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Climate Hustle

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 1 to 50 out of 67:

  1. Hopefully no-one's offended by this self-promotion, but I did a five-day series of posts that took apart common denier arguments for how Venus could be kept hot by means other than the greenhouse effect. This link goes to the first of the series.
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  2. I hadn't seen this before but I just added it to the Recommended reading
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  3. Thanks!
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  4. Kudos on an excellent post.
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  5. My one-line repsonse to climate denial bloggers who post about the Venusian atmosphere:

    "What happens on Venus, stays on Venus!"
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  6. 5 - Badgersouth

    Sometimes this site really needs a "like" button :-D
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  7. Thanks for the article, Chris - I haven't had a chance to read it in detail, but a quick perusal answered a few questions I had. I especially like the graph of emitted IR from Venus - it tells quite a story!
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  8. I had left a link to your 'Princeton' article on Jeff Id's blog, where he lauded Happer's WUWT article. That precipitated his interest in your post.
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  9. This is good. Best explanation I have seen of pressure broadening, whic is important to explain why band saturation is not occurring for CO2 absorption wavelengths.
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  10. The thing which struck me about Steve Goddard's venus article on WUWT (its all due to pressure not CO2) is that he used the diifferential form of the formula for variation of temperature with height. The normal formula would have had an integration constant T0. This means he managed to neglect/ignore/hide an important variable that in effect describes the overall the
    temperature of the atmosphere.
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  11. Observing the Heart’s temperature profile, we note that in its atmosphere there are two broad sinks (the tropopause and the mesopause) that collect the upwelling&downwelling thermal energy flows, held by the existing temperature gradients, and radiate them to space. The lower atmosphere, near the surface, is affected by the surface, the troposphere and the tropopause.
    Simplifying, let’s assume that the atmosphere is restricted to the troposphere.
    We can say without any doubt that the tropopause emits only a part of the needed heat because its temperature (Tt) is lesser than the effective one (Te) whereas the surface (which has a temperature Ts higher than Te) encounters some difficulties/resistances to radiate to space and its emission takes place with an efficiency (ε) lesser than one. Off course, simplifying, the balance of the thermal fluxes requires that there must be εTs^4 + Tt^4 = Te^4.

    Also, observing the brightness temperature vs wavelengths, ”(e.g. here)” we read that the Earth’s thermal sinks of the atmosphere are due to CO2 as well as for Venus and Mars (the absence of another sink for the mesopause temperature lets us to claim that it is due also to the CO2 and that it is overlapped by the tropopause sink). We read too that Earth has some others GHGs and so, while several gases take part in reducing the efficiency (ε) of the surface emission, the sole CO2 determines Tt. We can claim that if the Earth’s atmosphere was totally without CO2, both Tt and Ts would be higher and the surface would be warmer. It’s astonishing, the “vituperated” CO2 plays the role of to limit the GH effect.

    Further. The behavior of the atmosphere has to be analyzed from a fluid-dynamic point of view taking into account that a particle of the atmospheric gas, once heated by the surface, leaves it and climbs adiabatically.
    Assuming that the changes over the time vanish for all the playing variables, we read:
    1) The conservation of the momentum along the vertical direction states that, apart the viscosity, the vertical acceleration of the particle is generally (- g – (1/ρ)δP/δz) and for the adiabatic flow and for an ideal gas it is (- g - CpδT/δz). The acceleration is positive (the rising is accelerated, the falling is decelerated) if δT/δz is lesser than –g/Cp and vice versa. The rising/falling is uniform with δT/δz = -g/Cp.
    2) The conservation of the energy (in absence of sources and sinks within the adiabatically rising particle) tells us that the total energy (CpT + u²/2 + gz + … ) is constant, that’s, CpT + gz = constant for the uniform flow, i.e. δT/δz = - g/Cp. In other words a particle that leaves the surface at the temperature T0 is able to reach the height z = Cp(T0 – T)/g and if it has to reach the tropopause to yield a part of the heat that is there emitted, it needs to start from the surface at least at the temperature Ts = Tt + gH/Cp (H is the thickness of the troposphere). Conversely, the surface has to be at least at Ts to be able to heat the particle.

    Thus, the surface temperature is determined by the thermodynamics and fluid dynamics, once the tropopause has been set up at the height where the pressure allows the largest emission (Earth’s and Venus’ tropopause have similar pressures and temperatures, but CO2 densities tremendously different, as well as for Earth’s mesopause and Mars’ tropopause.

    All this in agreement with the consolidated physics. I think all others argumentations would integrate it without repudiate it.
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  12. Re 11 Michele - part of the problem, I think, is that you are using imprecise concepts, or at least imprecise language, which may lead you to confusion.

    First, the emission from the surface is not changed (in any simple direct way) by atmospheric radiation. What is changed is the amount of that radiation which reaches space, and the amount and distribution of absorption of that radiation by the atmosphere, and the amount of radiation from the atmosphere absorbed by the surface.

    Your first equation, εTs^4 + Tt^4 = Te^4, is simply incorrect. Even as an extreme simplication (of a grey gas isothermal atmosphere at temperature Tt overlaying a blackbody surface), the equation should be εTs^4 + (1-ε)*Tt^4 = Te^4 - but then the meaning of ε is 1 - atmospheric absorptivity, which is equal to atmospheric emissivity (the effective value over all directions, which I think can be used for an isothermal atmosphere). Really it would make more sense to use an ε for the atmosphere, and then you get (1-ε)*Ts^4 + ε*Tt^4 = Te^4. This is correct for this very simple case.

    But the atmosphere is not a single isothermal layer. It is helpful to consider emission weighting functions. You described the tropopause and mesopause as if they are surfaces that collect heat from the rest of the atmosphere and radiate to space. This is only partially true in a sense. The colder **layers** and surfaces (applicable to low-level inversions) will emit less than they absorb from warmer **layers** and surfaces. But depending on optical properties, the entire atmosphere can be emmitting radiation to space; it happens that, assuming well-mixed gases and setting aside pressure and doppler broadennning and temperature-dependent line strength, the fraction of radiation emitted upward that escapes to space increases going upward, toward 100 % at the top of the atmosphere. Rather than going over the details of fluxes that you find at any level, consider emission weighting functions (EWF for short here). For a radiation of a given direction, polarization, and frequency, the distribution of where that radiation is absorbed is equal to the EWF for radiation of the same type coming back from that direction at the same point. EWF is a density distribution over space, and taking the product of that with the Planck function at each location and integrating over volume (well, over a line if there's no scattering), gives the intensity of the radiation coming from a given direction; the temperature for which the Planck function equals this value is the brightness temperature of that radiation, and if it weren't for the nonlinearity of the Planck function, it would be equal to the EWF-weighted average temperature; if not for the (potential for) nonlinearity in both the Planck function and the temperature profile, it would be the temperature at the centroid of the EWF. Hence the brightness temperature may be equal to the temperature somewhere within the EWF (this must be true if the EWF and temperature vary continuously over space), and the location where this temperature occurs may be thought of as an effective emitting level (note that this varies with direction, so for the whole flux you have to have a weighted average of EWF's for each direction, etc.)

    The effective emitting level of radiation reaching space won't necessarily or generally be at the tropopause - even if it were, this is only a representative level - radiation is being emitted to space from a whole layer, potentially extending down to the surface.

    Regarding why parts of the atmosphere can be colder than Te, consider a case of pure radiative equilibrium with a grey gas. For a sufficiently thin layer at the top of the atmosphere (TOA), the emissivity and absorptivity of that layer can be approximated as zero in their effect on the flux from below, but the layer's temperature is still determined by those vary small quantities. It absorbs some fraction, a, of radiation from below, which must be approximately sigma*Te^4, and in radiative equilibrium, assuming no other heat sources, it must emit a*sigma*Ttoa^4 (Ttoa is the temperature at TOA) both upward and downward. Thus Ttoa^4 must be half of Te^4 (note that if space were radiating downward as if a blackbody at Te^4, then Ttoa = Te. But space's brightness temperature can generally be approximated as zero). This is the temperature of the skin layer. Temperature generally varies continuously through an atmosphere so T must drop below Te at some point below. For atmospheric absorption which is not grey, the formula for Ttoa will be different but at least for well-mixed greenhouse gases, it will still be less than Te. With solar heating, the equilibrium T in the upper atmosphere may be higher than Te, but if solar heating is not sufficient to prevent it, layers colder than Te may still be found as well. The ozone layer is responsible for the temperature maximum at the stratopause, and absorption of higher-frequency solar radiation is responsible for the thermosphere, but in between those regions and between the upper stratosphere and the lower troposphere, T can be below Te because their is sufficient transparency above such that not enough radiation is absorbed from above to prevent it.

    Convection within the troposphere doesn't all go to the tropopause; going higher up, the convective heat flux from the surface declines. This balances a net radiant cooling (including any direct solar heating of the air). It is theoretically possible to have a troposphere in which some layers have no net radiant cooling, in which the convective heat flux, on average in equilibrium, would be constant.
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  13. Patrick,

    you are right, I have some language issue because I am frequently using it only for a short time.

    Conversely, my concepts are very precise.

    I introduced ε to take into account the undeniable fact that the planet’s surface “encounters some difficulties/resistances to radiate to space”, that’s, the fact that the whole system surface-atmosphere emits to space less than the sole surface would do. I simply note the fact without doing any hypotheses on what occurs “to radiation” within the troposphere and so my first equation is perfectly correct. Really, I solely forgot to specify that I was assuming a unitary emission for the tropopause though it was implicit because the brightness temperature obtained by satellite measurements equals that of the vertical profiles obtained using the weather balloons.

    The formula you propose is heavily affected by a your personal point of view (isothermal troposphere and sole radiative heat transfer). Notice, I’d say “your personal uncorrected …” but, so doing, I’d expressed a too factious opinion rather than a skeptical opinion. In any case, it would be more correct to take into account all the known forms of heat transfer: conduction-diffusion, convection, radiation.

    I never described the tropopause and the mesopause as “surfaces” And I wouldn’t do it because they are two region of the atmosphere as large as the troposphere or, also, larger than it.

    Apropos, I would like to ask a very important question. Why and how a very large and isothermal atmospheric region, heated at its opposite edges and emitting uniformly is it able to transfer within it the heat maintaining constant its temperature? The tropopause and the mesopause behave as an evaporator-emitter and, for Earth, the stratopause behaves as a condenser-absorber. In this case we have always that the emission/absorption, as the evaporation/condensation, takes place at constant pressure and constant temperature, except the fact that now we have to do with the photonic pressure rather than with the molecular pressure. Again, why and how? As far as I know, I have not answers. Yet, I feel it is important to answer this question.
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  14. But for very dense atmosphere, frequent enough collisions between diatomic molecules can temporarily make a ”four-atom” molecule that behaves like a greenhouse gas.

    Good to see this, my Ph.D. was on the IR absorption spectra of these kind of entities ! :-)

    The other way that homo-nuclear diatomics absorb IR is through their isotopic variants e.g 15N-14N - Spectra here. Note the intensities values, and indeed the frequency, before concluding that they are significant to the Earth (unlike some people)
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  15. Re Michele 13 - Conversely, my concepts are very precise.

    Well they sound inaccurate and even if you understand them, just be forewarned they could be confusing to people used to more familiar conventions such as using ε for emissivity. Of course you can draw analogies and use analogous language that way, but using phrases like 'evaporator' and 'photonic pressure' may give the wrong impression. But I assume you aren't literally refering to evaporation in the mesopause region or the pressure exerted by radiation (not that this doesn't exist but it isn't important in this context).

    and so my first equation is perfectly correct. Really, I solely forgot to specify that I was assuming a unitary emission for the tropopause though it was implicit because the brightness temperature obtained by satellite measurements equals that of the vertical profiles obtained using the weather balloons.

