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The CO2 problem in 6 easy steps

Filed under: — gavin @ 6 August 2007


Step 1: There is a natural greenhouse effect.

The fact that there is a natural greenhouse effect (that the atmosphere restricts the passage of long wave (LW) radiation from the Earth’s surface to space) is easily deducible from i) the mean temperature of the surface (around 15ºC) and ii) knowing that the planet is roughly in radiative equilibrium. This means that there is an upward surface flux of LW around \sigma T^4 (~390 W/m2), while the outward flux at the top of the atmosphere (TOA) is roughly equivalent to the net solar radiation coming in (1-a)S/4 (~240 W/m2). Thus there is a large amount of LW absorbed by the atmosphere (around 150 W/m2) – a number that would be zero in the absence of any greenhouse substances.

Step 2: Trace gases contribute to the natural greenhouse effect.

The fact that different absorbers contribute to the net LW absorption is clear from IR spectra taken from space which show characteristic gaps associated with water vapour, CO2, CH4, O3 etc (Harries et al, 2001; HITRAN). The only question is how much energy is blocked by each. This cannot be calculated by hand (the number of absorption lines and the effects of pressure broadening etc. preclude that), but it can be calculated using line-by-line radiative transfer codes. The earliest calculations (reviewed by Ramanathan and Coakley, 1979) give very similar results to more modern calculations (Clough and Iacono, 1995), and demonstrate that removing the effect of CO2 reduces the net LW absorbed by ~14%, or around 30 W/m2. For some parts of the spectrum, IR can be either absorbed by CO2 or by water vapour, and so simply removing the CO2 gives only a minimum effect. Thus CO2 on its own would cause an even larger absorption. In either case however, the trace gases are a significant part of what gets absorbed.

Step 3: The trace greenhouse gases have increased markedly due to human emissions

CO2 is up more than 30%, CH4 has more than doubled, N2O is up 15%, tropospheric O3 has also increased. New compounds such as halocarbons (CFCs, HFCs) did not exist in the pre-industrial atmosphere. All of these increases contribute to an enhanced greenhouse effect.

Step 4: Radiative forcing is a useful diagnostic and can easily be calculated






The climate sensitivity classically defined is the response of global mean temperature to a forcing once all the ‘fast feedbacks’ have occurred (atmospheric temperatures, clouds, water vapour, winds, snow, sea ice etc.), but before any of the ‘slow’ feedbacks have kicked in (ice sheets, vegetation, carbon cycle etc.). Given that it doesn’t matter much which forcing is changing, sensitivity can be assessed from any particular period in the past where the changes in forcing are known and the corresponding equilibrium temperature change can be estimated. As we have discussed previously, the last glacial period is a good example of a large forcing (~7 W/m2 from ice sheets, greenhouse gases, dust and vegetation) giving a large temperature response (~5 ºC) and implying a sensitivity of about 3ºC (with substantial error bars). More formally, you can combine this estimate with others taken from the 20th century, the response to volcanoes, the last millennium, remote sensing etc. to get pretty good constraints on what the number should be. This was done by Annan and Hargreaves (2006), and they come up with, you guessed it, 3ºC.

Converting the estimate for doubled CO2 to a more useful factor gives ~0.75 ºC/(W/m2).

Step 6: Radiative forcing x climate sensitivity is a significant number

Current forcings (1.6 W/m2) x 0.75 ºC/(W/m2) imply 1.2 ºC that would occur at equilibrium. Because the oceans take time to warm up, we are not yet there (so far we have experienced 0.7ºC), and so the remaining 0.5 ºC is ‘in the pipeline’. We can estimate this independently using the changes in ocean heat content over the last decade or so (roughly equal to the current radiative imbalance) of ~0.7 W/m2, implying that this ‘unrealised’ forcing will lead to another 0.7×0.75 ºC – i.e. 0.5 ºC.

Additional forcings in business-as-usual scenarios range roughly from 3 to 7 W/m2 and therefore additional warming (at equilibrium) would be 2 to 5 ºC. That is significant.


255 Responses to “The CO2 problem in 6 easy steps”

  1. 201
    Ron Taylor says:

    Re 199- Steele begins with the words “The CO2 theory has a major inherent fallacy.”

    Categorical assertions like this are not only misleading, but seem silly, unless they come from a top climate scientist. Would you care to provide a link to something that establishes your qualifications to make such a statement? Otherwise, maybe you could tone it down a bit, practicing a little of the humility that marks real science.

  2. 202
    J. Steele says:

    Rather than ‘never [being] addressed or explored’ we addressed the reason why you don’t see a runaway effect here:

    Also my apologies for misudnerstanding. My reference to “never addressed or explored” was specifically aimed at your article on CO2 lag effects. In that article you only adressed the portion of the glacial-interglacial cycle that exhibits rising temperatures.

    I now have re-read your article on runaways and tipping points,that I had read over a year ago and forgotten about. To account for the fact that here is no runaway you said, “A simple example leads to a geometric series for instance; i.e. if an initial change to a parameter is D, and the feedback results in an additional rD then the final change will be the sum of D+rD+r2D…etc. ). This series converges if |r|

    [Response: this is cut off because you used a less than symbol, use & l t ; instead... - gavin]

  3. 203
    Patrick 027 says:

    Re 195 – Thanks, I’ll look at that.

  4. 204
    Jim Steele says:

    [Response: Sorry, but your example was a flawed thought experiment. Try coding this up with the following equations: c dT/dt = F_ext + 5.3*log(CO2/CO2_orig), dCO2/dt = a*(T-To) with suitable values for a,c, To etc. Then play around with the external forcing F_ext - sinusoidal maybe, and see what happens. If you get it right you’ll see T following F_ext with some lag (depending on a and c) and CO2 following along in both the ups and the downs. c is the heat capacity of the system, pick ‘a’ so that you get the observed glacial-interglacial difference for the peak to trough difference in F_ext. With large ‘a’ you’ll see a runaway affect, but for realistic values you won’t. - gavin]


    You have ignored my main point. yes, my choice of phrase “runaway warming” was ill-advised and you have properly corrected my statement. I should have more accurately said that CO2’s heat trapping ability will unceasingly push temperatures to some asymptote. And given the lag in changes of CO2, it is logical to expect that once the other external forcing stops, CO2 will push the temperature back towards that asymptote.

    dCO2/dt = a*(T-To)

    This equation assumes an instantaneous change in temperature due to CO2 changes or instantaneous changes in CO2 due to temperature. We know this is not the case as observed by the lag effects. If a given level of CO2 is causing an increased energy input, while external forcings cause a drop in energy input there is a theoretical rate of change at which the two opposing tendencies will offset. The change is not instantaneous. In addition if the external forcing only drops energy input by ½ or 1/5 as you have suggested, then the counteracting forcing of CO2 will prevent temperatures from returning to the glacial minima. Your equations showing instantaneous changes is not flawed just misapplied.


