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Learning from a simple model

Filed under: — gavin @ 10 April 2007

A lot of what gets discussed here in relation to the greenhouse effect is relatively simple, and yet can be confusing to the lay reader. A useful way of demonstrating that simplicity is to use a stripped down mathematical model that is complex enough to include some interesting physics, but simple enough so that you can just write down the answer. This is the staple of most textbooks on the subject, but there are questions that arise in discussions here that don’t ever get addressed in most textbooks. Yet simple models can be useful there too.

I’ll try and cover a few ‘greenhouse’ issues that come up in multiple contexts in the climate debate. Why does ‘radiative forcing’ work as method for comparing different physical impacts on the climate, and why you can’t calculate climate sensitivity just by looking at the surface energy budget. There will be mathematics, but hopefully it won’t be too painful.

So how simple can you make a model that contains the basic greenhouse physics? Pretty simple actually. You need to account for the solar radiation coming in (including the impact of albedo), the longwave radiation coming from the surface (which depends on the temperature) and some absorption/radiation (the ‘emissivity’) of longwave radiation in the atmosphere (the basic greenhouse effect). Optionally, you can increase the realism by adding feedbacks (allowing the absorption or albedo to depend on temperature), and other processes – like convection – that link the surface and atmosphere more closely than radiation does. You can skip directly to the bottom-line points if you don’t want to see the gory details.

The Greenhouse Effect

The basic case is set up like so: Solar radiation coming in is S=(1-a) \mbox{TSI}/4, where a is the albedo, TSI the solar ‘constant’ and the factor 4 deals with the geometry (the ratio of the area of the disk to the area of the sphere). The surface emission is G=\sigma T_{s}^{4} where \sigma is the Stefan-Boltzmann constant, and  T_s is the surface temperature and the atmospheric radiative flux is written \lambda A=\lambda \sigma T_{a}^{4}, where \lambda is the emissivity – effectively the strength of the greenhouse effect. Note that this is just going to be a qualitative description and can’t be used to quantitatively estimate the real world values.

There are three equations that define this system – the energy balance at the surface, in the atmosphere and for the planet as a whole (only two of which are independent). We can write the equations in terms of the energy fluxes (instead of the temperatures) since it makes the algebra a little clearer.

Surface:  S + \lambda A = G
Atmosphere: \lambda G = 2 \lambda A
Planet: S  = \lambda A + (1-\lambda) G

The factor of two for A (the radiation emitted from the atmosphere) comes in because the atmosphere radiates both up and down. From those equations you can derive the surface temperature as a function of the incoming solar and the atmospheric emissivity as:

G=\sigma T_s^4= {S\over(1 - 0.5\lambda) }

If you want to put some vaguely realistic numbers to it, then with S=240 W/m2 and \lambda=0.769, you get a ground temperature of 288 K – roughly corresponding to Earth. So far, so good.

Point 1: It’s easy to see that the G (and hence T_s) increases from S to 2S as the emissivity goes from 0 (no greenhouse effect) to 1 (maximum greenhouse effect) i.e. increasing the greenhouse effect warms the surface.

This is an extremely robust result, and indeed has been known for over a century. One little subtlety, note that the atmospheric temperature is cooler than the surface – this is fundamental to there being a greenhouse effect at all. In this example it’s cooler because of the radiative balance, while in the real world it’s cooler because of adiabatic expansion (air cools as it expands under lower pressure) modified by convection.

Radiative Forcing

Now what happens if something changes – say the solar input increases, or the emissivity changes? It’s easy enough to put in the new values and see what happens – and this will define the sensitivity of system. We can also calculate the instantaneous change in the energy balance at the top of the atmosphere as \lambda or S changes while keeping the temperatures the same. This is the famed ‘radiative forcing’ you’ve heard so much about. That change (+ve going down) is:

F_{Top}= \Delta S + \Delta \lambda (G_0 - A_0) = \Delta S + {{0.5 \Delta \lambda S } \over { (1-0.5\lambda) }}

where \Delta S, \Delta \lambda are the small changes in solar and change in emissivity respectively. The subscripts indicate the previous equilibrium values We can calculate the resulting change in G as:

\Delta G \sim {\Delta S \over { (1-0.5\lambda) }} + {0.5 S \Delta \lambda \over { (1-0.5\lambda)^2 }} ={ F_{Top}\over { (1-0.5\lambda)}}

so there is a direct linear connection between the radiative forcing and the resulting temperature change. In more complex systems the radiative forcing is a more tightly defined concept (the stratosphere or presence of convection make it a little more complex), but the principle remains the same:

Point 2: Radiative forcing – whether from the sun or from greenhouse gases – has pretty much the same effect regardless of how it comes about.

Climate Sensitivity

The ratio of \Delta G/F_{Top} is the sensitivity of G to the forcing for this (simplified) system. To get the sensitivity of the temperature (which is the more usual definition of climate sensitivity, \Delta T_s/F_{Top}), you need to multiply by {0.25\over\sigma T_s^3} i.e. {0.25\over\sigma T_s^3 (1 - 0.5\lambda) }. For the numbers given above, it would be about 0.3 C/(W/m2). Again, I should stress that this is not an estimate for the real Earth!

As an aside, there have been a few claims (notably from Steve Milloy or Sherwood Idso) that you can estimate climate sensitivity by dividing the change in temperature due to the greenhouse effect by the downwelling longwave radiation. This is not even close, as you can see by working it through here. The effect on G due to the greenhouse effect (i.e. the difference between having \lambda=0 and its actual value) is { 0.5\lambda S\over(1 - 0.5\lambda) }, and the downward longwave radiation is just \lambda A, and dividing one by the other simply gives \lambda – which is not the same as the correct expression above – in this case implying around 0.2 C/(W/m2) – and indeed is always smaller. That might explain it’s appeal of course (and we haven’t even thought about feedbacks yet…).

Point 3: Climate sensitivity is a precisely defined quantity – you can’t get it just by dividing an energy flux by any old temperature.


Now we can make the model a little more realistic by adding in ‘feedbacks’ or amplifying factors. In this simple system, there are two possible mechanism – a feedback on the emissivity or on the albedo. For instance, making the emissivity a function of temperature is analogous to the water vapour feedback in the real world and making the albedo a function of temperature could be analogous to the ice-albedo or cloud-cover feedbacks. We can incorporate the first kind of physics by making \lambda=f(T_s) dependent on the temperature (or G for arithmetical convenience). Indeed, if we take a special linear form for the temperature dependence and write:

\lambda (G) =\lambda_0 + \lambda^\prime ({G\over G_0}-1)

then the result we had before is still a solution (i.e. \lambda_0=0.769, G_0={S\over (1-0.5\lambda_0)}=390). However, the sensitivity to changes (whether in the greenhouse effect or solar input) will be different and will depend on \lambda^\prime. The new sensitivity will be given by

\Delta G \sim { F_{Top}\over { (1-0.5(\lambda_0+\lambda^\prime))}}

So if \lambda^\prime is positive, there will be an amplification of any particular change, if it’s negative, a dampening i.e. if water vapour increases with temperature that that will increase the greenhouse effect and cause additional warming. For instance, \lambda^\prime=0.1, then the sensitivity increases to 0.33 C/(W/m2). We could do a similar analysis with a feedback on albedo and get larger sensitivities if we wanted. However, regardless of the value of the feedbacks, the fluxes before any change will be the same and that leads to another important point:

Point 4: Climate sensitivity can only be determined from changes to the system, not from the climatological fluxes.


