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The CO2 problem in 6 easy steps

Filed under: — gavin @ 6 August 2007

We often get requests to provide an easy-to-understand explanation for why increasing CO2 is a significant problem without relying on climate models and we are generally happy to oblige. The explanation has a number of separate steps which tend to sometimes get confused and so we will try to break it down carefully.

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

Lessons from simple toy models and experience with more sophisticated GCMs suggests that any perturbation to the TOA radiation budget from whatever source is a pretty good predictor of eventual surface temperature change. Thus if the sun were to become stronger by about 2%, the TOA radiation balance would change by 0.02*1366*0.7/4 = 4.8 W/m2 (taking albedo and geometry into account) and this would be the radiative forcing (RF). An increase in greenhouse absorbers or a change in the albedo have analogous impacts on the TOA balance. However, calculation of the radiative forcing is again a job for the line-by-line codes that take into account atmospheric profiles of temperature, water vapour and aerosols. The most up-to-date calculations for the trace gases are by Myhre et al (1998) and those are the ones used in IPCC TAR and AR4.

These calculations can be condensed into simplified fits to the data, such as the oft-used formula for CO2: RF = 5.35 ln(CO2/CO2_orig) (see Table 6.2 in IPCC TAR for the others). The logarithmic form comes from the fact that some particular lines are already saturated and that the increase in forcing depends on the ‘wings’ (see this post for more details). Forcings for lower concentration gases (such as CFCs) are linear in concentration. The calculations in Myhre et al use representative profiles for different latitudes, but different assumptions about clouds, their properties and the spatial heterogeneity mean that the global mean forcing is uncertain by about 10%. Thus the RF for a doubling of CO2 is likely 3.7±0.4 W/m2 – the same order of magnitude as an increase of solar forcing by 2%.

There are a couple of small twists on the radiative forcing concept. One is that CO2 has an important role in the stratospheric radiation balance. The stratosphere reacts very quickly to changes in that balance and that changes the TOA forcing by a small but non-negligible amount. The surface response, which is much slower, therefore reacts more proportionately to the ‘adjusted’ forcing and this is generally what is used in lieu of the instantaneous forcing. The other wrinkle is depending slightly on the spatial distribution of forcing agents, different feedbacks and processes might come into play and thus an equivalent forcing from two different sources might not give the same response. The factor that quantifies this effect is called the ‘efficacy’ of the forcing, which for the most part is reasonably close to one, and so doesn’t change the zeroth-order picture (Hansen et al, 2005). This means that climate forcings can be simply added to approximate the net effect.

The total forcing from the trace greenhouse gases mentioned in Step 3, is currently about 2.5 W/m2, and the net forcing (including cooling impacts of aerosols and natural changes) is 1.6±1.0 W/m2 since the pre-industrial. Most of the uncertainty is related to aerosol effects. Current growth in forcings is dominated by increasing CO2, with potentially a small role for decreases in reflective aerosols (sulphates, particularly in the US and EU) and increases in absorbing aerosols (like soot, particularly from India and China and from biomass burning).

Step 5: Climate sensitivity is around 3ºC for a doubling of CO2

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. 151

    How to simplify the presentation of the greenhouse effect? Most of the focus is on forcings, which I think is the wrong way to go. Forcings are a convenient tool for those who do science but not for layman. For a layman, the forcing concept makes intuitive sense if we are talking about changes in solar output, in which case the amount of radiation impinging the Earth would increase. But the greenhouse effect intuitively understood is not about making the sun act like it is brighter. It’s about the atmosphere more effectively trapping the fixed amount of energy the sun bestows upon the Earth.

    In my treatment of the greenhouse effect (see link on my name) I start with the radiation balance:

    S(1-A)/4 = 240 = e*sig*T^4

    where S is the solar constant, A is albedo, e is emissivity, sig is the S-B constant and T is absolute temperature in Kelvins. The solar constant is a well known parameter for which I use the rounded value of 1370 watts per sq meter. Sig is a constant (5.67e-8) and the albedo is 0.3. Average temperature is 15 C (288K) Plug all these in and you get e = 0.615. This is the *apparent* emissivity of the Earth as viewed from space. If the Earth’s atmosphere was *transparent* to IR then the Earth’s emissivity would be that of its *surface*, which is about 0.96. The Earth’s temperature would then be below freezing, which it is not because the Earth’s emissivity is 0.615, not 0.96.