    That (unitary emission) is precisely why you're first equation is wrong. The only way the tropopause region can emit as a blackbody is if no radiation from below it can get past it. In order for some fraction (any nonzero fraction) of radiation from warmer layers below to get past a cooler layer above is if that cooler layer is partially transparent - it has absorbitivity less than 1 and therefore emissivity less than 1. Consider a situation where a layer and an opaque surface below it are both at the same temperature; assuming no reflection/backscatter from hotter sources, the maximum emitted flux possible (PS we're assuming LTE, of course) is sigma*T^4, where sigma is about 5.67E-8 W/(m2*K4) (the only way to get more is . Applying your formula to this situation, you'd have (1+ε)*sigma*T^4, which would then, a few steps later, allow you to build a perpetual motion machine.

    You can find brightness temperatures corresponding to different levels in the atmosphere at different wavelengths; at some wavelengths essentially no radiation from the surface or even the lower troposphere escapes to space. At other wavelengths a significant fraction of radiation from the surface can escape to space. Sufficiently thick clouds can act like blackbodies (so far as I know) and block essentially 100 % of the radiation from behind them, and at wavelengths where the atmosphere above is transparent, you can read the temperature of the clouds from the brightness temperature of the radiation. A given vertical layer is thicker at angles closer to horizontal, so you'll get different brightness temperatures corresponding to different regions of the atmosphere by varying the angle too. But it is important to note that the level with the temperature equal to the brightness temperature of the radiation is not the sole source of the radiation, it is merely representative; the source of the radiation is distributed according to the emission weighting function, multiplied by the local Planck function. You can think of the emission weighting function as describing how much of what you see is where. Imagine looking through a cloud of smoke. How much of what you see is within 1 meter of you? How much is between 1 and 2 meters? Etc.



    The formula you propose is heavily affected by a your personal point of view (isothermal troposphere and sole radiative heat transfer).

    That's not a personal point of view. The formula you propose is structured in such a way that this is the situation it would describe. Nowhere in my correction does it imply that convection doesn't occur, but you were refering to the radiative flux going to space, were you not? (essentially no convection or other non-radiant energy goes to space. Nothing of immediate climatological significance, anyway. H-escape has implications for geochemical evolution but very little energy is involved relative to radiant fluxes).

    Specifically, an atmosphere is of course not generally isothermal, but if a greenhouse effect is sufficiently weak, an isothermal approximation can be used - if the optical thickness of the atmopshere is small than the monochromatic emission weighting function would be, aside from variations in composition and line broadenning and line strenght, almost evenly distributed within the atmosphere (by mass), and in that case the emission from the atmosphere either to the surface or to space could be approximated as, for a grey gas, ea*sigma*Ta^4, where Ta is the mass-averaged atmospheric temperature and ea is the atmospheric emissivity (in effect for all directions) and the flux to space coming from the surface would then be, assuming the surface is a perfect blackbdoy, (1-ea)*sigma*Ts^4, where Ts is the surface temperature. And note that I am NOT saying that real atmospheres have only well-mixed grey-gas greenhouse effects, nor even that real surfaces are perfect blackbodies, though the later is a better approximation of reality than the former at least typically.

    In any case, it would be more correct to take into account all the known forms of heat transfer: conduction-diffusion, convection, radiation.

    Of course, **where applicable**.

    I never described the tropopause and the mesopause as “surfaces” And I wouldn’t do it because they are two region of the atmosphere as large as the troposphere or, also, larger than it.

    Tropopause, stratopause, and mesopause are, I think, typically defined as the top level of the troposphere, stratosphere, and mesosphere; these pauses are boundaries between layers and thus are surfaces. Of course, in reality the exact location of such a surface will be hard to determine down the the nearest molecule and so there is a region that the surface is within; of course the surface will also vary with weather and region and season, etc. But conceptually one can model an atmosphere as having a troposphere, stratosphere, and mesosphere, etc, and there is no actual air within the tropopause, etc, in that case - it is just a boundary between layers. Hence we may refer to the tropopause-level radiative forcing, for example.

    (And when considering radiation it is important to consider optical thickness, which aside for compositional variations and line strength and broadenning variations, would be proportional to mass, in which terms the troposphere on Earth is something like 85 % of the whole atmosphere. It isn't wrong to say that the stratosphere is thicker geometrically, but thinking in terms of mass is also a useful perspective.)




    The tropopause and the mesopause behave as an evaporator-emitter and, for Earth, the stratopause behaves as a condenser-absorber.

    To a good first approximation of at least the global annual average, the atmosphere above the tropopause (above the troposphere) is in radiative equilibrium. Convection can be approximated as zero. Were it not for direct solar heating above the tropopause (which in particular heats the ozone layer and thermosphere), the temperature would continue declining above the tropopause, but radiative equilibrium would maintain a sufficiently low lapse rate that convection would be inhibited - which of course is why the tropopause is there. When temperature variation is monotonic over large optical thicknesses, the net LW (non-solar) flux is locally from higher to lower temperature. Using the local Planck function instead as a measure of temperature, when the Planck function is concave or convex, the net LW flux will change such that there is an accumulation or depletion of energy - net LW heating or cooling, which must balance either net LW cooling or heating at other wavelengths, and/or convective and solar heating, when in equilibrium; this can occur even if the concave or convex regions are not local minima or maxima in temperature. When a layer is optically thin relative to the structure of the temperature profile, more or less net LW heating, or the opposite for net LW cooling, will tend to occur with minima and maxima in temperature, and there can also be some net LW heating or cooling due to emissions or lack-thereof from more distant regions being absorbed by the layer, and by emission of the layer. Emission increases and decreases (nonlinearly) with temperature, while absorption depends on the temperature at other locations, more distant if optical thicknesses are small over shorter distaces.

    The higher up you go, the farther, both geometrically and optically, you are from the surface, and the closer you are to space, which radiates approximately as a very cold blackbody, near zero K. Higher layers of atmosphere can recieve (setting aside the fraction they absorb) less or more LW radiation from above depending on the temperature of higher layers, but in addition, there is a tendency to recieve less LW flux from above because there is less air above to 'hide' the darkness of space. They also tend to recieve less LW radiation from below when the temperature is decreasing with height, thus the brightness temperature of the upward LW radiantion is reduced. This can still be true even if the temperature is locally increasing with height if the optical thickness is not too large and the increase not too great and over not too thick a layer, because then the emission weighting function may still be dominated by the surface and/or the rest of the atmosphere. Thus to reach radiative equilibrium there is a general tendency, underlying the potentially more variable effects of temperature as influenced by solar heating above the tropopause (and also local conditions where inversions may develop within the troposphere), to be colder going higher. Solar heating alters this by warming the upper stratosphere/lower mesosphere and the thermosphere. Some of this heat is radiated to space and some to other layers and some to the surface if the atmosphere is transparent enough, the cooler layers emit less to space (except for the effects of overlying layers) and less to the surface (except for the effects of underlying layers), and less to the warmer layers, but they can still emit to space depending on high high they are.

    Convection generally (global annual average) cools the surface and warms the troposphere (it is possible to have a situation where convection cools the lower troposphere and heats the upper troposphere, or some more complex distribution, but at least for Earthlike conditions the troposphere is mainly, so far as I know, and at least for globally representative conditions except (?) with no well-defined cloud layers (?), heated by convection throughout (but not evenly). The troposphere experiences net LW cooling that balances convective heating and direct solar heating. The surface experiences both net LW cooling (the difference between emission from the surface and absorption of the flux absorbed from the atmosphere) and convective cooling, which balance solar heating of the surface.
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  16. The "Greenhouse Effect" is an imprecise term.

    The effect of an atmosphere on the planet's surface temperature is affected by multiple atmospheric constituents. Greenhouse gases are the most obvious and most discussed, but suspended particles including liquid droplets, ice crystals, aerosols and dust also contribute.

    In the case of Venus, the top of the clouds are obviously opaque in the spectral region shown in figure 1 above. The regions in which CO2 is transparent show an emission brightness temperature corresponding to the temperature of the cloud tops.

    The contributions of different greenhouse constitutents are not additive. The CO2 in Venus' atmosphere only contributes to the planetary emission spectrum above the cloud tops - all the CO2 below the clouds does not affect the outgoing planetary spectrum.

    If one were to keep all else constant and replace all of Venus' CO2 below the 1 atmosphere altitude with dirt, the new equilibrium surface temperature would be a little less than Earth's, and the emission spectrum would be essentially the same. (Yes, I am ignoring the effect of the blocking of the very long wave emissions seen from Venus through the clouds - that is not the point...)

    The point is that the high surface temperature on Venus is clearly a result of the thick dense atmosphere through the lapse rate, and the IR absorption of CO2 is not a significant factor.
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  17. "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."

    This is a very one-dimensional view...

    A planetary atmosphere is on a sphere illuminated by a sun - resulting in heat sources and sinks from differences in insolation from day to night and season to season. The natural state of a non-trivial planetary atmosphere has a lapse rate in the troposphere.

    In this imagined isothermal atmosphere, any vertical movement of parcels of 'air' would necessarily result in a change in internal energy, and heat transfer to or from the parcel - moving the temperature distribution toward the expected temperature lapse rate. In other words, this isothermal atmosphere can only me maintained if there is no vertical exchange in the atmosphere.

    Also note that the equation for adiabatic lapse rate is not a function of the IR absorption - monotonic gases like Argon still have a significant adiabatic lapse rate.
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  18. guinganbresil,

    Your post #16 is really just full of assertions rather than any physics that can be usefully implemented in radiative transfer modeling. To treat even an Earth-like atmosphere radiatively can involve treating it as a stack of many near isothermal layers, with the temperature and absorber distribution as well as scattering. The upper atmosphere matters, but you can't just insert a cloud deck and watch the temperature soar to 735 K. Actually, in simplistic layer models with one blackbody absorbing layer, the surface temperature is constrained to be no more than the emission temperature multiplied by 2^0.25. This is especially the case where those clouds also make the albedo very large, and to first-order, offset their greenhouse effect.

    In post 17, there's no reason parcels of air will become bouyant, since the atmosphere will relax into a temperature required to eliminate convection.

    Also note that the equation for adiabatic lapse rate is not a function of the IR absorption

    Of course not, because in deriving that formula you turn off radiation.
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  19. Chris - Thanks for the feedback!

    I think we are coming at the problem from two different directions... Literally.

    1 - I argue that the planetary radiative balance is a result of the energy in vs. energy out of a sphere that encloses the entire planet plus its atmosphere. I think we should agree on this...

    2 - This large sphere can be looked at a series of spheres defined by different emission wavelengths - all co-located at a radius that encloses the planet and its atmosphere.

    3 - Each of these spheres will have a flux distribution mapped to its surface dependent on the properties of the planet and atmosphere below it - keep in mind day/night, hemispheric and geographic variations...

    3 - Now 'shrink wrap' each of these spheres - by this I mean reduce the radius until any further radius reduction would change the flux distribution. Now allow the spheres to locally deviate from a sphere and continue the 'shrink wrap' This set of surfaces should define the radiative balance of the planet.

    4 - The temperature profile of the atmosphere below these surfaces would be modeled using the 'shrink wrapped' surfaces as starting point.

    I understand this adds exceptional complexity, and should achieve the same results...

    Changing the point of view like this is important though.

    If you think of an Earth-like planet (~1 atm surface pressure, with ~15C average surface temperature) with a 100% cloud deck - to make it like Venus (please ignore albedo effects - we will hold that constant anyway.)

    Now use this method of modeling the atmospheric temperature downward to the surface - so far so good...

