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Climate Hustle

Stratospheric Cooling and Tropospheric Warming

Posted on 1 December 2010 by Bob Guercio

This post has been revised at Stratospheric Cooling and Tropospheric Warming - Revised

Increased levels of carbon dioxide (CO2) in the atmosphere have resulted in the warming of the troposphere and cooling of the stratosphere. This paper will explain the mechanism involved by considering a model of a fictitious planet with an atmosphere consisting of carbon dioxide and an inert gas such as nitrogen at pressures equivalent to those on earth. This atmosphere will have a troposphere and a stratosphere with the tropopause at 10 km. The initial concentration of carbon dioxide will be 100 parts per million (ppm) and will be increased instantaneously to 1000 ppm and the solar insolation will be 385.906 watts/meter2. Figure 1 is the IR spectrum from a planet with no atmosphere and Figures 2 and 3 represent the same planet with levels of CO2 at 100 ppm and 1000 ppm respectively. These graphs were generated from a model simulator at the website of Dr. David Archer, a professor in the Department of the Geophysical Sciences at the University of Chicago and edited to contain only the curves of interest to this discussion. The parameters were chosen in order to generate diagrams that enable the reader to more easily understand the mechanism discussed herein.

Prior to discussing the fictitious model, consider a planet with no atmosphere. In this situation light from the sun that is absorbed by the surface is reemitted from the surface. Figure 1 is the IR spectrum of this radiation which is known as Blackbody radiation.

Figure 1 

                  Figure 1. IR Spectrum - No Atmosphere

Consider now Figure 2 which shows the Infrared (IR) radiation spectrum looking down at the planet from an altitude of 10 km with a CO2 concentration of 100 ppm and Figure 3 which shows the IR spectrum with a CO2 concentration of 1000 ppm. Both figures represent the steady state and approximately follow the intensity curve for the blackbody of Figure 1 except for the missing band of energy centered at 667 cm-1. This band is called the absorption band and is so named because it represents the IR energy that is absorbed by CO2. IR radiation of all other wavenumbers do not react with CO2 and thus the IR intensity at these wavenumbers is the same as that of the ground. These wavenumbers represent the atmospheric window and is so named because the IR energy radiates through the atmosphere unaffected by the CO2. The absorption band and the atmospheric window is the key to stratospheric cooling.

Figure 2/3 

                    Figure 2. CO2 IR Spectrum - 100ppm                             Figure 3. CO2 IR Spectrum - 1000 ppm

The absorption band in Figure 3 is wider than that of Figure 2 because more energy has been absorbed from the IR radiation by the troposphere at a CO2 concentration of 1000 ppm than at a concentration of 100 ppm. The energy that remains in the absorption band after the IR radiation has traveled through the troposphere is the only energy that is available to interact with the CO2 of the stratosphere. At a CO2 level of 100 ppm there is more energy available for this purpose than at a level of 1000 ppm, thus the stratosphere is cooler for the higher level of CO2 in the troposphere. Additionally, the troposphere has warmed because it has absorbed the energy that is no longer available to the stratosphere.

One additional point should be noted. Notice that the IR radiation in the atmospheric window is slightly higher in Figure 3 than Figure 2. This is because the temperature of the troposphere has increased and in the steady state condition, the total amount of IR entering the stratosphere in both cases must be the same. That total amount of energy is the area under both of these curves. Thus, in Figure 2, there is more energy in the absorption band and less in the atmospheric window while in Figure 3, there is less energy in the absorption band and more in the atmospheric window.

In concluding, this paper has explained the mechanism which causes the troposphere to warm and the stratosphere to cool when the atmospheric levels of CO2 increase.

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Comments 201 to 247 out of 247:



  1. Hi All,

    Please note that in the above diagram, the ozone layer is about one third of the way up in the stratosphere. The UV from the sun interacts with the ozone and heats up the stratosphere. But why isn't the temperature the highest where the ozone is densest which is about one third of the way up?

    Thanks,
    Bob
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  2. Most of the heat is generated by the chemical reaction of O+02->O3+ heat. We also have the reaction UV+O2->O+O. The ozone expels the heat as it is formed. So the highest density of ozone is not related to the highest temperature. As the O3 is heavier than O2 it will tend to sink to the bottom of the layer I think.
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  3. Here is a basic course on the heat flows in the troposphere which explains how convection, latent heat and IR are transmitted to the troposphere.

