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The Planetary Greenhouse Engine Revisited

Posted on 15 June 2011 by Chris Colose

It turns out that significant discussion on the blogs came out of my recent “Even Princeton Makes Mistakes” posting, where I raised issues with an article on global warming by Princeton physicist Will Happer which contained a suspicious number of trivial errors, conspiracy theories, and fallacies.  A surprisingly disproportionate amount of response was dedicated to a side comment about the greenhouse effect on Venus that I made in passing-by (e.g., here, here, and Bart  Verheggen chipped in too).  I notice many issues still plaguing the web with regard to the basic physics behind the greenhouse effect, but also misconceptions behind some of the thermodynamics and radiative transfer in climate studies.  In particular, many people still think you can get super-hot temperatures on Venus without a greenhouse effect if you maintained a high surface pressure; others still think the greenhouse effect does not exist because its warming influence in some way violates thermodynamics.  Another that I really don't understand is that the lapse rate (the temperature change with height) itself causes high surface temperatures.  As such, I thought I'd take the opportunity to cover some of the inner workings behind the greenhouse effect while addressing these points.  This may  be a bit lengthy, but hopefully educational and a useful reference for future discussions that may arise.

 The Greenhouse Effect and Thermodynamics

When we think about problems in planetary climate-- whether it be the greenhouse effect of Venus, Snowball Earth, extreme orbits, the range of habitability around others stars, or what exotic atmospheres one might encounter on other planets-- we must be prepared to think well outside the "climate box" in terms of scenarios and possibilities.  Whatever alien situation we can think of however, we are necessarily constrained by the laws of physics to create a self-consistent picture that distinguishes reality from science fiction.  Among these laws of physics are the many well-established rules governing the behavior of radiant energy and its interaction with air, and also the statistical behavior of gases in local thermodynamic equilibrium.  Just as an incredibly trivial equation of state emerges in the thermodynamic limit from very complex molecular dynamics (which ultimately describes a relationship between fundamental variables in our atmosphere), we can make many general remarks concerning the energy balance and temperature structure of planetary atmospheres, even with exceedingly complex behavior at the interface of fluid dynamics, chemical interactions, and energy/momentum transfer.

The nearby rocky planets (e.g. Mercury, Venus, Earth, Mars) gain and lose energy radiatively, and come into thermal equilibrium when the magnitude of the absorbed solar radiation equals the outgoing emission by the planet (which is in the far-infrared part of the electromagnetic spectrum for all planets in our solar system, but could just as well be primarily in the visible for very hot planets orbiting close to their host star). This is not always the case: on the gaseous planets, observations show that the outgoing thermal radiation exceeds the incoming solar energy by significant amounts (this excess is nearly a factor of three for Neptune).  This is because the giant planets have an internal heat source.  On Earth or Venus, internal heating takes the form of radioactive decay, although it is negligible for energy budget purposes, since the energy flux is many orders of magnitude smaller than the incoming solar energy flux.  Radioactive decay is not responsible for the infrared excess on gas planets either; instead, the interior heat source takes the form of Kelvin-Helmholtz contraction—a way of converting potential energy into kinetic energy as the whole atmosphere contracts into the center (i.e., becoming more centrally condensed), heating the gas interiors.  This is a critical component of giant gas planet evolution, and the process is also what makes young stars hot enough in the center to eventually fuse hydrogen, although Jupiter is not nearly massive enough to reach this point.

 Introducing an infrared absorbing atmosphere into the picture complicates things, since now radiation is lost to space less efficiently than with no atmosphere (for a given temperature). In essence, the surface temperature acts as a slave to the way energy flows operate between our sun , the planet, and the overlying air and eventually adjusts to maintain equilibrium at the top and bottom of the atmosphere.  The critical ingredient for the greenhouse effect (aside from IR absorbers, obviously) is that the temperature structure of the atmosphere is one that declines with height.  This is because in order to make the planet lose radiant heat less efficiently, you need to replace the “radiating surface” near the ground with a weaker “radiating surface” in the upper, colder atmosphere (Fig 1)

Figure 1: Spectrum (Radiance vs. wavenumber) for a Planck Body at 300 K (purple dashed) and the OLR with an IR absorbing greenhouse gas

Figure 1 is plotted as a somewhat “contrived” greenhouse substance that works like this: Our ground has a temperature Ts, with a colder temperature above the surface (e.g. the stratosphere).  Plotted are the Planck function for the surface temperature (purple dashed) and actual outgoing radiation (OLR, curve).  The Planck function gives the distribution of energy intensity vs. wavenumber (or wavelength, or frequency, depending on your favorite characterization of an electromagnetic wave) for a blackbody at some specified temperature.