    The reason the emissivity is less than 096 is because the atmosphere is *not* transparent to IR. IR radiation from the surface is blocked by clouds and greenhouse gases which absorb the radiation and re-radiate it. But clouds and the atmosphere are *colder* than the surface (because they are at high altitudes), which means they radiate less energy (even if they are black bodies) than the surface does. For example, a thick cloud at 15000 ft elevation would have an average temperature of about 258K, which means it would radiate (258/288)^4 = 0.64 times as much energy as it would if it were at the surface temperature.

    The “effective” emissivity into space of the surface under this cloud would be lowered from 0.96 (the value for the surface)to 0.64 for the cloud. And the the greenhouse gases throughout the atmosphere absorb radiation and re-radiate it at their lower temperatures. Collectively, the effect of all the greenhouse gases and clouds (at their various heights) is to block most of the surface radiation (emitted with an e of 0.96) and replacing it with their emissions (emitted at a lower emissivity because of their lower temperature) so as to produce an emission that looks like (from space) that it comes from an object with e = 0.615.

    In my simple model I treat low, medium and high cloud as IR-opaque screens blocking and re-radiating surface radiation over the portions of the surface that they cover, on average. I obtain satellite-measured values of emissivity from real clouds to use for my screens and use observed average coverage values.

    The cloudless atmosphere is treated as a translucent “window” (between the opaque screens) having a true emissivity of Ea (which depends on the amount of greenhouse gases in the atmosphere). The effective emissivity of this “window” is the contribution of surface emissions that pass through the atmosphere (its translucent, meaning partially transparent) and the re-radiated emissions from the greenhouse gases at the window temperature Ta (the radiation average temperature of the atmosphere). It all falls out of a simple analysis using only high school algebra.

    So the effect of increased greenhouse gases is to make the atmospheric window a little more opaque. I use Beer’s law to describe the effect of greenhouse absorbers on opacity, which anyone who has had college chemistry might remember describes how colored (opaque) solutes make a solution progressively more colored (opaque) as their concentration rises.

    The model *is* naive, yet works surprisingly well. The key advantage of the approach I have taken is not that its mathematically easier than other approaches (its not), but that the model can be described in terms of simple physical concepts like screens and translucent panes of glass. Instead of a greenhouse analogy (which works by preventing convective heat loss) I use the carport analogy which prevents frost by acting as a radiation shield.

    Comments on my model are welcome

  2. 152
    Gerald Machnee says:

    Re #142 **Meanwhile, there has been an overwhelming glacial retreat observed in the last decade. The retreat of the Greenland ice sheet has accelerated from 21.33 m (70 ft) per day to 33.5 m (110 ft) per day in the period from 2001 to 2005 (Howat et al. 2006).**
    You are looking at the surface changes. Have you looked at the thickness or total mass of the Greenland ice?

  3. 153
    ChrisC says:

    Gerald Machnee (#152)

    I agree that surface ice cover is not the best way to measure ice sheet retreat. The mass balance (mass balance = accumulation – loss) is a better way to measure the total ice sheet loss. The data taken from the Greenland ice cap by the GRACE satellite program, launched in 2001, has acheived accurate measurements at low spatial resolutions.

    GRACE estimates that Greenland has lost 129 \pm 15 Gt/year from 2002 to 2005

  4. 154
    Kea Duckenfield says:

    I was very interested in Gavin’s dialogue with Bob Bergen (#19). Hoping that I didn’t miss a constriction on conceptual arguments, I’ve tried to respond to Gavin’s suggestion for a more widely accessible version of his six easy steps.

    Step 1: When you add energy to a system, it tends to warm up.
    Step 2: A greenhouse works by trapping some of the sun’s energy that comes through the glass.
    Step 3: The Earth’s atmosphere acts as a greenhouse, giving us an average surface temperature of 15oC (59oF).
    Step 4: CO2 and other trace gases contribute substantially to the atmosphere’s greenhouse capability.
    Step 5: The amount of these trace gases in the atmosphere has been increased substantially by human activities. (e.g., CO2 by more than 30% in the last 150yr.)
    Step 6: The increase in these trace gases represents a greenhouse effect of about +1.9ºC (about 62oF), or +13% of the average surface temperature given in step 3.