    Atmospheric thermodynamics
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  4. Bob @201

    According to the lecture notes posted by Tom@186 yesterday, solar destruction of ozone generates heat at the top of the stratosphere. So I guess you'd expect less of it.

    mars @202, you wouldn't expect gases to stratify according to density, in the same way we don't have a layer of CO2 at the ground. It's just a balance of relative chemical destruction and creation of ozone according the intensity of radiation and concentration of other gases (eg ozone depletors)

    http://www.ess.washington.edu/Space/ESS205/upperatmweb.pdf
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  5. Bob@201

    And froom Wiki,

    "The stratosphere is layered in temperature because ozone (O3) here absorbs high energy UVB and UVC energy waves from the Sun and is broken down into monoatomic oxygen (O) and diatomic oxygen (O2). Monoatomic oxygen is found prevalent in the upper stratosphere due to the bombardment of UV light and the destruction of both ozone and diatomic oxygen. The mid stratosphere has less UV light passing through it, O and O2 are able to combine, and is where the majority of natural ozone is produced. It is when these two forms of oxygen recombine to form ozone that they release the heat found in the stratosphere. The lower stratosphere receives very low amounts of UVC, thus monoatomic oxygen is not found here and ozone is not formed (with heat as the byproduct)."
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  6. VeryTallGuy 204 and 205

    As there is no convection going on in the stratosphere and the layer is very stable it is not like the troposphere where the gases are well mixed but I am not over confident that my suggestion is correct in relation to molecular weights. It is however definitely related to the heights where different chemical reactions occur. The sad part is I read an article on the net about 2 weeks ago that explained the issue in detail and now I can't find it.
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  7. VeryTallGuy - 205

    But this is exactly what my dilemma is. Heat is being released in the ozone layer that is about one third of the way up the stratosphere. Shouldn't this layer, therefore, be the warmest part of the stratosphere? But it's not. The top of the stratosphere is the warmest part.
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  8. mars - 203

    Great reference document!
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  9. Bob @207

    As I understand it (which is, painfully obviously, not all that well) there are several heat producing reactions with UV.

    1) O2 is split: O2 = 2O (absorbing a photon of UV)

    2) Ozone is created: 0+02=03 (releasing thermal energy)

    3) Ozone is destroyed: O3 = 0 + O2 (absorbing a photon of UV)

    4) Ozone is destroyed by other chemical reactions eg CFC catalysed

    At the top of the stratosphere you get more of (3) so despite absorbing quite a lot of UV, there isn't a very high Ozone conc.

    Each photon absorbed is a net energy & hence temp gain. Overall, there is more absorbed at top than bottom, hence the temp gradient.

    Lower down, the ratio changes hence the higher ozone concentration.
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  10. VeryTallGuy - 209

    Ditto on your remark on understanding.

    I think the problem is that in the study of Physics, you go into tremendous detail over single individual entities. For example, I remember going into mindboggling details over a mere water molecule.

    Atmospheric science involves everything which is why it is so complex. I could understand a water molecule but when combined with all the other chemistry of the atmosphere and other factors such as the spinning of the planet, it all becomes extremely difficult and very tricky. This is why I really will not feel comfortable about my blog until it is blessed by a professional.

    And that's the problem here. All we hear about is ozone but it is not just ozone that is generating heat. Oxygen is also and probably other chemicals that we have never heard of.

    So I guess the bottom line is that ozone is not primarily responsible for the generation of heat in the upper atmosphere. Oxygen is responsible for that!

    I think in the upper atmosphere, there is more of the process that you labeled "1".

    Bob
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  11. Bob,

    Oxygen and ozone absorb in different regions of the UV. There's a good overview description of the process here:
    http://eospso.gsfc.nasa.gov/science_plan/Ch7.pdf

    "The formation of ozone by the photolysis of molecular oxygen removes most of the incident sunlight with wavelengths shorter than 200 nm. The wavelengths between 200 and 310 nm are removed by the photolysis of ozone itself." - bringing out the point that different wavelengths are involved in the different reactions.

    For detailed chemistry try here
    http://www-tonycox.ch.cam.ac.uk/Download/ERCA2_Stratosphere.ppt
    It's complicated but not conceptually difficult I think.
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  12. Oh, and meant to add whilst this is interesting, overall for the stratospheric cooling issue all that matters is that UV is absorbed, heating the stratosphere.

    CO2 enables the heat to be released; more CO2 means more IR radiance at a given temperature, hence increasing stratospheric CO2 reduces stratospheric temperature.

    I've almost convinced myself now...
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  13. VeryTallGuy - 212

    I didn't talk about the issue of ozone with regard to cooling of the stratosphere.

    Ozone brings heat into the stratosphere. However, with the thinning of the ozone layer that occured several decades ago, it is now bringing in less heat and this has caused some of the cooling.

    Bob
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  14. mars at 19:39 PM on 9 December, 2010 says

    "The atmosphere at low levels is transparent to nearly all of the incoming radiation."

    I took that as a given, i was talking about LW.

    Mars says "The atmosphere is heated by contact with the surface. As a result a parcel of air close to the ground forms which is warmer than the surrounding air."

    The air is heated, by conduction and radiation, and as a result of the air being opaque to LW radiation in the lower troposphere, this energy is trapped, if it was transparent, it would simply pass through at the speed of light.

