2 molecules and then lost to space via its infrared radiation.â

That would mean that more CO2 in the stratosphere enables more IR to be lost to space, as CO2 is the main route for heat loss for the s-sphere.

And there's http://www.atmosphere.mpg.de/enid/20c.html

I had a discussion about this topic on http://ourchangingclimate.wordpress.com/2008/07/15/half-truths/ but didn't get to fully grasp the simple explanations. So trying again here...

[But "Since the heat gets trapped here [presumably the troposphere â red.] by greenhouse gases that absorb it, less heat travels outward to the stratosphere." is just wrong. Obviously, no? -W]

Maybe I'm just being a little thick here, but I interpret it as follows: Enhanced GHG cause more IR to be radiated downwards (e.g. Philippona) and less to escape to space (e.g. Harries).

Since most IR absorption and re-radiation occurs in the troposphere (effective radiation level is about 5-6 km, right?), that makes the above statement correct I'd say: With enhanced GHG, less IR reaches the stratosphere from below.

re 13 Patrick027

I think everything you've written makes sense but you've taken it further than I had intended - I was only thinking about the instantaneous effect rather than the final equilibrium fluxes.

Either way I've convinced myself that there are two separate effects which cool the stratosphere:

1) More CO2 = more emissions at a given temperature; total heating (from UV absorption) is the same, therefore temperature falls.

2) Long wave at the top of the troposhere is redistributed to be relatively more between CO2 bands (as the surface temperature has risen and the atmosphere is transparent at these wavelengths). CO2 in the stratosphere therefore has less IR to absorb from the troposphere therefore the stratosphere cools.

3) These are only handwaving and the only real answer is that a line by line heat transfer code shows cooling (and of course that experimental data confirms this)

Re 31 VeryTallGuy - Yes - however, if you only increase CO2 in the stratosphere, the wings of the CO2 band can intercept more radiation from lower down in the warmer parts of the troposphere or from the surface (depending on H2O vapor, clouds), and so that could end up heating the stratosphere - but there could still be cooling in some upper portion of the stratosphere because OLR must ultimately increase outside the center of the CO2 band and thus decrease - if not in the wings or even intermediate portions, at least in the central part of the CO2 band (setting aside any SW feedbacks)

- another way to look at it is that increased greenhouse gas concentrations increase the ability for a given small volume to emit and absorb; the (instantaneous) temperature change depends on whether the (intensity of the) radiation (averaged over directions) in that location is effectively warmer or cooler than the temperature at that location (for the part of the spectrum being considered**)

** - for LTE, the net flux of radiation from point of emission to point of absorption is always from higher to lower temperature regardless of spectra, but, for example, considering a surface of temperature Ti between two other surfaces of temperatures Tc and Th, the brightness temperature of the average of the radiant fluxes from Tc and Th will vary over the spectrum and can cross Ti at some point.

Re Greg Laden - if you have more middle men, then they take a greater share of the profit of the overall transaction. The more greenhouse gas molecules, the more individual transactions are required for heat to get to space. The profit for the whole set-up has to be that much larger so that there is enough motivation for each individual transaction to occur at a given rate (analogy strained a bit from both sides, perhaps). They will transact faster when the temperature gradient is larger per each transaction.

When there is a competing pathway for fewer middle men (such as the atmospheric window, etc.), then the increased expense of shipping heat out the CO2 band will motivate an increase in the shipping of heat out other bands. Those other bands bypass the uppermost atmosphere to a large extent - the middle men don't hang around there as much, and they don't recieve as much of this heat.

Thus, as the middle men slow the shipping of heat out of the atmosphere, the supply builds up (being continually supplied by the 'solar industry' - no wait, don't use that one, don't want people to think that renewables cause global warming too), the alternative pathways take advantage and increase their shipping volumes, thus depriving the uppermost middle men of some of the heat, so their economic situation cools off.

(you might want to clean that up a bit)

Re Bart Verheggen - And there's http://www.atmosphere.mpg.de/enid/20c.html - a very helpful illustration. The radiant cooling rate increases and decreases upward following increasing and decreasing temperatures, other things being equal. Things that are not equal - when the opacity is large, radiant fluxes are reduced, ultimately tending to reduce radiant heating and cooling too. This happens last for the smallest-scale lapse rate variations (when opacity is larger, net radiant fluxes depend more on local temperature gradients - in that case, the flux changes following the change in the lapse rate, thus causing some divergence or convergence of the flux). It is also interesting to see how things change going across the opacity variations over the spectrum, and note differences when the same opacity occurs at different parts of the spectrum. The water vapor cooling pattern is greatly affected by the 'precipitous' decrease in concentration with height through the troposphere.

Re Greg Laden - ... that being for the case with no upper atmospheric direct solar heating; with solar heating, there being a limited number of shippers available, the heat builds up until the shippers find it convenient to ship the heat out at the same rate it is coming in; this in addition to the heat coming from below that must be shipped to space. More shippers will ship the direct solar heat heat out faster, having a cooling effect (the shippers are also middle men for the heat coming from below).

Re Bart Verheggen -
http://www.atmosphere.mpg.de/enid/20c.html
specifically fig. 3 -
so without CO2, the radiant cooling from water vapor would tend to be concentrated in a continuous band running across the spectrum going up and down; where it intersects the surface and lessens, there is more cooling at the surface itself. Where it goes higher, the opacity from H2O is thicker and reduces the radiant cooling below; the top of the band itself is a sort of 'TOA' for what you would see if water vapor were the only greenhouse agent (the band itself follows an effective emitting level, sort of a centroid of what you can see looking down), as it thins sufficiently with height that there is little left above. In it's absorption band, CO2 hides the water vapor from space; it concentrates radiant cooling higher up (and the brightness temperature of the resulting flux is reduced because the effective emitting level goes into a colder region). It would be more clear that greater opacity concentrates the layer that radiatively cools to space if the y axis were in pressure.

But it is interesting that at the center of the CO2 band, there is some net radiant warming near the tropopause; this makes sense because the larger opacity gives the local temperature gradient greater control over the net radiant flux, and the relatively sharp change in the lapse rate leads to a net flux convergence (note that in general, the lapse rate doesn't need to change sign - however, it is the curvature of the lapse rate in terms of the Planck function that matters, and this can change as a function of wavelength).

In the shorter wavelength wing of the CO2 band, there is a vertically broader region of some net radiant warming; this is centered within the lower stratosphere, which is relatively cold and able to recieve heat from lower in the troposphere due to the CO2 being less opaque there (the lack of such warming in the other wing, perhaps as well as the asymmetric distribution of warming at the tropopause level, could be due to greater H2O opacity on that side - or maybe also due to the shape of the Planck function - see below).