    Since CO2 and other trace gases are a major factor in why the Earth is now at a viable temperature for us, increasing their concentrations — and hence raising the surface temperature by more than ten percent — can reasonably be considered a significant change with significant potential for impacting the physical and biological systems that depend upon the Earth’s average surface temperature.

    I’d also like to add that I appreciate Steve Horstmeyer’s comments here.

  5. 155
    Richard Simons says:

    The ‘easy’ steps outlined in the post, although suitable for an intelligent, motivated person, would be above the heads of the adult students I have dealt with. They would have been lost by the word ‘flux’ and get no more from equations than I do from Egyptian heiroglyphs.

    My own version is:

    The Earth is warmed by the sun but heat from Earth ‘leaks’ into space.

    Carbon dioxide absorbs some of the heat coming from the surface of the Earth, which increases the air temperature. Over 100 years ago, it was determined that without this effect Earth would be very much cooler. This has been referred to as the greenhouse effect, and CO2 as a greenhouse gas.

    The amount of CO2 in the atmosphere has been monitored for about the last 60 years and has been increasing steadily. As a result, more of the heat leaving Earth has been trapped. Several lines of evidence point to human activity as being the source of this extra CO2.

    There are other things that affect the Earth’s temperature, including water vapour, methane, pollution in the atmosphere, volcanic eruptions, the amount of energy produced by the sun and changes in the Earth’s orbit around the sun.

    Water vapour is also a greenhouse gas but the amount responds very rapidly to changes in the air temperature. An increase in the level of CO2 causes an increase in the amount of water vapour, which increases the temperature, which increases the water vapour . . until the temperature levels off. The effect is that the amount of water vapour depends on the temperature resulting from other factors, rather than the other way round.

    Clouds can either reflect energy coming from the sun or reflect energy leaving Earth (or both), depending on the type of cloud.

    Methane is a very effective greenhouse gas produced by decaying vegetation, cattle and other sources. However, it does not stay in the atmosphere for very long before being broken down (mainly to CO2).

    Other forms of atmospheric pollution and volcanic eruptions tend to lower the average air temperature, so the year after the Krakatoa eruption was known as ‘the year without summer’.

    The sun’s output does vary in strength, but all the evidence is that any recent changes have not been enough to cause the recent changes in global temperatures.

    The Earth’s orbit changes gradually in a predictable way and these changes have been linked to the Ice Ages. Currently, these changes should be leading to a gradual cooling of Earth but over a timescale of tens of thousands of years.

    When it was realized that the amount of CO2 in the atmosphere was increasing, predictions were made (in the 1960s if not earlier) that temperatures would rise and indeed that has happened. Computer simulations that try to include all the factors that affect the Earth’s temperature find that the only way to duplicate what has actually taken place is to include the effects of CO2 and that nothing else can explain the current warmer temperatures.

    I realize this is very ‘dumbed down’ but I hope I have not done excessive violence to the situation.

  6. 156


    Your summary was a very good one, clear, succinct, and to the point. My only quarrel is with

    [[Clouds can either reflect energy coming from the sun or reflect energy leaving Earth (or both), depending on the type of cloud.]]

    Clouds don’t reflect thermal infrared energy at all; they absorb it. Clouds are, in fact, a greenhouse agent. They cool more than they heat because they reflect visual wavelengths (and the near-infrared coming from the sun) so well.

  7. 157
    Richard Simons says:


    Thanks for your comment. I will modify my argument to correct the information on clouds.

    I think the best way to counter denialists (or skeptics if you prefer) amongst the general public is along the lines of:
    CO2 absorbs thermal energy that would otherwise leave Earth.
    CO2 is increasing in the atmosphere.
    This can be expected to increase Earth’s average temperature unless there is a massive, hitherto unknown negative feedback mechanism or violation of the laws of chemistry and physics.
    What is your suggested mechanism?