    There is nothing wrong with your description of convection, but the properties of the lower atmosphere are taken as a given, radiation is not considered, because the lower troposphere is opaque to the passing of LW, but at 6000m, radiation is the dominate means of energy transport(this is the average altitude of equilibrium with incoming and out going energy), not the sole, but dominate. As you rise further, the atmosphere becomes more and more transparent, and convection less and less important.
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  15. Bob Guercio at 04:25 AM

    The ozone's thinning can and has been quantified, variable UV through the solar cycle, also effects stratospheric T's, UV is the most variable wave length through the cycle. But smarter people than me, have done studies on these things... there is that paper that by Johanna Haige, that a thread was done on here that may impact these. But the reason why raising co2, should cause the stratosphere to cool, is because it causes more energy to be lost from the stratosphere through radiation.

    VeryTallGuy - 212

    Yes (-:
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  16. Joe Blog at 215
    I fully agree with that.
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  17. Joe Blog at 214
    And on refection
    I also fully with 214
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  18. Bob @201, as you surmise, temperature in the stratosphere is partially controlled by the mixing ration of Ozone to CO2, and if the flux of UV was constant with altitude, we would expect the highest temperature in the stratosphere to be where the highest mixing ratio was found. However, UV flux is not constant with altitude. Most UV-a, the most energetic form of UV, is absorbed above the level of maximum O3, apparently by the breakup of O2 (VGT @211).



    Considering UV-b, the next most energetic form of UV, nearly half is absorbed above 30km. Combined with the energy from UV-a, this should be sufficient to explain the temperature profile in the stratosphere.



    An interesting consequence of reduced O3 is that UV should penetrate further into the stratosphere. This should show up as a cooling at higher altitudes as they absorb less UV, but a warming at lower altitudes as more UV penetrates to the lower levels to be absorbed.



    The result is that in the lowest levels of the stratosphere, CO2 cooling is almost balanced by an ozone based warming, while in the upper levels they reinforce each other.

    PS: In preview, my first two images are not showing. I am leaving them in in case this is just a temporary bug, but in the mean time they can be found at the wikipedia article on the ozone layer.
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    Moderator Response: [Daniel Bailey] Fixed links. TIP: When linking to Wiki graphics, make sure you click on the graphic itself, bringing up the page with just the desired graphic and no text. If you see text still, click on the graphic again to bring up the source storage position for that graphic. That should take care of it.
  19. Joe Blog @214, heat is also passed from surface to atmosphere by evaporation and transpiration. This, together with conduction would be enough to heat the lowest layer of the atmosphere to surface temperature, even in the absence of radiant heat transfer. And that in turn would be enough to generate convection.

    Even if only conduction were available, that would still raise the lower atmosphere's temperature to near surface temperatures. Because conduction is a slow method of heat transfer, the lower atmosphere would not have a large day-night cycle in temperature, although land surfaces would have a very large cycle. But even this slow method of heat transfer would heat the entire atmosphere up to at least the mesopause in the absence of any absorption of radiant energy by the atmosphere.
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  20. Tom Curtis

    lol, yup, but i did say transparent. Not non radiating, so this energy could be radiated away by magical atmosphere.

    But i recall coming to a similar conclusion thinking about a non radiating atmosphere.
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  21. Joe Blog @196, having now understood what you are saying, I will not procede to criticize it.

    First, although the mechanism you describe sounds plausible, you fail to account for the characteristic rates
    characteristic rates of convection and radiant transfer. Specifically, while it only takes a few hours to restore thermodynamic equilibrium in the atmosphere by conduction, it can take as much as 50 days to do the same by radiation. This difference of rates is the primary reason why convection dominates radiation as a means of energy transfer in the atmosphere, and is still relevant at the tropopause.

    Given the example in 195 of a warm air parcel rising to 8km altitude, this means it would reach an equilibrium temperature by radiation over the period of about a month, or more. But it would still be able to reach an equilibrium temperature with the surrounding air in a few hours by convection, ie, by continuing to rise. Consequently, on these grounds, we would expect convection still to dominate as a heat transfer mechanism within the atmosphere.

    Second, radiant transfer is related to the fourth power of temperature, while heat conductive heat transfer is related to the difference between the temperature of the heated or cooled air parcel (Tap) and the temperature of the ambient air (Te) by the relation such that, a = g(Tap-Te)/Te
    , where a is the acceleration on the air parcel, g is the gravitational acceleration, and a is the acceleration of the air parcel. Therefore, given a 1% rise in temperature, we would expect heat transfer by convection to increase by about 1%. Heat transfer by radiation, in contrast, should increas by about 4%. Because radiant transfer becomes more effective with rising temperature, if radiant tranfer dominated, we would expect a rise in temperature to decrease the altitude at which radiant tranfer first started to dominate. Consequently, if the altitude of the tropopause where determined by where radiant energy started to dominate for heat transfer, then incraseing atmospheric temperature should decrease the altitude of the tropopause. Instead, the tropopause is highest in the tropics and lowest at the poles. Indeed, even cold fronts will lower the tropopause.