    This equation simply states that changes in temperatures are due to a change in all the external forcings plus a function of CO2 concentration as well as being proportional to the estimated heat capacity (will heat capacity be a constant?). No problem. I am just arguing that climate is more sensitive to the external forcings, and must be because observed temperatures drop to glacial minima despite the opposing warming by any given level of CO2.

    [Response: Hmm... thinking about it the CO2 equation isn't right. It should be something like b dCO2/dt = a (T - To) - (CO2 - CO2_orig). That makes (To, CO2_orig) a stable point and all stable CO2 levels must satisfy d(Co2)~a d(T) as is seen in the ice cores (a ~ 20 ppm/ºC ). The factor b provides the delay. Try that. - gavin]

  5. 205

    CO2 Problem Step 7:
    “All the coal that can be mined safely and inexpensively is gone”

    (From a news item I heard on NPR this morning. I think that’s a pretty good quote, but I might have a word or two wrong. If someone has the transcripts from this morning’s piece on the Utah mine collapse, you could get a better quote.)

  6. 206
    J. Steele says:

    I am a bit confused by your equations.
    Your new equation

    b dCO2/dt = a (T – To) – (CO2 – CO2_orig).

    Again with no external forcing to change temperatures the expression a(T-To) would equal zero. So this equation seems to be saying that b must be negative 1 to maintain the equality but that means a positive increase in CO2 will create a negative change in CO2?

    [Response: You could put in a forcing term if you wanted, but it's a distraction from the ice age story. But yes, if T=To, the CO2 system has a single stable point at CO2_orig. Perturbations in CO2 will be damped without the temperature feedback. That seems appropriate. But why should b=-1? This equation defines the growth rate d(CO2)/dt (i.e. the time differential). If CO2>CO2_orig, than the growth rate will be negative - i.e. it will bring it down to CO2_orig on a time scale define by 'b'. - gavin]

  7. 207
    John Mashey says:

    re: #205 F.C.H.

    [~40 years ago, I did summer jobs at the US Bureau of Mines Pittsburgh Center; my first-ever paper was "A computer program for the stereographic analysis of coal fractures and cleats." I never expected any of that experience to become even slightly relevant again...]

    cActually, it is far safer and inexpensive to do surface mining, like in the big deposits in Wyoming, Montana, etc, than in underground mines, and there is a strong trend towards more of the former and less of the latter.

    Jeff Goodell’s “Big Coal” is useful. So are:,
    which compares surface and underground

    The latter has a map of 28 fatalities in coal mining in 2004: most are in the Appalachians. has many useful tables; one can compare the growth of Western & surface mining to slow decline of Eastern & deep mines, from 1990 to 2006:
    In one can find that 2006 estimates give “Production Per Miner Per Hour” of:
    3.99 underground
    10.39 surface mines

    So, maybe what they meant on NPR was that all the coal in the Utah mine that an be mined safely and inexpensively is gone, because clearly, the trends are otherwise: it is becoming safer and more efficient to *mine* coal.

    Whether it is safe to *burn* it without CO2 sequestration is another story.

  8. 208
    Dermod O'Reilly says:

    Re 201 Rod you say “Categorical assertions like this are not only misleading, but seem silly, unless they come from a top climate scientist.”

    I think you have a problem here. How do you choose a “top” scientist of any sort? (whatever that may mean.) The IPCC chooses thousands it would seem, for me most of them are very nice guys, if you look at their websites they are good with children, know how to use a keyboard and they are very condescending about people who are not scientists (what is a scientist?)

    Perhaps you know a top scientist when you see one. Do you think Einstein was a top scientist? If so do you share his views on his pupil Werner Heisenberg’s ideas about uncertainty?

    I have a big problem with anybody who is not up to speed with thermodynamics but all I require is that they get curious about it, I don’t know everything but I sure as hell try to find out.

  9. 209
    Peter Brunson says:

    Every time I discuss AGW the question comes up about temperature leading CO2 increase. Can anyone point me towards information that shows CO2 driving the temperature?

  10. 210
    Dermod O'Reilly says:

    Gavin, in 196 you responded “[The lapse rate arises because any larger gradient is unstable to small perturbations. Those perturbations in the atmosphere are associated with convection, since the profile is to a large extent heated from below. - Gavin]” If you mean the lapse rate does not derive from gravity then you are stuck with the problem of where the pressure gradient comes from. It is basic physics that energy tends to be equally distributed in an unperturbed system e.g. equal pressure and temperature in a pressure vessel.

    The situation on the planets is different from a pressure vessel because of gravity (holding the atmosphere on the planet), the mass of the atmosphere is no longer distributed uniformly but the energy (Joules/kg.) remains uniformly distributed, 1kg. of air (CO2 or anything else) at the tropopause contains just the same energy as 1 kg. at the surface, the difference being that the 1kg. at the t(r)op. has potential energy because it has been raised from the surface (remember zero volume a 0K) to the troposphere, while the 1kg. at the surface has equal potential energy because it is compressed by all the stuff on top of it. This is not immediately obvious because the temperature gradient (lapse rate) might appear to contradict the 2nd law of thermodynamics (why doesn’t the heat at surface flow to the cooler place “up there”). This would be a too simple interpretation; it is the energy that is uniform, not the temperature, the lapse rate is built in with the bricks because of gravity.

    Energy arriving from the sun keeps everything nice and warm, the heat is taken to the top of the atmosphere by adiabatic convection (remember adiabatic, the energy remains constant, pressure, volume and temperature change) takes energy at a high temperature and delivers the same energy to the tropopause at a lower temperature where it is radiates to deep space, courtesy of polar gasses. Here is the sting in the tail, it matters little what the radiating gas is, in the case of Venus it is >90% CO2, if this CO2 were replaced by air the temperature at the surface would be much higher because of the different gamma of the O2/N2 mixture.