    Now remove ~65 km of dirt and replace it with atmosphere in a way that maintains pressure and temperature profile of the previous atmosphere above the former surface level.
    Perform the calculations again down to the new surface - you will find a very high surface temperature...

    Looking at the planetary surface as a 'zero point' is an anthropocentric point of view - some planets might not even have surfaces...
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  20. Chris -

    In post 17, I think you missed my point.

    I agree with you on the isothermal layers in a one-dimensensional analysis.

    The simplest three-dimensional scenerio would be a tidally locked planet in orbit around a single sun. In this case there would be a large temperature difference between the day-side and night-side of the planet which would support vigorous convection and resulting tropospheric mixing.
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  21. Re guinganbresil - adding a specific point, consider that if you have a layer of clouds and a much hotter surface some distance below it, those clouds will be heated by that layer from radiation. Having gases that block some of that radiation will reduce that.
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  22. Patrick 027 -

    That is a good scenerio. If the atmosphere below the cloud deck is initially transparent to IR - say Argon or something like that, then the bottom of the clouds would absorb the upward radiation. Since the cloud bottom is in a saturated state, its altitude would be determined by those conditions.

    By adding and absorbing gas below the cloud deck you would block that radiation lower in the atmosphere. Convection in the troposphere should keep the lapse rate essentially the same. Since the cloud bottom is no longer exposed to the long wave radiation from the surface I would expect its altitude to lower a bit since it is no longer being 'burned off' by the radiation.

    As viewed from the space there is no change in the outgoing radiation spectrum since the cloud tops have not been affected by what is going on below. Therefore, the planetary heat balance is as it was before - no change...

    Granted this is a thought experiment only - Earth is quite a bit more complicated - spotty cloud deck, etc... But it does show an example of increasing GHG w/o an impact on the planetary heat balance.
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  23. Let’s maintain apart the radiative transfer trying to explain the behavior of the atmosphere only from a point of view of the thermo kinetics and fluid dynamics. Of course if this wouldn’t be sufficient then we will see what to do.
    Viewing the Earth’s and Venus’ temperature profiles ”(see here for example)” we read that there are some convective layers (the troposphere and the mesosphere for Earth, the sole troposphere for Venus) where the atmospheric gases rise by buoyancy.

    The spectra of brightness temperature ”(see here for example)” point up that the minimal values of the temperatures, which occur at the top of the convective layers having their bottom closer to ground, are due to CO2 (By the way, notice that Earth without oxygen would be Venus-like also if its pressure is circa one hundredth).

    Really, we can think the CO2 molecules behave as heat engines which, colliding with the surrounding molecules, absorb thermal energy from them, and transform it to EM energy.

    The thermal energy density (J/m³) of the rising air particles changes continuously according to δT/δz and, above all, their EM energy density (J/m³) varies according to T³δT/δz. Both the gradients are negative because the continuous growth of the geo-gravitational energy that phagocytizes them. So, the rising CO2 molecules never are in LTE, the thermal energy (needed to excite them until the resonance) is used for other different purposes (the rising of the entire air particle), and there can’t occur any radiative emission.

    In other words, the gases of the convecting troposphere rise until they aren’t trapped by the thermosphere and stratosphere, and they can emit heat radiation only at least at its top, within the isothermal layer above.

    It seem that the temperature profiles of the atmospheric gases are fully explained by the thermo kinetics and by fluid dynamics. The surface temperature is determined by the lapse rate and above all be the altitude where the rising air particles are stopped by the inverted slope due to the external radiative heating of a layer of the atmosphere above it.

    Of course, also the surface radiation around 15μm forces and excites the CO2 molecules which could scatter it. I think this isn’t the case, otherwise, the brightness temperature around 15μm should be higher. The CO2 fully wastes the EM energy to heat close the ground and this can be partially converted back and emitted to space only at the top of the first convective layer above the ground.
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  24. Re guinganbresil - If you made the atmosphere transparent below the cloud deck, and the temperature of the surface were sufficiently high, so that the heating of the cloud deck by radiation from the surface were sufficient, if the cloud deck were completely burned off as a result, then the surface radiation would simply go off to space (unless there's another cloud deck or some other source of opacity above) - furthermore, the backradiation at the surface from the original cloud deck would be lost. The net LW (radiant) cooling of the surface would be increased, which would be taken away from energy available for convection. The net LW flux at the tropopause level (above convection) would increase, cooling the whole surface+troposphere, so even if the lapse rate were maintained, the surface temperature would fall. This is setting aside the effect on solar radiation.

    The burning off of a cloud deck is a feedback of the same category as water vapor feedback and surface albedo feedback. Lets' keep the cloud deck and see what happens. The increased net LW flux in the space between the surface to the cloud deck must be balanced by a reduction in convection - if the convective flux was originally not big enough, convection could go to zero and the lapse rate could decrease, creating a stable layer and necessarily tending to reduce surface temperature while increasing the temperature at the cloud deck.

    But looking for what happens at equilibrium, it's easiest to get to the effect at the tropopause level and then get back to convection. Even if there remains some convection beneath the cloud deck and the surface temperature is sustained, the cloud deck must then get warmer and the emission from the top of the cloud deck will increase. This will tend to increase the net LW flux out of the tropopause and out to space (effect modulated by absorption by overlying layers). Thus this situation cannot be sustained; energy is being lost from the troposphere and surface; there must be a temperature reduction. If both the cloud deck and surface remain in/adjacent to the troposphere, the nonlinear relationship between temperature and emission will reduce the net LW flux from the surface to the cloud deck. Whether or not the reduction is sufficient to allow convection to be the same or greater than it was originally (before removing opacity from the space between clouds and surface) is not determined as this description is too general.
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  25. Re 20 guinganbresil - I think that's an interesting issue and I tried to estimate some things myself at another post - I think it was in comments at an earlier post by Chris Colose on his own blog. Perhaps a scale analysis (this may be over or underdetermined and there may be some errors, but at least this gives a sense of what might be done):
    U ~ L/T,
    Area ~ L^2,
    heat flux ~ R*L^2, where R is *a* radiative forcing,
    heat flux between hemispheres ~ U*L*(Th-Tc)*H*cp*density,
    rate of kinetic energy production by horizontal motion ~ L*H*U*L*(ph-pc) = U*H*L^2*(ph-pc) where ph-pc is a representative pressure difference between the cold and hot side and proportional to Th-Tc (at surface the difference will have an opposite sign than at the top of the overturning layer of depth H - or H could be an e-folding scale), kinetic energy supply ~ R * L^2 * 1-Tc/Th, viscous kinetic energy sink ~ viscosity * L^2 * U/H - or is it U^2/H, or U/H^2, I'll have to get back to that...

    mixing kinetic energy sink (mixing heat downward) ~ ?
    (could be negative or zero on the hot side - or incorporate thermally direct localized overturning on the hot side into the mixing term, and it would be negative if the export of heat by horizontal winds is sufficient to maintain a greater than adiabatic lapse rate),

    Actually I need to go back and specify R farther; Rh could be the net radiant heating of the surface in the warm hemisphere; Rc could be the radiant cooling of the surface in the cold hemisphere; 1-Rc/Rh ~ (1-Tc/Th), except that whatever kinetic energy is produced is eventually converted to heat anyway, which in terms of necessary heat flux would be divided into an addition to Rc on the cold side (kc) and an effective addition to Rh on the warm side (kr) so that for the actual Rc and Rh, 1-(Rc-kc)/(Rh+kr) ~ (1-Tc/Th), and Rc-kr = Rh+kr ... no wait, that can't be right...

    Rate of conductive heat supply to surface on cold side ~ L^2 * (THc-Tsurfacec)/H * K , where THc is the temperature at height H above the now go play with it.

    Some of the above clearly needs more work, but some things are clear:

    Note that you could have overturning with cold air masses sliding under warm air masses without actually having an adiabatic lapse rate. In fact, that kind of overturning decreases the lapse rate. With cold air coming in over a warm surface you could get something more like a troposphere, and perhaps some stable layer of air in the 'winter/night' hemisphere/region would be considered part of the global tropopshere as it is on Earth (although the troposphere is still not as stably stratified as the stratosphere - except maybe (I'm not sure) in the inversion near the surface, which is not the whole troposphere). However, in the polar nights on Earth, the troposphere, heated by horizontal import of warm air from warmer places, can lose that heat to the surface by radiation and conduction/mixing and can lose that heat to space (and the stratosphere) by radiation as well. With no greenhouse effect (specifically of the emission/absorption kind), the troposphere cannot cool by emitting radiation, and so either it must be warmer or the surface must be cooler to get the same heat flux, which must be entirely to the surface. Kinetic energy from the large scale overturning may drive downward mixing of heat; otherwise you have to rely on conduction/diffusion. Possibly the lapse rate would be such that the stratosphere does reach the surface. The troposphere might perhaps be a bubble on the hot side, which may extend somewhat into the night/winter side. The depth of the overturning layer in the night/winter side must be small enough for conduction to make up for what mixing cannot accomplish, to balance the heat supply - itself limited by the depth of the layer and the wind. Thus the layer may tend to be shallow. The tropospheric thickness on the hot side would be determined in part by the supply of cold air from the cold side, which would be determined by the wind speed and the depth of the layer which can lose heat to the surface at the necessary rate. So the troposphere on the hot side may also be forced to be shallow. If there is any solar heating of the air itself, this also has to be mixed and/or diffused/conducted downward.
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  26. Re Michele - the mesosphere on Earth is not convective. It is less stable than it would be with a zero or negative lapse rate, but there isn't much convection there.

    Generally, the convection that does occur in the Earth's stratosphere and mesosphere is thermally-indirect motions (heat pumps) forced by kinetic energy produced by thermally-direct motions (heat engines) in the troposphere; the kinetic energy - actually the fluid mechanical energy which is a combination of kinetic energy and APE (although the ultimate conversion of remaining kinetic energy to APE is the heat pump part) in the form of fluid-mechanical waves, propogates upward as gravity waves, equatorial waves of various types (associated with the QBO; I haven't read of this being thermally indirect or driving meridional overturning but I would think it has to be thermally indirect), and Rossby/PV waves (associated especially with the Brewer-Dobson circulation within the stratosphere and 'sudden stratospheric warmings'). The energy is absorbed above when and where kinetic energy is dissipated mechanically (mechanical damping of the waves) and otherwise converted to APE in thermally indirection motion with the resulting APE being dissipated radiatively (thermal damping of the waves).

    Really, we can think the CO2 molecules behave as heat engines which, colliding with the surrounding molecules, absorb thermal energy from them, and transform it to EM energy....Both the gradients are negative because the continuous growth of the geo-gravitational energy that phagocytizes them. So, the rising CO2 molecules never are in LTE, the thermal energy (needed to excite them until the resonance) is used for other different purposes (the rising of the entire air particle), and there can’t occur any radiative emission. ... The surface temperature is determined by the lapse rate and above all be the altitude where the rising air particles are stopped by the inverted slope due to the external radiative heating of a layer of the atmosphere above it.

    No, very much wrong and confused, sorry. The tropopause level doesn't necessarily or generally correspond to the effective emitting level. The fact that you can see spectra where some freqencies have brightness temperatures higher than the tropopause temperature should alone be a clue. Note also that the CO2 band is not only that part with the lowest brightness temperature; it extends outward from there. Same for water vapor, too.

    See
    374
    http://www.realclimate.org/index.php/archives/2011/06/unforced-variations-june-2011/comment-page-8/#comment-208838
    383
    http://www.realclimate.org/index.php/archives/2011/06/unforced-variations-june-2011/comment-page-8/#comment-208856

    and some clarifying comments in between.