Ozone concentration increases going into the stratosphere and is within a region of minimal H2O vapor opacity, so the ozone band should be especially able to cause warming by absorbing radiation from relatively low in the troposhere and/or from the surface. It appears that ozone in the upper tropopshere is also being heated from the radiation from below. The warming extends higher into the stratosphere in the wings of the O3 band, which makes sense; the middle of the band may block the effect of the greater flux of radiation from the lower trosphere/surface from reaching higher. Meanwhile the warmer temperature of the upper stratosphere/lower mesosphere makes net radiant cooling more likely.

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It is also interesting that there is net radiant warming again for ozone and for the shorter-wavelength LW H2O band going up into the colder part of the mesosphere. This would happen if the band were sufficiently transparent to allow some of the greater flux from the warmer lower troposphere to filter through, or opaque enough for the radiation from the warmer upper stratosphere/lower mesosphere to be sufficient to overcome the net cooling from emission to space. Yet water vapor causes some net cooling throughout the upper atmosphere at longer wavelengths and there is no net warming in at the top of the figure anywhere from the CO2 wings to the CO2 band center (although there is a minimum in net cooling). For the CO2 wings, the opacity of tropospheric water vapor would take away from any warming, but if radiation from the upper stratosphere itself were the cause for the mesospheric warming in the ozone and shorter-wavelength water vapor bands, then somewhere within the CO2 band, opacity should be sufficient to allow emissions from near the stratopause to be warming the colder part of the mesosphere without being so large as to reduce the fluxes to near zero.

Another contributing factor is the shape of the Planck function. It is almost linear with temperature at the longest wavelengths, while it drops by very large percentages for small percentage declines in temperature at shorter wavelengths.

In terms of the Planck function, the lapse rate will be relatively smaller at longer wavelengths, perhaps allowing the effect of proximity to space to be a more dominant factor (in an isothermal case, net radiant cooling must involve emission to space, and this increases with height (for well mixed gases, setting aside variations in line strength and broadenning), being more concentrated toward TOA (other things being equal) when opacity is larger)), whereas at shorter wavelengths, a relatively small temperature minimum may cause a larger drop in emission and thus make net warming more likely (and a relatively small temperature maximum would lead to greater net cooling (?etc. for curvature of the lapse rate?)).

Of course, the Planck function also varies over wavelength, which would make net radiant warming or cooling values smaller toward the shortest and longest wavelengths.

Re my but if radiation from the upper stratosphere itself were the cause for the mesospheric warming in the ozone and shorter-wavelength water vapor bands,
intended as a hypothetical statement. While both have significant opacity in the stratosphere in some bands, the warmer upper stratosphere is thinner still; ozone concentration varies (it peaks somewhere below the stratopause); I don't think water vapor concentration varies a lot in the stratosphere but I'm not sure.

Re my but if radiation from the upper stratosphere itself were the cause for the mesospheric warming in the ozone and shorter-wavelength water vapor bands,
intended as a hypothetical statement. While both have significant opacity in the stratosphere in some bands, the warmer upper stratosphere is thinner still; ozone concentration varies (it peaks somewhere below the stratopause); I don't think water vapor concentration varies a lot in the stratosphere but I'm not sure.

There has been a large negative stratospheric air temperature anomaly over the Chukchi, East Siberian, and western Beaufort Seas from March to October since March 2007.

The NCEP/NCAR Reanalysis Composite Anomaly for 2000-06 and 2007-11 can be viewed here: http://i256.photobucket.com/albums/hh197/ktonine/potentialtemp2000s.jpg

What is the most likely reason for this regional stratospheric temperature anomaly?

Re Kevin O'Neill - I don't have any specific answers, but this may be helpful background information:

In a one-dimensional model (vertical extent of the atmosphere from the surface) radiative-convective equilibrium, a stratosphere forms where pure radiative equilibrium is not unstable to convection while convection is occuring where a convectively-maintained lapse rate sustains a vertical distribution of net radiant heating and cooling, which are balanced by a convective heat flux

(thermodynamics: there is a heat engine aspect where rising warmer air and cooler sinking air produce a net conversion of heat to kinetic energy (the most energy that can be converted via adiabatic circulation is called available potential energy (APE) and is the amount of energy converted to reach a state of zero horizontal temperature variation, loosely speaking**), which may either be converted back to heat and APE in 'thermally indirect' circulations, or dissipated viscously and converted to heat; for the purposes of balancing fluxes, the conversion from heat to kinetic energy in one location and the reverse conversion in another effectively acts like a convective (or advective) heat flux; but the kinetic energy budget for the climate system is relatively small compared to the heat budget).

In the full four-dimensional climate system, parts of the troposphere are stable to convection locally (but are still linked by the overall large-scale circulation (Hadley cells, monsoons, extratropical storm tracks, etc.) or may become unstable to moist convection, and there is some 'leakage' of mechanical energy (in the form of fluid mechanical waves - such as gravity waves and Rossby (vorticity) waves), that is produced by the tropospheric heat engine, into the upper atmosphere. This can and does drive thermally indirect circulations (such as Brewer-Dobson) there, acting as a heat pump or refrigerator (most obviously in the case of the summer polar upper mesosphere, which, so far as I know, is the the most naturally frigid place in the whole planet (see Holton, "An Introduction to Dynamic Meteorology", 1992, p.404), ) (the circulation also is important to the distribution of stratospheric ozone).

This thermally-indirect circulation keeps part of the winter hemisphere stratosphere warmer than otherwise. Sometimes (if not most of the time? I'm not clear on that point) this occurs in bursts called 'Sudden Stratospheric Warmings" - it happens when long-wavelength vorticity waves propagating from below attain a large amplitude and break (there is such a thing as 'surf' in the air!).

Long story short, my understanding is that the stratosphere is only approximately in radiative equilibrium in the global average (there is some net upward flux of work energy; I'm not sure but I think there may be a net downward forced-convective flux of heat), and regionally and seasonally there are significant deviations related to atmospheric circulation.

The response of the stratosphere to global warming or any climate change may also have some component that is due to changes in atmospheric circulation, though I'm unclear about which component this is (I may have a couple articles that explain it but I haven't gotten around to finishing reading them yet).