  8. 158
    Lawrence Coleman says:

    Re: Levenson. Can it therfore be proven that the countries or areas of countries that have a significant cloud cover for most of the year have not had a ‘greenhouse’ rise in temp if if they had not as much as the global mean, and that countries like australia which have very little permanent cloud cover would then tend to record the most dramatic daytime temperature extremes?.

  9. 159
    Lawrence Coleman says:

    Re: Levenson. based on that thought we have nothing to worry about. The warmer the ocean gets the more cloud formation there will over the face of the globe so that will in it self stabilise world temps and we wont get hotter??

  10. 160
    Lawrence Coleman says:

    This shows just how complex the climate sciences and meterology are. If you take all the negative feedback loops and the value of their impact and weight them against all the positive feedback loops and their relative value of affect you will arrive at either a nett positive or negative value. What is happening now is that due to the warming of the earth and biosphere we are creating more positive feedback loops than negaive ones. ie. The warming of the tundra..releasing millions of tonnes of methane..being quickly converted into many more millions of tonnes of CO2 every month..less ice to reflect sunlight back into space where much of belongs, thus heating the polar oceans. The one variable scientists are not sure or can agree upon is the value of importance they can place on each feedback system..they do not understand each in enough detail and how each affects every other feedback system in turn.

  11. 161
    Dermod O'Reilly says:

    Re 156. Barton, can you explain a bit more why clouds don’t reflect? They fulfill all the physics requirements for reflection e.g. they contain (mostly) water, a dielectric, their particle size is good for scattering, rather similar to reflection, light is retroreflected by water droplets. True enough it isn’t a case of “mirror mirror on the wall” but it doesn’t have to be specular to qualify as reflection.

  12. 162
    Rod B says:

    re #9, etc: I was never sure where the 5.35 came from. But you deduce that it comes from the answer that it is supposed to generate! That makes no sense.

  13. 163
    Nick Gotts says:

    Re #86 [Given that Hubbert’s Peak for world oil = 2015 (+/- 5 years, depending on reality level of OPEC numbers), it seems unlikely that the amount of air travel is going to keep going up for very long. If it does, it means somebody will be converting a lot of coal to kerosene, not A Good Thing for The Climate. Note that petroleum (down) may not be a good thing if it means (unsequestered) coal (up).]

    I don’t get the impression that the aviation industry shares your belief about the future growth of air travel; nor that the nearness of Peak Oil is generally accepted. I certainly don’t see this as a reason not to campaign against airport expansion (airport capacity seems to be the main constraint on the expansion of air travel, at least in the UK). The more the aviation industry grows, the harder it will be to resist the pressure to make kerosene from coal in order to keep that expansion going if Peak Oil does happen in the near future.

  14. 164
    Darran P says:

    Given the state of world fossil fuels – I doubt there is another 50 yrs of supply left to burn (at current usage) and our ability to consume the leftovers may be even less.

    I like the bacteria analogy, we grow and consume all available resources as rapidly as possible, overshoot and then die off. So far no previous human civilisation has avoided this fate.

    In more recent times, the dot-com bubble showed me that people will stare disaster in the face and fail to see it coming. Sadly I think this shows a continuation of the trend (head, sand, buried)

    Maybe this is actually good news for planet Earth afterall?

  15. 165

    [[Re: Levenson. based on that thought we have nothing to worry about. The warmer the ocean gets the more cloud formation there will over the face of the globe so that will in it self stabilise world temps and we wont get hotter??]]

    Richard Lindzen actually proposed such a mechanism in the peer-reviewed literature; he referres to it as an “iris” mediated by tropical cloud-cover. Later satellite observation showed the relation he described was too weak to matter (i.e., not statistically significant). The relationship between world temperature and world cloud cover is still unclear, I believe.

  16. 166

    [[Re 156. Barton, can you explain a bit more why clouds don’t reflect? They fulfill all the physics requirements for reflection e.g. they contain (mostly) water, a dielectric, their particle size is good for scattering, rather similar to reflection, light is retroreflected by water droplets. True enough it isn’t a case of “mirror mirror on the wall” but it doesn’t have to be specular to qualify as reflection.]]