    "As can be seen in the figure above, the tropopause altitude steadily drops from about 12.5 km to 11 km as the DC8 flies west from The Azores toward a cold front in the western Atlantic Ocean. At ~10:15 UT there is evidence of stratospheric tracers (O3, NOy up, CO down) from in situ sensors. At the same time, the tropopause altitude drops abruptly more than 1 km and MTP sees a warm finger of air extending through this tropopause drop, apparently because the descending stratospheric air is being adiabatically heated. Later, at 11:17UT the Langley Research Center DIAL lidar saw the beginning of a stratospheric intrusion at the same time that MTP saw a second tropopause altitude drop"
    (Caption quoted from source.)

    Finally, I think my comments about the mesosphere in 193 above are still relevant.
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  22. Tom Curtis at 13:23 says
    "Specifically, while it only takes a few hours to restore thermodynamic equilibrium in the atmosphere by conduction, it can take as much as 50 days to do the same by radiation."

    Again, the reason for this, is the opacity, radiation, is an inefficient mover of energy in the lower layers of the atmosphere, where it is opaque, because what is radiated, is absorbed in a very short distance. As the atmosphere thins with altitude, the path length shortens, radiation travels further before it is absorbed.

    When air convects, it looses its energy, performing work, displacing the air above it, this energy is put into the air it is displacing, this is why it cools... Now if radiation wasn't moving this energy, out of the upper layers of the troposphere at the rate convection was carrying it there, the energy would accumulate. And because energy is still coming into the system, it would lead to a build up of energy in the system, raising the T at all layers. And it would continue to do this, until it had heated the higher layers(shorter path length) up enough until they were radiating the energy away.

    Convection, cannot take energy out of the system, it does not work in a vacuum. And energy cannot be created or destroyed, it can only come into the system, via radiation, and leave via radiation. If more is coming in, than what is being radiated away, the system will accumulate energy, until it can radiate the incoming away. You are violating, the first law of thermodynamics.

    For your second point, the same applies, it dosnt matter that at the surface, it is warmer and radiating more, because the energy is simply swapping between molecules, This is why convection occurs, energy accumulates... In the tropics, it receives a lot more energy from the sun than at the poles, there is vastly more water vapor in the atmosphere, to much higher levels(due to convection)... again making the atmosphere opaque to radiation, inhibiting it. Causing convection to much higher altitudes, until the energy can be lost via radiation.

    The bottom line is, if convection was moving more energy up to the tropopause, than what was being radiated away, it would heat, moving the tropopause up, until it got to a level, that it could radiate the energy away. You have to be able to explain, where your energy is? It doesn't vanish.

    Now if there was no solar absorption in the upper atmosphere, we would have a T gradient, starting from the surface T, and decreasing until the outer layer at 2.7K The back ground T o space.
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  23. Oh and tom, there is a thread over at Science of Doom about this stuff.
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  24. Joe Blog at 22
    Re Para 3
    When convection takes place the work is done by expanding the air parcel in the first phase of warming until this happens the air parcel will not ascend. The air parcel once it starts to rise continues to do so because it is less dense than the surrounding air mass but as it rises the external pressure is lower and therefore it expands.

    The process is adiabatic that means no heat is added or taken away from the system during the ascent phase. To put it another way the same amount of heat in a large space translates to a lower temperature.

    Physically due to gravity the heavier air parcels fall to the bottom of the atmosphere and the lighter rise. The colder air having been displaced downwards is now at a higher pressure and therefore its temperature is higher but again this process is adiabatic so no work is done, and yes heat does accumulates at higher levels during the day but of course it is lost again during the night.

    The bit I am not sure about is whether this is agreement with Joe or Tom.
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  25. mars at 09:40 AM says
    "When convection takes place the work is done by expanding the air parcel in the first phase of warming until this happens the air parcel will not ascend."

    Yes, the same as a cylinder compressing air, you apply work to the piston, squishing the air, the energy applied to the piston, is now contained in the air, as well as the prior existing energy is now more tightly compressed... now the rise... pushing up the piston, putting the energy applied by the piston back into the piston, until the air is back at equilibrium, with the same amount of energy contained in the volume of air prior to the compression.

    The same applies to the atmosphere, work is done, by energy being added to a parcel of air, the air rises, displacing the air above it(the piston) expanding, with the energy from the work being used to displace the air above, redistributing it into this, until it is at equilibrium with its surroundings... If the air didnt have more energy in it than the adiabatic rate dictated, it wouldn't rise, or less it wouldn't sink...

    So work goes both ways, it takes work to apply pressure/add energy... when it expands, it releases this energy, work is done, until it is at equilibrium. otherwise it would never stop rising, it would always contain more energy than the adiabatic rate dictates.
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  26. Joe 255
    at Para 3

    There is a problem here as the process is adiabatic that means no heat is added or subtracted from the system and that in turn implies no energy has either. So what did the work ?
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  27. mars at 10:15 AM
    Read here the section on adiabatic heating and cooling, and if you still think im wrong get back to me and i shall try to clarify.
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  28. Joe at 227
    The way I understand it, is the work that is done, is internal to the parcel of air. Work is done when the air parcel expands and the temperature falls. During compression the work energy is in effect returned as an increase in temperature.