    [Response: Of course gravity is important. Who ever said it wasn't? That sets the relationship between the integrated density and pressure. Given that, you can then determine whether a particular temperature profile is stable or not. Gradients shallower than the adiabat are unstable, therefore the adiabat sets the minimum gradient. The greenhouse effect works regardless of the lapse rate as long as there is one. - gavin]

  11. 211
    Dermod O'Reilly says:

    Re 210 (your response) You accept that gravity is important, well do you think it is important enough to explain the 30K difference between the surface temperature and the tropopause? If you don’t accept this then: why is gravity important to you? Your response “Gradients shallower than the adiabat are unstable, therefore the adiabat sets the minimum gradient.” has got nothing to do with this 30K difference; it is in connection with local conditions that determine the weather, morning calm to hurricanes. Of course the local weather changes the lapse rate, but locally; amazingly I happen to know that also. The current argument is, if I am not mistaken, not about the weather but about effects that are averaged over the whole planet. I do not appreciate having the discussion deflected in this way.

    [Response: The difference between the surface and the tropopause is more like 100 K in the tropics. And frankly, I have no idea what point you are trying to make and so any deflection is purely accidental. - gavin]

  12. 212
    David B. Benson says:

    Re #209: Peter Brunson — This has been the subject of comments and replys on many previous threads. Also, on the sidebar you will find a link to the AIP Dicovery of Global Warming site. The page there on carbon dioxide as a greenhouse gas ought to serve you well.

  13. 213
    Hank Roberts says:

    Dermod, what sources are you drawing on for the point you’re trying to make? Perhaps if you give a pointer to your sources it will help understand what you’re trying to get at. I’ve tried your terms and phrases with Google Scholar and not found anything that seems likely, but you seem to be trying to develop a basis for some point.

  14. 214
    Patrick 027 says:

    Re 210 – but it does matter what the compostition is, not just because of the convectively maintained tropospheric lapse rates depending on specific heat and molecular mass as well as latent heating; both SW and LW radiative properties matter. The height of the tropopause is climate-dependent and will be affected by these things. Some net LW radiative energy transfer does take place within and from and to the troposphere on Earth because it does not approach infinite optical depth.

  15. 215
    Patrick 027 says:

    Re 210 – and gravity, yes, the convectively maintained lapse rates depends on gravity, and in general gravity determines the relationship between density and vertical pressure gradient which is just an important feature of the atmosphere. But more stably stratified layers can and do exist as has been mentioned.

  16. 216


    Aren’t you ignoring thermal energy? A kilogram of air at the tropopause is a lot colder than one at the surface, and therefore carries less thermal energy.

  17. 217
    Dermod O'Reilly says:

    Re 216 You are nearly there Barton but the road is a bit rocky. The short answer is that the energy is the same but the volume is bigger, the energy of 1kg. is spread about a lot more (energy/kg. is the same).
    The process is called adiabatic because the heat content of the kg. gas at the bottom surface is the same as the kg. at the top surface; if you are familiar with transformers it is a very similar process, energy is taken at one pressure (voltage; temperature) and delivered at another. When gas is compressed adiabatically work is done on it, it gets hotter; when it expands adiabatically it does work. This is not quite so obscure as it looks because the work compressing the ground level gas corresponds exactly to the work (against gravity) needed to lift the top level kg. to its top level; it may not be obvious but the different kg.s will have different temp. for the same energy.
    This last point is a major pitfall when getting into thermodynamics, tutors always baffle undergrads. at this point by introducing the term “enthalpy” which is a measure of the total energy, it does not alter the explanation, the point remains the same, a mass of gas can have the same energy at two different temperatures.

    I have just noticed an error in my post 210 (patrick remarks on it in 214) it DOES matter what kind the gas is because of the different heat capacities between e.g. CO2 and N2. In thermodynamic terms gas masses are comparable if they have the same number of molecules, in this case they will have masses in proportion to their molecular weights, thermodynamics refers to “mole(s)”, a mole being (to some) the weight (in kg.) of “Na molecules of gas” where Na is Avagadro’s number (approx. 6x 10to23 (big!)) Some use the “gm. mole” instead of the “kg. mole”. The purpose of this is to enable comparisons to be made between different gases.
    YOU ARE NOT finished yet, not all molecules are the same, some are monatomic with 3 degrees of freedom, others diatomic with more degrees of freedom; this gets huge!

    I have gone so far with explanations not because I am a teacher, I am not (I got out of university as fast as I could) but because few contributors seem to consider this whole global warming/CO2 thing as a problem of thermodynamics; it is PURE thermodynamics, like rocket science and lots more. Anybody who thinks that it is just a matter of radiative transfer does not understand the technical content and will have a hard job recognizing the real answer when they see it. I am strongly of the impression that the whole group of IPCC experts does not contain anyone who is informed about thermodynamics because they are not using the right words. It isn’t because I am good at thermodynamics, I’m not, it is just that, when I see the words I know where I have to start looking.

    Just to finish, I am not saying that CO2 doesn’t heat the atmosphere , it does, it also cools it, the net effect is zero.

    Patrick re #215, I hope you refer to “stably stratified layers can and do exist as has been mentioned” you mean troposphere, stratosphere etc. otherwise I do not understand you. The troposphere , apart from local inversion etc. (e.g. weather processes), does not have layers on a global basis, the apparent layers of clouds all derive from lapse rate but not the global lapse rate due to the mass of the atmosphere.

  18. 218
    Patrick 027 says:

    Re 217 – actually the entirety of the energy content is a bit tricky – work is done to lift a kg of air up, but the air does work on it’s environment by expanding at nonzero pressure as the pressure drops – this is where the cooling comes from. The work done to lift the air is related to work done by the surrounding air which sinks around the rising air, and if that air at a given pressure level is more dense than the rising air as it passes through that same level, then more work is done by the sinking air than is done on the rising air; thus there is a net decrease in gravitational potential energy as it is converted into kinetic energy in convection (or in the reverse case, kinetic energy is converted into gravitational potential energy).

    Also, there are a few different ways one may refer to layers in the atmosphere. Well-defined layers (defined by characteristics that would be lost by mixing and would take awhile to be restored) may tend to exist or be more likely to persist when and where the air is more stable, where there is reduced vertical mixing.