    I’m not sure what the reason is that scattering can be neglected for the thermal IR; if I had to guess I’d say it had something to do with the long wavelengths not being susceptible to Mie scattering. But I don’t really know.

  17. 167
    Lynn Vincentnathan says:

    RE #88 and Currently “average” is based on the 30 year period 1971 – 2000 and next it will be based on the 1981 – 2010 thirty year period.

    So the average (when weathermen say, “it’s below average”) is a sliding average….and I assume the averages for 1981-2010 may be on the whole a bit higher than the averages for 1971-2000 due to global warming. It will be a bit misleading to viewers who don’t realize it is a sliding (upward) average.

  18. 168
    Daniel Pedersen says:

    Re: explaining CO2 warming
    When explaining the increase in the greenhouse effect, I like to use the analogy that the natural effect traps heat like a coat, which has a zipper that allows some of the heat to escape (the “atmospheric window”). When the CO2 in the atmosphere increases, it is like closing the zipper, thereby trapping more heat and we get warmer.

    Great topics, great posts, great site. I think I’ve learned more in the past 2 hours reading this site than in the last 6 months >grin

  19. 169
    B Jackson says:

    Konstantin (reply 6) wonders what he can say to people who simply don’t seem to care what happens to anyone or anything outside their own sphere:
    1) You can’t safely assume that your part of the world will manage. No one knows that.
    2) Imagine the consequences of the world blaming you/us for deliberately abandoning them to catastrophe. What happens to you when hundreds of millions hate you and have nothing to lose?
    3)”Was grandpa one of the bad people who didn’t care?”

  20. 170

    #157 Richard,

    Very good summary. I’ve been giving talks in Northern California that have followed essentially the same logical pathway. People have been getting it and really appreciate me leaving the too-technical bits out.

    As for your question to the denialists (“What is your suggested mechanism?”) I think it’s important for everyone’s sanity to insert an important step before engaging with them. The step is to check whether you are speaking with someone who has a genuine commitment to understand the situation. If the commitment is there, go ahead and have the conversation. If it isn’t, don’t bother.

    When a person has made up their mind, they will do one of two things with evidence to the contrary a) they will adjust it so that it fits their world view or b) they will reject it completely as absurd.

    It’s an easy human mechanism to watch and understand…I do it with my wife sometimes when we have arguments. If I can catch myself in the moment, I will realize that I’m just arguing to be right. If I don’t catch myself in time, then I often (but not always, sigh) take responsibility for that and apologize.

    Bottom line: if you’re dealing with someone who has made up their mind (like the people who believe the Earth was created 6000 years ago), arguing is pointless — and you’ll just feed your need to be right. (Which is what causes arguments in the first place. Authentic inquiries are a different matter.)

  21. 171
    Patrick 027 says:

    (formerly just “Pat”) – my apologies if somewhere above this has been asked, but I was thinking, since (outside sea level rise) it is the regional climate effects and some other specific ones (implications of a rising tropopause) where the ecosystems and economies will really ‘feel the heat’, it might be helpful if there were also “6 easy steps” (I realize it might be more like 60+ and they wouldn’t all be easy) for explaining why we should expect whatever such effects would be expected. Some are relatively easy to explain – why the lower troposphere and surface warm most at the poles (ice albedo feedback) in winter (water releasing summer heat before freezing, whereas the unfrozen water in summer absorbs more solar radiation but does not increase much in temperature) while in the tropics the greatest warming would be in the mid to upper troposphere (in one phrase, temperature dependence of moist adiabatic lapse rate), and of course increased water vapor allowing more intense precipitation, but others are trickier – for example, I haven’t figured out what to expect from the effect of the pattern just described on baroclinic instability and extratropical cyclone life cycle and motion – because it suggests increasing temperature gradients in the upper troposphere but decreasing temperature gradients near the surface; I can speculate but I won’t know if I’m right or not. I could speculate that increased moisture causes a greater role in latent heating for extratopical storms, that an increase in the dry static stability would favor development of horizontally larger anticyclones (dry) (because there is a short-wave cuttoff for growth and it depends on vertical stratification among other things) but not larger cyclones (because of the latent heating), and that the latent heating favors narrower more intense upward movement relative to the downward movement; thus I’m guessing horizontally larger anticyclones and more intense cyclones, although the increased depth of the troposphere should favor larger systems overall (although poleward shifts in storm tracks should reduce these effects, and also favor smaller systems due to increased coriolis parameter f, but perhaps allow larger systems to grow as beta (df/dy) also decreases? – also, I would expect a poleward retreat of extratropical storms based on reduced temperature gradient at lower levels (and therefore poleward shift of subtropical dry zones), but what of the effect of the upper level gradient?), and for that matter, Also, while the moist adiabatic lapse rate decreases with increasing temperature, the total difference in temperature from top to bottom still increases as the tropospheric depth increases, so that the efficiency of the ‘heat engine’ aspect of thunderstorms and hurricanes would increase – for the same amount of heat energy carried upward, a greater portion is converted to kinetic energy … and would that lead to larger hail? (and would greater moisture overall allow for greater contrast of moist and dry air, allowing for stronger supercell storms via more intense evaporative cooling where dry air impinges on the cloud, etc.?) Of course, some fraction of that energy propogates away as gravity waves, and if that fraction changes… And then, for a given speed of westerlies, there is a wavelength of planetary wave that can remain stationary and thus be excited by longitudinal variations in topography and temperature (land-ocean contrasts, ocean currents), so is there a significant effect from changing westerlies (and regional temperature contrasts) affecting wavelengths of stationary planetary waves? What exactly does happen to the Hadley cells – I’m imagining greater latent heating tending to make them stronger overall, greater direct change in greenhouse forcing in the subtropics (due to relative lack of clouds and moisture) tending to weaken them (although allowing poleward expansion), and might poleward expansion allow for greater seasonal motion of the ITCZ? And what happens to anticyclone tracks and blocking anticyclones, … and that doesn’t even include ocean currents … well, that sort of thing is what I’ve been wondering lately. I might yet find it in the IPCC AR4 WGI but I’m not sure. (PS nice job on these “6 easy steps”)

  22. 172
    Patrick 027 says:

    … well, another way of looking at some of the above: I’ve ready mid-latitude storms would shift poleward, be fewer in number, but with more intense storms (I had previously misinterpreted something to mean larger horizontally when it may have meant larger central pressure drop) – is the reason for more intensity, despite decreased lower level thermal gradient, compensation by the upper level gradient, greater latent heating, or both, or neither? And is the reason for fewer storms due just to the storm tracks becoming crammed into a smaller area – (at higher latitudes), to the lower level temperature gradient reduction (in the background mean state, I mean), or to both, or something else? – actually, that brings up another point – if there were fewer storms in a smaller area, there could be the same number per unit area within the given area, but what if they lasted longer (yes/no?) – then storm per unit area per unit time could increase … and while the average thermal gradient at lower levels would decrease (in the zonal average, I mean), there could be longitudinal variations in that, but also temporal variations – one could imagine a moving region in which the thermal gradient is the same but the north-south distance across it is smaller, and the motion of this region would just average out to having a reduced average thermal gradient (and then I automatically think of implication for the vertical wind shear and baroclinic dynamics) …

  23. 173
    Patrick 027 says:

    … in addition to the latent heating synchronized with midlatitude eddy circulations, there are other circulation-synchronized diabatic processes that could weaken or strengthen those circulations – advection-induced thermal anomalies should tend to decay via radiative heating/cooling; cloud and moisture anomalies create variations also create radiative heating/cooling anomalies. I think that the generalized increase in the greenhouse effect should decrease the rate of radiative heating/cooling of thermal anomalies, which would slow energy loss from the eddies – in the lower troposphere, anyway – in the stratosphere, I would guess the opposite could be the case (I don’t know much about the associated stratospheric structure of extratropical circulations except that in the average state, meridional thermal gradient and thus vertical wind shear are reversed, except in winter in some places). For the same cloud and moisture distribution, increased CO2,CH4,etc. should weaken the radiative anomalies, but then again, moisture increases and I expect cloud heights generally would rise, so … (That’s it for now, I’m done.)