The blue curve titled “OLR” is the actual spectrum of this hypothetical planet with a hypothetical greenhouse gas in the atmosphere.  The difference between that blue spectrum and the Planck (purple) spectrum for the ground temperature arises because our greenhouse gas happens to be blocking radiation from exiting directly to space at 600 cm-1 and the surrounding regions.  Even toward the “wings” at 400 or 800 cm-1 it is making the atmosphere “partially opaque.” This is fairly standard qualitative behavior for a greenhouse gas, especially CO2, although there are exceptions.

This plot is computed for a fixed temperature, so the end result of adding the greenhouse gas is to reduce the total outgoing radiation (the specific amount is whatever chunk is taken out of the Planck curve).  This creates a situation where the planet temporarily takes in more energy than it loses, and as a consequence the ground temperature must rise to increase emission and restore equilibrium.

To think about this another way, emission at wavenumbers where the atmosphere is strongly absorbing will always be closer to a "sensor" that is recording the emission than wavenumbers where the atmosphere is transparent.  If the sensor is a satellite looking down from space, it will see warm, surface emission in transparent ("window") wavenumbers, but for opaque wavenumbers, emission emanates from the high atmosphere.

Similarly, for a surface sensor looking up, emission from opaque regions is seen to come from very near the surface, whereas for transparent wavenumbers the sensor is recording the  ~3 K temperature of microwave background radiation in space. In this post, we're thinking about the sensor looking down.  

Brief Technical aside: Let’s define a “mean radiating pressure" of the planet, which we’ll call pr, where the atmosphere becomes optically thin enough to lose its radiation to space directly rather than being absorbed in a higher layer. Since pressure decreases with height, the radiating pressure will decrease as the optical thickness of the atmosphere increases (i.e., more radiation is preferentially leaking out higher in the atmosphere where it is colder when you add greenhouse gases).  Conversely, the radiating pressure is at the surface (pr=ps) with no greenhouse effect. It is easy to show that for an atmosphere whose temperature profile is dry adiabatic, that the radiating pressure is given by:


where the ratio cp/R is approximately 7/2 for Earth air; the numerator in the brackets is the absorbed solar radiation, σ is the Stefan-Boltzmann constant, and Tis the surface temperature.  For Earth, the mean radiating pressure would thus be at ~650 millibars, rather than at sea level (1000 mb) with no atmosphere (in reality, it would be smaller than this, since the real lapse rate is less steep than the dry adiabat).  See also Figure 2, to show how decreasing pr increases the surface temperature.

Figure 2: Depiction of how increasing the radiating height of a planet increases the surface temperature.  Equilibrium is reached when the outgoing long-wave energy curves intersect the absorbed solar radiation curve.

Does this all violate Thermodynamics?

The reason greenhouse warming does not violate thermodynamics is because the planet is not an energetically closed system, and receives a constant influx of energy from the sun.  The reduction in outgoing energy flow by the atmosphere can therefore heat the planet toward a value slightly closer to the solar temperature.  If the sun turned off, the greenhouse effect would be irrelevant (even assuming you could keep your atmosphere in the air at all without everything condensing out).  Some people on the blogs have claimed that because a colder atmosphere radiates toward a warmer surface, there is some thermodynamic inconsistency with the second law.  First, note that I have not said a word about back-radiation to the surface, primarily because it doesn’t give proper insight into the way energy balance is adjusted and determined.  But to the point, cold objects still radiate energy and a photon doesn’t care whether it’s traveling toward a warm object.  So yes, colder objects can and do radiate toward (and heat!) warmer objects.  Standard measurements (from Grant Petty's Radiation book) of back-radiation should be simple proof that this occurs.  Keep in mind that the net two-way energy flow is always from warm to cold.

Let’s now compare the theoretical Fig. 1 spectrum with a real Venus spectrum (Fig 3).


Figure 3:260 K blackbody spectrum (red) with observed Venus spectrum from The Venera 15 orbiter (blue). 