Let me first say that I am impressed with the explanations of stratospheric cooling (elevator pitch or otherwise) from each one of you here. It seems to me though that we are all trying to explain the same thing with different wording on how the stratosphere cools. Increase CO2 in a warm stratosphere will radiate more IR, and thus cool the stratosphere.

Incidentally, since it is warmer than either space or the troposphere, this should mean that a stratosphere with more GHG will not just cool more to space, but also (counter-intuitively) warm the troposphere by radiation, no ?

What I do not see is, specifically for the polar regions, what the effect of increased GHG (or ozone) is between winter and summer. In absence of SW warming, does the winter stratosphere get warmer with increased GHG, rather than cooler in summer ? And what is the difference between CO2 and ozone when looking at summer and winter stratospheric temperatures ?

[I have a third explanation coming along, based on some more comments I solicited. But I haven't read an understood the reply yet, so I'm not going to say more until I have -W]

Re 41 Rob Dekker - even increasing GHGs in a cold stratosphere will tend to warm the surface/troposphere, because without opacity in the stratosphere, there is only the dark of space.

Polar stratospheric winter - is warmer than local radiative equilibrium because of atmospheric circulation. From what I remember of graphs in IPCC AR4 WGI Ch9, I think pretty much the whole stratosphere cools from increased well-mixed GHGs. Actually, that's probably a good graph to check out for this discussion (latitude-height atmospheric cross sections). To what extent the distribution of cooling is due to direct radiative effects or circulation changes, I'm not sure. I think the patterns in the troposphere may be a bit easier to understand (if I'm not mistaken here) - positive albedo feedback at the surface at high latitudes in relatively stable air (although I read something else about that once...?), negative lapse rate feedback due to physics of moist convection manifests itself as the mid/upper 'tropospheric hot spot' at low latitudes.

Thanks Patrick,
That explanation makes sense (even in absense of SW, in polar winter, GHG in the stratosphere still cools). Let me take that thought one step further and quantify it :

In Arctic/Antarctic winter, if the stratosphere would be devoid of GHG, it would slowly warm up due to heat convecting from the 'warm' troposphere. But if the stratosphere would be laden with GHG, then at radiative equilibrium, this GHG will receive say X energy flux from below, and radiate 1/2 X back down, and 1/2 X to space. So the equilibrium temperature envelope should be 0.5^0.25 = 0.84 T where T would be the temperature of the tropopause (assuming that's where the radiative energy exchange overtakes convection).

Even though GHG does not cover the entire black-body IR spectrum, this means that at least the stratosphere's average temperature should fall (cool) in the presence of GHG's in the troposphere.
Note that this should be true for all well-mixed GHGs in the stratosphere, CO2 and methane and ozone alike, although each would have to be analyzed separately to quantify their effect, since (as Gavin points out) the spectrum on where they absorb (and their vertical concentration through the troposphere and atmosphere) matter.

In the summer, things may be a bit more complex.
Well-mixed GHG in the troposphere still would like to cool the stratosphere to 0.84 T, but since SW insolation heats up the stratosphere, through O O2 and O3 interaction, the cooling effect of GHGs should be stronger than in winter.

Also, the role of ozone is certainly interesting : ozone is not just a GHG and will act as a stratospheric cooler, but is an essential ingredient of stratospheric heating in summer. So it seems clear (and this is where I agree with William) that ozone IS important and it is not entirely clear up-front under which conditions ozone cools or warms the stratosphere.

Re Rob Dekker - generally upward radiation going into the stratosphere may originate anywhere from the surface to the tropopause; in bands where well-mixed greenhouse gases (example: CO2) dominate, if the upward radiation is coming from near the tropopause then the downward radiation will be from near the tropopause as well, but at less opaque parts of absorption bands, radiation can come from a a greather depth within the troposphere and be absorbed over a greather thickness of the stratosphere - as with the emission from the stratosphere. The skin temperature is not necessarily brightness temperature / (2^(1/4)) when the absorption spectra are at all colorful (not grey); if all absorption/emission were occuring at shorter wavelengths the skin temperature will be closer to the brightness temperature; if at the longest wavelengths, it may approach half the brightness temperature. Granted, the CO2 band is at an intermediate position in the spectrum for the temperatures involved; if it is near the peak in the spectrum (graphed over wavelength), then skin T ~= brightness temperature / (2^(1/5)) ; for a band near the peak when given in terms of frequency or photon energy, the denominator would be 2^(1/3); near the peak per unit log(wavelength or frequency), it would be 2^(1/4) - of course those formulas require the approximation that the skin and brightness temperatures are similar enough that their corresponding Planck functions's peaks are near each other so that the band involved can be near both.

Re 21 Paul S - I'm not sure about volcanic aerosols, but I wonder if it might be that, while having an overall cooling effect, they might cool the surface+troposphere more than their forcing at TOA - that is, perhaps they, like ozone, might add solar heating to the stratosphere. Otherwise, if they absorbed LW (terrestrial) radiation in bands where the stratosphere and upper troposphere were otherwise relatively transparent, they could intercept radiation with a higher brightness temperature such that they would absorb more than they would emit, thus having a warming effect. (PS if I'm not mistaken, volcanic aerosols, ozone depletion, and CO2 increase have some similar effects on atmospheric circulation in some aspect that concerns the stratosphere - maybe increased solar forcing too? - although I got the impression solar forcing would have a different effect from an article I half read a couple years ago (I really should get back to it...).)

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I was thinking about my first comment here and I think, in so far as the OLR-based arguments are concerned, I could simplify some of what I said:

When LW optical thickness (greenhouse effect) is added to a band - either in the troposphere, stratosphere, or both, but in any case, such that it reduces OLR and reduces the net flux at the tropopause level (with some of that forcing remaining, with the same sign, after stratospheric adjustment), then the OLR remains reduced until the troposphere and surface warm so as to restore it - if some fraction of that increased upward radiation at the tropopause level is in bands where the stratosphere is sufficiently transparent that it adds directly to OLR (as opposed to indirectly by heating the stratosphere causing it to emit more), then the OLR has increased in those bands, so absent SW feedbacks, the OLR must decrease elsewhere. Unless by some combination of factors (tropopause rising sufficiently so that it can be colder than previously, and a large opacity band in the troposphere with a transparent upper atmosphere in the same band) this decrease occurs in another location where the upper atmosphere is also transparent, then the decrease must occur in some bands where the atmsophere optically-near TOA would interact with it. Thus it reduces the skin temperature (where the thickness of the skin layer depends on the opacity of the upper atmosphere in thos bands). In other words, if OLR can be displaced overall from those bands which exert more infuence on the skin temperature to those which exert less, then there is a tendency toward cooling. However, this only addresses the skin layer(s), which, depending on optical thicknesses and their distribution (well-mixed vs __), may or may not include the whole stratosphere.