    Of course, also the surface radiation around 15μm forces and excites the CO2 molecules which could scatter it. I think this isn’t the case, otherwise, the brightness temperature around 15μm should be higher. The CO2 fully wastes the EM energy to heat close the ground and this can be partially converted back and emitted to space only at the top of the first convective layer above the ground.

    Actually near the center of the CO2 band, it is so opaque that much/most of the radiation emitted at the tropopause level is absorbed, relatively nearby. The net LW flux at the tropopause is or is close to zero; the effect is or nearly is saturated. Adding CO2 doesn't have much effect on the tropopause radiative forcing at the center of the band. It DOES have an effect a bit outside the center of the band, where it's opacity is intermediate (it will also have some indirect effect as stratospheric adjustment will affect the downward flux from stratospheric water vapor and ozone as well as CO2). The opacity for a given level of CO2 drops roughly exponentially away from the band center, which is why each doubling of CO2 effectively widens the band by a given amount and has a corresponding amount of radiative forcing (if there were only a tiny amount of CO2 then the band center wouldn't be saturated and the forcing would tend to be more linearly proportional to CO2 amount; for the amount of CO2 on Venus, other bands become important and the proporitionality if forcing to amount of CO2 is different again. (Also, the climate itself affects the forcing per unit amount change - different wavelengths have different relative importances at different temperatures; the radiative fluxes change; there are variations in water vapor and cloud overlap on Earth (etc. for Venus, though I'm not sure how the feedbacks work there), and the vertical temperature profile is important. Also there are variations in line broadenning and line strength, ... etc.)
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  27. @ Patrick
    Not at all, the mesosphere has to be convective as well as the troposphere.
    If the tropopause emits as BB the outgoing power should be σT^4= 138 W/m² and, assuming the CO2 is the sole emitting gas with a width of band of 1% of the total spectrum (we well know it is very higher), the real outgoing power should be 13.8 W/m² and this can be obtained with a δT/δz = 13.8/(2.5e-3) = 55284 K/m !!!!!!!! The same compute for the mesopause gives δT/δz = 6.8/(2.5e-3) = 2480 K/m !!!!!!!!
    Any other comment becomes worthless. The emitting CO2 is able to make up the convective upwelling motion and so the quasi adiabatic lapse rate with an outgoing power a little greater than (2.5e-3)10/1000 = 2.5e-5 W/m², i.e. always.

    The brightness temperature diagram ”(see here)” point up the fact that broadening of the CO2 band is quasi the same for the three planets having CO2 densities abysmally different. That means that the CO2 limits its action to set up the altitude from where the lapse rate starts, obtained by the balance of incoming and outgoing fluxes, and to do that are enough only a few ppm. Its effect is merely qualitative, not quantitative.
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  28. Michele, sorry, no, that's not right at all.

    CO2 optical thickness decreases roughly exponentially away from the band center. With optical thicknesses of intermediate value, a thick layer of air emits to space, or in any direction from any level (a thicker layer of the upper troposphere, potentially extending to and including the surface, will be the source of radiation upward at the tropopause, for example). Not that it's impossible to have a convective layer aloft, but this just isn't the case for the mesosphere.

    The CO2 band actually encompasses somewhere on the order of ~ 30 % of the blackbody radiation in a spectrum for temperatures in the range of the surface and most of the atmosphere. This includes parts where the atmosphere is partially transparent, though.

    Radiative forcing: When you increase the density of a component with cross section (opacity), cross section density, optical thicknesses over the same paths increase in proportion. The distances photons can travel shrink. The emission weighting functions become more concentrated and overall closer to the location for which they are based. With a potential for some variation when starting with great transparency, eventually the brightness temperature approaches the actual temperature; if there is not a disconinuity in optical properties or temperature, the net flux goes to zero. (At the effective TOA, an effective discontinuity, the net upward flux is just the upward flux.) The net upward LW flux at the tropopause must (global annual average, in the approximation of zero convection across the tropopause) balance the net downward SW flux, equal to solar heating below that level, or else energy is being gained or lost from the troposphere+surface.

    Where CO2 is saturated at the tropopause level, the net flux is already zero and can't be farther lowered. But doubling CO2 approximately shifts the same range of optical thickness values out from the center of the band, into where the atmosphere was more transparent. This reduces the net upward LW flux at the troposphere - for upward LW radiation at the tropopause, it 'lifts' the effective emitting level (which is just a representative concept for the emission weighting function) off the surface (if it was there) and to higher and higher levels, and for downward LW radiation, it pulls the effective emitting level from the dark of space, into the stratosphere, and lower into the stratosphere.

    Think of the effective emitting levels (EELS) forming a landscape; the net LW flux can be large when the EEL for upward radiation is on a warm surface and the EEL for downward radiation is in space; bringing them close together eventually makes their temperatures nearly equal and so the net LW flux goes to zero. For radiation at the tropopause level, the two EELs are, around the CO2 band a hill rising upward from the surface and/or clouds and water vapor within the troposphere, and a valley dropping down from space. When the two meet at the band center, adding more CO2 continues to widen the hill and the valley, reducing the interval of relatively larger transparency and increasing the interval where the net LW flux is zero.

    If the climate was previously in equilibrium, the radiative fluxes are now imbalanced, and energy accumulates below the tropopause level - until the the warming that results increases the upward LW flux (which occurs outside the saturated part of the spectrum) to restore balance. It is here where the lapse rate matters - without convection, the radiative fluxes at each level would combine to determine equilibrium temperatures; but with radiative equilibrium being unstable to (moist) convection within the troposphere and surface, the whole of the two warm to balance the radiative fluxes at the tropopause level (and at TOA) while the distribution of that warming is determined by the convective lapse rate, which itself may be temperature dependent (hence the lapse rate feedback), and from various other complexities that arise when considering the full 4-dimensional climate system.

    I have up to this point skipped the effect on the stratosphere; adding CO2 cools the stratosphere, due to a combination of the temperature profile being as it is and the spectra being as they are. The stratosphere has little heat capacity relative to the convectively-coupled troposphere+surface (including the ocean, or at least the upper more rapidly mixed portion of it) and tends to reach radiative equilibrium much faster. This reduces the downward flux at the tropopause level, having a cooling effect, and so rather than using 'instantaneous forcing', we often refer to the tropopause-level forcing with stratospheric adjustment - this is the forcing that the tropopause+surface must respond to.

    However, there is also a feedback when the warming below the tropopause increases the upward LW flux, as some of that is absorbed by the stratosphere, increasing the LW flux emitted by the stratosphere by that amount, some of which is downward - however the stratosphere on Earth is relatively transparent to much of the LW radiation upward from below, perhaps even more so to the increase in LW radiation.

    I
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    Response:

    [DB] I took the liberty of breaking your comment up into paragraphs for improved readability.

  29. ... I didn't even mention the mesosphere or thermosphere in that last part because - while their meager optical thicknesses are important to their own energy balances and in determining radiative equilibrium, they are so tiny compared to the stratosphere (as a whole, anyway) and troposphere that they barely make any difference.
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  30. Re [DB] - thanks.
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  31. re my 26, first big paragraph: The energy is absorbed above when and where kinetic energy is dissipated mechanically (mechanical damping of the waves) and otherwise converted to APE in thermally indirection motion with the resulting APE being dissipated radiatively (thermal damping of the waves).

    Sometimes conditions favoring absorption are what cause energy and momentum of the wave to be absorbed where they are. Sometimes nonlinear wave breaking from sufficient increases in amplitude cause the wave energy to be absorbed when and where it is.
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  32. re my 28 -
    Think of the effective emitting levels (EELS) forming a landscape... and a valley dropping down from space.

    That last part highlights the importance of recognizing that an 'EEL' is a representative concept for something more complex (an 'EWF' - emission weighting function). Because the stratosphere, or at least the upper stratosphere, on Earth, has temperature increasing with height, pulling the EEL out of space and down through the stratosphere would appear to suggest that the radiation goes from having a brightness temperature approximately at zero to having some higher value and gradually dropping down toward the tropopause temperature. But for a well-mixed gas, aside from line broadenning and line strength variations, the first little bit of emissivity added to an otherwise transparent atmosphere produces an EWF such that, for whatever portion is in the atmosphere, it is evenly distributed (over mass for constant optical thickness per unit mass path; otherwise more generally, over optical thickness) So if the inversion of the stratosphere is sufficiently thin relative to a lower isothermal part (and/or sufficiently weak), it may never come to dominate, and having the EEL come down from space may only gradually increase the brightness temperature (and for upward radiation, an inversion at the surface that is sufficiently thin wouldn't keep the brightness temperature of the upward flux at the tropopause from decreasing - unless the surface is colder than the troposphere's average temperature (or averaged in terms of the Planck function, and then weighted by EWF)); and even if the inversion runs all the way through the stratosphere and is sufficiently strong, etc, the downward LW radiation would gradually go from zero to a peak before coming down.
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  33. @ Patrick

    I would like your point of view about the arising of the heat sinks and sources ”(Venus-Earth-Mars Profiles)” within the uniform temperature profile of a perfectly transparent atmosphere later than a GHG is added.

    Perhaps, absit iniuria verbis, a greater synthesis would be more effective for our purposes.
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  34. Re http://ju1zjq.blu.livefilestore.com/y1pjEa2b4sDI2I3SchEL6t4570vOnfDE4gRu7wLOOZTAm1VzBsqmUm9UCRtbhmf_jwW6imVJMR6dGxFLYqu-Cou412qaJDdkXzl/Profiles%20Earth-Venus.jpg?psid=1 -
    I'm not sure but it looks like a Venusian tropopause may exist at ~ 60 km. (this is similar to what is stated here: http://en.wikipedia.org/wiki/Atmosphere_of_Venus) The lapse rate decreases sharply above that. Note that a positive lapse rate can still be stable.

    It's also interesting that the lapse rate is a little lower below 50 km. Perhaps an effect of latent heating/cooling associated with cloud layers. And the gas becomes less than ideal at some point.

    Both Venus and Earth have temperature increasing with height above some point. Earth's temperature goes down and up twice; this is because the ozone layer allows a seperate solar heating maximum below the thermosphere. Oxygen is involved in the solar heating of the thermosphere, but I don't think it's necessarily alone in that role; there is some water vapor in Venus's atmosphere which could be source of atomic oxygen at sufficiently high altitudes. At least on Earth, solar heating of the highest, very thin (by mass) layer of air (the thermosphere) involves a very small fraction of the solar radiation being absorbed by a very small heat capacity which has a very very small emissivity and thus must get to very high temperatures to achieve radiative equilibrium.

    If there were no greenhouse effect (of the emitting/absorbing type), then direct solar heating of the air would have to be balanced by downward mixing (requiring some work input) and diffusion/conduction (requiring larger negative lapse rate to be significant) of heat to the surface. Other things being equal, the negative lapse rate would get larger and large going down through layers with direct solar heating as a greater and greater downward heat flux is required to balance the total solar heating above. Sufficient vigorous mixing in a layer at the surface could 'erode' this profile and set up a convective lapse rate, with a strong inversion on top; but work must be down to accomplish this. See above on the potential for horizontal variations in solar heating of/near the surface to provide some APE. With no greenhouse effect of any kind and a blackbody surface, setting aside horizontal and temporal variability, the equilibrium temperature of the surface would be such that the surface would emit the flux that balances the total solar heating of the planet.

    With a greenhouse effect of the absorbing/emitting kind, radiative equilibrium can occur wherein, with all solar heating at the surface, a constant upward net LW flux would have to be maintained, which requires the surface being warmer than the atmosphere, and generally that the temperature decreases with height - more so with larger optical thickness, as this decreases the photon mean free path, thus requiring a greater temperature gradient to sustain the same net flux. Adding more optical thickness from a grey gas would tend to increase temperature (in full equilibrium) at all levels except at TOA, which would tend toward the same skin temperature (the temperature profile would get compressed toward TOA). But if one adds optical thickness only at some frequencies, the response in temperature can change fluxes at other frequencies as well to compensate, so that the temperature may not have to increase at all levels for radiative equilibrium to be reached. Radiative equilibrium may be unstable to convection in some layers - this has been gone over.