While this is just a simple model that is not really very Earth-like (no convection, no clouds, only a single layer etc.), it does illustrate some relevant points which are just as qualitatively true for GCMs and the real world. You should think of these kinds of exercises as simple flim-flam detectors – if someone tries to convince you that they can do a simple calculation and prove everyone else wrong, think about what the same calculation would be in this more straightforward system and see whether the idea holds up. If it does, it might work in the real world (no guarantee though) – but if it doesn’t, then it’s most probably garbage.

N.B. This is a more pedagogical and math-heavy article than most of the ones we post, and we aren’t likely to switch over exclusively to this sort of thing. But let us know if you like it (or not) and we’ll think about doing similar pieces on other key topics.

296 Responses to “Learning from a simple model”

  1. 201
    Chuck Booth says:

    Re 196 You don’t hear of biologists being good at physics

    Actually, you do, if you try…Andrew Biewener at Harvard(, and Steve Vogel ( and Steve Wainright at Duke ( are three that come to mind. Biology and physics are well integrated in the fields of biophysics and biomechanics.

  2. 202
    Jon C says:

    If you used the GSMs from the “Big Five”, made logical assumptions, applied those assumptions to the models, at about what period in the future would we reach the Point of No Return? This exercise appears to be worthwhile because it is doubtful that man will do much to address warming for many years.

  3. 203

    the Wonderer:

    That’s very well put and I agree its easy to lose focus. I have to add that the rigour we need to discuss climate science is at first frustrating, because some of the people “bucking” the consensus aren’t honest, and the others seem a little odd in what they’re willing to believe or not, but when a scientific topic comes up on other forums, it’s interesting how often I think, man, that level of vagueness, lack of sources, double standards, whatever, would never fly discussing climate change. Although we compare it with things like the evolution debate, I’d say the “opponents” are more formidable in climate science than in most controversies.

  4. 204

    also to clarify and definitely not to stoke anything i was speculating that there might be community differences between Mechanical Engineering culture and Electrical Engineering culture, with the latter taking a broader spectrum of math. Hence, an MS in EE would be, by what I was saying, taking a broader spectrum of math, not a narrower one, so that reinforces the question I was musing over, not contradicts its premises.

    I literally took only one grad engineering class, and it happened to be in ME. I noticed that as a big difference with my undergrad and grad physics classes, but that’s obviously too small a sample for me to have learned anything definitive. It just seemed to me at the time that Mechanics and Mechanical Engineering have lengthy calculations where things can go wrong and having a sense of what you’re doing is important, whereas my E&M stuff and Thermal and Statistical were more wide-ranging idea classes. It seemed to me E&M was definitely more arcane in the math involved.

    Also, I sometimes see parallels in science between things like engineering and things like physics to US military interservice rivalries. Some of it is tradition.

  5. 205

    Re 195:

    Gavin, won’t virtually any IC engine produce N02?

  6. 206
    Craig Allen says:

    Re: 199: Minor hiccup on the link there – this one should work

    Does anyone know of a good comparative summary of the various models currently in use or in development? And for that matter information about what we can expect in future. How much better will they get and at what rate? Are we going to approach some limit any time soon in prediction capacity that is inherent in the chaotic nature of the atmosphere? What are the key areas for improvement? What are the key hurdles to be overcome. Etc.

  7. 207

    [[As I understand it (correct me if I'm wrong!) it's believed that on Venus there was a runaway greenhouse effect involving temperatures rising to the boiling point of water and all the water evaporating. But now the atmosphere of Venus is almost all CO2 (??), so currently the Venusian greenhouse effect is all due to CO2, and the temperature is something like 735 K. I'm a bit confused about how that's consistent with us (Earth) being anywhere close to saturation of CO2 absorption and only being around 300 K. I think Venus is less than 10% closer to the Sun than we are: does that make such a big difference, or is there another reason?]]

    Venus has a semimajor axis (distance from the Sun in Earth-Sun units) of 0.723. When it formed and the primordial nebula cleared away, it was too hot to keep its oceans liquid — there was CO2 and H2O in the air, that heated the atmosphere, H2O evaporated from the oceans, that heated the atmosphere more, and so on in a cycle that “ran away” until there was no ocean left. Then sunlight dissociated the water vapor in the upper atmosphere. The hydrogen escaped, the oxygen combined with Venus’s surface rocks.

    Most analyses of planet climate histories (Rasool and deBergh 1970, Hart 1978, 1979, Kasting et al. 1993) conclude that any planet that formed closer than about 0.95 AUs to the sun would have undergone such a runaway greenhouse effect. Earth was just far enough out that the process never ran away.

    The Venus greenhouse is maintained mostly by carbon dioxide, but also by the 75% sulfuric acid droplet clouds that cover the whole planet, and by minor gases such as water vapor, sulfur dioxide, hydrocholoric acid and hydrofluoric acid.

    The idea that CO2 absorption is “saturated” in Earth’s atmosphere is wrong. It was developed in the early 20th century in response to Arrhenius’s 1896 global warming paper, and was standard doctrine until more careful spectra of CO2 and H2O were developed in the 1940s, and the process of radiative transfer at many levels in the atmosphere was better understood.

  8. 208

    [[The educations of both are very very similar. You are implying that scientists by education are more savy than engineers.]]

    No, that’s not what I said at all. I said that what engineers do and what scientists do are two different things, and that some engineers don’t seem to understand the difference, and claim to be scientists (and in many cases, better scientists than the real scientists). No matter how much engineers like science, love science, or admire science, what they do in their jobs is not science. It is not empirical research and does not get published in peer-reviewed science journals. Engineers are engineers. Scientists are scientists. They’re both admirable professions, but they are not the same profession. That’s all I’m saying, and I’m saying it not out of “snobbery,” but because we’ve had engineers come in here claiming to be scientists, and telling the climatologists here that they were wrong about this, that and the other thing (the models, how the greenhouse effect works, etc.).

  9. 209


    Sorry, I saw that response after I posted my last message. Withdraw that one if it’s out of line.


  10. 210
    Fredrik says:

    Barton, what is a scientiest and what is an engineer? Is a professor doing research in a subject like structural dynamics or control theory a scientist according to you? I am interested because I want to know if I am a scientist or not.

    Why this bs about scientist and engineers anyway? Engineers do mistakes, scientists do mistakes and both belives and write incorrect things as can be seen on this very website.

  11. 211
    Steve Funk says:

    The difficulty I have in following this piece is not the mathematical operations, but understanding and retaining the concepts that are expressed as a single letter. If you put up a sidebar with 1-2 sentence definitions of each letter variable, that might help. Also, it would help to include the English pronunciation of the Greek letters. I retain this stuff by vocalizing it, and never actually studied Greek. (I Googled the Greek alphabet, and that helped.)