    There are other layers that may be defined by different characteristics – the troposphere is defined by weaker stratification. Within the troposphere, there is an atmospheric boundary layer defined by the mechanical and sometimes thermal effects of contact with the surface. There may be other layers which have dry adiabatic lapse rates within them and therefore can be expected to be well-mixed layers. There can be a layer of persistent low clouds over some parts of the ocean. There are the ionosphere and magnetosphere, defined by electric and magnetic characteristics; there are the homosphere and the heterosphere, defined by the relative importance of eddy diffusion (which, dominating in the homosphere, tends to evenly distribute the gasses which are not rapidly added to or removed from the atmosphere, or otherwise rapidly undergoing chemical or physical reactions (such as ozone and water vapor)) over molecular diffusion (which, in the heterosphere, above the turbopause, where molecular collision frequencies are quite low, allows gasses of greater molecular mass to settle out – mathematically, it is as if each component forms it’s own seperate atmosphere, with it’s own rate of roughly exponential decrease of partial pressure with height (variations due to changes in temperature or some net upward or downward diffusion rates feeding chemical reactions, etc.); thus there is a region where atomic oxygen is the most abundant component).

    But more generally, one may speak of layers of atmosphere in the sense that each step (such as those one would use in numerical modelling) in a vertical coordinate, like geometric height, gravitational potential energy, pressure, or potential temperature, can define a layer of atmosphere. I may have refered to these arbitrary layers when discussing radiation exchange among layers of air or between them and the surface or space.

    PS in the discussion of net radiation fluxes – either SW or LW – each can be subdivided by contributions from different wavelengths, and there can be interesting variations, for example, in LW fluxes, the total net flux upward is always positive, at least for the global average, although this is probably the usual case even locally (one exception could be within a low level inversion capped by clouds). But the net LW flux at wavelengths where the atmosphere is very opaque (perhaps at a narrow peak in CO2 opacity around 15 microns), if it is opaque enough, might actually be downward in the middle of the stratosphere – because looking up one would mainly see the warm upper stratosphere and lower mesosphere, while looking down one would mainly see the cold lower stratosphere and top of the troposphere. But at other wavelengths, the net LW flux is upward throughout the stratopshere, because one can see farther, to the cold upper mesopshere and space, and to the warmer mid-troposphere (unless clouds get in the way), or maybe even the lower troposphere, and even some of the surface (unless high-humidity air masses get in the way).

    The net effect of additional CO2 is to raise the temperature of the surface and troposphere and cool the stratosphere.

    Which words are the IPCC experts not using that you think they ought to? (I really think at least some of them do understand thermodynamics – at least as well as they need to for climatological applications.)

  19. 219
    Hank Roberts says:


    That’s exactly what happens, and while the CO2 level is stable, so is the net effect.
    Add CO2, and with the various lag times involved, the planet warms over a period of some centuries.
    The net effect is again zero when the planet returns to radiative equilibrium.

  20. 220
    ray ladbury says:

    I’m afraid we are having trouble understanding what point you are trying to make. Could you please state your thesis simply and succinctly?

  21. 221
    Dermod O'Reilly says:

    Re #220. Surface temperature (288K) is determined by (global average) lapse rate and effective radiation temperature of the Earth. These two temperatures are a function of the adiabatic compression of the atmosphere by gravity; the size of the compression is determined by the atmospheric mass and the planet’s gravity (this is why Venus has 460C surface temp.). Incoming absorbed radiation becomes outgoing long wave radiation that is, in turn, sourced by the surface, H2O gas and CO2; reflected radiation is per albedo. Radiative transfer to the atmosphere is very small compared to evaporation and convection.

    Models used by IPCC etc. that rely on “blocking” or “trapping” of infrared are known to occur e.g. the radiation zone in the sun. This “blocking” or “trapping” is in fact diffusion processes similar to conduction (of heat). Diffusion processes are very slow and are not applicable to the physical reality of the Earth and Venus; they cannot co-exist with the dominant (much faster) convection process (the Sun has a convection zone also).

    I hope I have not lost anything in this (adiabatic) summary!

  22. 222
    Dermod O'Reilly says:

    Re #220 & #221 I did miss something. The adiabatic lapse rate accounts for the 33K difference between the mean surface temp. (288K) and the effective radiation temp.(255K).

  23. 223
    Ray Ladbury says:

    I mostly agree with your summary, but the fact that convection, latent heat, etc. decrease in importance the further one gets from Earth’s surface is also important. In the tropopause and stratosphere, radiation is the dominant transport mechanism for outgoing radiation. Details of absorption and the balance between re-radiation and other relaxation processes do become important here in quantifying the magnitude of the greenhouse contribution and especially the changes in that contribution due to increasing ghg concentrations.

  24. 224
    Dermod O'Reilly says:

    Re #223 ” In the tropopause and stratosphere, radiation is the dominant transport mechanism for outgoing radiation.(YES) Details of absorption and the balance between re-radiation (don’t understand) and other relaxation processes do become important here in quantifying the magnitude of the greenhouse contribution.”

    I don’t think that the tropopause is where the greenhouse effect is supposed to take place, the density is far too low; that is why thermal processes such as convection cease. With even more certainty there are no diffusion processes to be found in the tropopause such as the absorption/emission process that characterises the greenhouse hypothesis. May I ask someone to explain just how the greenhouse process causes a temperature gradient? For me the perfectly good gradient due to the adiabatic lapse rate is quite sufficient, it is out there to see on the top of the mountains, why is another one needed?

  25. 225
    Hank Roberts says:

    > just how the greenhouse process causes a temperature gradient?

    Incoming sunlight warms the planet; outgoing radiation at the top of the atmosphere from CO2 cools the planet.
    Add CO2 rapidly, faster than biogeochemical cycling removes it.
    Heat is delayed leaving the planet, while incoming sunlight continues at its usual rate.
    The lower atmosphere warms.
    The warmer atmosphere expands.
    The expanding atmosphere lifts the top of the atmosphere higher.
    When lifted higher, gas expands and becomes cooler.
    The upper atmosphere is where CO2 emits infrared that has a good chance of leaving the planet.
    The upper atmosphere has been cooled by being lifted, so it’s emitting lower energy cooler infrared.
    Since the outgoing infrared is less effective in removing heat, the planet continues to warm.
    Eventually the warming of the atmosphere extends to the top, and energy balances again, after some centuries.