Here, the red curve is a 260 K blackbody Planck spectrum and the blue is a typical Venus spectrum I plotted which was obtained from the Soviet Venera 15 orbiter.  Keep in mind that the Venusian surface radiates at ~735 K, so the fact that the whole spectrum is seen to radiate at Earth or Mars like temperatures is a good indication that the atmosphere is highly opaque in the infrared spectrum.  Most of this is CO2, but other constituents like water vapor, SO2, and sulfur-water clouds are very important too, along with some other minor species.

Some Remarks about Pressure

It has been argued on some blogs that high pressures can cause high temperatures, and the argument has taken a variety of forms.  One is that p= ρRT (the ideal gas law) implies that a high p means a high T.  Of course, the pressure is 90x higher on Venus but the temperature is only 2-3 times higher than Earth, so such a straightforward proportion obviously doesn’t work.  The temperature must satisfy energy balance considerations, so a better way to think about the problem is to fix T (with other information, namely radiation) and solve for the density, which is of course much higher on Venus.  You can't get all the information from the equation of state alone.  The other argument is that some “insulative” property of gases could keep Venus hot at high pressure, even if the whole atmosphere were transparent to outgoing light.  One way to heat Venus would be to compress its atmosphere, but this would be temporary and eventually the temperature must relax back to its equilibrium value determined by energy conservation considerations.  The way things work is that heat is sluggishly migrated upward by radiation or convection until it finally reaches a point where the air is optically thin enough to let radiation leak out to space.  This doesn’t happen in a transparent atmosphere.

So does pressure matter for the greenhouse effect? The answer is yes, and the prime reason it matters is that collisions between molecules act to “smooth out” absorption and fill in the window regions where air is transparent.  Unlike the quantum nature of absorption and emission, the kinetic energy of moving molecules is not quantized, so it is possible for colliding molecules to impart kinetic energy on the absorber and make up the energy deficit required to make a quantum leap from one energy level to another.  There are some other broadening mechanisms too, but this is by far most important in the lower atmosphere.

Aside from the fact that a 90 bar atmosphere can hold much more greenhouse gas, pressure broadening is huge on Venus, but you can only smooth things out and fill in the windows so much.  Where pressure broadening would really make a difference is to put in a 1 bar atmosphere (even N2) on a very low dense atmosphere like Mars.  The reason why Mars does not currently generate a strong greenhouse effect, even at over 90% CO2, is that the spectral lines are too narrow to have a sizable effect.  Even with almost two orders of magnitude more CO2 per square meter than Earth, the equivalent width is less on Mars.  The equivalent width is a measure of the area of absorption taken out by a molecule (see the wiki article for further explanation on its definition).  The following diagrams illustrate the OLR change in a 250 ppm CO2 atmosphere at Earthlike pressure (Fig. 4a) and 100x Earth pressure (Fig. 4b) (note that the same mixing ratio in the 100 bar atmosphere implies more greenhouse gas overall).  


Figure 5: 250 ppm CO2 mixing ratio for an atmosphere at a) Earthlike pressure and b) 100x Earth pressure

Note that at very high CO2 concentrations, a lot of new absorption features come into play that are irrelevant on modern Earth.  The water vapor and sulfur-bearing compounds on Venus also help to fill in some window regions considerably.   Also unlike Earth, Venus has a non-negligible scattering greenhouse component too (by inhibiting cooling through IR scattering rather than absorption and emission).  These make direct planetary comparisons useless, except that Venus is a case in point of how much a greenhouse effect can matter in planetary climate discussions.

Note also that very dense atmospheres also raise the albedo through Rayleigh scattering; this is the same process that make our skies blue.  A pure Venusian CO2atmosphere raises the albedo to a moderately high ~40%, somewhat short of its current albedo (~77%, because of clouds), but still higher than Earth.  This remark is primarily true for planets orbiting sun-like stars, but for lower temperature stars (like M-dwarfs) the Rayleigh scattering is much less important, since the spectrum of the starlight itself is red-shifted, and Rayleigh scattering favors shorter (bluer) wavelengths.

Could a purely diatomic molecule atmosphere generate a greenhouse effect?

The answer, again, is yes.  This may be surprising because something like H2 or N2doesn’t have the molecular symmetry (to make a dipole moment) that we commonly attribute as a defining characteristic of greenhouse gases.  Similarly, Pressure broadening doesn’t broaden anything that isn’t there to begin with.  But for very dense atmosphere, frequent enough collisions between diatomic molecules can temporarily make a ”four-atom” molecule that behaves like a greenhouse gas.  This effect is much more pronounced at colder temperatures, since the time of collision is longer at low velocities.  Collision induced (as opposed to broadened) absorption has been best studied on Titan, but it’s important on the gaseous planets, as well as some theoretical atmosphere with several tens of bars of H2 or He that are relatively dense and cold.  It’s unimportant on Earth, since the temperatures are high enough and density low enough.