    Adding direct solar heating to some layers of air, the necessary net LW flux profile has to change to restore radiative equilibrium. Start with a constant upward net LW flux above where solar heating originally occured, and add some additional net LW flux that diverges from regions of solar heating and converges towards areas that have reduced solar heating. This requires the layers with solar heating to be relatively warmer than some other layers, so that they can emit more than they absorb to balance the solar heating. With small optical thickness, larger temperature changes are required to get sufficient emission; with large optical thickness, larger temperature gradients are required for the same net LW fluxes. The radiation will be most responsive to temperature changes in spectral bands where the distances over which solar heating (or convective heating, etc.) are on the order of unit optical thickness, so there should be some tendency for the LW fluxes in these bands may largely determine the required temperature profile for equilibrium. For example, if solar heating goes from a low to a high value and back to a low value over a distance of ~ 10 km, then the temperature variation required might be approximated by that which would sufficiently adjust the net LW fluxes in spectral bands where a 5 km distance would be on the order of unit optical thickness.
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  35. Of course, if you add a small concentrated region of solar heating, then there will be a temperature response with net LW flux divergence out of that region at relatively more opaque bands; but this will heat neighboring regions, so the larger region warms up so that a net LW flux can come out of that, at somewhat less opaque bands, etc. The process would continue until the additional net LW flux is escaping to space; this will require more 'steps' if the atmosphere as a whole (depending on spectral structure) is more opaque, and each of those steps added warmth, so the original affected region gets warmer (When the LW flux out of the solar heated region reaches a layer that can radiate where other layers are more transparent, the next step will have some of that LW flux travelling across thos transparent layers, and this may include escape to space).

    Alternatively if we are only rearranging solar heating (or rearranging it via convection), then the following approach may work to some extent: the changes in solar/convective heating could be represented by a linear sum of sinusoidal functions over mass path or some other convenient variable. Then the temperature response to each component would tend to first involve LW radiant net flux changes in those parts of the spectrum where the Planck function changes the most and where the optical thickness over ~ 1/4 of the wavelength of the heating distribution change is ~ 1 (or actually a bit less then 1 since radiation is travelling over all directions, not just vertically). For small changes one could find temperature responses for each component and add linearly, but for larger changes nonlinearities become important and so one would have to evaluate the temperature response for one component, then the next, etc.

    The radiation will be most responsive to temperature changes in spectral bands where the distances over which solar heating (or convective heating, etc.) are on the order of unit optical thickness, so there should be some tendency for the LW fluxes in these bands may largely determine the required temperature profile for equilibrium.

    Of course that depends on band width and where it is in the spectrum relative to the relevant Planck function(s). If the bands with optical thickness ~ 1 on the spatial scale involved, in the best part of the spectrum, are insufficient, the temperature response will be large enough to have significant effects on LW fluxes in bands with somewhat larger or smaller optical thicknesses or in less optimal parts of the spectrum, and if that isn't sufficient, even larger or smaller optical thicknesses or even less optimal parts of the spectrum will have significant net LW flux changes.

    --------

    Starting with an atmosphere transparent to all radiation, adding a tiny amount of GHG will instantly bring the whole atmosphere's radiative equilibrium temperature to the skin temperature (for the spectrum involved); the atmosphere will be colder but as it can now emit radiation whereas before it could not, 'backradiation' increases at the surface and so the surface equilibrium temperature increases.

    If there is some solar heating of the air, adding a little GHG to a LW-transparent atmosphere reduces the equilibrium temperature profile of the atmosphere by allowing the atmosphere to emit radiation to help balance solar heating. Parts of the atmosphere still may remain warmer than the equillibrium surface temperature. As GHG concentration increases, the solar heating is effectively spread out over greater LW optical thickness, and the temperature at TOA will eventually come down toward a skin temperature (the effect of direct solar heating is in a sense 'diluted'), although within the atmosphere, increasing LW optical thickness can eventually start to trap solar heating in a layer and cause the temperature to increase.
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  36. ... of course that assumes a LW blackbody surface. With sufficient LW albedo at the surface, I think adding GHGs could at first cause some surface cooling, but eventually adding more would cause warming.

    ----

    Going back to an earlier point:

    I had (roughly) estimated a mean free path for photons near the peak of the CO2 band to be about 1 m (see Real Climate comments) (setting aside variations over height in line broadenning and line strenghth). But this is a narrow peak; I think the mean free path may only be about 100 m or less over a band width of ~ one micron, though this is a rough estimate. Anyway, the density in the mesosphere is roughly 1/1000 to 1/100000 of the surface value, and (setting aside variations over height in line broadenning and line strenghth), this implies photon mean free paths on the order of 1 km to 100 km at the peak and less than or about the same as 100 km to 10000 km over a band width of about a micron.

    The temperature gradient of the mesosphere is considerably less than a dry adiabatic lapse rate - I graphically estimated 2.8 K/km for the steepest part of the profile in a CRC handbook of Chemistry and Physics graph - 3.8 K/km for an older profile in the same graph; whereas the troposphere had around 6.4 K/km, which is typical for a moist adiabatic lapse rate there).

    I think about 3 % of incident solar radiation (~ 342 W/m2) is absorbed by the ozone layer - that's about 10 W/m2 solar heating, distributed over more than a 10 km thick layer, including down into the stratopshere where photon mean free paths are smaller.

    The temperature at the stratopause gets up to around 270 K, where at 15 microns the blackbody flux is almost 15 W/m2 per micron bandwidth (it's 7 W/m2 per micron at 225 K).

    While I haven't completed the analysis, it seems like radiation within the CO2 band should have little trouble responding to the temperature gradients here (going farther down into the atmosphere, when the center part of the band is too thick, you can find intermediate opacity farther out from the band center). Over sufficiently thick layers, water vapor can also contribute (it is on the order of unit optical thickness for the whole upper atmopshere in the most optically thick portionss of the water vapor spectrum).
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  37. ... also, ozone itself can emit radiation somewhere around 10 microns wavelength.
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  38. re my 32 even if the inversion runs all the way through the stratosphere and is sufficiently strong, etc, the downward LW radiation would gradually go from zero to a peak before coming down.

    Provided optical thickness has no complete spatial gaps (z varies continuously over optical thickness when the later is used as a vertical coordinate), then for any inversion which reaches all the way down to the level being considered, the downward LW flux will saturate at a value that is less than what it is some point before, in a progression toward larger optical thickness.

    Earth's lower stratosphere is in some places roughly isothermal; the lapse rate is negative down to, or to near, the tropopause in lower latitudes, while in winter polar regions the lower stratosphere can have a small positive lapse rate. (PS what I refer to as the lower stratosphere can/may be as much as 90 % or more of the mass of the stratosphere.)
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  39. @ Patrick

    Venus and Earth have the same behavior at the bottom of the thermosphere where starts a large cooling layer which, thermally, can solely radiate to space. Of course, this is due to the fact that the molecular CO2 appears just at that altitude, not above because the EUV, and it is the easiest vibrationally excitable molecule by means of the thermal molecular collisions. The temperature shifts leftward simply because the CO2 is able to heat-radiate. At the equilibrium the sum of the thermospheric downward flux (by diffusion) and the mesospheric/tropospheric upward flux (by convection) must balance the outgoing radiative flux.

    Why the altitudes and the temperatures of the two planets are about equal? I don’t know.

    For Venus the underlying convective layer starts from the surface and thus an air particle (which reaches the radiating layer as a sounding balloon), has to fill up its enthalpic tank at least with an amount equivalent to the geo-potential energy that it must acquire to carry aloft whatever little thermal pay load that will be elaborate within the radiating layer. That’s, the particle, at least, needs a temperature T0 = T + gH/Cp, where T is the temperature at the altitude H of the radiating layer.

    This means that Earth and Venus would have temperatures about equal at the surface, if Earth had also a sole convective layer below the radiative one. Fortunately Earth’s atmosphere contains oxygen that absorbs the UV creating an heating middle layer (stratopause) which breaks the convection and produces the constitution of the stratosphere that transfers downwards part of the absorbed heat. The temperature shifts again leftward simply because the strato pause and the surface aren’t able yield the heat that the CO2 heat-radiates between them. At the equilibrium the sum of the stratospheric downward flux (by diffusion) and the tropospheric upward flux (by convection) must balance the outgoing radiative flux.

    That’s, the lower atmosphere repeats the same behavior of the higher one. The convective layer starting at the surface with a negative lapse rate (troposphere) and the stratosphere produce the constitution of the middle cooling layer (tropopause) where the CO2 once again radiates . In this way the oxygen avoid to Earth a lethal overheating of about 450°C.
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  40. It is worth to point up the cooling/heating places are large isothermal regions which show with extreme evidence the fact that the radiative exchange of energy between the atmosphere and the external space is not at all easy. The transformation heat->photons and vice versa requires the cohesive contribution of a very an very large amount of gas, so it cannot occur within a little rising particle or if there is present also the sole temperature gradient.

    The emitting/absorbing region has to be isothermal because the transformation above behaves as a phase transition in the same way than the ionization/deionization.
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  41. Re 40 Michele -

    The transformation heat->photons and vice versa requires the cohesive contribution of a very an very large amount of gas, so it cannot occur within a little rising particle or if there is present also the sole temperature gradient.

    Almost completely untrue.

    A single molecule with the necessary properties can emit a single photon (or absorb one).

    The only need for a large number of molecules (but still a very small amount of material) is in order to be statistically sufficient for fitting the distribution of energy at LTE (PS photons could still be emitted and absorbed when not at LTE, it would just be quantitatively different. Heck, you could even(theoretically) have a greenhouse effect based on fluorescence).

    The only need for a large amount of material (relatively speaking, and depending on optical properties of the material) is to provide sufficient optical thickness to be able to emit a given fraction of the blackbody flux for the temperature (or a representative temperature, etc.) of the material.

    The sizable isothermal regions exist at least in part because the solar heating is not more concentrated into even thinner layers or excluded from only even thinner layers.

    Regarding your comment 39:

    Yes, the ability to emit more radiation while absorbing less at a given temperature will cause the temperature to fall (unless solar heating and convection or diffusion make up the difference). Relative to optical thickness, the closer one goes towards TOA, aside from other factors, the less downward LW flux there is to absorb, so aside from other factors, equilibrium temperature tends to decline with height.

    Yes, the temperature at the base of a convective layer (a sufficiently vigorously convective layer, (?perhaps with sufficient localized overturning in particular?) is to a first order approximation coupled to the temperature at any other height in the same layer including the top of that layer, by a convectively-sustained lapse rate. This doesn't determine the temperature of the whole layer, merely the lapse rate of the layer.

    But it is entirely mistaken to assume that the net radiant cooling which balances convective is isolated to the top, or near the top, of such a layer. It is possible to have such a situation but it is also possible to have net radiant cooling of almost the whole layer. What determines the temperature of any reference level in the layer, given the lapse rate it will have, is the balance of non-radiant fluxes going into the top or base of the layer - THIS DOES NOT MEAN THOSE FLUXES ARE EMITTED OR ABSORBED ONLY AT THE BOUNDARIES; they can be emitted or absorbed anywhere within the layer. The only caveat is that the distribution of net non-convective heating and cooling must not stabilize the layer to convection, or else the convection would stop shaping the lapse rate, and we'd be back to a radiative or radiative-diffusive/conductive equilibrium.