    Here I may be misunderstanding what you are saying. I was under the impression that you are saying that heat from the parcel of air is being lost to its surroundings. My understanding is that is not the case.

    My simplistic understanding is that a parcel of dry air cools at a rate of 9.8 Deg C per 1 Km of altitude but the atmosphere on average is cooler by 6.8 Deg C for every 1 Km of altitude.

    For example if the surface temperature is 16 Deg C
    and a parcel is heated an extra 6 degs C to 22 Deg C
    At 1 Km air parcel cools to 12.2 Deg C local temp is 9.2 C
    At 2 Km air parcel cools to 2.4 Deg C local Temp is also 2.4 C
    Here equilibrium is reached and and convection stops.
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  29. mars, Joe,

    on the adiabatic lapse rate point Science of Doom has a new post setting this out very well:

    http://scienceofdoom.com/2010/12/07/things-climate-science-has-totally-missed-convection/
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  30. No saturation.

    Es ergibt sich folgende Kurzdarstellung des Treibhauseffektes in 5 Punkten:
    1. Die Atmosphäre ist im Wesentlichen zweigeteilt: unten die konvektionsreiche Troposphäre, in der das Wetter ist und wo wir leben und oben die konvektionsarme Stratotosphäre, wobei sich die Grenze zwischen beiden Sphären verschieben kann.
    2. Der Temperaturgradient in der Troposphäre ist (fast) konstant - auch wenn sich die Dicke der Troposphäre ändert. Diese Konstanz ist konvektionsbedingt.
    3. Die fast konstante optische Dicke einer sich ändernden Stratosphäre. Diese Konstanz ist strahlungsbedingt und ergibt sich aus der Skalierung (Maßstabsänderung) der Strahlungstransportgleichung bei Änderung der optischen Dicke bei Konzentrationsänderung des CO2.
    4. Wenn der Temperaturgradient einen bestimmten Grenzwert überschreitet kann die Luftschichtung nicht ruhig bleiben und wird instabil = Konvektion = Kennzeichen der Troposphäre
    5. Im stationären Zustand (d.h. auch wenn Zeit vergeht, ändert sich der Zustand nicht) ist im Mittel die Wärmeabgabe der Erde genau so groß wie die Wärmeabsorption - andernfalls müßten sich die Temperaturen laufend ändern. Das aber widerspräche der Stationarität.

    Diese 5 Punkte liefern eine Grundsensitivität der durchschnittlichen Oberflächentemperatur als Folge von Konzentrationsänderungen des CO2.

    Ergänzung: Die dickere Tropopsphäre hat eine größere Temperaturdiffernz zwischen oben und unten, wobei diese größere Temperaturdifferenz sich als Abkühlung oben und Erwärmung unten so verteilt, daß die Gesamtabstrahlung der Erde gleich der Gesamtabsorption ist.

    MfG
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  31. Mars, Joe, and TallGuy,

    The environmental lapse rate is not the same as the adiabatic lapse rate. There are other factors at work; one of them is the loss of energy through radiation.

    My take is that stratospheric cooling has two components: less radiation getting out from the troposphere and greater ability to radiate LW. The less radiation leaving bit is only until a new, higher point of equilibrium is reached.

    One thing I'd like to mention is that the leveling off to a new equilibrium temperature will not even start until after CO2 levels are stabilized. The leveling off of CO2 is not guaranteed to remain within our ability to affect depending on how the feedbacks play out.
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  32. Guten Tag Ebel, aber, mein Deutch ist nicht sehr gut. :-)
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  33. @ Chris G at 08:32 AM on 13 December, 2010. Sorry my English is not good (automatic translation)

    It results in the following outline of the greenhouse effect in 5 points:
    1. The atmosphere is divided into two parts, in essence, bottom the troposphere with a lot of convection, where the weather is and where we live, and top the stratosphere without convection, with a possible move the border between the two spheres.
    2. The temperature gradient in the troposphere is (almost) constant - even when changing the thickness of the troposphere. This consistency is result of convection.
    3. The almost constant optical thickness of a changing stratosphere. This constancy is due to radiation and is due to the scaling (scaling) of the radiation transport equation for change in optical thickness with change in concentration of CO2.
    4. If the temperature gradient exceeds a certain threshold, the air can not stay calm and stratification becomes unstable - and the convection is the characteristics of the troposphere
    5. In the steady state (ie, even though time passes, the state no changes) does mean the heat of the earth just as great as the heat absorption - would otherwise be the temperatures change constantly. But this would contradict the stationarity.

    These 5 points provide a basic sensitivity of the average surface temperature as a result of changes in concentrations of CO2.

