2011-06-11 18:24:12The Planetary Greenhouse Engine...One more time
Chris Colose


Hey guys, putting this in for review...I'd like to get it out fairly quickly since it is directly relevant to commentary on my last SkS article



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 error-and-fallacy ridden article by a Princeton physicist.  However, an unusually high amount of response was dedicated to a side comment I made in passing-by.  That topic is Venus.  This eventually led to accusations of scare mongering on my part, even though I never compared Earth to Venus in any way.  This also led to another article devoted to a discussion of thermodynamics and the greenhouse effect, where a lot of confused (but also some interesting) issues were raised in the comments concerning the physics of the extraterrestrial atmospheres (including Venus, Mars, or the gaseous planets).  Bart Verheggen chipped in too.   A lot of people seem to have their own theories, like "Venus is hot because of its pressure, not its greenhouse effect" or "the greenhouse warming violates thermodynamics" or "the lapse rate causes enhanced warming."  As such, I thought I would take this opportunity to clarify a number of points concerning these topics.  This may be a bit lengthy, but hopefully a handy reference for future blog discussions on this topic.  There are several other online resources that cover the basics more thoroughly, and are linked for recommended reading at the bottom, yet there's still a lot of confusion into how radiative transfer works with respect to atmospheres.


 The Greenhouse Effect and Thermodynamics


The nearby rocky planets 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 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 (at the same temperature).  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 to make the planet lose heat less efficiently, you need to replace the “radiating surface” near the ground with a colder “radiating surface” in the 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 (i.e., into the stratosphere).  Plotted are the Planck functions for the surface temperature (purple dashed) and the blue curve titled “OLR” is the actual spectrum of this hypothetical planet with a greenhouse gas in the atmosphere.  The difference between that spectrum and the Planck spectrum for the ground temperature arises because the 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 the chunk taken out of the curve by the gas).  This creates a situation where the planet temporarily takes in more energy than it loses, and the result is that 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.  So, let’s define a “mean” radiating pressure of the planet, which we’ll call pr.  Since pressure decreases with height, the radiating pressure will decrease as the optical thickness of the atmosphere decreases (i.e., more radiation is preferentially leaking out higher in the atmosphere where it is colder).  The radiating pressure is at the surface (ps) with no greenhouse effect. It is easy to show, based on a generalized application from Poisson's equation for potential temperature, that for an atmosphere whose temperature profile is dry adiabatic, that 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 Ts is 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 moist adiabatic lapse rate declines less sharply).  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 planet 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 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 CO2 atmosphere 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 N2 doesn’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. 

The argument is a bit different on Earth.  In the tropics, the opacity of water vapor plays a secondary role in making the tropopause higher than the poles; rather, the chief reason for a higher tropopause is due to the fact that the moist adiabat is less steep than in a dry atmosphere (due to condensation).  One therefore needs to go a further distance before convection gives out.  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 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 gives out and the tropopause migrates to the surface, developing a deep isotheral 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

2011-06-11 22:17:19thanks
Otto Lehikoinen

There's been quite a long time since I last read this technical an article carefully. Didn't see the images, though.

The few (unhelpful?) notes:

How's Mercury emitting more IR? (might be the ground acts as a conductor to the dark side.)

(Some) lapse rate is a function of the greenhouse gases present, and their possible condensation.

"Could a purely diatomic molecule atmosphere generate a greenhouse effect? The answer, again, is yes."  This was surprising, but the explanation below was clear enough.

The pressure is directly proportional to the amount of the mocelular collisions at the specific pressure in gaseous phase (as was said in the entry level chemistry course of the university).

The bit on sensors (observing intsruments) on the sky was a different approach to what i've come to think (usually thinking heat transport by the winds), but clear enough ( I guess even for those who are obsessed with quantum nature of quanta dismissing the whole other lot of molecules present in the atmosphere.)

So no errors that I can see, and that is saying a little :-) (M.Sc.)

2011-06-12 01:08:26
Chris Colose


I mentioned some of the gas planets, not Mercury

2011-06-12 02:03:27ok
Otto Lehikoinen

oh yes, that was just a random thought, sorry, the rest of the notes were just hightlighting the differences in physics/chemistry terminology. your take on this is more physics oriented than mine (didn't do too well in physical chemistry)

2011-06-12 02:51:59comments?
Dana Nuccitelli

"error- and fallacy-ridden"

"All of the old goodies-- like Venus is hot because of its pressure, not its greenhouse effect, or and even “the greenhouse effect violates thermodynamics” line came up"

"One is that p= ρRT" => I'd suggest clarifying that this is the ideal gas formula

Gotta get those images working, but looks good otherwise.

2011-06-12 03:43:47
Andy S


I don't understand this sentence:

 On Earth or Venus, internal heating takes the form of radioactive decay  (although it is negligible for energy budget purposes, since the formation of a surface sharply curtails the diffusion of heat into the atmosphere).