    Regarding Venus vs Earth - and now I see why some are saying that Earth would be like Venus without oxygen (I used to think they just meant that there wouldn't be a stratosphere/mesosphere division without an ozone layer, or some equivalent UV-shield operating in a sufficiently similar manner) -

    Take away the ozone layer and the upper stratosphere and lower mesosphere get colder. That's pretty much it. There isn't much change to the troposphere; except there is some added warming effect because some portion of the solar heating of the ozone layer is now solar heating below the tropopause (warming effect for the surface and troposphere - small, nothing that would get you anywhere at all near Venus, not even close, not even remotely), while the downward LW flux from the ozone layer is also gone (cooling effect - reduces the greenhouse effect).

    Why wouldn't the troposphere extend up to much greater height? ****Because the radiant heating and cooling just aren't there to support it.***** Most, maybe nearly all, of where the stratosphere is now would remain stable to convection in pure radiative equilibrium there. If you tried to heat the surface up to 700 K, without adding a sufficient amount more CO2, etc, then the surface and troposphere would be emitting a lot more radiation then they'd be absorbing (LW + solar) and they'd cool off.

    There is no physical basis for the idea that photons are emitted to space just from the two cold layers or levels. CO2 does not form a layer just at the mesopause and tropopause - it is almost evenly distributed up through the mesopause and I think a little beyond that. How could you get CO2 at the mesopause emitting to space and not CO2 just above it or (given the thinness of the layer and CO2 spectral properties) just below it? How could tropopause CO2 emit radiation and not the CO2 in the stratosphere or stratopause or lower mesosphere? It makes absolutely no sense. Line broadenning and line strength vary but they don't take everthing away and they tend to vary gradually with height withe the pressure and temperature that determine them.

    Photons are emitted whereever molecules with sufficient energy can emit them, and also tend to be emitted more at higher temperatures; it's just that photons are also being absorbed and not all emitted photons escape to space or travel beyond any particular given distance. Cooler temperatures tend to be found where there is less radiant energy (including solar) available to be absorbed (and less convective heating - where some of the troposphere is, it would be colder without convective heating), so equilibrium requires less emission. At any given location, generally the flux of photons reaching that location are emitted over a range of distances away. Sometimes there is a concentrated source, like a surface, or the boundary of a cloud layer, but otherwise the source of the photons reaching some location is not a single level but a distribution. On Earth, the photons escaping to space come from all levels of the atmosphere, but more from one or another depending on frequency and the thickness of that layer. Adding greenhouse gases changes that distribution.

    Yes, at sufficient heights CO2 is reduced by photolysis, but that is just reducing the optical thickness there, making that layer of the atmosphere thinner in terms of optical thickness - it's like lowering the TOA. It's not that special. And conduction/diffusion becomes significant at some height because of long mean free paths. The vast majority of the mass of the atmosphere is below such levels.

    And the mesosphere is not convective - at least not in the sense that the troposphere is. Not all positive lapse rates imply convection.
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  42. I would remember that we are not arguing about the global fluxes assuring the planetary energetic balance, but about the GH effect that found on any modification of the temperature profiles with regard to the isothermal one that would be there if the atmosphere was perfectly transparent.

    Venus has one cooling region, determined by the CO2 as we read from the space, where the heat arrives from both above and below. The equilibrium temperature of this region is simply due to outgoing radiative flux through the CO2 window around 15 microns, which represents only a small part of the total outgoing flux, but enough to set up the temperature profile.

    Notice that the radiating region takes place always between two layers both producing an inward heat flux, so while Venus, heated solely at the surface and within the thermosphere, has one middle region which avoids the runaway warming of the planet, Earth, with its three heating region, has to present two emitting regions, whose thermostat is the CO2.

    A single molecule with the necessary properties can emit a single photon (or absorb one).

    Yes in an EM radiating field. Not at all for the processes based on the collisions among the molecules as heat->EM and vice versa.

    Mesosphere.
    Really, I do not care one bit if the mesosphere is convective or not. It is enough for my aim that there exists a upward heat flux within the mesosphere.
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  43. Re Michele 42 -

    Heating of the thermosphere has nothing to do with avoiding runaway. Take away solar heating of the thermosphere. What happens? The thermosphere gets colder. Actually there'd be less downward heat flux due to that, so there would be a cooling effect below, too. But not much, because it's a very, very, very, very small amount of flux involved in maintaining the thermospheric temperature.

    Clarifying my earlier point:
    Take away the ozone layer and the upper stratosphere and lower mesosphere get colder. That's pretty much it. There isn't much change to the troposphere; except there is some added warming effect because some portion of the solar heating of the ozone layer is now solar heating below the tropopause (warming effect for the surface and troposphere - small, nothing that would get you anywhere at all near Venus, not even close, not even remotely), while the downward LW flux from the ozone layer is also gone (cooling effect - reduces the greenhouse effect). -
    The cooling effect is both from the loss of a greenhouse gas, and from the reduced temperature of that part of the upper atmosphere, which would reduce the downwared LW flux at the tropopause. We can focus on the effect of solar heating by considering what happens if ozone's UV absorption is eliminated while retaining the greenhouse properties of ozone; in that case, the cooling effect on the troposphere from the reduced LW flux from the cooler upper atmosphere remains, as does the warming effect of increased UV heating below the troposphere; setting aside any effects on/of UV albedo, the warming effect would be greater because the reduction in net LW cooling of the ozone layer is only equal to the reduction in solar heating there, which is equal to the increased solar heating of the surface+troposphere, while the cooling effect can only be some fraction of the reduced LW flux out of the ozone layer. But this is a matter of ~ 10 W/m2; if solar heating below the tropopause increased by 10 W/m2 and the downward LW flux at the tropopause decreased by 5 W/m2, then the forcing would be a bit more than that of a doubling of CO2, so you'd get between 1 and 2 K warming without compositional feedbacks, and with feedbacks (as in Charney sensitivity, not getting into ice sheets and some other things), that may be a bit over 4 K, give or take. It's no Venus territory.

    More on that at the end of this...

    Emission to space is occuring from both the colder and warmer levels; it increases going upward because of less optical thickness above. Otherwise it is actually more from the warmer levels than colder levels because emission rates increase with increasing temperature (Planck function). Think about it - at any frequency, the fraction of radiation emitted at some level that escapes to space always increases going upward. This will tend to be true for the whole LW spectrum, unless there is a sufficient change in spectral properties with height. If radiation is emitted from CO2 at the tropopause to space then surely it is emitted from the CO2 in the stratopause, and except for line broadenning and line strength variations, the CO2 in the stratopause is emitting more radiation, per unit CO2, than either the CO2 at the tropopause or mesopause.

    --------------


    Yes in an EM radiating field. Not at all for the processes based on the collisions among the molecules as heat->EM and vice versa.

    But all the processes that do occur, including those which excite or relax a molecule so that it may emit a photon or so that it may not emit a photon after just absorbing one, are occuring in any sufficient population of molecules with sufficient collisional frequency. At LTE among the non-photons, which can be approximately maintained by sufficient collisional frequency, the distribution of energy among states is such that the fraction of molecules with some probability of absorbing any incident photons and the fraction that will emit photons in a given time period fit the temperature of the material, and it will emit according to the Planck function and absorb according to incident radiation and do both according to the same absorption/emission spectrum.

    Spontaneous emission occurs. Absorption also occurs when photons are present - which they generally are.

    ---------------

    Venus has one cooling region, determined by the CO2 as we read from the space, where the heat arrives from both above and below. The equilibrium temperature of this region is simply due to outgoing radiative flux through the CO2 window around 15 microns, which represents only a small part of the total outgoing flux, but enough to set up the temperature profile.

    The surface of Venus would be considerably colder if CO2 only absorbed in a 1 micron bandwidth at 15 microns.

    Notice that the radiating region takes place always between two layers both producing an inward heat flux, so while Venus, heated solely at the surface and within the thermosphere, has one middle region which avoids the runaway warming of the planet, Earth, with its three heating region, has to present two emitting regions, whose thermostat is the CO2.

    In the absence of direct solar heating of the atmosphere and in the presence of greenhouse gases, temperature would tend to decrease with height all the way up to TOA, even above the tropopause, even in layers with no convection! Radiation is not only radiated to space from relative minima in temperature; in fact more radiation is generally emitted from layers with higher temperatures (for the same layer thickness), and the amount reaching space depends on height.

    Again, heating of an upper layer doesn't cool a lower layer; it can be an indirect heat source via the increased emission from the heated layer, and the cooling effect (absent compositional feedbacks/linkages) only comes from using energy to heat the upper layer that would otherwise have heated the lower layer.

    Aside from redistributing solar heating, merely adding solar heating, in any layer, will increase the temperature in general, but will tend to have the greatest impact where it occurs, because increased net LW fluxes out of that layer are necessary to balance the increased solar heating.

    ---------

    Consider this: What if the Earth, without direct solar heating of the ozone layer, had a troposphere all the way up to where the mesopause now is - let's say 85 km (it might be a bit off of that but I think it's close) Well, first, the lapse rate of what is now the mesosphere would have to increase as presently it is stable to convection. But let's suppose the mesosphere already had a convective lapse rate.

    In this very high tropopause situation, if we now add solar heating around the level of the stratopause - and let's say, remove it from the surface, what happens? In order to balance the reduced radiant heating of the surface and reduced radiant cooling around the stratopause, the convective flux between those two levels is reduced. But unless you have to reduce it all the way down to zero, the tropospheric lapse rate remains and it still goes from the surface to 85 km; there has been no net forcing on this layer (we only redistributed the solar heating within it), so the surface temperature is unchanged, as is the height of the tropopause and the temperature at the tropopause.

    Setting aside redistribution of solar energy, adding solar heating to a layer above the tropopause could reduce the tropopause height by raising the temperature at the tropopause level. The indirect heating effect (via LW flux) would tend to warm the surface and troposphere. The cooling effect if this solar heating was not added to the system as a whole but taken from beneath the troposphere will tend to be stronger than the indirect heating effect from the LW flux. But see above for a quantitative example.


    Mesosphere.
    Really, I do not care one bit if the mesosphere is convective or not. It is enough for my aim that there exists a upward heat flux within the mesosphere.


    Which is mainly radiative. Not convective.

    I will add that I recently realized (from this paper
    http://journals.ametsoc.org/doi/pdf/10.1175/JCLI3829.1
    "The HAMMONIA Chemistry Climate Model: Sensitivity of the Mesopause Region to the 11-Year Solar Cycle and CO2 Doubling"
    Schmidt et al. )
    that some or much solar heating of the upper atmosphere, going into chemical reactions, is not all realized as sensible heat right away; some portion can exist as latent heat (chemically) which can be transported before conversion to sensible heat. But motions are mainly thermally indirect, driven by fluid-mechanical wave energy from below the tropopause. I

    PS see fig 10 of that paper - note the solar heating of the atmosphere above the 1 mb level (1 mb = 100 Pa) is less than 1 W/m2.
    (With surface gravity at 9.81 m/s2, a flux of 0.118 W/m2 per mb is required per K/day heating rate. At 100 km height, with the slight reduction in g, this is 0.122 W/m2 per mb per K/day. So from the surface up to 100 km, we could just get by using 0.12 W/m2 per mb per K/day)
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  44. @ Patrick

    Heating of the thermosphere has nothing to do with avoiding runaway.
    I clear my thought. There is the CO2 that avoid the runaway. An atmosphere perfectly transparent and heated solely at its bottom would be isothermal at T=Te. The thermosphere adds a heating source at its top and this heat has to reach the surface so that it can be radiated to space. Thus the surface would have a temperature Ts greater than Te (how much?), just below the thermosphere there would be a temperature Tt = Ts + 1.2e5*Ф/λ, i.e., we had Tt – Ts = 4.8e7*Ф and, even with a specific thermal flux Ф = 1W/m², we had Tt – Ts = 48000000 °C.