Lapse Rates and Tropopause Height

Several other bloggers have been under the impression that the lapse rate “causes” high surface temperatures on a place like Venus, the idea being that the tropopause is very high and so one can extrapolate down the adiabat very far to reach a high temperature.  As should be obvious from the preceding section, the entire reason why you’re allowed to extrapolate such a far distance is because of the greenhouse effect, which increases the altitude where emission in the opaque regions of the spectrum take place.  In fact, on Venus the high tropopause is a a consequence of the high optical thickness. 

In radiative-convective equilibrium, the atmosphere transports sufficient heat vertically (by convection) to prevent the lapse rate from exceeding some critical value, so that a stratosphere can exist in radiative equilibrium (with a thermal balance between ozone heating and CO2 cooling) atop a troposphere where both radiative and dynamical fluxes are important.   The lapse rate just describes the manner in which temperature changes vertically; it isn’t some supply of energy and you need to specify the temperature at the surface by some other means.  The reason an adiabatic lapse rate might develop and the height to which it extends is most certainly not independent of radiation, which provides a basis for global energy flows.

An adiabatic lapse rate only needs to develop by convection where air parcels at the surface become buoyant with respect to the air above it.  In an infrared transparent atmosphere with no sources and sinks of energy, convection would eventually give out and the tropopause would migrate to the surface, developing a deep isothermal region.

In conclusion, the "greenhouse effect" is a very real physical phenomenon and has no inconsistencies with thermodynamics or any other field of inquiry (and in fact,emerges from these disciplines).  It can be just as important in determining the global temperature as the distance to the sun, and is especially important on Venus.

Acknowledgments: I would like to thank Ludmila Zasova for the Venus Venera spectral data used in Figure 3 (which was provided by David Crisp).  I also made use of Dr. Ray Pierrehumbert's online Python code that supplements his new textbook for image production.

Further Recommended Reading: Pierrehumbert RT 2011: Infrared radiation and planetary temperature. Physics Today 64, 33-38, online here [PDF]

Greenhouse Effect Revisited, by yours truly

ScienceofDoom - no specific link, as he has a large number of articles on Energy Balance and radiative transfer...great multi-series introduction if you wade through the pages

Comment On "Falsification Of The Atmospheric Co2 Greenhouse Effects Within The Frame Of Physics", by Joshua B. Halpern, Christopher M. Colose, Chris Ho-Stuart, Joel D. Shore, Arthur P. Smith And Jörg Zimmermann, in IJMP(B), Vol 24, Iss 10, Apr 20, 2010, pp 1309-1332

Several part series on Venus, by Brian Angliss, starting with this post

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Comments 51 to 67 out of 67:

  1. It is still incorrect to refere to the top of the troposphere and mesosphere as radiating layers; aside from net radiant heating or cooling or gross emission and absorption or net fluxes among layers, for Earth, much radiation escaping to space is emitted from within the troposphere, some comes from the stratosphere, very very little comes from above that; more comes from the warmer layer around the stratopause than from the mesopause region, and more would come from a warmer layer than a cooler layer of the same thickness except for variations in height, line broadenning and line strength (actually I think line strength may tend to increase with temperature but I'm not sure), and composition (ozone in particular in the upper atmosphere).
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  2. ... Actually, I need to review just how good a radiative equilibrium fits the global average upper atmosphere. The point that a 1-dimension column can reach radiative equilibrium or will only be perturbed from that by diffusion at very high levels (or if chemical latent heat release involves very slow reaction rates?) is still important - that spontaneous convection doesn't occur above the tropopause in particular, and the lapse rates are shaped by the distribution of solar heating combined with the need to balance that with net LW cooling. But earlier I wrote that very small fluxes can be important to the upper layers. And a heat pump can pump a greater heat flux than the work input. So what is the work input from the troposphere that goes into the upper atmosphere? PS regionally/seasonally, their is sinking at higher winter latitudes, and rising motion in the summer high latitude mesosphere - the later produces the cold spot at the mesopause there. Sinking in the winter polar stratosphere, particularly in the mid-stratosphere (but not near the stratopause) may still be thermally direct (?) if the rising motion is in the tropics, depending on height and hemisphere. (but it is still forced motion); however, sinking in midlatitudes, or high latitudes at the tropopause, is thermally indirect relative to rising motion near the equatorial tropopause (but now I'm not sure if there is sinking motion in the midlatitudes ? - sorry I'm a bit rusty there. See textbooks, etc.). The coldest part of the atmosphere is the *summer* polar mesopause; other cold spots are the equatorial tropopause, and the mid-stratospheric winter polar region, which is still warmer than it would be without the sinking motion forced to occur there (see Holton, "An Introduction to Dynamic Meteorology", ch 12). I suspect the changes in APE (in the form of temperature anomalies produced by forced motions) produced by the forced circulation are generally balanced by the radiative disequilibrium associated with them - the net LW cooling or heating will tend to destroy those APE changes. But so far as I know, a global annual average of radiative fluxes might still be nearly in balance above the tropopause, until you get to where diffusion becomes important. I'll have to go back to that fig. 10 in that article I cited above to see if it is for a global average. If so, it indicates radiative equilibrium at least in the lower mesosphere.
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  3. That article again: "The HAMMONIA Chemistry Climate Model: Sensitivity of the Mesopause Region to the 11-Year Solar Cycle and CO2 Doubling" Schmidt et al.
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  4. It is the case of pointing up some consequences that follow to the preceding simulation of the atmosphere. The CO2 affects heavily the behavior of the atmosphere but not in the way commonly claimed. It produces the arising within the Earth’s atmosphere of the tropopause and mesopause heat sinks where are collected all the forms of wasted energy which are sent to space once converted to EM radiative energy. Then the CO2 makes the atmosphere able to emit the heat which else would be continuously accumulated within it, thus producing a runaway warming. The atmosphere without CO2 would be very hot (I think it would be thermally vanished). The cooling effect occurs within the isothermal sinks because the conversion heat->EM radiation, in effect, is a phase transition because the excitation/disexcitation takes place as change of the internal molecular energy which doesn’t affect the translational molecular KE ant thus the temperature. The most important result is that the emission power is simply proportional to T^4, i.e., it is a purely intensive property, as moreover is explicitly stated by the Einstein’s relation F=1/(M0/M1-1) claiming that the photonic density is not an extensive property. We can assume whatever value for M=M0+M1, in this case the amount of CO2 present within the atmosphere, and M0/M1 will remain constant. This is also shown by the Earth’s and Venus’ temperature profiles. That means that even increasing about 4e5 times the atmospheric CO2 we don’t have any serious effect on the atmospheric temperature profile. Thus, the alarmists’ claims about the GW caused by CO2 seem to be physically unfounded and this matter would be totally upset.
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  5. 54 - Michele "Thus, the alarmists’ claims about the GW caused by CO2 seem to be physically unfounded" I'm seeing the physics words but not the physics. Do you have a link to a paper or proper analysis demonstrating your claims? There are plenty of links on this site showing how "greenhouse" gasses produce warming (e.g. the ScienceOfDoom pists) are well founded. So, equally, could you show where the errors (and thay must be very big and obvious) are?