Note that adding CO2 only to the troposphere should cool the stratosphere overall; the upward flux at the tropopause is displaced from the CO2 band; some is added to where stratospheric water vapor or ozone can absorb it, but this is less than the amount removed from the CO2 band because some of it slips through stratospheric 'windows'.

Adding CO2 only to the stratosphere would cool some upper portion of the stratosphere but could result in warming of the lower stratosphere by absorbing radiation with larger brightness temperatures coming up at the outer edges of the CO2 band in the troposphere; it will warm the surface+troposphere by increasing the downward radiation from the stratosphere. The cooling effect can be enhanced where there is solar heating, depending on the position and optical thickness of such a layer (generally, if the solar-heated layer is already (optically) too far below TOA then farther increases in the greenhouse effect just bury it under a blanket).

Adding CO2 evenly doesn't (setting aside the shape of the Planck function, overlaps with other gases (tropospheric water vapor), and any bumpiness in the CO2 absorption spectrum (as opposed to fitting the approximation of halving optical thickness per unit spectral interval from the band peak)) by itself change fluxes through spectral intervals that are shifted following the band widenning, but the addition of a new central interval can instantaneously change the skin temperature among other things. The eventual surface+tropospheric warming increase OLR not just outside the CO2 band but also in some outer part of the band; there is a point where OLR is the same, within which it must remain lower (setting aside SW feedbacks), and so some layer of the atmosphere extending downward from TOA must cool, at least to a depth depending on where in the band the OLR remains reduced. Unless the tropopause itself cools (and by an amount depending on where it has migrated), the radiation going up into the stratosphere from below will be the same or increase, even at the CO2 band peak, so this could warm the lowermost stratosphere, but that may be a relatively thin layer(?).

Re Rob Dekker - on ozone: see http://www.atmosphere.mpg.de/enid/20c.html (fig. 3). The net effects for LW radiation would be found by integrating over the spectrum (see my comment 36 above, an attempt at explaining the features of that figure); there isn't any obvious disagreement with fig. 3.18 from Hartmann, "Global Physical Climatology", 1994, p.71 (the figure itself cites Manabe and Strickler 1964).

In this figure, the dominant net radiant effects are net radiant cooling of the troposphere, generally from 1 to 2 K/day in most of the troposphere, tapering off toward zero near the tropopause(balanced by convection, balanced by net radiant heating of the surface, which isn't shown) and no net radiant heating of the stratosphere, which to a rough first approximation is from a balance between net LW CO2 cooling and SW O3 heating (but the LW CO2 cooling is a bit smaller than SW O3 above ~ 25 or 30 km (eyeballing it) and larger below there; both increasing with height from near the tropopause to the highest level shown (2.3 mb, a bit above 40 km, perhaps ~ 7 km or so below the stratopause level).

There is LW cooling of the troposphere by H2O generally between 1 to 2 K/day tapering toward (but not reaching zero) near the tropopause (similar to the net radiant cooling but a little larger except near the surface; the LW cooling profile is lumpy, with a broad stretched out minimum region from near the surface to the mid-troposphere (~ 1.4 to 1.5 K/day, eyeballing it) and peaks at the surface (almost 2 K/day) and in the upper troposphere (~ 1.8 K/day, eyeballing it) - this structure may make more sense when looking at the spectrum in the link above. it reaches a minimim in the lower stratosphere (~1/6 K/day, eyeballing it) and then increases with height to ~ 1.25 K/day at 2.3 mb.

SW heating by H2O is a little above 0.5 K/day from the surface up through the mid troposphere, with a slight increase with height (because the upper H2O blocks solar radiation from reaching the lower H2O), then tapers toward near zero near the tropopause (because H2O concentration is decreasing with height through the troposphere), then increases slightly going up through the stratosphere (because less solar radiation in the bands that absorb it has been blocked, and H2O concentration doesn't drop with height as it does in the troposphere), reaching ~ 1/7 K/day (give or take) at 2.3 mb.

LW cooing by CO2 is ~ 0.7 K/day at the surface, decreasing to a minimum just below 0.5 K/day just above the surface, then increases again to just above 0.5 K/day a little above that; in the rest of the troposphere it decreases with height, slowly at first (perhaps stopping for a bit in the mid troposphere) and then more rapidly in the upper troposphere, reaching a minimum (sign uncertain) very near or maybe just below(?) the tropopause; it then increases again, getting larger than LW H2O cooling just below LW H2O cooling's minimum; it gets to 1 K/day somewhere around 25 km (eyeballing it) and increases more rapidly with height to a little less than 4 K/day at 2.3 mb.

CO2 SW heating is too small to discern in the graph until near the tropopause - it increases with height to ~ 0.3 to 0.4 K/day at 2.3 mb; it appears (in this figure) to be generally double stratospheric SW H2O warming except near the tropopause where the graph is harder to read (a few lines converge with small heating rates).

O3 LW cooling might be just larger than zero above the surface (there's a nonzero value there from something other than H2O or LW CO2; LW O3 is the only logical candidate for that); it is otherwise ~ 0 until a little bit below the tropopause, where it goes negative (net warming); it is larger than H2O, CO2, or O3 SW heating (individually) until a little bit above the tropopause where SW O3 heating overtakes it; it remains greater than SW CO2 and SW H2O heating (at least individually) up until just above it peaks at maybe a little less than ~ 0.4 K/day (a bit above 25 km); the net LW effect is still warming until a bit above 30 km, near 10 mb; it then turns to net cooling and increases to ~ 3/4 K/day at 2.3 mb.

SW heating by O3 is near zero until at or maybe a bit below the tropopause (hard to tell); it stays relatively small until near 20 km (where it is ~ 0.4 K/day); it increases more rapidly with height from near the tropopause up to 2.3 mb (**although it looks like this is interpolated over the last 15-20 km so I can't say from this graph that it doesn't actually peak at or below 2.3 mb, but it would make sense that the peak should be near the relative temperature maximum of the stratopause, which is above 2.3 mb); at 2.3 mb it is ~ 5.5 K/day.