  12. 212
    tamino says:

    Question for the mods (or anybody, off the topic of this thread).

    Something’s been nagging at the back of my head. A while ago, a post was made about CO2 change leading temperature change during deglaciations. It was stated that “something” starts warming, which then increases CO2. In discussion (here and elsewhere), much was made of the uncertainty in the “something starts warming” statement. What starts warming?

    Isn’t it obvious? Milankovitch cycles start melting, and the albedo change induced by melting starts the warming.

    So … what am I missing?

  13. 213
    Ken Coffman says:

    Regarding N2 as greenhouse gas.

    Thank you, Gavin, for your comment. To be sure, you’re saying N2 has zero effectiveness as a greenhouse gas, compared to CO2? It has no capability to absorb or reflect radiant energy? Zero sounds like a troublesome number. 5%? 1%? 0.1%?

    [Response: The ability to absorb in the infrared is a function of various vibrational modes. Symmetric two atom molecules do not possess the requisite degrees of freedom that tri-atomic (and higher) molecules have (think of all the different ways that O-C-O can oscillate compared to N-N). Thus for all intents and purposes N2 is not a greenhouse gas. Nothing is ever truly zero, and it's conceivable that isotopic variations/higher energy bands make a difference - the HITRAN database would be the place to look for them - but I would be astounded if they were even a thousandth as important as CO2. If someone knows the exact number, let me know. - gavin]

  14. 214

    #212, Tamino, you not missing much ! As an example, In modern times, Arctic Ocean ice use to be more spread out:

    now a days it is much less expansive particularly around Novaya Zemlya

    This has tremendous impact on not only temperatures, Polar wildlife and sea transportation, but on the very time when the sunrises from the long night:

    When the sun was seen while it was -5.7 degrees below the horizon, an historical record established in 1597, not broken since.

  15. 215
    lars says:

    The sun’s photochemical action on carbon dioxide. Ultraviolet photons of wavelengths less than 169 nm can photodissociate carbon dioxide into carbon monoxide and atomic oxygen.

    Will the sun save us?

    [Response: This sink is tiny and only occurs in the mesosphere, and so the answer is no. -gavin]

  16. 216
    Ike Solem says:

    RE#212, The problem with basing the initiation strictly on the milankovitch cycles seems to be that over the past 900,000 years the main signal has been the 100,000 year cycle, while in the 2 million years prior to that the main glacial was 41,000 years, which was ascribed to the Milankovitch obliquity (the onset of N. Hemisphere glaciation was 2.75 million years ago). So, there seems to be no agreement on what sets the timing for the more recent 100,000 year glacial cycle. There is a paper that discusses the problem (and proposes their solution) at :

    Paleoclimatic evidence from ice cores, ocean sediments and other sources reveal oscillations in climate and atmospheric CO2 over the last million years, with major signals in 20, 41 and 100 ky (thousands of years) frequency bands (Hays et al., 1976; Petit et al., 1999; EPICA, 2004). While changes in solar radiation caused by perturbations to Earth’s orbit appear to be directly responsible for the 20 ky and 41 ky cycles, the explanation of the dominant 100 ky cycles remains elusive (Imbrie et al., 1993; Roe and Allen, 1999; Wunsch, 2004).

    It is increasingly clear that internal feedbacks in the Earth’s climate system play a major role in the 100 ky cycles, whether it is pacemaked by orbital forcing or not. Atmospheric model simulations show that the 80-100 ppmv lower CO2 is the dominant factor in producing about 5C cooler glacial climate, with additional contribution from ice-albedo and other effects 5 (Broccoli and Manabe, 1987; Lorius et al., 1990; Weaver et al., 1998). It is very difficult, if not impossible, to simulate the observed glacial cooling in comprehensive models without changing CO2. Thus carbon-climate interaction may provide key internal feedbacks that have rarely been included in comprehensive models interactively.

    CO2, CH4 and N2O levels were all well lower during the glacial-interglacial period, (by 100-200 ppm relative to current values for CO2) CO2 and other gas levels changed much slower during the transitions than they are today (by a factor of 30 or so). Thus, it’s difficult to related such changes to current circumstances – multiple factors appear to control the glacial/interglacial cycle, but they produced a semi-stable periodic response. However, it’s doesn’t seem that current warming will be a repeat of a glacial-to-interglacial transition, of which there is only one well-recorded example, that of the Holocene.

    In the Pliocene period that preceded the onset of glacial cycles, temps were ~3C higher and sea levels were 10-20 meters higher, and CO2 levels were some 30% higher than present values. Some people say that this is the best model of what future climate will be like. The main real issue still is the speed of the climate response to the accelerating greenhouse forcing… for which there is no good ‘recent’ historical analogue.

  17. 217
    lars says:

    The sun’s photochemical action on carbon dioxide. Ultraviolet photons of wavelengths less than 169 nm can photodissociate carbon dioxide into carbon monoxide and atomic oxygen.

    Will the sun save us?

    [Response: This sink is tiny and only occurs in the mesosphere, and so the answer is no. -gavin]

    So all we need is a ultraviolet photon generator…..

    [Response: Sorry, but no again. CO in the lower atmosphere oxidises to CO2 very quickly (due to the OH formed from photolytic reactions involving water). -gavin]

  18. 218
    Carol says:

    [Isn't it obvious? Milankovitch cycles start melting, and the albedo change induced by melting starts the warming.

    So ... what am I missing?]

    Add in the air cooling that takes place from the heat of fusion melting the ice. The calories required to melt ice can only come from the air. Need to have something happen that raises temperatures (and then the carbon dioxide levels), and keeps pumping calories into the air to make up for the calories absorbed by the ice to make it turn to liquid. The likely candidates could include massive geothermal events or variations of the sun. Solar variations probably account for most of the climate variations that have occurred.

    [Response: Milankovitch forcings makes differences of ten's of W/m2 on these timescales - plenty enough energy to melt the ice. -gavin]

  19. 219
    Lynn Vincentnathan says:

    I’m glad nitrogen was brought up. So N20 is a GHG. Now don’t laugh, I’m not a chemist, but what about N02 or NOx (whatever they are)? It seems I’ve read something somewhere about them being GHGs. Also that car & power plants emit them, and that synthetic fertilizers emit them.

    And also one of these guys is a ozone depletor, as well.

    So much for a little knowledge…(well, you know the rest).

  20. 220
    Jim says:

    One more comment and then I will leave it alone.

    Barton, alot of engineering is purely empirical, that is the part that you are missing. (I am taking that you mean empirical is the for the furthering of knowledge not so much to create a product for the market.) Engineering is not just about making products, it is also about researching new ideas, processes or things. (Yes they do get published in peer reviewed journals too!) Which, to me, is what science is all about and no one discpline of science (Whether you like it or not engineering is an applied science) has exclusive abilities to further science and to learn new science outside of their fields. You said that becuase engineers can plug numbers into some math eqs that they think they know science. I am sure there are some which mostly comes from the emphasis in our later classes in practicality and about the requirement to produce timely results. (This tends to make a lot of engineers confident and pragmatic and very cynical about “blue sky” ideas.) Whereas empirical research does not obey deadlines and often does not yield the desired results. (It is research after all.) In any case, overconfidence and cyninism are not unique to engineers, it is present in any science profession and you were making a broad generalization of one displine of it. What you were saying was exactly snobbery and you knew that when you said it.