    Addition: The thicker troposphere has a greater temperature difference between top and bottom, and this greater temperature difference is so distributed to warming bottom and cooling top, that the total radiation of the Earth is equal to the total absorption.
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  34. addition to #176



    The same pressure difference = same number of molecules
    200 mbar - about 11 km altitude



    Pressure difference across the height of an air layer with CO2 in which the initial intensity of a vertical infrared beam to 1 / e is dropped (Lambert.Beer)



    The Comparing the two charts above give the narrow spike at 15μm (= 666cm-1). There, is much absorbed, emits a lot, but according to the temperature. Therefore, the bright peak due to the narrow tip of the ozone area.
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  35. Re my comment at 228
    It has just occurred to me that of course work is done when a parcel of air is lifted to a higher altitude which must be equal to MGH. That is Mass X Gravity X Height so that means the temperature drop per KM will work out as the same number as G provide of course the air is not saturated. This must be true for any planet.
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  36. @ mars at 19:52 PM on 13 December, 2010

    This is not true. The cooling does not follow from the increase in potential energy, but from the pressure decrease during rapid ascent.
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  37. Ebel, Mars 235/236

    You are both right!

    The adiabatic lapse rate is simply set by the Cp of the gas and g, dT/dZ = -g/cp, see textbook extract at bottom of this post

    However, it’s also true to say that cooling is a function of pressure loss; the thing is that the pressure loss depends on g.

    For adiabatic expansion,

    The point is that the pressure at any given height is a function of g and gas properties, so the two are coupled.

    My understanding is that the real lapse rate differs from this due to latent heat, radiation, lateral mixing etc.




    (Extract from Elementary Climate Physics, F.W. Taylor (2005)
    sourced from Science of Doom)
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  38. The condition (dQ about 0) requires a fast vertical circulation
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  39. Joe Blog @222, I went through the discussion at Science of Doom, and found that though the issue we are discussing was raised, it was not often adressed. One interesting titbit was the claim by DeWitt Payne that it takes "...on the order of a few months ..." for the stratosphere to reach an equilibrium temperature. This compares well with the approximately 50 day characteristic time for radiative transfer to reach equilibrium in the troposphere in the absence of convection, showing that it is not an increase in the rate of heat transfer by radiation which changes between troposphere and tropopause. What does change is path lengths.

    I did notice, however, a comment in the extract of Goody and Walker posted by SOD to the effect that the lapse rate due to radiative transfer is small at high altitudes, and becomes large at low altitudes, so that at low altitudes, radiation will generate sufficient heat differences to generate convection, but at higher altitudes it will not (p 63). This seems to be what you are saying, so I followed up on it and found out something very interesting.

    Specifically, I found a graph of the radiative-convective equilibrium for atmospheres including H2O, H2O and CO2, and H2O, CO2 and O3 (fig 3.17, page 19/35). This clearly shows that, in the absence of ozone, atmospheric temperatures decline in lapse rate above 15 km to a point at which convection no longer operates. However, they also show that: in the absence of ozone, there is no temperature inversion; and that with ozone, temperature passes from a convecting zone to 0 lapse rate at around 12 km.

    In other words, based on this graph, I was correct in ascribing to ozone the particular temperature profile and altitude of the tropopause; but you were correct in assigning the cessation to convection as a dominant player at about that altitude to the improved efficiency of radiation as a heat change mechanism. I should also note, though it is not shown on the graph, that the mesosphere would not exhibit convection where it not for the presence of ozone either - a point on which you were correct.

    Also of interest is the graph on figure 3.16 (p 8/35), which shows temperatures profiles for radiation only, for radiation plus convection on the dry adiabat, and for radiation plus convection with a lapse rate of 6.5 degrees per km. As convection becomes more efficient in transferring heat, the tropopause climbs, in these graphs from 10, to 11, then to 15 km. Presumably sufficiently moist air, and sufficiently high surface temperatures will cause it to rise still higher, to 18-20 km as found in the tropics. Conversely, drier air, and colder will cause it to drop.

    If the radiative lapse rate where constant with altitude, then the strength of convective forces it generates would also be constant with altitude, so that in the absence O3, the adiabatic lapse rate would be sustained to the edge of space. Clearly that is not the case, and the fact that the radiative lapse rate drops below a level that can sustain convection at around 15 km is clearly relevant to the altitude of the tropopause. However, this evidence, together with the emperical evidence previously indicated, suggest to me that while the drop in radiative lapse rate determines the general region of the tropopause, the actual altitude depends critically on a variety of factors, some of which (such as water vapour, and surface temperature) govern the strength of convection, while others (such as the presence of ozone) govern the particular temperature profile.