  26. 226


    That would be true only if the entire thermal structure of the atmosphere were due to convection. It isn’t, there are also radiative effects. The thermal energy per kilogram is NOT the same at ground level and at the tropopause.

  27. 227

    [[I am not saying that CO2 doesn’t heat the atmosphere , it does, it also cools it, the net effect is zero.]]

    Completely wrong. You’re arguing against the greenhouse effect here, which is well established physics.

  28. 228


    This is wrong from beginning to end. The static compression of an atmosphere by a planet’s gravity cannot possibly maintain the temperature of the atmosphere; unless work is being done, no heat will be generated. If high pressure were all there were to it, Neptune would be hot. Venus is hot because of the greenhouse effect, not because of some compression effect.

    [[Radiative transfer to the atmosphere is very small compared to evaporation and convection.]]

    On the contrary. The Earth contributes about 350 watts per square meter of longwave radiation to the atmosphere, but only 24 watts per square meter by conduction and convection and 78 watts per square meter from evaporation of seawater. Non-radiative effects are important, but they are in no way very large compared to the radiative effects. See:

  29. 229
    Ray Ladbury says:

    Dermod, the very change in density of which you speak could contribute to a thermal gradient via radiation: At higher altitudes, 1)absorption decreases, but still remains high; 2)the balance between re-radiation and other relaxation processes (e.g. collisional) shifts toward re-radiation. Thus, more energy is lost at higher altitude. Once in the stratosphere, the situation changes significantly due to absorption of UV by O3–this means that the atmosphere is warmer than would be expected in LTE, so CO2 and other ghgs have a net cooling effect.

  30. 230

    So this won’t be just a war of words, let me do a little relevant math here.

    The equation for the heat content of a substance is:

    H = m c T

    where H is the heat content (in Joules; I’ll use the SI), c the specific heat or heat capacity of the substance (in J kg-1 K-1), and T is the temperature (K).

    For dry air the heat capacity is 1,004 Joules per Kelvin per kilogram. A kilogram of air near the surface might have a mean global annual temperature of 288 K, a kilogram near the tropopause might be at 217 K. The heat content of 1 kilogram of air is therefore 289,000 Joules near the surface, and 218,000 Joules near the tropopause (maintaining the proper number of significant digits). The tropopause kilogram therefore has about 25% less thermal energy than the one near the surface.

  31. 231
    Fred Staples says:

    As a retired Physicist I have been trying for many years to find a convincing explanation of the atmospheric greenhouse effect. My difficulties all stem from the statements in your step 1.

    The radiative fluxes you mention appear to come from the Trenberth analysis. If the upward radiation energy from the surface is 390 watts per square meter, an anisotropic balancing downward flux from the atmosphere of 324 watts per square meter from the atmosphere is required.

    The net upward radiation from the surface is necessary, because otherwise there would be a net heating effect at the (warmer) surface, prohibited by the second law of thermodynamics. But if there is no heat transfer from the atmosphere to the surface, how can atmospheric radiation explain the observed surface temperature, and how can an increase in atmospheric radiation from increased CO2 plus additional H2O further increase the surface temperature?

    Incidentally, why does the atmosphere not radiate istropically in the Trenberth model?

    [Response: The numbers are similar to those in Kiehl+Trenberth because they used the same observational constraints. There is no ambiguity there - TOA LW out is measured, surface LW up is also measured (and fits a near blackbody curve). The difference between the two is evidence of net LW absorption in the atmosphere. Your confusion I think stems from thinking of the atmosphere as a single layer at a single temperature. It is not, and given the temperature gradient, the mean emission level (at 255 K) does not have to be at the same height as the mean absorption level. You can in fact simply add an extra layer to the KT analysis to make it all work out as you expect. - gavin]

  32. 232
    Patrick 027 says:

    Re 226,230,219, – nice job.

    Re 228 – but don’t forget that near the surface, the net LW radiation flux is smaller than net convective flux. But as I tried to explain before, this does not mean that LW fluxes are relatively unimportant. (But neither is convection – if convection were artificially held back, then the lapse rate would change until pure radiative equilibrium could be attained – the lower tropospheric lapse rate would be higher and the surface warmer. If there were no LW radiation at all, then the Earth would heat up until it was hot enough to emit SW significantly (as convection does not go into space). if there were no downward LW flux from the atmosphere to the surface, than the net LW flux from the surface would rise drastically, cooling the surface and warming the atmosphere, while reducing the upward convective flux…etc…)

    Re 229 – I thought that LTE was still a good approximation for reality up to … well, very high up – maybe into the lower thermosphere? I don’t think it is necessary to have a departure from LTE (local thermodynamic equilibrium) to explain things – SW energy is absorbed – there are chemical reactions involved, but the end effect of that is solar heating of the upper atmosphere, particularly the upper stratosphere. It heats up until LW radiative flux divergence balances the SW flux convergence.

    Re 221 – models used by the IPCC take both convection and radiation into account – if they did not, the results would be WAY off. (I’m not sure if this is your point, but some people try to argue that since convection greatly reduces the equilibrium temperature of the surface and lowermost troposphere (relative to pure radiative equilibrium), which is true, then the warming by any additional greenhouse effect will be drastically reduced or maybe completely whisked away by convection – well, that last version is certainly false – maybe it is reduced, but the thing is, this (convective adjustment) is included in the models, and thus cannot support a ‘models are wrong’ arguement).

    Re 225 – the thermal expansion of the troposphere is not why the upper atmosphere cools – the thermal expansion of the troposphere lifts the pressure levels upward a bit, so the upper atmosphere (setting aside shifting location of the tropopause) is lifted up by the same amount that the pressure levels are raised – there is no expansion of the upper atmosphere associated with this process, and thus no cooling. (Except maybe that, being further from the center of the Earth, gravitational acceleration is weaker, so that the weight of the upper atmosphere is reduced (shifting pressure levels back down some amount) – but that would be a rather small effect, considering the tropopause is less than 20 km high and the expansion would be around 1% (with some additional expansion due to additional water vapor content) – and perhaps reduced or cancelled or reversed by the contraction of the upper atmosphere that occurs as it does cool.)