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  6. Re 54 Michele - you keep coming back to the same basic errors. 1. In your description a few comments back, it seems you rigged the setup to have two levels radiating to space. You then said that the physics may be simpler than we are making it. But I think the underlying physics is simpler than you are making it (what physics could cause two radiating levels independent of composition and at odds with temperature), although the consequences are complex, they are complex in a simple way - I mean, it takes a lot of number crunching to get the results right, but you can understand qualitatively how a lot of it works just by picturing it (think about seeing through a fog. How far can you see. An object fades into the distance. Now consider instead smoke that glows incandescently. Given a particular temperature distribution within the smoke and whatever objects are present, how does the brightness of the radiation vary with location and direction? Sum over direction (properly weighted by geometrical considerations) to find gross and then net fluxes of radiant energy; the divergence is a net radiant cooling rate. Now consider a smoke that is not spectrally grey but rather has absorption and emission lines or bands, of various shapes, etc. You have to use the Planck function now, a more complex relationship than the T^4 proportionality, but nonetheless it always increases with increasing temperature. Absorptivity = emissivity at LTE. If not at LTE, quantitatively things change, but there can still be some qualitatively similar behavior up to a point. In the limit of particles absorbing and then emitting photons of the same energy, this becomes like scattering. You can have a greenhouse effect based on that, too, or also based on scatteriing involving photon energy changes (Raman, Compton, others...)) The cooling effect occurs within the isothermal sinks because the conversion heat->EM radiation, in effect, is a phase transition because the excitation/disexcitation takes place as change of the internal molecular energy which doesn’t affect the translational molecular KE ant thus the temperature. Molecular collisions redistribute the energy among translational, vibrational, rotational, and if hot enough or depending on other things, electronic or chemical forms. The Planck function describes the intensity of radiation that can be emitted given a thermodynamic equilibrium distribution of the energy over these forms (but you can exclude disequilibria that are not 'in play' in the relevant timescale - ie the surplus unoxidized CH4 in the atmosphere doesn't perturb LTE much for the given composition) - and it applies to any volume possessing material of some optical thickness with some temperature, provided the volume is statistically large enough, which is generally not a severe constraint, and also that the volume is isothermal, which is easily approximated by using small volumes. It applies over any time period statistically long enough, also not a severe constraint. Thus a change in temperature over space and/or time only requires using sufficiently small grid resolution to do calculations. Emission of radiation from vibrational/rotational/other de-excitation results in a cooling via providing a sink for translational kinetic energy; likewise absorption results in warming. A layer of given thickness and composition, setting aside line broadenning and line strength variations, will emit more intensely if at higher temperature. The stratopause region doesn't dominate radiation emitted to space at most wavelengths because it is so thin in terms of optical thickness. The mesopause region is much much much thinner. And if, at the same frequency, the tropopause and mesopause can both emit radiation, the would also absorb each other's radiation, to the extent the intervening space is transparent (which it isn't!) and to the extent they can emit (relative to the Planck function). If the mesopause region were sufficiently opaque you couldn't see much radiation from the stratopause or tropopause reaching space. But from the spectra I've see, the upper mesosphere and above is so optically thin you could hardly see any radiation from it reaching space and just about all radiation reaching space is coming from below. At most wavelengths it is coming mainly from below the upper stratosphere - the warmth of the upper stratosphere is responsible for the narrow spike in outgoing LW radiation (OLR) near 15 microns, where CO2 is most opaque; this is within a broader valley of OLR where CO2 is opaque enough for the brightness temperature to approach that of the upper troposphere and lower stratosphere; outside of that CO2 is only opaque enough to block some of the radiation from the lower troposphere and surface. Going outward from 15 microns, the net upward LW flux at the tropopause level increases; adding more CO2 has the effect of broadenning the spectral interval over which a given opacity is exceeded, thus reducing the net upward LW flux at the tropopause (even after stratospheric/upper atmospheric cooling due to the increased net outward LW flux from the stratosphere through both top and bottom) - conservation of energy requires that this results in a build-up of energy below the tropopause. This continues until the resulting temperature changes restore approximate radiative equilibrium at the tropopause. The distribution of the temperature change **below** the tropopause is greatly affected by convection. You can't begin to successfully argue against the assertion that doubling CO2 tends to increase Earth's surface temperature about 3 K, +/- some range (Charney sensitivity - excluding some feedbacks) when you are supporting points that are false or unsupportable while the assertion itself is supported by true facts and supported points.