PS diurnal temperature variations should tend to be larger (other things being equal) where the SW heating rates are larger; from this graph one would then expect a minimum in the diurnal temperature range from the tropopause into the lowest part of the stratosphere, and relative small diurnal temperature ranges from above the the boundary layer up to somewhere within the stratosphere. (Assuming a 10 cm effective penetration depth for diurnal temperature variations and a heat capacity ~ 2000 J/(K*L) (see p. 85 of Hartmann), that's an effective heat capacity of 0.2 MJ/(K*m2); if surface solar heating ~(roughly) 120 W/m2, given 86400 s/day, that's ~ (rounding) 10 MJ/m2 per day; together this suggests a surface SW heating rate of ~ 50 K/day (land! - bare soil?). Of course, the boundary layer's heat capacity should really be included in this (on the order of 1 MJ/(K*m2), but varies; so the effective SW heating rate would be ~ 8 K/day, give or take).

Unless the tropopause itself cools (and by an amount depending on where it has migrated), - the shifting of the tropopause height and tropopause temperature themselves would depend on (for a given surface warming) lapse rate feedback and stratospheric changes.

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(generally, if the solar-heated layer is already (optically) too far below TOA then farther increases in the greenhouse effect just bury it under a blanket).

Another way to look at something:

For a given LW band, If there is some flux of heat in or out of a mass of air that is either non radiative, SW (solar), or at other LW bands, then at equilibrium, the difference must be made up for by a difference between emission and absorption rates per unit mass in that band. Increasing optical thickness in that band would by itself increase the emission and absorption rates by the same proportion (assuming constant temperature and incident fluxes), thus increasing the difference. So in order to balance the same net heating or cooling at other parts of the spectrum or by convection, etc, the temperature would change to bring emission closer to absorption - this brings the temperature closer to whatever equilibrium would be determined at that band alone.

However, this only generalizes to changing optical thickness of just a small parcel of air such that the incident flux from the environment are relatively unaffected by either the change in optical thickness or the changes in temperature of surroundings in response to changes in fluxes from and through that parcel of air. If the temperature generally decreases coming toward the parcel (over sufficient optical thickness), the effect of increasing optical thickness at other locations in the same way would decrease incident fluxes and at least the instantaneous effect would be to enhance cooling or reduce warming; however, if the air above is sufficiently optically thin, then increasing optical thickness will increase the downward flux even if temperature increases with height, thus reducing cooling or enhancing warming (at least instantaneously; additional effects are from temperature changes occuring elsewhere altering the incident radiant fluxes at that parcel, aside from changes in circulation, etc.).

(PS if a portion of the LW opacity were from scattering then some of the upward radiation from warmer layers below would locally come from above and some portion of the darkness of space, if visible, could be seen below).

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Net fluxes from warm layers to cool layers are greatest when the opacity of each layer is significant but the opacity in between is not too large; if temperature followed a sinusoidal profile, setting aside boundaries (surface, space), the net fluxes would peak near where the slopes are largest; they would be small for small opacity because each individual hill and valley in T would be nearly invisible and the radiant intensities would tend toward a some wavelength-averaged value of the Planck function. The net fluxes would peak when the optical thickness over a half wavelength is on the order of 1 (I won't bother finding the precise value). At larger opacities the net fluxes would decrease toward zero as the radiant intensities tend toward local Planck function values.

Once the center of the CO2 band is saturated (with respect to a given location and distance scale, layer thickness, or temperature profile), the band widenning leaves the intervals of intermediate opacity at roughly the same size, so setting aside bumpy details of the absorption spectrum, the shape of the Planck function, and any spectral overlaps, farther increases in CO2 wouldn't directly change the net cooling of a warm layer of air in that case (this includes the surface and space - the layer of air would absorb the same flux from the surface and emit the same flux to the surface, and would emit the same flux to space; note that CO2 can't be saturated in this context if the layer of air is too close to the surface or space). From see http://www.atmosphere.mpg.de/enid/20c.html (fig. 3), it looks like CO2 is not saturated in this way in the ozone layer or in general in the stratosphere; radiant cooling is maximum near the center of the band, rather than falling back to near zero (exception near the tropopause, but that's due to a sharp curvature in the temperature profile causing net LW heating where opacity allows it, so it isn't saturated there at least with respect to the distance scale of that temperature profile feature). Thus increasing CO2 should, via band widenning, increase the cooling.

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Interestingly there is also net LW CO2 cooling higher up; it decreases toward a minimum (still siginficant cooling) just below the 0.1 mb level, then it increases again with height. This is actually way below the mesopause, so presumably the cooling is increasing with height due to getting closer to TOA. (It also starts to increase with height below 0.1 mb within the long-wavelength H2O band, but within the domain of the figure, this increase isn't found at other wavelengths except around 1300 to 1400 cm-1 and also maybe in part of the ozone band (it's hard to tell), (and one other place that I think was > 1500 cm-1 but I have the website closed now so ?)).

But the colder upper mesosphere is still generally warmer than it would be without direct solar heating of the upper atmosphere - (because of indirect heating from the ozone layer and maybe, at very high levels, from the thermosphere? (or is it only the lower thermosphere that is heated by the upper thermosphere?) - see fig. 10 of
"The HAMMONIA Chemistry Climate Model: Sensitivity of the Mesopause Region to the 11-Year Solar Cycle and CO2 Doubling",
H. SCHMID et al.,
Thttp://journals.ametsoc.org/doi/pdf/10.1175/JCLI3829.1 - (if you want, see fig. 7 for H2O distribution up there) - PS a lot of info there, I've only gone through a drop in the bucket). Keep in mind the stratopause is around 1 mb, give or take (1 mb = 1 hPa), the mesopause is around 0.001 mb, give or take, and the tropopause is around 100 mb in low latitudes and lower (higher pressures) at higher latitudes (Holton, "An Introduction to Dynamic Meteorology", 1992, p.404) - from Hartmann, "Global Physical Climatology", (I think 1994), fig 3.17 (also cites Manabe and Strickler 1964), the temperature without ozone (but note that that presumably includes removal of LW ozone effects) is down to ~ 153 or 154 K at 2.3 mb; the existing mesopause (even higher up) doesn't get that cold except at summer latitudes > ~ 55 or 57 deg (rough semi-eyeballing it) (Holton, p.404).