    The reason the upper atmosphere cools is that 1. as the LW opacity increases, less of the warmer surface and lower troposphere can be ‘seen’ from the upper atmosphere – it looks colder looking down, and 2. the upper atmosphere can be seen better (in the LW) from space, meaning that it becomes a more effective emitter, radiative more LW to space at a given temperature, so that it cools until LW balance is restored. The cooler upper atmosphere reduces the change in LW radiative forcing at the tropopause, but not greatly – radiative forcing still exists – that is, there is an imbalance that causes the troposphere and surface to warm. As the troposphere warms and stratosphere cools, the tropopause height rises – not just by thermal expansion, but by redesignation of the air in lower edge of stratosphere – in other words, I think the tropopause height rises to a lower pressure surface (surface in the abstract sense of the word). The warmer troposphere does reduce the cooling of the upper atmosphere by some amount (by increased LW heating from below) but it still ends up cooler.

    Re 224 – The greenhouse effect creates the troposphere. With no greenhouse effect, the surface could cool directly to space by radiation. There would be no convection without the greenhouse effect (another reason why LW radiation is important even at the surface) (setting aside large-scale horizontal variations – see previous comments) because there would not be a radiative heating distribution that would tend to destabilize a portion of the atmosphere (at least not while near an equilibrium state). Increasing LW opacity generally tends to increase the depth (in pressure coordinates as well as geometric or geopotential height coordinates) of the troposphere at the expense of the remaining upper atmosphere.

    The greenhouse effect is weaker in areas of higher elevation – all else being equal (at a given pressure level) – the remaining atmosphere above an elevated region has less optical depth, so more LW radiation can escape directly to space; there is also less remaining troposphere in particular, so more LW radiation can escape to the relatively cooler upper troposphere and lower stratosphere – these effects may not be as significant if the optical depth remaining in the whole atmosphere or in particular the mid-troposphere is still high (which can be expected if there are clouds or high humidity, or in some wavelength ranges, although in clear sky, I would expect significant effects within or on the edges of the atmospheric window (a band of relative transparency between 8 and 12 microns, interupted by ozone around 9 or 10 microns, and blocked by clouds or low-level high humidity, partially blocked by lower level humidity, bounded by CO2 absorption/emission at the long wavelength end), or on the edges of other absorption bands, etc. Anyway, as colder parts of the atmosphere can be ‘seen’ in the LW in general, the net LW emission from the surface will be higher at a given temperature as there is less downward LW emission, thus the equilibrium surface temperature will be cooler. Even comparing high elevation to low elevation in very opaque circumstances (fog/clouds), that the air tends to be cooler at higher elevations anyway (because a cloudy layer will have a net LW radiation from the top of the clouds, or would tend to convect upward if it became warmer, as upper level air may be advected from somewhere and still be cold, etc…) means that there is less downward LW radiation at the surface. Overall, less downward LW radiation (and to a degree, a tendency for a greater amount of SW radiation to reach higher elevations) places greater relative influence on the SW radiation flux in maintaining the temperature, which means that there will be a tendency for greater diurnal variation. That’s not all; while the greenhouse effect is lower at higher elevations, I don’t think it automatically follows that the equilibrium temperature will be the same as at the same pressure level over lower elevations – direct solar heating of the surface can increase the temperature over a plateau relative to that at the same level over a lower plain. This can drive wind upslope. In the diurnal cycle, there are mountain-valley breezes (at night, the mountain cools off faster) as well as land-sea breezes, and similarly, the Tibetan plateau plays a role in the seasonal Asian monsoons. In the summer or in midday, dry air (if not cloudy air) blowing up a slope can have a cooling effect on the upper elevations owing to the adiabatic lapse rate.

    PS the optical properties of each unit of atmosphere change with pressure as well as composition (the heterogeniety of water vapor, clouds, aerosols, ozone). An individual atom or molecule has a line spectrum. Quantum uncertainty causes some (relatively small, I think) broadenning of those lines. Collisional (pressure) broadenning occurs, as energy levels are altered. The doppler effect due to molecular motion also broadens the lines. Interaction among molecules can also create more lines, which may happen with water vapor at relatively high concentrations (the atmospheric window closes up with high enough water vapor concentration, even before it becomes cloudy (if the temperature is high enough)). Bands may contain many lines, etc…; going upward, there is generally less line broadenning, so gaps between the lines become clearer, but this is balanced by increased optical cross sections (at a single wavelength, cross section per molecule * molecules per unit volume = optical depth per unit distance) – that is, for line broadenning mechanisms, I think the total cross section integrated over wavelength remains the same (without weighting by radiation as a function of wavelength); however, the same is not true for optical depth when the optical depth is not very close to zero. The average effective optical depth over wavelength should decrease when line broadenning decreases because the increased optical depth at line peaks has a saturation effect (each unit increase in optical depth has progressively less impact on remaining trasmission). Anyway, this (changes in line broadenning) alters the optical depth per unit distance as a function of height, but this modifies the major effects discussed; it doesn’t really create them – it is not the reason the upper atmosphere above the tropopause cools in response to increased greenhouse effect.

  33. 233
    Hank Roberts says:

    Patrick, can you add some references for those many statements?

  34. 234
    DeWitt Payne says:

    Re: #230


    Correct, but you’re still leaving out gravitational potential energy. A kg of air at 10 km will have 98,000 Joules of gravitational potential energy (g*h/kg, where g=9.8m/sec2 is the acceleration from gravity and h is the height in meters. An atmosphere with just nitrogen and oxygen would still have a lapse rate of about 10 K/km. It would be a lot colder, though.

  35. 235
    Patrick 027 says:

    Re 233 – well, I did that mainly by memory and reasoning – are there specific parts you disagree with?

  36. 236
    Hank Roberts says:

    Just too many statements to sort out what’s what, and I’ve become convinced that I need cites to be sure I understand what I read.

  37. 237
    Dermod O'Reilly says:

    Re 215 Patrick, quoting you “Re 210 – and gravity, yes, the convectively maintained lapse rates depends on gravity” Er, Patrick what is a “convectively maintained lapse rate”? Is this a new physical mechanism, finally it is discovered that the cause produces the effect!! I tried this when I was at school but it didn’t work, lucky you!

    Re#230 quoting Barton “The equation for the heat content of a substance is:

    H = m c T


    For dry air the heat capacity is 1,004 Joules per Kelvin per kilogram.”

    Very interesting Barton, but is there a good reason for using the Cp (constant pressure) specific heat?