    I have participated in many empirical research activities such as building 33Tesla, 54 Tesla and 900Mhz DC continous (not pulsed) magnets. (BTW what have you done?) We designed and built most of those beasts from scratch.

    New methods in Controls,Neural Nets, Digital Signal Proccessing, materials synthesis new transistors, and random process research, also count as empirical. (Along with lots of other things.)

    If all you are basing your opinions of engineers on is how some guys post on a blog, well then you are definitly using flawed judgement. In any case a quick set of google searches reveals that it is not just engineers that challenge AGW or say silly things about it, but some physicists/geologists/biologists etc.etc don’t preach from the AGW bible either. Does that make all phycists idiots too just becuase of a few bad apples? If I used your line of reasoning it would.

    Re 201.

    You will have a couple of outstanding folks in any field. That is what the Nobel Prize is for after all!

    Take your average biology grad and ask them to work out some ODEs or a couple fourier series, Laplace Transforms, or to show a time domain function in the frequency domain. (The eyes will glaze over.) See if they can do it. Then go ask a physics/math/engineer grad if they can.
    Post the results. Of course, ask those some physics/math/engineer about the details of cellular mitosis and you will also some eyes glaze over! The point being is what I said ealier no one discpline in science is any better at grasping the other disciplines that are outside of their core competencies. What is required of anyone is an open, agile, and thoughtful mind.

  21. 221

    Great article – the maths is always welcome. Certainly more welcome than politics – I know this is an important issue and we need people to understand…

    Through pure coincidence, I imagine, Kerry Emanuel talked about this model a few weeks back (the basics, not the feedbacks) in his Tropical Meteorology Course at MIT. It is always amazing to me how well simple models can do. Take this model, add a few more levels and some sort of tropospheric lapse rates and we can get very close to reality!

  22. 222
    Adam Nealis says:

    More like this please.

    Consider these threads in a forum I am a regular reader of and contributor to.

    I could not find anything online that was simple enough to support my views and at the same time objective.

    For me, there is still a paucity of publicly available data from simple, basic science experiments that demonstrate the fundamentls of greenhouse warming, etc. I did find some of the raw data used in the IPCC models, but it was not clear to me what the data were. It seems this information may be locked away in science journals whose publications are not publically available.

    I am an ex scientist, whose field was not in cliamte science. When I apply my scientists’ skepticism to the climate change debate I find the available data to be wanting. Which means I cannot be in support of the case for climate change as much as perhaps I should. And this is from someone who wants to believe in the reality of climate change.

  23. 223
    David B. Benson says:

    Re #222: Adam Nealis — Once a scientist, always a scientist. :-)

    Seriously now, have you read the AIP history of climatology linked in a sidebar? How about any of a number of textbooks, beginning perhaps with W.F. Ruddiman’s Earth’s Climate: Past and Future?

    But for AGW, the issue is very simple. Cardon dioxide is a so-called greenhouse gas. Humans have been producing a huge slug of it by burning fossil carbon, especially in the last 50 years. Therefore it will become even hotter, globally…

  24. 224
    Jim says:

    Re 223.

    That made it soooo clear!
    He is wanting more raw data, not polished answers. He wants to try to figure it out for himself. You telling him “we say we did so you can believe us” is not what I thought he was asking.

  25. 225
    Mark A. York says:

    “Who ya gonna believe, the people who pretend they’re on your side, and feed you lies and spin? “Just because you’re on their side doesn’t mean they’re on your side.” — Teresa Nielsen Hayden.”

    Where does this come from Hank? The author and I aren’t on speaking terms because she said I wasn’t a real Democrat. In fact, I wasn’t one at all according to St. Teresa. She disemvoweled me and there’s been hard feelings ever since. Public blog comment humiliation isn’t much fun. I thought her tactics resembled the Puritan stock treatment. I’m a Democrat, and have been since McGovern. I’m also a biologist. She’s a vehement partisan. I wouldn’t expect anything resembling objectivity from her anymore than the wingnuts. I do assume a sci-fi editor respects science itself, unlike these co-opted shills. If not those of us who do science for a living.

  26. 226
    Alexander Harvey says:

    It might amuse to consider this simplified model at the point where there are no greenhouse gases in the atmosphere. By which I mean that the atmosphere is totally transparent at all frequencies.

    Such an atmosphere can neither absorb nor emit radiation.

    Its only source of heat exchange is with the surface. What sort of atmosphere would this produce? What would be its equilibrium state?

    Unlike the original model I will be assuming that the greenhouse affect is distributed in a vertical gas column capable of convection, and conduction but not much else.

    At equilibrium there would be no net heat exchange at the surface as the atmosphere can not dissipate heat to space. This atmosphere would have no net source nor sink for heat, it would be thermodynamically dead.

    On course to equilibrium it may manifest many of the aspects of our atmosphere, it may pass through adiabatic equilibrium with a lapse rate but that lapse rate would necessitate a net upward flow due to conduction which, as the top of the atmosphere can not dissipate heat, does not represent an equilibrium condition.

    Equilibrium would be reached when the atmosphere was evenly heated throughout with no macroscopic temperature gradients. Its temperature thoughout would be the same as the earth’s surface.

    Given that all of that is true (comments welcomed) what would be the effects of adding greenhouse gases to this dead atmosphere.

    Well a major impact would be that the top of the atmosphere could now dissipate heat into space. The atmosphere would be alive again. Now do not think for a minute that I am going to hint that this indicates cooling.

    As space above the top of the atmosphere is now a net sink the only other location for net heat exchange, the surface, must represent a net source. This could be in the form of warming there resulting in a conductive flow, as well as the absorption of infrared radiation by the atmosphere. The effect of both would be to create a temperature gradient with the surface hotter than the atmosphere. With increasing greenhouse gasses added the atmosphere would reach adiabatic equilibrium and convection would increasingly become a significant transport mechanism. With increasing greenhouse effect, convective flows would increase and radiative flows would decrease as proportions of the total flow. It might help to consider the limiting state at which the atmosphere is totally opaque, a dark gas at all infrared frequencies yet still transparent to shorter wavelengths. The only significant means for transport would then be convection, ignoring any increase shorter wavelength radiation from the surface due to excessive temperatures.

    An important point of this model is that the temperature gradient needs only to be sufficient to maintain the flow necessary to match the radiative loss at the top of the atmosphere by either radiative of convective means.

    I realise that this is a different way of looking at things but hopefully, perhaps with some corrections, it might be useful.

    In this view it is the ability of the greenhouse atmosphere to dissipate heat into space that is the significant driver. The flows of heat in the atmosphere are the result of a need to supply that loss in a sustainable fashion.

    A key question is: what temperature does this indicate for the top of the atmosphere?