Interestingly the difference between just H2O and H2O+CO2 is a warming everywhere shown (from 1000 mb (surface) to 2.3 mb), of ~ 10 K, but less in the lower stratosphere. If Manabe and Strickler 1964 is correct, then adding (an amount similar to the present amount?) of CO2 (to an atmosphere with no CO2 and no ozone) warms the stratosphere; but that doesn't mean that additional amounts wouldn't cool it, or part of it, even without solar heating of the upper atmosphere (initially adding a little CO2 allows absorption of radiation from below with higher brightness temperature due to not being in those parts of the spectrum where H2O is more opaque; setting aside Planck function shape, that would tend to have a warming effect). As the CO2 band widens with increasing CO2, with each addition (thus refering to forcing, which can be different then the ongoing effect after equilibration)
...
I'm guessing (running out of time now so I'm going quickly; error risk increases) the general tendency should be for a net LW warming in the CO2 wings to shift outward from the center, with some net LW cooling eventually developing in the center of the band at some height as the upward flux from below is reduced; this then gets more concentrated toward TOA as net fluxes below TOA fall toward zero while the flux at TOA has to be nonzero as long as the temperature is nonzero - note this implies a warming effect below the cooling effect as the net flux falls to near zero above the level where the net flux has already fallen to near zero. So...
... meanwhile, after equilibration presumably there remains net warming in the CO2 band wings because the temperature doesn't equilibrate fully to just the fluxes in those wings. But a sufficiently thin skin layer will be dominated by CO2 alone once the center of the band has sufficiently larger opacity than any other gas in any other part of the spectrum, so, integrated over a sufficient width about the band center, the temperature will respond so that the net LW cooling or warming would tend toward zero.
(... end hurried portion of comment...)

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I should note that figs 3.17 and 3.18 (citered earler) of Hartmann, and also , I would guess, fig 3 of http://www.atmosphere.mpg.de/enid/20c.html, are for clear skies (no clouds). Clouds would reduce the spectral variation in upward flux at the tropopause because they partly fill in the atmospheric window - so the stratospheric warming from adding a small amount of CO2 when none was there would be reduced (other things being equal) - however, clouds don't eliminate this spectral variation (they would if there were global thick cirrus cloud cover at the tropopause level). Clouds would also alter the temperature (cooling effect from SW effects dominate, at least going from no clouds to the clouds we have; since OLR would be reduced I'm guessing the stratosphere would also be colder from that effect, although less than otherwise since some CO2 and H2O is above some of the clouds).

It would be interesting to consider what cloud feedback does to the stratosphere.

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PS I had wondered why stratospheric cooling from well mixed GHGs would be greater at high latitudes (see http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch9s9-2-2.html) - but a closer look reveals that going up toward higher levels where SW heating is greater, the cooling effect generally decreases toward higher latitudes out to about 45 or 60 deg latitude, before increasing again. Lower in the troposphere, the pattern of cooling and warming seems like it may follow the latitudinal variation in tropopause height, so to some extent one could say that cooling just increases going up from near the tropopause where it must be near zero (since the troposphere is warming) (well, actually one could at least hypothetically have cooling down to where the new tropopause level is; anyway the height of the tropopause varies with weather and seasons and meridionally so it's not going to be a sharp feature in such a graph anyway) - and then the tropopause slope shapes the changes in horizontal temperature gradients; however, that isn't the whole story; in particular, there is a bit of an 'overhang' in the maximum in warming/minimum in cooling near 100 mb in the lower southern midlatitudes and the northern high latitudes, just below which cooling decreases with height.

To the extent that surface and tropospheric warming do warm the stratosphere, it should tend to warm the lower stratosphere more and be greater when that tropospheric or surface warming is closer to the tropopause. The initial tropopause-level forcing itself is smaller at higher latitudes at least in part because (as far as reduction of upward radiation from below is concerned) of the smaller temperature decline from the surface to the tropopause (the reduction in upward radiation from increased CO2 should be largest where the lapse rate is large, the tropopause is high, and there are few clouds - especially high clouds - and low humidity - thus, the subtropics, I think).

And maybe the convection-caused warming in higher polar latitudes can play the role of solar heating elsewhere in terms of enhancing the ability of GHG's to cause cooling. There is upward motion in the lower tropical stratosphere which would cause cooling, which by the same logic could tend to reduce GHG-caused cooling there.

Meanwhile, at colder temperatures a larger temperature change is required to cause the same change in emission (but colder temperatures also reduce the forcing that can occur, other things being equal).

Of course changes in circulation can also affect the distribution of warming/cooling.

--------

PS Fig. 3.16 from Hartmann - (also citing Manabe and Strickler 1964) - shows that switching from pure radiative equilibrium to radiative-convective equilibrium results in some stratospheric cooling above some height in the lower stratosphere; the lower part of the stratosphere warms. The switch cools the surface and lowermost troposphere and warms the rest of the troposphere; this can shift OLR from the atmospheric window to where absorption bands are found. The lower stratosphere could warm due to absorbing greater radiative fluxes from the warmer middle and upper troposphere. Interestingly, switching from a dry convective lapse rate to 6.5 K/km convective lapse rate has relatively little effect on the stratosphere above ~ 22 km and has a warming effect below that; there is a smaller surface temperature change involved in that switch and - maybe that's why? (Also, the tropopause level gets higher, so upper tropospheric warming is closer to any given stratospheric level.) Meanwhile, the lower tropospheric cooling (going from 9.8 K/km to 6.5 K/km tropospheric lapse rate) extends up higher than in the switch from pure radiative equilibrium to either radiative-convective equilibrium.

Wow that took way longer than I thought it would. I'm taking a break for awhile (moderators rejoice?)...

I'm taking a break for awhile - oops, except for this: meanwhile, after equilibration presumably there remains net warming in the CO2 band wings because the temperature doesn't equilibrate fully to just the fluxes in those wings.

Yes, but (and distinguishing between ongoing cooling/heating at equilibrium vs forcing)-

when the same optical thickness values are shifted out from the center of the CO2 band, initially the net LW heating or cooling should stay about the same (setting aside running into varying overlaps with (tropospheric) H2O, and variation in the Planck function). But whatever the newly inserted interval of larger opacity (the new band center, the interval with higher opacity values than were previously found) does (combined with temperature responses elsewhere and H2O, O3, etc, feedbacks), the temperature response will tend to change the net LW heating or cooling on the wings. So for example, if the net LW heating or cooling is of the same sign in the center as in the wings, then, nonlocal effects aside, there would be a temperature response that would then reduce that net LW heating or cooling. If the CO2 band were the only absorption band in the stratosphere, then in equilibrium the net LW heating/cooling could not be the same sign everywhere in the band - it has to be a balance between heating and cooling (in the approximation of LW radiative equilibrium). Assuming it changes sign between the wings and the center, adding more CO2 would then tend to exert local forcing with the same sign as the center, thus pulling the temperature in a direction away from where the wings would have it, thus increasing the net cooling or heating of the wings. Nonlocal effect (well one of them?): the concentration of upward flux from the warmed surface+troposphere outside the band tends to (but maybe depending on spectral variability of H2O feedback and the OLR response to that, etc.) filter into some part of the wings, and expansion of the wings into that increased upward flux from below means the wings will have greater warming effect after each addition of CO2.