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  7. Holton (1992), p. 405, (in contrast to/with the troposphere): "In the stratosphere, on the other hand, infrared radiative cooling is in the mean balanced primarily by radiative heating owing to the absorption of solar ultraviolet radiation by ozone. As a result of the solar heating in the ozone layer, the mean temperature in the stratosphere increases with height to a maximum at the stratopause near 50 km. Above the stratopause temperature decreases with height owing to the reduced solar heating of ozone." p.404, the troposphere: "Because very little solar radiation is absorbed in the troposphere, the thermal structure of the troposphere is maintained by an approximate balance among infrared radiative cooling, vertical transport of sensible and latent heat away from the surface by small-scale eddies, and large-scale heat transport by synoptic-scale eddies. The net result is a mean temperature structure in which the surface temperature has its maximum in the equatorial region and decreases toward both the winter and summer poles. There is also a rapid decrease in altitude with a lapse rate of about 6[K/km]." I should add that you can account for the solar heating of the air simply by using net radiant cooling (net LW cooling minus solar heating). And the small solar heating of the troposphere is in terms of K/day, or heating rate relative to mass. In terms of the total flux, solar heating of the troposphere is considerably larger than that of the rest of the atmosphere. The solar heating in K/day is smaller in the lowest part of the stratosphere than it is in the troposphere, but gets larger going into the upper stratosphere (Hartmann).
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  8. And if, at the same frequency, the tropopause and mesopause can both emit radiation, the would also absorb each other's radiation, to the extent the intervening space is transparent (which it isn't!) and to the extent they can emit (relative to the Planck function). Of course the whole upper atmosphere is nearly transparent over some spectral bands, over a broader interval than the 'atmospheric window' and more transparent than the 'atmospheric window'. (the atmospheric window, roughly 8 to 12 microns (interupted by ozone somewhere around 9 or 10 microns) is a band where a sizable fraction of radiation from the surface can reach space, absent clouds or high humidity levels. Aside from ozone, Most of the non-cloud opacity in the atmospheric window comes from water vapor and most of that is in the lower troposphere) But there isn't a particularly greater abundance of greenhouse gases near the tropopause or mesopause than in between (in fact ozone has a maximum in between), so at wavelengths where emission from the regions of the tropopause or mesopause is significant (relative to the layer thickness, which is extremely small for anything above the stratosphere), so would be emission and absorption from the intervening layer.
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  9. In the same vein as my 57, see fig 10 from source in 53. It is a global annual average. It shows solar heating generally almost in balance with net LW cooling. However, I think it may be showing the part of solar heating via chemical latent heat at the point where the chemical latent heat is released. Hence the location where solar radiation is absorbed may not be the same, althouth I think it has a similar general pattern in the lower mesosphere. Anyway, that's a bit different than conduction/diffusion of sensible heat and though circulation may be involved, it wouldn't be necessary to bring fluxes into balance there (temperature would adjust as necessary to bring net LW cooling into balance with the others). There is an interesting descrepancy between the cooling and heating rates higher up - I'll have to look again but I think it may not be balanced by conduction/diffusion; perhaps there is a fingerprint of convection in the global average? But a reminder that this is forced motion, not locally spontaneous.
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  10. Re Michele - The cooling effect occurs within the isothermal sinks because the conversion heat->EM radiation, in effect, is a phase transition... That last term - maybe part of the problem? Granted, energy is changing forms and so that could be considered a phase transition, but when I here 'phase transition', I generally think of a substance or mixture changing from a solid to a liquid and/or to a gas, etc., or various changes between different crystal structures. Sometimes I think this may also involve changes in chemical equilibria (I think in some cases a liquid may react with a solid to form a different solid during a phase transition in which each solid is a different substance (though with dissolved impurities); it certainly can involve solid vs liquid vs gas solubility. For a pure substance, generally (so far as I know) such physical phase transitions occur isothermally (if provided they are also isobaric) - meaning that the two or more phases only coexist in equilibrium at a single temperature (for a particular pressure). And any latent heat involved must be given off or taken up at that point. However, in mixtures, it can often be the case that a phase transition occurs gradually. This may be punctuated by some isothermal (if isobaric) phase transitions (for example, if I remember correctly, the point at which the remaining liquid freezes into two different solids in a eutectic phase transition (this can happen because two substances may be miscible as liquids but only have limited solubility in each other as solids)), but in between there are spans of temperature in which different phases coexist, with proportions varying gradually - the phases will generally have different compositions that vary with temperature and the composition of the whole is maintained by changing the mix of phases. This is commonly the case between a liquid and solid phase. In a phase diagram, this is illustrated with lines/curves, I think they're called the solidus and the liquidus. Other interesting terms - peritectic, syntectic, etc. And of course, chemical equilibrium varies gradually (although maybe sometimes quickly) over a span of temperature. Anyway, none of this really is quite the same as changing the form of energy from a difference in vibration/rotation mode to a photon. Each type of transition behaves according to the relavent physics. Photons don't 'boil off' a material like steam from liquid water at a single set temperature.
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  11. (PS of course liquid water coexists with vapor over a range of temperatures, but the vapor phase is in a mixture in such familiar conditions. If the vapor phase were chemically pure, then the vapor pressure would be the pressure that the liquid is at as well.)