    Well in the totally IR transparent regime it will be the same as the surface temperature. In the totally IR opaque regime it will be the same temperature. In that state, for IR emission purposes the top of the atmosphere is the IR surface so it must have the same temperature as the surface of the earth in the totally transparent case as the same amount of heat needs to be dissipated. So at each extreme the temperature of the top of the atmosphere is the same. I can only speculate that it is the same at all greenhouse gas densities (comments welcomed).

    So if the temperature of the effective IR top of the atmosphere is basically unchanged, greenhouse gases must give rise to a net warming of the earth surface.

    Just how hot the surface gets in this model depends on the likely contributions of convective and radiative flows.

    Both depend on the temperature gradient. This may not be obvious.

    As IR passes through the gas column it is constantly absorbed and emitted. This applies to both upward and downward flows. The net upward flow is only sustained by the temperature gradient causing the upward flow from each lower level to the next higher level to be greater then the downward from the upper level to the lower one.

    I have no figures, but I would not think that convection is a particularly good heat transport system considering the large amounts of heat that need to be transported to fuel the IR being emitted at the top of the atmosphere. I think that the world would be a very nasty place before the primary transport mechanism was convection. (Comments welcomed.)

    So in the simplified model all we really need to know is the amount of heat being dissipated into space by the top of the IR atmosphere which given that the temperature up there would be relatively constant under increasing GH effects will reach a maximum at the point where all IR in the range of the GH gas is being absorbed and emitted close to the top of the atmosphere. So the increase in temperature necessary to feed this loss is a function of the opacity, which gives us the temperature gradient, which in turn must be integrated over the effective depth of the atmosphere to give the surface warming.

    Hopefully, given the restraints of the model I have not strayed too far away from the physically possible. And further that some points like the relationship between temperature gradients and net IR flows may be useful.

    All comments welcomed.

    Alexander Harvey

  27. 227
    Hank Roberts says:

    Mark, I don’t recommend arguing about other bloggers’ policies here, if anywhere.

    Berkeley advice:
    “Don’t argue with crazy people on the streeet — passers-by can’t tell which of you is crazy.”

    Any writer’s name (however many people use it) is easy to find with Google. I can search for
    “some name” +banned
    and find a lot of hits, but it’s impossible to tell who’s behind each instance of the name.

    – When when a host says a tone is not acceptable and uses disemvowelling, it’s their call — it’s their blog.
    It happens. Some hosts stir up shit; some don’t care.

    – When a host says several names are sock puppets all coming from one IP, it’s their call — it’s their blog.
    It happens. Some hosts let it to stir up shit; some don’t care; most consider it a reason to block the IP.

    – Trolls pick up names and post stupid stuff under them as recreation. Only the host can see the IP; we bystanders can’t tell who’s using the name. It happens.

    Posting to someone else’s blog is like sending them unsolicited email—-if they like it well enough to keep it and show it to their friends, that’s great; if they don’t, learn not to take offense. No point arguing.

    “Ever tried. Ever failed. No matter. Try again. Fail again. Fail better.” —-Samuel Beckett

    I recommend calling attention to your good work, not your troubles, when using other people’s forums.

  28. 228

    [[At equilibrium there would be no net heat exchange at the surface as the atmosphere can not dissipate heat to space.]]

    It can’t do so by conduction or convection, but it can dissipate heat by radiation, and does. Even worlds without atmospheres (or without significant atmospheres) — Mercury, the Moon, asteroids — can lose heat that way. Otherwise they’d steadily heat up in the sun until they melted and then vaporized.

  29. 229
    Pat says:

    Re 226 – That’s one good way to approach the matter. There are some complexities, of course, but we’re starting with the idea of a simple model here.

    (PS I prefer to use SW and LW rather than IR –
    SW = short wave, the kind of radiation mainly from the sun;
    LW = long wave, the kind of radiation that can be emitted at typical terrestrial (Planet surface and atmospheric) temperatures.
    This differentiation is more convenient because SW includes UV, visible, and some IR (out to around ~ 4 microns – of course the sun emits some radiation even in the LW band and the Earth emits a tiny amount of radiation even in the SW band but the great majority of the energy in each case can be seperated into non-overlapping bands. (Are you familiar with black body radiation as a function of wavelength?)

    There is an idea of an effective emitting level in the atmosphere that radiates to space; this level must then have the temperature that corresponds to the temperature of the surface with an atmosphere transparent to LW, assuming same overall albedo. This would be at the top of the atmosphere if the atmosphere were perfectly opaque in LW.

    It does become a bit more complicated when the atmosphere has a varying degree of opacity. The source of emission to space is distributed over the vertical thickness of the atmosphere; along a vertical coordinate corresponding to optical depth, the source would be concentrated at the top. But if the optical depth of the atmosphere is low, some still comes from the surface of the Earth. Then, all of this varies over wavelength, even within the LW band (in the absence of clouds and tropical humid air, the atmosphere is somewhat transparent between 8 and 12 microns.) There is also some atmospheric absorption in parts of the SW band, mainly from water vapor in the troposphere and ozone in the stratosphere, and there is some absorption, I think by molecular and atomic oxygen, at the very top of the atmosphere. The air’s absorption/emission spectrum varies with height in part because H2O and O3 concentrations vary, and also because at higher pressure and temperature near the surface, discrete molecular absorption lines are spread out into bands, while higher up in the atmosphere they are less spread out.

    Typically a planetary atmosphere has a troposphere, in which temperature falls with height, and a thermosphere, in which temperature rises with height; because of the Earth’s ozone layer, the Earth’s atmosphere also has a stratosphere and mesosphere in between.

    I think generally convection tends to maintain a representative lapse rate in the troposphere close to a moist adiabat (the rate that air cools at while it rises if condensation is occuring). This actually decreases at increasing temperature because at a given x % relative humidity, the concentration of water vapor increases with temperature so moist updrafts starting at a higher temperature cool off less quickly with height.

    I’m leaving some loose ends here, …

    But see my comment 105 above.

    For a simple one dimensional radiative-convective equilibrium model, one can set a maximum allowable lapse rate – a constant or a moist adiabat, for example – then the resulting temperature profile requires in places which are at such a lapse rate (the troposphere) that the total radiative heating or cooling rate is nonzero. The surface will also typically have a net radiative heating rate. This must equal the convection rate from the surface, and the variation in convection with height can be infered by the radiative cooling rate (which at equilibrium equals the convective heating rate, which is the convergence of the convective heat flux, or the negative rate of change with height of upward convective heat flux).

    I would guess that you’re right that convective heat transport should generally increase as the greenhouse effect increases. Some effects which would reduce that increase are that radiative transfer across a difference in temperature increases with an acroos the board temperature increase, especially at the shorter end of the LW band (not as much at longer wavelengths). Also, there is the SW absorption by water vapor. On the other hand, an increase in temperature would reduce the moist adiabatic lapse rate, which would slow radiative transfer within the lower atmosphere.