But CO2 is not the only LW band in the stratosphere; the longer-wavelength H2O band (fig 3 of http://www.atmosphere.mpg.de/enid/20c.html) contributes cooling; absent other bands and absent solar heating, the CO2 band would tend**(?) to contribute warming and would not be self-balanced at any given vertical level (the center and the wings could still have opposite signs, though - or not).

** based on the Planck function - other things being equal (and they probably won't be) the same optical thickness at longer wavelengths would tend to hold a smaller equilibrium temperature relative to the brightness temperature of the incident flux (from below) - thus the longer wavelength H2O band will tend to pull the stratosphere toward cooler temperatures and the CO2 band would have to pull in the opposite direction at equilibrium. In addition to that, for the same stratospheric optical thicknessess of H2O and CO2, there is more H2O opacity in the lower troposphere, so the upward flux will be reduced farther in the H2O bands.

However, without solar heating, the reduced temperature may mean that the shorter-wavelength H2O band would contribute net heating. *If* the H2O bands self-balanced then the CO2 band would also self-balance when at equilibrium (absent other bands). It isn't so obvious that CO2 could come to completely dominate in determining the temperature just by adding more and more relative to H2O because at some point the center of the band will (at any given level, for some amount) saturate in it's effect, and adding more does nothing (directly locally; indirectly/nonlocally still increases OLR outside the band) as it will then be the intermediate-opacity interval with the greatest influence; one has to have a sufficiently optically thin amount of H2O for CO2 to reach a given level of dominance before saturation occurs - thus, thinner layers (closer to TOA).

with some net LW cooling eventually developing in the center of the band at some height as the upward flux from below is reduced; this then gets more concentrated toward TOA as net fluxes below TOA fall toward zero while the flux at TOA has to be nonzero as long as the temperature is nonzero - note this implies a warming effect below the cooling effect as the net flux falls to near zero above the level where the net flux has already fallen to near zero. So... - well no, actually, in the perspective of following the same opacity values as they shift outward from the center, what is happening in net is that stratospheric window outside the band (where there is no net heating or cooling and the net flux is constant with height) is being replaced by the widenning band center - which might have net heating below some level or not; it will tend to have net cooling (forcing) sufficiently near TOA because if the temperature was previously held in equilibrium at smaller optical thicknessess, the upward flux within the new center will be too small to maintain the same equilibrium. (Also in this perspective (that we are swapping stratospheric or atmospheric window for additional band center width), the shifting outward of the wings has no forcing except for the shape of the Planck function and changing spectral overlaps (and irregularities in the absorption spectrum shape); it is the additional center which is the major concern in the forcing).

So maybe after adding some CO2 warms the stratosphere (when it was previously just H2O) via intercepting what was relatively higher brightness temperature OLR, that warming reduces the ongoing net warming in the wings, so the next additional band center has less local warming forcing than otherwise since it is already warmer (but somewhat counteracted by the increased upward flux from below that filters through the band); at some point the reduced upward flux from below may allow the next additional amount to have a cooling effect, if saturation doesn't happen first. Does this ever cool the whole stratosphere or just some upper portion? Eventually I'm thinking it would only cool the upper stratosphere as the effects in the lower stratosphere are saturated (except for some part of the wings, which will heat up a little by intercepting some fraction of the increasingly concentrated upward flux from below).

PS stratospheric feedbacks may include H2O feedback and O3 feedback from temperature changes, circulation changes, and also maybe H2O and O3 feedback from those circulation changes.

Okay now I'm done.

Yet another way to say something:

On the spatial scale of photon paths, if the lapse rate - in terms of the Planck function - is convex or concave, there is a tendency for net radiant cooling or heating.

- depending on the temperature profile, the lapse rate expressed in terms of the Planck function may vary from being convex to linear to concave over the spectrum

- when optical thickness increases, the scale of photon paths shrinks. For pure radiative equilibrium in a particular band, the temperature is such that the Planck function lapse rate is linear - at TOA there is generally a drop off to near zero (space) but on a particular spatial scale it is effectively linear between TOA and space (via the skin temperature). For the same temperature and band, shrinking the spatial scale makes the Planck fuction at TOA convex (whereas at sufficient depth within the atmosphere it must still be linear (assuming the relative distribution of optical thickness is held constant), just with a smaller gradient relative to optical thickness) - so there is a cooling tendency at/near TOA.

Of course for a grey gas (LW, with all SW heating sufficiently far below TOA, and zero SW feedbacks), once complete radiative equilibrium is restored, warming below will restore the skin temperature, but otherwise some fraction of the restoration of OLR can bypass the band(s?) where the change was made (at least if the change was made at the optically-thickest bands, which tend to dominate in the skin layer) and leave some uppermost portion of the atmosphere colder (but not as cold as immediately after the change, assuming a quick radiative relaxation time of the upper air and relatively large heat capacity in part of the system below).

---

(not really pertinent to stratospheric cooling, but does the discontinuity at the surface lead to a similar issue (in the absence of convection)? Assuming zero LW albedo at the surface (and no scattering in the atmosphere - or else the same single-scatter albedo for both?), one can just graph the surface as if it were an effectively infinitely thick lower part of the atmosphere. But scaled that way, the lapse rate will go to near zero because conduction is so effective over millimeters in a solid or liquid, and we aren't (in this context) changing the optical thickness of this layer anyway.)

(PS I remember going through some of this a year or more ago and I thought there was some issue with the fact that photons are going in all directions - so that the radiative equilibrium lapse rate will be a bit larger than if radiation with the same flux/area were purely vertical - and also adding some complexity to how to deal with the surface and TOA. ...
It even occured to me that there could be a 'skin layer catastrophe' with the skin layer having a skin of it's own where the temperature is determined largely by the OLR intensity at angles near horizontal, where the original skin layer may be optically thick - and then that skin would have another skin determined by an even smaller ranges of directions closer to horizontal, etc. Maybe there's a flaw in that reasoning, though? Or otherwise, perhaps the curvature of the planets, the eventual loss of LTE and the rise of importance of molecular diffusion in the uppermost atmosphere render this moot?)