    Finally, you suggest that my proposal violates the first law of thermodynamics. This cannot be the case in that the altitude at which radiation absorbed by water vapour becomes optically thin is about half that as for the average of the atmosphere. At that altitude, convection dominates the temperature profile. Clearly, you can have a larger escape of radiant energy to space coupled with a convection dominated (ie, adiabatic) lapse rate without violating the first law.
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  40. Ebel at 21:10 PM says
    "This is not true. The cooling does not follow from the increase in potential energy, but from the pressure decrease during rapid ascent."

    Yes, the decrease in potential energy, as it performs work, as i understood it that is what mars said. The pressure decreases because it expands, and displaces/pushes the air around it. The opposite is true of adiabatic heating.

    Tom Curtis at 03:01 AM

    Good post, my comment about "violating the first law" was simply saying, that if radiation wasnt moving the energy that convection was lifting, it would result in a build up of energy, raising the troposphere until it was able to shift it. So radiation, must at some stage become the dominant mover. And at equilibrium must be moving out the same amount of energy that is coming into the system.

    I dont disagree with anything in this post however.
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  41. I admit that I have not studied all the previous posts in detail. What I am interested to know is whether there is agreement that the 2nd mechanism that Bob refers is valid or not?
    My view at this stage is that while it true for Bob's model, it is overridden by other factors when considering the Earth's atmosphere, particularly the extra heat gained at altitude from latent heat in a warmer more humid world.
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  42. mars @241, whether the 2nd effect is over ridden by other factors is a complex issue, involving, as I see it, four factors.

    1) With the addition of extra CO2, the amount of CO2 leaving the troposphere is reduced by two effects. First, because of increased optical thickness, the average altitude of emmission increases and hence becomes cooler. On an emmission spectrum, this means the trough around 15 microns (due to CO2) will be deeper. Second, because of a variety of factors, that emmission/absorption band will also be broader, as shown in figure 2 in the revised article.

    Both effects reduce the amount of energy escaping the atmosphere around 15 microns, requiring more to escape at other wavelengths to maintain equilibrium, which in turn requires the Earth's surface to heat. However, the emmission/absorption band of CO2 in the stratosphere is much narrower than that in the troposphere due to its low partial pressure. The stratospheric emmission band can be seen as the small spike at the center of the tropospheric emmission/absorption band in the graph below. Because the stratospheric emmission/absorption band is so narrow, broadening of the tropospheric band has no (or almost no) effect on amount of IR energy absorbed by CO2 in the stratosphere. Therefore, Bob's seoond mechanism is entirely a function of the first effect (increased altitude of emmission), and how strong it is depends on the relative strengths of the two effects I have just described. Unfortunately, I cannot tell you what the relative strength is.



    The first factor describes completely the initial responce to the addition CO2 to the atmosphere. However, after that addition, the atmosphere adjusts bringing in factors that act as negative feedbacks to Bob's second mechanism. Consequently, Bob'second mechanism will undoubtedly cool the stratosphere initialy, but may not do so in the final state. Indeed, it is possible it will slightly warm the stratosphere in the steady state. Dealing with these feedbacks, we come to:

    2) As the atmosphere responds to the greenhouse effect, the surface warms, and with it all altitudes above it in the troposphere. This increases the temperature at the effective altitude of emmission, reducing the effect of Bob's second mechanism.

    3) Further, warming the atmosphere drives a water vapour feedback. The enhanced greenhous effect due to the water vapour feedback will also increase the temperature at the effective altitude of emmission, again reducing the effect of Bob's second mechanism.

    4) Finally, as you mention, the lapse rate feedback (the reduction of the lapse rate due to the presence of additional water vapour) will also reduce the temperature at the effective altitude of emmission.

    How these factors play out is beyond my means to calculate. If only factors 2 and 4 were involved, then I could confidently state that they do not eliminate the second mechanism in the steady state, for if they did so, net radiation from around the 15 micron band would not have reduced, meaning there was no increase in the greenhouse effect. However, because of the broadening of the band (factor 1) it is possible that factors 2, 3, and 4 could result in a net increase in temperature at the altitude of effective emmission while still reducing outgoing IR radiation because of line broadening. This is one reason I would like to see comments by someone who was genuinely expert on this topic (eg, Gavin Schmidt).

    Finally, there is at least one positive feedback on both mechanisms. Specifically, as tropospheric temperatures increase, a greater proportion of CO2 will be found at a higher altitude, thereby increasing optical thickness. I suspect it is a miner effect compared to the others mentioned.
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  43. The radiation of the entire 15μm bands at 220K is from the stratosphere, which has over the entire thickness almost 220K (yellow line). The small spike in the middle is caused by a particularly strong absorption, so that the emission comes almost exclusively from the height of the ozone area. See also # 234th
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  44. Ebel @243, the majority of emmissions near the 15 micron band comes from CO2 in the troposphere, from about an altitude of 8 - 10 km. If you use the Modtran model linked to several times in this thread, with a look down altitude of 10 km, you will see the main part of the emmission spectrum still present (as in fig 2 above).