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  12. @ Patrick … (what physics could cause two radiating levels independent of composition and at odds with temperature) … For the radiative sweeping of the wasted energy, we have two spatial locations defined by the thermal orography of the planetary atmosphere. If we analyze the temperature profile we can view very well its likeness with an unique closed drainage basin (Venus) or with two closed basins (Earth), divided between each other by a watershed (stratopause) where the showered water converges to a single/double bottom valley lake which behaves as a sink and disposes of the collected water by evaporation (phase transition) and where the level of the water will be determined by the balance of the incoming/outgoing mass. Well then. Where is it the physics inconsistency?
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  13. Re Michele Well then. Where is it the physics inconsistency? Radiation doesn't behave just like water flowing under gravity, but borrowing your analogy anyway, what you've forgotten is that evaporation doesn't only occur in the valley, it occurs on the hill as well. In fact there is more evaporation, per unit area, on the hill than in the valley (the analogy gets tricky here as to why, but we could say it is because the wind is stronger on the hill. Actually it is by said evaporation that the water reaches the valley as well as space, and here the analogy falls apart almost completely. So please consider radiation physics.)
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  14. Re Michele - Also remember, in your analogy, liquid water is the enthalpy contained in the non-photons. Thus, the topography you speak of is not a landscape that directs water flow - it is the liquid water itself! And given that (except at sufficiently great heights) there is little conduction and no spontaneous convection in the part of the atmosphere being considered, in a radiative equilibrium the only flow of water from one place to another is by evaporation and condensation. But to get a better understanding, again, please try going right to the physics of radiation; this analogy could lead you astray.
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  15. @ Patrick I never argued that the radiation flows because I am strongly convinced that it doesn’t occur. What flows is the wasted energy which is collected into the one/two cul-de-sac and then converted to radiation and so disposed of. I think that if you continue to argue about the total radiative balance we could leak the true causes leading to actual temperature profiles (GH effect). Of course the radiation/evaporation also takes place on the way but it seems to be very tiny as its contribute to the lapse rate seems to be negligible: if it had a real weight the lapse rate of troposphere, e.g., would be always hyper-adiabatic, whereas we well know it is, at large scale, adiabatic or at least hypo-adiabatic. Aside that, it is undeniable that the atmosphere, by means of the temperature gradients, behaves as a scavenger which sweeps and collects the waste energy toward the tropopause and the mesopause where the heat has only one way to escape to space: it has to be converted thermally to radiation. as the results of my simulation show, also if roughly. The temperature profiles are determined by the conduction/convection and, above all, by the conversion heat->radiation localized within the collection regions where the heat remains confined.
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  16. Michele, I'm seeing a very bizarre interpretation of the physics of the atmosphere, at odds will all previous observation of it. Your second paragraph in #54 is wrong in every sense. If extra CO2 emitted energy trapped by the rest of the atmosphere (a weird concept), one of its implications would be that glacial periods, with low CO2, would be very hot! Large ice sheets tend to suggest that they weren't... I seriously think you need to rethink your ideas about radiation physics, as there is an awful lot of experimental evidence and working modern technology that suggests your physics is wrong.
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  17. Re Michele - as the results of my simulation show, You're simulation was designed based on your assumptions; it doesn't show those assumptions to be correct. I think that if you continue to argue about the total radiative balance we could leak the true causes leading to actual temperature profiles (GH effect). I and others already did. You refused to accept it. Of course the radiation/evaporation also takes place on the way but it seems to be very tiny as its contribute to the lapse rate seems to be negligible: if it had a real weight the lapse rate of troposphere, e.g., would be always hyper-adiabatic, whereas we well know it is, at large scale, adiabatic or at least hypo-adiabatic. No. We've been over that. The lapse rate is in radiative disequilibrium; the troposphere has to have net radiant cooling. See Real Climate thread - June 2011 Unforced Variations. Aside that, it is undeniable that the atmosphere, by means of the temperature gradients, behaves as a scavenger which sweeps and collects The temperature profile shapes the radiant flux profile. There's no 'scavenging', 'sweeping', 'collecting', except in limited analogy; - the radiation just goes where it goes; it's emitted at higher rates at higher temperatures, at lower rates at lower temperatures; optical properties determine the rate of emission per unit volume or for a given temperature; they also determine the rate of absorption per unit volume for a given incident flux. Radiation from all levels can reach space in so far as the intervening layers are transparent - but they can't be transparent if they can also emit, hence, greater fractions of what are emitted from higher layers can reach space. If you can't be bothered to distinguish reality from fantasy, I can't help you. I'm done.
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