_________

This is a more subtle thing that doesn't pertain to the basic 1-dimensional model, but:

Given that CO2 is not so saturated even in the center of it's band that net LW cooling (to balance SW heating and effects of other LW bands) peaks in the center of the band or doesn't fall back to near zero through most of the stratosphere (going from memory from that fig 3 of http://www.atmosphere.mpg.de/enid/20c.html), maybe increasing CO2 would also decrease the radiative relaxation time for perturbations from convection (the rate at which APE perturbations, created by KE, are diabatically destroyed by radiation (a.k.a. thermal damping)) - such as from the various fluid-mechanical waves that drive motions in the upper atmosphere. H2O feedback in the stratosphere could do something too. (And even if CO2 were saturated in the center of the band (note that band widenning, aside from Planck function shape, spectral overlaps, and bumpiness in the real absorption spectrum, would not change radiative relaxation time in this context if the center is too optically thick) for some spatial scales, waves with smaller vertical wavelengths (so that there isn't saturation) could be affected). On the other hand, overall colder conditions would increase the radiative relaxation time. Wonder what that would do.
(Absorption of waves can 'freeze in' the redistribution of PV, so that the changes in wave-averaged circulation become permanent (until something else happens) - however, when this happens by thermal damping (setting aside mechanical (viscous) damping), the PV distribution should tend toward a less-perturbed state, which I would guess (emphasizing that I'm not an expert on this) would reduce the effect, relative to if it happens by wave breaking (but it can't cancel it, because I (think I)know that the QBO is driven via wave-damping rather than wave breaking - but maybe the combination of viscous and radiant damping does something else?))

Corrections/clarifications:
which I would guess (emphasizing that I'm not an expert on this) would reduce the effect, relative to if it happens by wave breaking (but it can't cancel it, because I (think I)know that the QBO is driven via wave-damping rather than wave breaking - but maybe the combination of viscous and radiant damping does something else?)

Maybe there's a difference between ageostrophic waves ((inertio-)gravity, Kelvin, etc.) and quasigeostrophic waves (Rossby/vorticity/planetary) in that regard, but the resulting steady circulation must be quasigeostrophic or gradient wind balance or balanced in some way ...
(and for zonal winds, it should tend to be quasigeostrophic even near the equator, right? (As I recall, at the equator the thermal wind shear is related to the curvature of the temperature) - however, smaller temperature gradients support larger thermal wind shears going near the equator, so there would be less of a thermal anomaly involved in a given velocity anomaly.)
... and so something like PV invertability should be applicable, right? (Note to self to review chapters 10-12 of Holton sometime) (While vertical vorticity wave propagation involves a rearrangment of PV in each isentropic surface/layer, which is then reversed when wave activity propagates away, perhaps the absorption of gravity waves into a layer itself changes the PV of a given parcel through the damping processes in such as to support the changed steady motions, whereas non-absorption doesn't ...? Will have to set aside time to figure that one out.)

It even occured to me that there could be a 'skin layer catastrophe'
Oops, nevermind (I was thinking about how the absorptivity of an infinite horizontal layer will tend to aproach 1 going toward horizontal directions even if absorptivity is near zero everywhere else. However, it helps to consider individual molecules, which are (generally/time-population averaged) just as able to absorb photons from any direction, and most directions are not infinitesimally close to horizontal, etc.)

For pure radiative equilibrium in a particular band, the temperature is such that the Planck function lapse rate is linear

to clarify:

Deep within an opaque expanse with constant net upward LW flux, this will be true (with vertical distance in terms of optical thickness). The constant (in terms of the Planck function) lapse rate (PFLR for short) leads to anisotropy where the radiant intensity varies smoothly between a minimum from straight upward and a maximum straight downward. It approaches an intermediate value at horizontal directions because a larger optical thickness is required to cover the same vertical distance.

This would remain true at TOA and the surface if PFLR remained constant going into space and into the surface material - hypothetically the later could happen but in more familiar conditions the opacity is so large for a thin layer (through which heat may be conducted) that PFLR could be near zero in the surface material. With an isothermal surface with the same temperature as the air in contact with it, keeping the same PFLR in the air, the upward flux is less than it otherwise would be (if the surface material got hotter going down into it over only a moderate optical depth). Space in this context can be thought of as a blackbody approximately at zero K - in order to continue the same PFLR into space with the downward flux at TOA being zero, the Plank function has to become negative past some point in order for negative radiant intensity straight downward at TOA to balance the positive radiant intensity from angles closer to horizontal (this would require some interesting temperatures - for a grey gas, T would be proportional to i+1).

So with space and the surface being isothermal, to keep the same net fluxes, the Planck function profile has to be discontinuous there - the surface temperature has to be warmer and space at TOA has to be colder (it's zero K). At the surface this increases the upward flux. But the upward intensity is constant (for a perfect blackbody surface) over all upward directions - thus it is still smaller closer to vertical but larger closer to horizontal than it would be with constant PFLR; since radiation at greater angles from vertical is aborbed over shorter vertical disances, this would cause heating of the air just above the surface and cooling some distance above (probably on the order of a unit optical thickness). Thus equilibrium requires temperatures higher and then lower than the profile for a constant PFLR going up from the surface. By the same reasoning the temperatures near TOA must decrease close to TOA and increase some distance below TOA. These perturbations produce additional heating and cooling effects in their optical neighborhoods, so the equilibrium effects will be spread out and partly cancel each other to a larger extent than otherwise; still the Planck function profile (PFP for short) would end up being concave near the surface, convex near TOA, and have a smaller slope in between (it would seem odd for multiple oscillations to occur, so I'm assuming the magnitude in the curvature in PFP would decrease away from either boundary and approach zero in between). The discontinuities would still remain at TOA (considering the reasoning for skin temperature) and at the surface (similar reasoning as for skin temperature). The smaller PFLR would support a smaller net upward LW flux between atmospheric emission and absorption, but this would then be supplemented by contributions from the surface and space - as optical thickness increases, those contributions would approach zero in the middle of the atmosphere and then over larger thicknesses, while PFLR would approach a value where the net flux is supported entirely by the local PFLR, and the regions of the atmosphere which deviate from constant PFLR would get thinner. In the other direction (decreasing optical thickness), the atmosphere would eventually tend towards being isothermal at the skin temperature, with the net flux being mainly emission from the surface to space.

The explanations continue:

http://itsnotnova.wordpress.com/2012/01/31/hot-spot-the-difference/#mor…

which points to:

http://www.atmosphere.mpg.de/enid/20c.html

"At present, however, our understanding of stratospheric cooling is not complete and further research has to be done...."