    I was using an adiabatic model and I said so more than once; if you use another we will never get to a common position and we are wasting everybody’s time. This whole matter is not the easiest to grasp and this kind of approach produces endless playground arguments, ’tis, ’tisn’t, ’tis, ’tisn’t etc. etc.

  38. 238
    Patrick 027 says:

    Re 237 – a convectively maintained lapse rate will tend to occur when convection is allowed, which will be when and where the lapse rate without convection would become great enough to be unstable to that convection.

    Cp is used in the atmosphere for specific heat because it is held at (essentially) constant pressure by it’s own mass under gravity. It is not held at constant volume. Of course air can move up and down and change pressure that way, and then one gets adiabatic temperature changes (or moist adiabatic if at 100 % relative humidity – if water phase changes are occuring). A way to view this is in very small steps, that is, for example, if air is rising, there is a change in pressure per unit time. There is a dry adiabatic temperature decline per unit decrease in pressure. If at 100% relative humidity, there is an amount of latent heat release …

    (a diabatic process for the air by itself – it can also be called moist adiabatic because as long as the condensed water does not get seperated from the same air (or as long as there is not mixing between air parcels of different characteristics), the process is isentropic and reversable)

    … per unit decrease in pressure due to the cooling. There could also be some other diabatic heating from radiation flux convergence. The latent and other diabatic heating causes a change in temperature, which can be found using Cp if at constant pressure. This can be done if the diabatic heating is added not during but after each increment in change in pressure. This can be made to be realistic by shrinking the increments toward size zero – that’s calculus.


    Another thought on upper atmosphere cooling by adiabatic expansion – even if that were to occur, it would be an instantaneous effect that, if radiative or radiative-convective equilibrium were not changed, would eventually disappear from radiative heating. It is the change in radiative-convective equilibrium that causes upper atmospheric cooling.

  39. 239

    [[Very interesting Barton, but is there a good reason for using the Cp (constant pressure) specific heat?]]

    Okay, use the constant volume specific heat and see if it changes your results substantially. You still get that the one at the tropopause has 25% less thermal energy.

  40. 240
    Joanna says:

    To all who respond:
    [edit] There are some of us who are not skeptics, but do not want to blindly copy the words of others either. I for one just want to learn more before I start formulating an opinion. Information seems to be conflicting. One chart shows CO2 lagging temperature, and levels as seen before, and others show CO2 at levels double than ever before. Having a forum like this is great because I can ask people who might actually gather their own data.

    So are we experiencing the highest temperature and CO2 ever? Or has the earth been through this before?

    Offer information so we can all learn.
    If they don’t understand, explain it more clearly.
    Thank you to those who choose not get angry.

  41. 241

    [[So are we experiencing the highest temperature and CO2 ever? Or has the earth been through this before]]

    Neither is at a record level when the records under discussion span the history of the Earth. But it has been 10,000 years since we’ve experienced a climate change this major, and our agriculture and our economy depend on the climate we have now — or had before 1970, say. The increased droughts in continental interiors, increased violent weather along coastlines, and gradually submerging of coastal cities, will play merry hell with our civilization. If we can mitigate the worst effects by acting now we ought to try.

  42. 242
    Hank Roberts says:

    Joanna, try the “Start Here” link, at the top of each page, for answers to frequently asked questions like yours.
    Also try the list in the right hand column of each page, for major topics discussed earlier at RC, and the Science links.
    (I’m just another reader here, not one of the climate scientists).
    (You can usually find the answers to off-topic questions, in the links and lists provided.)

  43. 243
    David B. Benson says:

    Re #240: Joanna — At the top of the page ther is a link to the

    Start Here

    page. After that, there is a link on the side bar to the

    AIP Dicovery of Global Warming

    page. Both a great resources to help you get started. Enjoy!

  44. 244

    Re #240


    The Earth has been through this before, but not mankind. One case was during the PETM see

    But also during the Jurassic and Cretaceous, when the dinosaurs ruled the world, carbon dioxide levels were much higher and the climate was much warmer. The cold blooded reptiles would not have survived if had not been warmer.

    During the warmings which end the glaciations the temperature rise does lead the CO2 rise. However, we are pretty sure that it is variations in the orbit of the earth around the sun (Milankovitch cycles) which causes us to enter and leave those glacial periods. The CO2 acts as a feedback amplifying those astronomical effects.

    Milankovitch cycles explain why we go in and out of glacial periods, but they do not explain why this ice age has started. Milankovitch cycles happened during the Cretaceous but there was no ice then. It seems that the reason is that during the PETM a new type of plant, C$ grasses, evolved to survive the heat. These plants are more efficient at using carbon dioxide and they have reduced the level of global CO2, eventually causing the start of the current ice age.

    So we are fairly confident that past climate change has been caused by changes in CO2 level, along with other factors.

  45. 245
    Patrick 027 says:

    Re 240 – on the matter of “So are we experiencing the highest temperature and CO2 ever? Or has the earth been through this before?”

    I’m not sure of the sustained rate of CO2 rise, but in terms of the amount of CO2 and the potential increase in global temperature we will see, the Earth certainly has been through such conditions before. It has been hotter, and has been colder, perhaps even much colder. It has had much lower sea levels, and also much higher sea levels (not just from an absense of large ice sheets – there is also the matter of geological forces changing the relative heights of continental and oceanic crust). And the continents have been in a number of different arrangements. But that’s not really at issue. Humans wouldn’t necessarily have wanted to be around at certain times in the past (not in large numbers, anyway). Changes which are both sufficiently large and rapid can cause mass extinctions (it takes time for species and ecosystems to adapt and migrate to change). And sufficiently large and rapid changes will be of concern for us, our economies and societies.

  46. 246
    Patrick 027 says:

    Re 240 – another point – even if, on occasion, a large and even somewhat rapid change can take place, there is the matter of would we be expecting such a change in the forseeable future besides those we could cause or control. I think the likelihood of a sizable asteroid impact, prolonged flood volcanism (which I don’t think would even be all that rapid compared to our effects, or even iceage-interglacial transisitions), or supervolcano eruption occuring within the next few thousand years is small enough that we should be concerned about anthropogenic global warming. (The next ice age is likely a few tens of thousands of years into the future.)