    Take away the ozone layer and the upper stratosphere and lower mesosphere get colder.
    Not at all. The absence of the heating will make all convective the atmosphere between the surface and the thermosphere and that will establish Venus-like conditions.

    But all the processes that do occur, including those which excite or relax a molecule so that it may emit a photon or so that it may not emit a photon after just absorbing one, are occuring in any sufficient population of molecules with sufficient collisional frequency. At LTE among the non-photons, which can be approximately maintained by sufficient collisional frequency, the distribution of energy among states is such that the fraction of molecules with some probability of absorbing any incident photons and the fraction that will emit photons in a given time period fit the temperature of the material, and it will emit according to the Planck function and absorb according to incident radiation and do both according to the same absorption/emission spectrum.
    Here is missing the thermal flux that the surface yields to the atmosphere by conduction and as sensible heat which can leave the atmosphere only once the KE of the colliding molecules has been transformed to radiative energy within the isothermal regions that allow the phase transition from the non-excited to excited state and so the photons emission.

    Just a point. Why do you continue to argue that all the thermo kinetics is founded on the radiative transfer, completely omitting the conduction and, over all, the convection, or leaving them a very marginal role? As far as I know, the heat output of a column radiator for room heating plan has the ratio radiative-heat/convective-heat equal about to 1/3, i.e., the convective effect is the 300% of the radiative one. Then neglecting the convection would be very hazardous and non-real.
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  45. On the idea that heating of the thermosphere heats the surface -

    Keeping Te constant - that is, keeping the total solar heating of the climate system constant:
    No. Without any greenhouse effect of the absorption-emission kind, if the surface is a blackbody for LW radiation, then the surface temperature will be Te regardless of where solar heating is occuring. No matter how hot the stratosphere/thermosphere gets. Except for the effect that at sufficient temperature, the upper atmosphere could start to emit a significant amount of radiation in the SW part of the spectrum - in which case the surface would be cooler.

    Not at all. The absence of the heating will make all convective the atmosphere between the surface and the thermosphere and that will establish Venus-like conditions.
    Not at all. The absence of sufficient solar heating and/or sufficient greenhouse effect will not allow that.

    Yes, the potential (depends on albedo effects) removal of ~ 10 W/m2 solar heating from the surface/troposphere required to give that heating to the stratosphere/mesosphere (I think mainly the upper stratosphere), minus the effect of the increased downward LW flux from the upper atmospheric warming (perhaps half of the heating, maybe 5 W/m2, give or take - well, it's somewhere between zero and the involved solar heating of the upper atmopshere), will have a cooling effect on the surface+troposphere, which will tend to reduce tropopause height. Reversing this - eliminating solar heating of the ozone layer and allowing that to heat the surface+troposphere, will warm the surface+troposphere and, via that and maybe also the cooling of the upper atmosphere, will raise the tropopause level. But (see Hartmann, "Global Physical Climatology", 1994, p. 70), the warming of the troposphere (without compositional feedbacks) from removing ozone is small - it doesn't even show up in the graph on Hartmann, p.70 - although this could be because of the additional cooling effect of removing ozone's LW opacity, which is seperate from the issue of solar heating. Also, the height of the tropopause stays below 20 km in that graph (the graph has a relatively old citation but the basics of radiation have been understood for a long time), although it is not as sharply defined, the lapse rate definitely does decrease with height going up above roughly ~17 or 20 km or so, the tropopause stays below 20 km, perhaps going to maybe somewhere around 70 mb, whereas before removing ozone it was ~ 150 mb, give or take (I'm very quickly estimating from a graph, but it definitely doesn't get much above 20 km). Ozone could still heat some of the upper atmosphere by absorbing a LW flux from below, and this effect is also presumably removed in this graph.

    And why should this be so? Well with a difference of only 10 W/m2 (minus counteracting effects), you can only heat the surface+tropopause so much. How much of a convective heat flux would be required to sustain a troposphere up to ~ 85 km with the 85 km level remaining at it's present temperature? Consider how much you'd be shifting the temperature profile, and the kind of radiative disequilbrium (net radiant cooling) that would cause. And that would have to be balanced by net radiant heating at the surface. How could the surface be warmed up so much, and yet still have enough net radiant heating to supply the necessary convection? You'd need to boost solar heating and/or the greenhouse effect considerably.

    Let's make this simpler and just give the ~ 10 W/m2 to the troposphere+surface while retaining solar heating of the upper atmosphere, let the surface+troposphere warm up a little, the tropopause shift a little, but it still looks pretty much the same as now (in a big picture, purely abiotic way, a not caring about economic and environmental effects sort of way). The tropopause temperature is not much different. If it were only the solar heating of the ozone layer that stood in the way of having continuous convection from the surface to 85 km, then the surface would have to be warm enough for an adiabat from the surface to intersect the temperature profile as is at about that level, 85 km; - actually higher then that, because they'll be some cooling effect when you let convection from the troposphere get higher by removing overlying solar heating. The thing is, if you draw such a line you'd see it would be warmer than all points are in between already. How can removing solar heating of the ozone layer result in warming there?

    Here is missing the thermal flux that the surface yields to the atmosphere by conduction and as sensible heat I never said that the atmosphere doesn't recieve heat from the surface by more than radiation
    which can leave the atmosphere only once the [energy] of the colliding molecules has been transformed to radiative energy
    Yes.
    within the isothermal regions that allow the phase transition from the non-excited to excited state and so the photons emission.
    Well that's probably the most fundamental mistake you are making. You do not need to have an isothermal region in order for photons to be emitted (or absorbed). Have you ever seen the incandescent glow of an electric range on a stove top? Consider what happens when you turn it off - the range cools off - but while the temperature is changing, it still has a non-zero temperature that is actually quite high, and it continues to glow for a while. It may also glow unevenly because the temperature isn't constant throughout it - this doesn't prevent smaller pieces of it from having high nonzero temperatures and thus they can still emit such radiation.

    If you are thinking that the air can't have net radiant cooling while it is undergoing an adiabatic process - well, for individual parcels that are undergoing perfectly adiabatic processes, yes. But convective heating has to be balanced by some non-convective cooling, and this doesn't all happen only at the tropopause, etc. (See http://www.realclimate.org/index.php/archives/2011/06/unforced-variations-june-2011/comment-page-10/#comment-209281 ). Really, convection tends to bring the lapse rate towards being adiabatic, and under the right conditions this can be done very effectively, but this only happens spontaneously (as opposed to being forced from some external work input like large tides - or alien spaceships sticking giant blenders into the atmosphere - you get the idea) if the lapse rate without convection became unstable to said convection; the convection causes radiative disequilbrium, meaning there is net radiant heating and net radiant cooling in some places. This can't be avoided - unless radiant equilibrium just happens to line up that way, an adiabatic lapse rate requires diabatic processes to be sustained - if this ever meant that the lapse rate can't actually be exactly adiabatic, so be it (PS see point in Real Climate comment regarding moist adiabatic rising and dry sinking, although what I'm saying still generally applies to a dry atmosphere as well). Related point: certainly the idea of a single radiative-convective temperature profile is not meant to imply that nothing deviates from it even the slightest, or you couldn't even have a convective heat flux (what goes up has to be at a different temperature than what goes down in order for a sensible heat flux to exist; and the latent heat eventually becomes sensible heat).

    For Earthly conditions (global annual average) the net radiant heating is at the surface and net radiant cooling is distributed throughout the troposphere. Which, by the way, is not entirely all directly to space (see the last part of that Real Climate comment). Convection tends to bring the troposphere toward an adiabatic lapse rate because otherwise the atmosphere gets more unstable and convection becomes even more likely to happen or more vigorous, but ongoing convection requires in heating and cooling that must be balanced by radiation - entirely and purely adiabatic processes would have the same warm air coming down after going up, along the exact same adiabat, and thus you wouldn't have a net nonzero convective heat flux that way. What comes down has to be cooler. Also, not all parcels reach the tropopause before turning around (related: have you ever noticed cumulus clouds that never became cumulonimbus?).

    Just a point. Why do you continue to argue that all the thermo kinetics is founded on the radiative transfer, completely omitting the conduction and, over all, the convection, or leaving them a very marginal role? As far as I know, the heat output of a column radiator for room heating plan has the ratio radiative-heat/convective-heat equal about to 1/3, i.e., the convective effect is the 300% of the radiative one. Then neglecting the convection would be very hazardous and non-real.

    I've left conduction/diffusion and convection all the role they need to have. Convection is very important in the troposphere / between the surface and troposphere (and conduction/diffusion being a part of that at the surface-air interface). Conduction/diffusion become significant again very high up where the mean free paths are sufficiently large - I had earlier not thought of this. And there is some transport of heat (I guess some of it is latent-chemical) in the stratosphere and mesosphere - but this is driven by work supplied from below, and the stratosphere and mesosphere are not convective in the way the troposphere is. To a good first approximation the stratosphere, and I think much of the mesosphere, is in radiative equilibrium; the vast majority of the upper atmosphere by mass is the stratosphere so perhaps I didn't pay enough attention to the potential for radiative disequilibrium higher up; but anyway, certainly the ozone layer is not preventing the Earth from becoming like Venus as far as temperature is concerned. Why should the upper atmosphere act just like a room with heater?
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  46. If it were only the solar heating of the ozone layer that stood in the way of having continuous convection from the surface to 85 km, then the surface would have to be warm enough for an adiabat from the surface to intersect the temperature profile as is at about that level, 85 km; - actually higher then that, because they'll be some cooling effect when you let convection from the troposphere get higher by removing overlying solar heating. The thing is, if you draw such a line you'd see it would be warmer than all points are in between already. How can removing solar heating of the ozone layer result in warming there?

    Actually I didn't account for moist advection; the lapse rate of the mesosphere as is is significantly less than the typical moist adiabatic lapse rate in the troposphere; however, starting at ~ 260 or 270 K at a pressure ~ 1 mb with saturation vapor pressure for water vapor, you have a much higher mixing ratio than you would at the same temperature at lower tropospheric pressures, so the moist adiabatic lapse rate could be much reduced. Still, if we add 10 W/m2 heating to the troposphere+surface, and are still such a long, long way from Venus territory, with the tropopause still well below where the stratopause is now, then, after that, removing 10 W/m2 of solar heating from the ozone layer cannot have any warming effect anywhere (at least in the 1 dimensional equilbrium climate - maybe with some complexity in the feedbacks in the 4-dimensional system you could find some warming somewhere). With less solar heating in the ozone layer, the ozone layer now has excess emission (more than absorption) and so the temperature falls there. And then what? The emission falls there. Some fraction of that emission had been absorbed elsewhere in the system, and so the cooling effect now spreads there. Etc. The tropopause may rise, but only because the layer above it is colder, not because the troposphere and surface are warmer.


    Have you ever seen the incandescent glow of an electric range on a stove top?
    Well I think you're not supposed to leave a burner on with nothing on it, but you can look sideways and see the glow; you may notice the glow fading after you turn it off and remove the pot/whatever. Safety first! Okay, I'm done here.
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  47. If it helps, here's one way to picture dry convection along adiabats with net radiant cooling:

    Picture the temperature profile with an adiabatic lapse rate through the troposphere. Now zoom in and notice that the temperature profile splits into two lines at the tropopause and remains split down to the surface. There are two lines both following adiabatic lapse rates, one with higher temperature and one with lower temperature. So rising air can follow the higher temperature adiabat and sinking air can follow the cooling adiabat. Notice that air parcels do not all need to follow each of these adiabats all the way from the surface to the troposphere; they can rise or fall to some height and then shift over to the other and reverse direction. This shifting requires a diabatic process, and so we can have net radiant cooling or heating within such a troposphere (the surface air would make the shift with a contribution from conduction/diffusion from the surface). In Earth's case it will tend to be net radiant cooling.