    While increasing the LW opacity decreases radiative energy transfer at longer distances (with the temperature profile held steady), it can increase radiative energy transfer across shorter distances (the cut off between longer and shorter is itself reduced by increasing opacity – across a fixed distance, with a fixed temperature distribution, increasing opacity from zero at first results in increasing radiative energy transfer, which reaches a peak, and then declines). What happens with increasing opacity is that radiation is exchanged across shorter distances, which tend to involve smaller differences in temperature, and so there is less of an imbalance in radiation – that is, the net radiative energy transfer decreases…

  30. 230
    David says:

    I’m relatively new to Realclimate (been following for about a month), and like the site a lot. I think this type of post describing the modelling is well worthwhile and very interesting.

    A few comments on detail.

    I’m not surprised some people found the geometric factor of 4 hard to understand. I don’t think it’s immediately obvious. I think the way I’d express it as something like “the solar constant gives the energy when the sun is due overhead, but for this model we are interested in the average over the whole globe, day and night as well as all latitudes.”

    It took me a little while to get my head round “atmospheric radiative flux is written lambda A = lambda sigma Ta to the fourth” because my natural reaction was to cancel the lambdas. I’d be tempted to leave the temperature part out altogether until after the basic formula has been derived, and then have a separate little bit as part of the ‘Climate Sensitivity’ section to point out that these changes in energy are expressed through temperature.

    I can’t decide whether the equation of emissivity with absorptivity (Kirchoff’s Law) is so obvious that it’s not worth mentioning, or so profound that it merits a whole exposition in itself. I think it probably does need to be explained that lambda is variously representing emission and absorption at different places in the three energy balance equations.

    But those are bagatelles. The part that really confused me (and to an extent still does) is the ‘Radiative Forcing’ section. To me, the second (Delta G) equation is almost obvious because all you are doing is differentiating your first (G) equation (it’s a fine-balanced decision whether the equations should be numbered as nothing screams ‘impenetrable techy geekiness’ to the typical reader like numbered equations, IMO), whereas the FTop equation to me comes out of nowhere. Where are you going with it and why are you introducing this concept?

    In the end I had to look up ‘radiative forcing’ on Wikipedia (not a bad thing in itself, but I suspect you are losing readers right there). I’m still not sure I’ve understood why radiative forcing is a useful concept – it seems to me it’s being used like a sort of convertible currency for any external stimulus to the climate: “we can (in the model) treat any externally (including human) generated change, such as an increase in the amount of carbon dioxide in the atmosphere, just as if it were a change to the amount of energy coming in at the top of the atmosphere. The magnitude of this energy is known as the radiative forcing. This feature carries over to more complicated models as well as the real atmosphere [I assume that's true]. This is useful because…” I think this is really what you are getting at with your Point 2.

    I think some of my confusion arose from the use of the phrase “instantaneous change” in this section. The trouble is that by this time I was thinking in terms of the model, where time is not represented (the ground and atmosphere have undefined heat capacity), so my reaction was “how can there be a change in the energy balance? It’s always zero by definition” and it took me a little while to sort myself out.

    Finally, there’s a cultural trap here. If I’d read the substance of this post in a textbook, or heard it in a lecture, I would have expected to get a pen and paper and do some sums before I was sure I’d got it all. Because I read it on a blog, I expected to read it through once and understand it first time and was mightily affronted for a while that that didn’t work.

    I hope this hasn’t come off as an ‘it’s really all about me’ comment, but I’m starting out from the assumption that the post is not really about climate, but about effective popular communication of science, and I wanted to record some of the false starts and blind alleys as likely being relevant to other readers and other attempts to do this sort of thing.

    Finally, I have to say I love the argument that, because greenhouses don’t use the greenhouse effect to keep warm, the earth can’t be using it either, and so it can’t be warming.


  31. 231
    Alexander Harvey says:

    # 228

    I think that you misunderstand me.

    You wrote:

    “It can’t do so by conduction or convection, but it can dissipate heat by radiation, and does.”

    Actually I think that you will find that a non-greenhuose gas can’t!

    If a gas can not absorb SW radiation it can not emit SW radiation and vice versa.

    The planetary surface would be the only source of SW radiation. If a gas can not radiate heat into space then that sink is not present.

    #229 Many thanks for your comments. I think I am aware of some of the complications. In particular the detailed way that real greenhouse gases must absorb and emit radiation and the factors that determine its emissivity at each frequency. Unfortunately this seems horrible complex and intractable and I presume certain rule of thumb parameterizations are used instead.

    I must read your postings again before commenting further.

    For know thanks.

  32. 232

    [["It can't do so by conduction or convection, but it can dissipate heat by radiation, and does."
    Actually I think that you will find that a non-greenhuose gas can't!
    If a gas can not absorb SW radiation it can not emit SW radiation and vice versa.
    The planetary surface would be the only source of SW radiation. If a gas can not radiate heat into space then that sink is not present.

    Any body at a temperature above absolute zero is constantly emitting photons, non-greenhouse gases as well as greenhouse gases. Nitrogen at 288 K emits radiation just like carbon dioxide does, though there may be a different emissivity in the equation. But the idea that an atmosphere — any atmosphere — can’t radiate heat into space is just wrong.

  33. 233
    Alexander Harvey says:


    I suggest you go looking for the LW absorption spectra for the monatomic gases. I doubt you will find one.

    I have found something quotable from

    “Homo-nuclear diatomic molecules such as O2, N2, H2 and Cl2 and monatomic gases such as helium, and radon do not have infrared bands and therefore must be measured by non-infrared means.”


    There is a significant difference between the ways that different gases absorb and emit EM radiation. The monatomic gases simply lack the rotation and vibration modes that produce LW emissivity in greenhouse gases.

    If you are saying that all gases emit some radtiation at atmospheric temperatures no matter how small and no matter which part of the spectrum then you are right but risk pedantry.

    According to this definition all gases are greenhouse gases.

    For the purposes of what I have written the monatomic noble gases do not radiate at room temperature. Get them hot enough (thousands of degrees) and they will radiate via electon state transitions but this I think largely confined to the UV, and visible bands. The same is true, or perhaps nearly true of the symmetric diatomic molecules. (I am not sure that the quote above is strictly true of N2.)

    There is something special about the greenhouse gases. Which is that they are “significant” radiators at room temperatures. This is what makes them greenhouse gases.

    If you are saying that a Helium atmosphere at Earth atmospheric temperatures and pressures must radiate miniscule amounts of UV and visible radiation then I suppose you are right and I am wrong.

    If you are going to protest that planets do not have pure monatomic atmoshperes then all I can say is that I never suggested they did. I was merely considering how this simplified model might perform if ours did.

    If I am wrong give details, not bald statements, and I will fall on my sword like a gent. As it stands I know of no mechanism by which the noble gases can emit significant radiation at standard atmospheric temperatures and pressures.