  47. 247
    Timothy Chase says:

    Re: Joanna (#240)

    CO2 levels have both lead and followed temperatures in the past. For example, during the Permian-Triassic Extinction (the greatest major extinction – approximately 251 million years ago, you could look it up in Wikipedia – but I wouldn’t worry too much about our reaching levels quite like that), CO2 levels lead, being the result of a Siberian supervolcano resulting from the continental collision. The CO2 levels rose to perhaps over 3000 ppm, and the volcano continued to erupt lava for over a million years.

    CO2 absorbs longwave thermal radiation from the earth’s surface (a process that is well-understood), making the atmosphere opaque to radiation in those parts of the spectra, reemits much of it to the earth’s surface, warming the surface, causing higher levels of water evaporation. More water vapor means more absorption of thermal radiation and more reemission to the surface. This amplifies the effects of carbon dioxide – as does the melting of ice and consequent greater absorption of sunlight by the earth’s surface. However, water vapor won’t stay in the atmosphere for very long without the continued presence of other greenhouse gases. It falls out as rain or snow. But carbon dioxide tends to stay in the atmosphere for a very long time.

    With higher temperatures you have the reduction in the ability of the ocean to absorb gases, including both carbon dioxide and oxygen. Depending upon how high the temperatures rise, the ocean may even become a net emitter – much like soda going flat. If temperatures go high enough, thawing permafrost and shallow water methane cathrates may become an emitters as well, but methane tends to degrade into carbon dioxide within a matter of decades. Higher temperatures will result in plants suffering from heat and drought stress (higher temperatures mean more evaporation from the soil and the expansion of the Hadley cells), and thus they will be less able to absorb carbon dioxide.

    So basically there is a great deal of positive feedback between temperatures and carbon dioxide. It doesn’t really matter what gets the process rolling so much as the fact that the system is in disequilibrium and positive feedback will shift the climate system away from the original equilibrium to a new equilibrium. Ultimately the excess CO2 will end up being mineralized before a final equilibrium is reached, but it will start to decline well before then.
    In any case, setting aside the extinctions, we have the ability to cause a great deal of damage by human standards. While the IPCC has projected that business as usual will result in less than a meter of sea-level rise in this century, they have assumed that it is a linear process, we are seeing more and more that it is anything but. The arctic warms as more dark ocean is exposed by melting sea ice, melting snow is darker and absorbs more sunlight, drainage from glaciers lubricate the bottom of those glaciers so that they slide more quickly towards the ocean, and if either Greenland or the West Antarctic Peninsula melts enough, positive feedback will be come into play where the rising sea-levels will reach more ice and even lift the glaciers so that they descend more rapidly into the ocean. It is possible that under business as usual we will see five meters this century due to such feedback.

    Since half the world’s population lives within sixty miles of the coasts, this is something to worry about. Since we expect the glaciers of the Tibetean Plateau to be gone by the end of this century and they are what feed the six major rivers of Asia, this is something to worry about. Since global warming is already resulting in droughts becoming more frequent (with the amount of the world being in drought at any given time rising from 20% in the 1950s to 30% today and projected to rise to 50% by the end of this century), this is something to worry about. We are talking about large populations of people being displaced, drastic reductions in agricultural output, and drastic reductions in fish harvests (due to the increasing acidity of the ocean – another effect of rising atmospheric levels of carbon dioxide).

    Cities aren’t that portable. There is a great deal of infrastructure that they depend upon – and even if they aren’t permanently flooded by rising sea-levels, they will be more vulnerable to stronger storms and the rising sea levels may render them uninhabitable if the subways or sewers become flooded. Farmland isn’t portable – and we are looking at the United States being unable to grow even wheat in the lower forty-eight by 2080.

    So the economic consequences are projected to be quite severe. We may be looking at an economic crisis which will be deeper than the Great Depression and which will last far longer if we do not adjust our course. Finally, if we encounter a major economic recession before that, it will quickly reduce the amount of aerosols which have been masking much of the effects of the carbon dioxide which is already in the atmosphere. Temperatures could rise much more quickly.

    I hope this helps.

  48. 248
    Fred says:

    Great post which has certainly improved my understanding particularly in relation to saturation, and an explanation of why the stratosphere has cooled. Is it correct to say that the two key factors are the temperature required at the top of the troposphere where the radiated heat is effectively transmitted into space and the height at which this occurs? From this the lapse rate determines the surface temperature (average temperatures of course). Additional CO2 has two effects. One is additional absorption by the “wings” which has to be made up by an increase in temperature at the top of the troposphere. The second effect is an increase in the opacity of the atmosphere at infrared which therefore increases the height at which the effective radiation occurs. So the temperature of the atmosphere required to generate 240W/m2 of radiation needs to occur higher and again this translates directly to a higher surface temperature. In which case, is it also true that the increase in temperature occurs relatively quickly (weeks/months) from the time of the increase in concentrations, and if this is the case can the effect be directly observed in areas where the CO2 (and methane) concentrations are highest (it appears from this that there are quite wide seasonal and regional variations in the concentrations of GHG’s). The reason why the adjustment would occur quickly is that the additional heat being added to the atmosphere by absorption of the wings is not what is actually doing the heating, the whole of the solar flux is available to drive the system to it’s new equilibrium.

  49. 249
    Fred Staples says:

    – Sir Arthur Eddington

    This very interesting debate gets very close to the heart of the AGW “greenhouse” theory.

    Without any radiative effects, Mr O’Reilly’s thermodynamic arguments leaves the atmosphere with an approriate pressure/temperature gradient, and the earth’s outgoing and incoming radiation in balance at the tropopause.

    The crucial issue is contained in an aside from DeWitt Payne:


    Would it? Do the greenhouse gasses warm the earth to any significant extent?

    Almost 100 years ago Mr RWWood attempted to settle the matter. He constructed a radiative (glass) and non-radiative (rock-salt) enclosure, exposed them both to sunlight, and found no detectable radiative effect from the glass. The temperature in both the enclosures reached 65 degrees centigrade.

    He concluded:



    His generation of Physicists ignored Arrhenius. Would it have been a good idea to have taken him seriously, and to have foregone the technological developments in the 20th century to avoid his predicted 6 degree rise in surface temperature?

  50. 250
    Ray Ladbury says:

    Fred Staples, the greenhouse effect is known physics. It’s good for about 33 K warming of the planet. There is nothing that is even the least bit controversial there.

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