    You will not see the spike at the center, of course, because it comes from the stratosphere and hence from above 10km. If you use Modtran, and a 10km look up altitude, you will see the spike, but not the main band. Clearly, though, the spike, being an increase of outgoing energy, must be an emmission rather than an absorption.
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  45. It is less important to explain "how it is", but the more important, "why it is so". And to just heard the important role of the vertical circulation and where be the begin of vertical circulation. (see #233 and #234).
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  46. tcflood,

    This is a response to this comment from The Big Picture...

    You asked:

    Does anyone have a good physical explanation (like I have presented above, not mathematical) of why the stratosphere must cool for the troposphere to heat during the greenhouse effect?

    Yes.

    As explained earlier, there are two answers to this. 

    Molecular Reasons

    Let's start with the first, in which there are two interlocking mechanisms at work.  One is the absorption and emission of IR by CO2.  The other is the transmission of energy between molecules as a result of a collision.

    So in the lower troposphere, where the air is dense, there is a lot of CO2 to absorb IR.  But there are also far more O2 and N2 molecules, and so many collisions, such that energy is quickly transferred through collisions to O2 and N2 molecules.  What was vibrational energy in the CO2 molecule turns into translational (and perhaps very slightly rotational) energy in an O2 or N2 molecule.

    Of course, everything is rate of reaction:

    1) * + CO2 --> CO2*

    2) CO2* + O2 --> CO2 + O2* (O2* is just accelarated, not "excited", O2)

    3) CO2* --> CO2 + *

    4) O2* + CO2 --> O2 + CO2*

    Equation 1 happens a lot, but is dependent on the concentration of CO2 and * (IR photons in the right wavelength).

    Equation 2 happens a lot more, but is dependent on the concentration of excited CO2* molecules and O2 (or N2) molecules.

    Equation 4 happens pretty much, and is dependent on the concentration of unexcited CO2 and O2 (or N2) molecules.

    Equation 3 happens not so much in the denser parts of the troposphere, because equation 2 happens so often and so frequently that excited CO2* doesn't have much chance to re-emit IR.  Of course, it does happen, but then what matters is rates of reaction, and which equations dominate the system in which states.

    As we move into the less dense upper troposphere and stratosphere, we find that there is less IR to absorb, and also with more rarefied air, less collisions.  So the relative rates of equations 1 and 2 go down, while 3 and 4 go up.  We reach a point where rather than absorbing IR and heating the surrounding atmosphere (1 and 2), the surrounding atmosphere is "heating" (exciting) CO2 which then is able to emit the IR (in all directions, obviously), some of which makes it into space.

    So, on a molecular level, this explains why CO2 cools the stratosphere but warms the troposphere.

    Emission Reasons

    I've thought about this less, so my explanation will be somewhat vague... and honestly, we've recently had a discussion (argument) about both of these reasons, and which is more correct (molecular or this one, for which I don't have a good name)...

    As you have recognized, the earth must emit exactly as much as it absorbs, once it achieves equilibrium.  This means that at a warmer temperature it will still emit the same level of radiation, but the profile of that radiation will have changed.  This can be seen in figures 2 and 3 of this original SkS post above.  What it means is that the same total amount of radiation is emitted, but the spectrum will have less emissions in the "CO2 window".  This in turn means that there is less IR for the CO2 in the stratosphere is to absorb (again, equation 1 happens less often in the stratosphere, but it does happen) and so equations 1 and 2 are even less likely to happen.

    Summary

    1.  Raising CO2 in the troposphere increases the chance of IR being absorbed and transferred to the surrounding atmosphere.

    2.  Raising CO2 in the stratosphere increases the chance of energy being "stolen" from the stratosphere and emitted as IR into space.

    3.  Raising CO2 in the troposphere changes the profile of outgoing radiation, such that there is less radiation in the CO2 IR band for the stratosphere to absorb to "stay warm."

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  47. tcflood,

    I just noticed that the phrasing of your question was also inaccurate.  No one says the statosphere must cool for the troposphere to heat.  The real fact is that the nature of CO2 (unlike other forcings) will heat the troposphere and cool the stratosphere, independent of each other, for the reasons explained above.

    This is different, for example, from an increase in solar insolation, which would warm the surface and atmosphere directly, causing the earth to radiate more (more in, more out), but would leave the atmosphere unchanged (except for whatever effects the increase in incoming radiation would have directly on the stratosphere).

    Or consider the case of less ice, such as when the ice sheets retreat at the end of a glacial period.  Less ice reflects less radiation.  With less radiation reflected in the visible spectrum, the earth will heat more, until it emits enough IR to compensate for the increased absorbed radiation.  The earth is receiving and will emit the same total amount of energy, but more of it must be in the IR (and the planet is warmer).  But this would have minimal effect on the stratosphere.

    This is one reason why stratospheric cooling is itself a signature -- a fingerprint -- that adds one more bit of evidence that CO2 is the cause of our current warming.  The theory predicts stratospheric cooling, and we see it, when other warming mechanisms would not show this.

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