  34. 234

    [[I suggest you go looking for the LW absorption spectra for the monatomic gases. I doubt you will find one.
    I have found something quotable from
    "Homo-nuclear diatomic molecules such as O2, N2, H2 and Cl2 and monatomic gases such as helium, and radon do not have infrared bands and therefore must be measured by non-infrared means."
    There is a significant difference between the ways that different gases absorb and emit EM radiation. The monatomic gases simply lack the rotation and vibration modes that produce LW emissivity in greenhouse gases.
    If you are saying that all gases emit some radtiation at atmospheric temperatures no matter how small and no matter which part of the spectrum then you are right but risk pedantry.
    According to this definition all gases are greenhouse gases.

    I know the difference, thank you, between a greenhouse gas and a non-greenhouse gas. I think part of your problem seems to be that you think if something doesn’t emit at IR wavelengths, it doesn’t emit at all, leading to your idea that an atmosphere without greenhouse gases wouldn’t emit any radiation.

    How does such an atmosphere work? I can only think of a few possible mechanisms:

    1. It is at absolute zero temperature.

    2. It is a perfect insulator (the emissivity term in the Stefan-Boltzmann equation is identically zero). The planet beneath it absorbs sunlight, but nothing gets out, which means the planet will heat steadily until it melts and then vaporizes.

    Which explanation do you favor?

  35. 235
    Alexander Harvey says:


    At Earth like temperatures and pressures blackbodies only emit any significant amount of radiation in the Infrared. You can check this, go outside on a dark night.

    If a gas has no significant spectra in the infrared than it does not radiate any significant amount of energy at earth like termperatures and pressures.

    I have never said that the surface does not radiate, quite the contrary.

    I have said that an atmosphere that can not radiate LW radiation, does not radiate LW radiation and at earth like conditions and does not emit any signifcant amounts of SW radiation

    Please explain the mechanism by which you say that it must. Other than that you say so. Or is your augument that the emission is not precisely zero and as miniscule is not precisely zero, you are right and I am wrong, which I have alredy accepted.

    Which state transitions correspond to LW transmissions in noble gases?

    A substance does not radiate simply because it is warm. It does so because it is warm and a mechanism exists. If there is no mechanism by which it can radiate LW radiation then it can not do so. If it is not hot enough to radiate any significant amount of SW then for all intents and purposes (except it seems yours) it is dark. I have accepted that small amounts of SW will be emitted but as the night sky is not aglow with light generated by the atmosphere I do not accept that it makes any material difference to what was a model suitable to aid thinking about generalized atmospheres.

    As I have said; show me some evidence that noble gases emit significant amounts of energy at Earth like temperatures and pressures and I will retract.

  36. 236

    [[I have never said that the surface does not radiate, quite the contrary.]]

    Ah! Now we’re getting somewhere.

    Your original discussion seemed to be saying that without greenhouse gases, heat would be transmitted to the atmosphere by conduction and convection but would have no way to dissipate the energy to space. If it doesn’t dissipate the energy, where does the energy go?

    If your reply is that such an atmosphere would heat up without limit — well, we’re back to Olbers’s paradox. A sufficiently hot atmosphere, whatever its composition, will radiate. It will not have zero emissivity. That’s why dust veils in the way of the starlight can’t explain the dark night sky. With a uniformly bright sky, the dust would heat up until it glowed.

    So would the greenhouse-gas-less atmosphere you describe.

  37. 237
    Alexander Harvey says:

    I am afraid that you do not seem to have understood the original posting. Or that I did not make it completely clear.

    The satement: “At equilibrium there would be no net heat exchange at the surface as the atmosphere can not dissipate heat to space.”

    meant no net heat exchange between the surface and the atmosphere. I thought that the obvious heat exchange between the surface and deep space would be understood.

    That said I am still waiting to hear from you a statement about which mechanism noble gases can use to emit significant radiation into space at Earth like temperatures and pressures. I think that this is the crux of your augument.

    Please advise.

  38. 238
    Joseph O'Sullivan says:

    This type of post with some simple math that demonstrates some of the relevant points behind the most important topics is very useful. I welcome this as an easier alternative to reading a textbook on atmospheric science.

    Instead of these types of posts maybe Gavin could go on the Daily Show again! ;)

    [Response: [grin] – gavin]

  39. 239

    [[meant no net heat exchange between the surface and the atmosphere.]]

    What would stop conduction and convection from happening?

  40. 240
    Ray Ladbury says:

    Alexander, Actually, your model, as phrased is not physical. All matter radiates at finite temperature–it doesn’t require an atmosphere at all. Moreover, all matter has absorption bands–and that is why the true black body does not exist in nature. So, in the absence of greehnouse gases, the effect would be that light is incident on the surface. The surface absorbs the light and warms. It then re-radiates back into space with a spectrum appropriate to its temperature. This heats the atmosphere, and heat is transported by convection (very effective, by the way) and radiation through the atmosphere and out into space. At equilibrium, input equals output–same as always. Adding greenhouse gases simply changes the spectrum of the light incident on the surface and leaving the atmosphere–it has gaps in the absorption bands. The reason there is a net greenhouse effect is because sunlight peaks in the green, while, the peak of thermal emission from the surface is in the IR. Voila, an extra 30 degrees to make life possible

  41. 241
    Pat says:

    Re 239,240

    Well, I understood’s Alexander’s post to be a look at what happens if a dimension of the atmosphere is varied from one extreme to the other (LW opacity), and so will necessarily have unphysical aspects at the extrema but be instructive nonetheless.

    With the (unphysical) simplification that there is no SW absorption within the atmosphere, it seems quite clear that in a perfectly LW opaque atmosphere, essentially all heat flow starts as SW absorption at the surface, flows only by conduction to the air and then convection through the atmosphere, and then is emitted to space only at the top of the atmosphere (which is all troposphere, no stratosphere, mesosphere, or thermosphere). This is assuming of course that the surface and lower atmosphere do not get so hot as to emit in SW – of course, with the simplification of no SW absorption in the atmosphere, it would only be SW emission from the surface, and so all significant heat transfer from the surface to the atmosphere and within the atmosphere would still be conduction and convection. In the opposite extreme, a completely transparent (at both SW and LW) atmosphere, the surface would be (at equilibrium) in radiative equilibrium with SW absorption and LW emission to space. Given that, at equilibrium there could be (in a 1 dimensional atmospheric column, at least) no heat transfer to or from the atmosphere, suggesting the atmosphere would approach by conduction an isothermal equilibrium state. If some atmospheric SW absorption were thrown in, then heat would be conducted downward from an entirely thermospheric atmosphere to the surface, etc…

    This could be expanded in three dimensions – in terms of cross section per unit mass, for example, LW emission/absorption cross section, SW absorption cross section, and SW scattering cross section (for any given surface characteristics – SW albedo and LW emissivity). This would be a simple scenario where the atmosphere is chemically homogeneous, the effects of clouds (if counted) being smeared out, etc…

  42. 242
    Alexander Harvey says:

    Hi All,

    I do not have a lot of time right now.

    Can I separate things out and deal with just one bit at a time.

    The statement that all matter radiates at finite temperature seems blindingly obvious. But how true is this statement. Can it be used as a maxim?

    To answer this it is necessary to be very careful about what we mean by matter and temperatures.

    At one extreme it is “believed”, not known, that most of the mass of the universe is both warm (estimates of a few degrees to thousands of degrees) yet does not emit any detectable radiation.