I'm not sure what you mean by "formation of a surface". I suppose you are referring to the contrast between the rocky planets with the gas giants. And, surely, the energy balance bewteen the solid earth and the atmoshere/ocean must be in equilibrium(otherwise the interior of the Earth would be heating up); so what does curtailing of diffusion of heat into the atmosphere mean? It's true that geothermal energy flux is orders of magnitude less than the solar energy flux to Earth (and is therfore irrelevant in the overall energy balance) but that's because of the rate of radioactive decay within the solid Earth, not, in the long term, because of the low thermal conductivity of rocks or the nature of the solid earth/ocean or atmosphere interface.

It's entirely possible, alternatively, that I have misunderstood your point.

2011-06-12 03:51:34


when you discuss the lapse rate near the end of the post, i'm afraid that many will miss the big picture. I think you should add a few words explaining (the obvious?) that the emission altitude (as well as the tropopause) for a transparent atmosphere would be zero and then surface temperature will be set by the energy balance of the whole planet, no matter what the laspe rate is.

In fig. 1, the colors of the linea are too similar.

Here the correct links for your figures:
fig. 1: http://s4.postimage.org/5oxix6763/OLRspec.png
fig. 2: http://s4.postimage.org/5zblyd8ej/OLRchange.png
fig. 3: http://s3.postimage.org/6j0bb2vhn/Vspec.jpg
fig. 4: http://s4.postimage.org/5u3mj93nv/Planck2.png
fig. 5: http://s4.postimage.org/5u5tx1rd7/Planck3.png

2011-06-12 05:00:58
Chris Colose


Thanks Riccardo,

I didn't realize the images were problematic since they show up fine on the preview here.

Andy-- I'm not too familiar with the internal heat within Earth, but my impression was that there's a lot of it, it's just irrelevant because the rate of flow that actually gets out to the surface only amounts to a small trickle when compared to the rate of energy flow from the sun.  It does matter in localized situations, like beneath ice sheets or near geysers, or what have you.  I'll change the wording regardless.

2011-06-12 05:10:45
Chris Colose


I just changed the links, and on my screen at least I went from being able to see the images to not being able to.  Somewhat let me know what's up, I always manage to screw this up...

2011-06-12 05:34:16
Rob Painting

Chris, still can't see the images.

2011-06-12 08:29:26
Andy S



Here's the Wikipedia summary of geothermal heat flows (my emphasis). 

Heat flows constantly from its sources within the Earth to the surface. Total heat loss from the earth is 44.2 TW (4.42 × 1013 watts).[12] Mean heat flow is 65 mW/m2 over continental crust and 101 mW/m2 over oceanic crust.[12] This is approximately 1/10 watt/square meter on average, (about 1/10,000 of solar irradiation,) but is much more concentrated in areas where thermal energy is transported toward the crust by convection such as along mid-ocean ridges and mantle plumes.[13] The Earth's crust effectively acts as a thick insulating blanket which must be pierced by fluid conduits (of magma, water or other) in order to release the heat underneath. More of the heat in the Earth is lost through plate tectonics, by mantle upwelling associated with mid-ocean ridges. The final major mode of heat loss is by conduction through the lithosphere, the majority of which occurs in the oceans due to the crust there being much thinner and younger than under the continents.[12][14]

The heat of the earth is replenished by radioactive decay at a rate of 30 TW.[15] The global geothermal flow rates are more than twice the rate of human energy consumption from all primary sources.

The distribution of surface heat flow is controlled by geology but the global amount released is controlled by (mainly) the amount of radioacticve decay of U, K and Th isotopes that have half lives comparable to the age of the Earth and is very slowly winding down.

2011-06-12 16:18:30
Chris Colose


There is one more attempt at all the images...it looks good on my screen here.  Anyone else having an issue seeing them? I just uploaded the blog post (with a few minor changes to the above post here), so let me know if anyone spots anything criticial


2011-06-13 00:34:40Recommendation
John Hartz
John Hartz

I suspect there are relevant aritcles (equations) posted on the Science of Doom website that could be referenced in this article or in a reference tab to it.

Edit:  Oops! I see that Chris has addressed this in an end-note.

2011-06-13 00:39:10No Images
John Hartz
John Hartz

The images do not apper here or on the blog post.

2011-06-13 00:58:52
Chris Colose



Well if anyone wants to look at what the issue might be (John?) that would be appreciated.  They are all in JPG format and I'm just copying and pasting the image link into the little green square above that loads images to SkS.  And they're all appearing fine on my page.  Might have something to do with me being on a Mac?


2011-06-13 03:57:03


Use the upload page to upload them to the SkS server.  Then use those links.

2011-06-13 06:19:56
Chris Colose



Try the linked post again

2011-06-13 06:26:30


The good news is that the images are ok now; the bad is that in some way you screwd up the  links :)

2011-06-13 07:05:47Images look good to me now
John Cook


Now they're uploaded to SkS

2011-06-13 11:43:04
Chris Colose


Whew..should be good now