    Now you can have a continuum of adiabats, closely spaced, and the parcels follow trajectories up, down, and around within the range of adiabats.
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  48. @ Patrick

    On the idea that heating of the thermosphere heats the surface -
    The EUV dissociates/ionizes all molecular gas within the thermosphere and so, whatever is the characteristics of the molecular gases below the thermosphere, they will be heated from above and, if the layer surface-thermosphere is perfectly transparent, this heat will be radiated to space only by the surface where it can be carried only by conduction. In this case all the heat radiated by the mesosphere in the reality must be subtracted to albedo and Te increases.

    You do not need to have an isothermal region in order for photons to be emitted (or absorbed).

    Yes if the photon is absorbed/emitted with a EM forcing. Not at all if the photon is created/destroyed with a thermal forcing.

    We can continue to argue until infinity if we don’t know the order of magnitude of all the contributes, or their weighted contributes, because you continue to consider very marginal (pretty negligible) the role of the fluid dynamics. In the preceding post I saw that,e.g., the heating power yielded by a column radiator within a room is about 75% by convection, 25% by radiation, as certified by the engineering physics laboratories. What occurs, really, within the atmosphere, what will be the ratio convective/radiative? We cannot say anything (at least we cold guess something) without a well-advised synthesis of the fluid dynamics and the radiative transfer which, actually, represents the one way to obtain weighted answers and so to have realistic reasons for neglecting or not some aspect.
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  49. The EUV dissociates/ionizes all molecular gas within the thermosphere and so, whatever is the characteristics of the molecular gases below the thermosphere, they will be heated from above and, if the layer surface-thermosphere is perfectly transparent, this heat will be radiated to space only by the surface where it can be carried only by conduction. In this case all the heat radiated by the mesosphere in the reality must be subtracted to albedo and Te increases.

    You were correct up to the part about the mesosphere. (Except I'm not sure you can say that *all* molecular gas is ionized - I think some neutral (as well as multiatomic) molecules do remain, but I'll have to double check.)
    Heating of the mesosphere just adds to the downward flux of heat that must be carried to the surface before emission to space. If you don't change the total amount of solar heating but only rearrange it, whether among different layers of air or between them and the surface, Te stays constant. Of course you can change the effective TOA albedo by changing atmospheric solar absorption of some layers so that more or less can be reflected by other layers or the surface, but that changes the total solar heating, which of course will change Te. Generally reducing absorption of solar radiation in the upper atmosphere should tend to reduce Te because of a greater potential for reflection by clouds or the surface or the scattering of the air itself, although this might not be a strong effect if the layers below mostly absorb the same radiation.

    Yes if the photon is absorbed/emitted with a EM forcing. Not at all if the photon is created/destroyed with a thermal forcing.

    The vast vast majority of radiation emitted by the Earth - surface or atmosphere - is from thermal processes, and in accord with the Planck function for the temperature and optical properties of the material. Aurora are different (I think 'fluorescence' applies), but that involves a very very very small amount of energy.

    And you can have stimulated emission without isothermal conditions, too. You don't need isothermal conditions for either.

    The Planck function is a function of temperature, and not of temperature gradient or time derivative. When temperature varies in space and time, the material in each location in space and time still has a temperature.

    If you still think otherwise, please explain how CO2 molecules at any temperature found in the Earth's atmosphere, which are continually colliding and thus at any given moment with some fraction in various excited states, could be prevented from emitting radiation, when it otherwise happens spontaneously (as has been observed).

    This is the last time I will address this issue; look it up in physics books if you need more.

    We can continue to argue until infinity if we don’t know the order of magnitude of all the contributes, or their weighted contributes,

    But you don't know; I at least know some things.

    because you continue to consider very marginal (pretty negligible) the role of the fluid dynamics.

    Not at all. Did you not notice my discussion (maybe some of this on the Real climate thread) on the mechanics behind the tendency for warmer air to rise and cooler air to sink. On the conversion between APE and kinetic energy, where, when APE is in the form of heat, APE to kinetic energy is thermally direct and acts like a heat engine, while the reverse is a heat pump (converts work to heat whil pumping heat from lower to higher temperature). In case you needed this link, the mechanism by which kinetic energy is produced from APE is the flow from higher to lower pressure - a pressure gradient is a force per unit distace per unit area, and work is done when there is flow across isobars - energy = force * distance; and if I'm not mistaken the kinetic energy (per unit mass) gain or loss is equal to the loss or gain in pressure, divided by density - thus in accord with Bernoulli's Law/principle ( http://en.wikipedia.org/wiki/Bernoulli's_principle ) - or for vertical motion, the combination of change in pressure and gravitational potential energy is converted to or from a change in kinetic energy. Regarding the deviation of the upper atmosphere from radiative equilibrium, I did discusss the work done on the upper atmosphere (running heat pumps there, driving thermally indirect circulation) by fluid mechanical waves which propagate vertically from the troposphere which has the heat engines that supply their kinetic energy.Now I could go into the coriolis effect, geostrophic balance, gradient wind balance, cyclostrophic balance, baroclinic instability, Hadley cells, etc, but it's not necessary - not because they're unimportant, but because it isn't specified in a simple first-order explanation of radiative-convective equilibrium.

    (In the full four dimensional climate system, horizontal radiant heating variations, in combination with the vertical variation, and along with latent heating, produce APE which drives Hadley cells, monsoonal circulations, and midlatitude storm track activity - the later provides kinetic energy to the zonal mean Ferrel cell, which itself is thermally indirect. This extratropical storm track activity in particular involves colder air sliding under warmer air and thus can have a stabilizing effect (these large-horizontal scale overturning can produce lapse rates that are stable to localized overturning). the troposphere and surface in high winter latitudes in particular is heated from horizontal transport from lower latitudes, and, especially when/where there is land or sea ice or ocean circulation is otherwise not supplying this heat, the heat goes through the troposphere and down to the surface, and I think both have net radiant cooling. Because of this pattern, the lower troposphere can be especially stable at high winter latitudes.)

    (Off on a tangent - when you create a warm air mass surrounded by cooler air, the warmer air rises and flows out over the cooler air, which sinks and slides underneath the warm air. But if this is taking place on relatively large horizontal scales, the coriolis effect will eventually stop this circulation before it is completed; geostrophic adjustment occurs, with the wind blowing parallel to isobars; the temperature contrast is stabilized and some APE remains. However, in the right conditions, there remains baroclinic instability, wherein wavy displacements (PV anomalies) of the air alter the wind field and induce other displacements such that the displacments at different vertical levels mutually amplify each other; this transfers some APE from the prexisting temperature contrast and puts it into the temperature variations of the waves, which convert some of that APE into kinetic energy. Aside from some other things, this is how extratropical storm tracks work.)

    (Having achieved geostrophic balance, warmING air tends to rise and coolING air tends to sink, even if the warmING air is still cooler than the coolING air.)

    All in all I think I've paid more attention to dynamics than you have. But it remains that to a good first approximation the upper atmosphere (at least up through the stratopause, maybe most of the mesosphere) is, in a global annual average, in radiative equilibrium. The effects of circulation cause some interesting deviations from that which I think may be much more important when considering the seasonal and latitidunal variations in temperature, rather than a global average or globally representative temperature profile. (Note in figure 10 of http://journals.ametsoc.org/doi/pdf/10.1175/JCLI3829.1
    "The HAMMONIA Chemistry Climate Model: Sensitivity of the Mesopause Region to the 11-Year Solar Cycle and CO2 Doubling"
    Schmidt et al.
    how the distribution of solar heating and LW radiant cooling match up in the lower mesosphere. Note also that heating rates are proportional to fluxes absorbed or emitted and inversely proportional to mass, so the fluxes involved in large heating or cooling rates higher up are much smaller than they might appear in a graph which uses geometric height rather than pressure as a vertical coordinate. Which isn't to say that the small fluxes are not important at those heights, but they are small compared to what is going in and coming out of some layers far below.)

    In the preceding post I saw that,e.g., the heating power yielded by a column radiator within a room is about 75% by convection, 25% by radiation, as certified by the engineering physics laboratories. What occurs, really, within the atmosphere, what will be the ratio convective/radiative? We cannot say anything (at least we cold guess something) without a well-advised synthesis of the fluid dynamics and the radiative transfer which, actually, represents the one way to obtain weighted answers and so to have realistic reasons for neglecting or not some aspect.

    But that work has been done. If you don't believe my account, read it yourself.
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  50. @ Patrick

    I downloaded the free software FreeFem++ at http://www.freefem.org/ff++/ which solve the PDE systems and I used it.
    I used a domain 90x120. The abscissas between X15 and X75 represent an entire Earth’s meridian circumference, that’s, X15 is the equator at midday, X30 the North Pole, X45 the equator at midnight, X60 the South Pole, X75 again the equator at midday. The abscissas 0-X15 and X75-X90 have been used only to obtain a perfect symmetry of the range X15-X75 with respect to X45. The ordinates represent the Earth’s atmosphere layer high 120 km above the surface.

    The assumed surface temperatures change sinusoidally along the meridian being 200K at poles and at equator 290K at midnight, 320K at midday.

    Using FreeFem++ I have solved the two-dimensional problem in the steady state using the follow system:

    ∇•u = 0 //continuity
    u •∇u + gk + Cp∇T – νΔu = 0 // momentum
    u •∇(CpT + gz) – λΔT = 0 // total energy without KE

    imposing
    a) T = 270 K at 120 km (within the thermosphere) and at 50 km (top of the stratosphere)
    b) T = temperature of equilibrium due to the emission 6e-8*T^4 for the thermal sinks of the tropopause at 10 km and the mesopause one at 90 km
    and plotting
    a) the temperatures ”(temperature)”
    b) the vertical velocities ”(vertical velocities)”
    c) the vectors velocity ”([u,v])”
    d) the lapse rates at X15 (equator at midday) ”(X15-equator at midday)” , at X22.5 , mid latitude at midday, ”(X22.5-mid latitude at midday)” , at X30, poles, ”(X30-poles)” , at X37.5, mid latitude at midnight, ”(X37.5-mid latitude at midnight)” , at X45, equator at midnight, ”(X45-equator at midnight)”

    I have to make amends for my mistake. The mesosphere lapse rate is not able to activate the convection.

    I have reduced the ordinates to 10 km and plotted also the horizontal and vertical components of the velocities which are quantities with sign so it is possible to understand the sense of the eddies thermally induced. ”(velocities X90)”

    I have plotted some lapse rates for different latitudes. At the equator the concavity of the lapse rate is positive showing that the energy of the lower atmosphere is increasing both in daytime and nighttime; for the mid latitudes the lapse rates day/night are linear; at the poles the concavity of the lapse rate is negative because the falling air is losing its energy.” (lapse rates of temperatures)”

    The results of this very simple simulation confirm what was well known:
    - we need different temperatures on the surface to activate circulation induced by convection
    - the turbulence is present almost exclusively within the lowest region of the tropopause
    - if the Earth is not rotating and then without the Coriolis forces, the global circulation occurs according to a simplified one-cell way between the equator and the poles, as we can see, e.g., at http://www.physicalgeography.net/fundamentals/7p.html or at many other sites of physical geography on the web.

    The most important result is that it is enough to add two radiating layers at the top of both the troposphere and the mesosphere and the behavior of the entire atmosphere seems satisfactorily (even if grossly) explained. May be, the physics is more and more simpler than we tend to depict it.
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