    This is highly exotic stuff but is this sufficient to challenge the statement that if it has a finite temperature it “must” radiate.

    Less exotically Helium gas, lacks the normal mechanisms by which gases radiate at room temperature. So does it radiate at this temperature, I do not know for certain. What I know is that “I do not know how it can”.

    I know not the mechanism by which it can.

    Helium detectors use the atoms internal excited states to produce a spectra because of the lack of other excitations (rotation-vibration).

    The energy required to produce a spectra is around 19.8eV (first excitation state). At 300K the energy distribution is centred around ~0.07 eV, less than 1/250th of the required energy.

    Rememering that the energy distribution is dependent on the exponent of this ratio, I think that the chance of a random 19.8eV collision event is very small, possible but very, very small. Even then I do not know if such a collision could be inelastic, I do not know if it corresponds to a permitted transition.

    You see there is a lot that I do not know, but I do know that in order to agree with you and say it must radiate I need to know that it does (a spectra, or a measured emissivity at 300K). Or in the absence of that evidence, sound reasons why, in this particular case, it must. For that I need to know how it can radiate and why it must do so.

    If anyone here can elucidate the mechanism by which Helium gas can, by itself, from only its Helium – Helium interactions, radiate at 300K I would be very much obliged to you.

    I have pointed out what I see to be the difficulties and what makes the noble gases and particularly Helium a special case. Gases do not just radiate, they radiate via mechanisms, permitted pathways.

    I am not saying I am right or that you are wrong.

    If you know that you know that you are right just explain the mechanism or point to the evidence. If you only think that you know then perhaps the matter can not be decided either way.

  43. 243
    Ray Ladbury says:

    Well, that’s all very interesting, Alexander, but we weren’t talking about dark matter or anything exotic; nor were we talking about pure helium (and you’re wrong here, also)–we were talking about a planetary atmosphere. The radiation we are talking about here is blackbody radiation–nothing to do with molecular levels, except as those levels absorb wavelengths out of the blackbody spectrum. As a matter of fact, matter is not necessary at all–space itself radiates as a black body at 3.2 Kelvin. And most black body radiation experiments actually look at emissions from an evacuated cavity. You can read about it here:

    but basically blackbody radiation is a result of scattering between the atoms and the incident radiation.

  44. 244
    Fredrik says:

    Ray, take away all green house gases in the earth atmosphere.

    Would some radiation from the earth be absorbed by the atmosphere? If yes, how many procents? Would the atmosphere radiate something out in the space? If yes, how much?

    I belive that the answers to the above questions it for all practical considerations no. Isn’t that the difference between C_2 and H_2 0 for example? One is transparent for the radiotion from the earth and one isn’t.

  45. 245
    Ray Ladbury says:

    All matter absorbs radiation. Whether there is a significant effect depends on what spectral range the matter has its absorption bands in and whether the radiation source radiates in that range. Earth, being roughly 300 K radiates in the IR predominantly, so the relevant greenhouse gases are H2O, CO2, CH4 etc. On the other hand, if Earth radiated significantly in the UV, Ozone would be a “greenhouse” gas (not to mention that it would be bloody hot!). So, basically, if you take away all the gasses that absorb where Earth radiates, yes, there’d be no absorption of radiation from Earth into space, and aside from effects of albedo (which would be considerable on a frozen Earth), the planet would radiate like a black body.

  46. 246
    Alexander Harvey says:


    Regarding the emission of radiation from a gas: I think that the quantum transitions are critical in determining how a gas absorbs and radiates energy.

    A gas is not a blackbody. Its absorption and emission are in origin discrete. Check HITRANS. I think that this is very important.

    One of the initial puzzles is how a line spectra can result in any significant absorption or radiation. This is allowed for by the broadening of the lines due to natural broadening (Uncertainty Principle), doppler effects and collisions. This results in a continous spectrum in the vicinity of the lines in the unbroadened spectrum.

    Without the line spectra there can be no broadening to produce the characteristic spectra of gases like CO2. My understanding is that in the 300K range the spectral lines are due to a combination of vibrational and rotational quantum state transitions. Which I further believe are absent in Helium gas at atmospheric like conditions.

    How do you think that the absorption/emission spectra are produced?

    You say that I am wrong concerning Helium. If you know how I am wrong, please say so. E.G. characterize the type of radiation and the mechanism.

    I am not the sort of person to be happy with a “it does”.

  47. 247
    tamino says:

    Re: #242 (Alexander Harvey)

    My net searches indicate that collision processes can lead to both emission and absorbption or radiation by helium gas.

  48. 248
    Hank Roberts says:

    Alexander, you’re aware that helium does emit a characteristic set of spectral lines, right? You’re basically asking why it happens?

    So were these people:

    This might help, if your librarian can borrow a copy for you:

    “A closer look at the spectrum of heliumâ��[The Physics Teacher 36 …
    When observing the spectrum of helium in an introductory physics laboratory, a complete and satisfactory laboratory experience that provides insight into …”

  49. 249
    Ray Ladbury says:

    Alexander, you are complicating things far more than they need to be. We’re not talking about atomic transistions at all when we talk blackbody radiation. Rather, we are talking about scattering of light by material. The thermal spectrum of energies of the material gives rise to a characteristic spectral shape determined by the temperature. Yes, the process is quantized, but it has nothing to do with atomic transitions. Read the primer on blackbody radiation. To a first approximation, when it comes to thermal radiation (e.g. blackbody radiation) the material is not important–you still get a spectrum characterized by Plank’s distribution.
    CO2 absorption on the other hand has to do with atomic transitions–specifically vibrational excitations of the CO2 molecule cause by IR radiation.

  50. 250
    Rod B. says:

    Not being encumbered with a plethora of detail knowledge, I’ll try my hand at the sandbox-1 level (with a couple of minor excursions). So-called “blackbody” radiation, covered by the Stephan-Boltzman (you’ll find differing spellings) law is a different physical process (predominately) from the spectra absorption/radiation of say greenhouse gasses. It basically stems from the orbital and vibrational acceleration of electrons and some molecules/ions. Accelerating charges radiate EM waves proportional to their acceleration, which is proportional to their kinetic energy — proportional to their temperature. All matter does this, unless it’s at absolute zero, which none is. (btw, true space doesn’t, but the universe debris floating in near vacuum does, which is the “background” radiation in the microwave bandwidths.)

    Also, the body doesn’t have to be a true “blackbody” to radiate. Anything above a perfect reflector will radiate something. (It’s called “blackbody radiation” because it’s shorter and simpler.) Radiation emission and absorption capabilities are identical, and both are opposite of reflective capabilities for any specific body. Which leads to the complicating exception to the above: perfect reflecting bodies (matter) won’t radiate anything at any temperature.

    The spectra absorption/radiation process is different. Too complicated to explain simply but it has mainly to do with the atomic bonds within molecules and/or differing energy levels of the molecule or its electrons. I’m pretty sure all chemicals/elements are capable here, though some more and some less. Helium certainly does — it’s how we get He spectral lines from the spectroscope.

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