  24. 174
    Patrick 027 says:

    Re 166 – (on reflection vs absorption of water droplets) I would guess it’s due to the drop in single scatter albedo as one moves away from the visible band. I’m no expert on Mie scattering but based on geometric optics (not taking into accout the droplet’s surface’s tight curvature’s effect) I would imagine that for each individual scattering, a considerable amount is forward scattering, where the angle change is less than 90 degrees; some of that comes from diffusion around the droplet, some from passage through the droplet – some from glancing reflection near the edge of the droplet’s cross section. Some backscatter from a cloud, especially thicker clouds, would come from successive forward scatterings. As some of that radiation passes through the droplets, it is subjected to absorption within the droplet. (Some backscatter could also be from reflection off the ‘back side’ of the droplet, passing through twice before coming out, so that could also be absorbed within the droplet. Reflection becomes stronger as the rays hit the droplet’s surface (from inside or out) from more glancing angles. With the more complex effects that come into play when a droplet’s size approaches the wavelength of radiation, I don’t know – maybe absorption within the droplet affects radiation reflecting off the surface? (Because I think there is some short distance penetration of the electromagnetic field into the material even if the ray reflects off the surface?)

    Re 162: yes, if you forget 5.35, you can deduce it from the change in radiative forcing per doubling CO2; if you forget the later, you can find it using the former – so it sounds like circular reasoning if taken in isolation, but as I understand it, the logarithmic formula is a useful approximation fitted to the results from more coplex computation where the input would be the known optical properties of CO2 and some other things (probably optical properties of other atmospheric components and the temperature variation with height).

  25. 175
    Patrick 027 says:

    … other thoughts on circulation:

    Actually, for contant optical properties, the radiative decay of thermal anomalies would be weaker for vertically thicker anomalies, which would be the effect in the lower troposphere of reduced lower tropospheric wind shear. As absorptivity increases from increasing CO2 or other greenhouse agents, relatively thicker anomlies to begin with would decay less rapidly then, but for thinner anomalies, the opposite could occur, and the boundary between thick and thin as defined by this behavior would get thinner. … My reasoning for guessing a reverse effect in the stratosphere on thermal anomalies was not because of reversed thermal gradients but because the layers would be optically thinner and more ‘exposed’ to space, etc.

    I wonder if, with reduced wind shear in the lower troposphere, downdrafts in supercells might start more from higher up and perhaps have greater kinetic energy per unit evaporative cooling? But I know the ideal graph of wind velocity with height for supercell development is a lower curved portion and an upper straight portion – and I’m infering that in the future the lower portion becomes less curved and the upper portion becomes more curved… or on the other hand it could be that the lower portion simply gets thicker relative to the upper portion…? – based on generalized zonal mean trends, of course – effects would vary with location and time (and occurence of any given weather phenomenon does the same, so using an average background environment could easily not give the right answer…)

  26. 176
    Patrick 027 says:

    In 174 I meant diffraction where I wrote diffusion.

  27. 177
    Al S. says:

    Re 19: Please, Bob, a more simplified version would be very helpful. Otherwise, I may have to use the analogy (admittedly ill-suited) that if we put an extra jacket on, we should expect to be warmer.

    It would be best if it were a separate topic, rather than being buried among 150+ subsequent postings.

  28. 178

    In step 5, you assume that there is one climate sensitivy to radiative forcings indpendent of differences in how those forcings couple to the climate. In particular solar couples to 10s of meters of the ocean while CO2 to a millimeter or so. Hansen’s model based efficacy work, doesn’t reflect this difference in the coupling to the climate, or the different time scales over which these different couplings would impact the climate, so his conclusion that the forcings can be summed is a mere artifact of treating these different forcings unrealistically similarly.

    [Response: Not so. All of the efficacy analyses were done with coupled models that include all of that physics. – gavin]

  29. 179
    Dermod O'Reilly says:

    Re 174, 175 and 175. I have a lot of difficulty with imprecise terms used in all of these discussions, absorption, reflection, etc., are often used indiscriminately, if the electromagnetic/thermal processes are not used accurately then meaningful discussion becomes impossible. It was Pat’s slip of the pen that caused me to question this whole matter. The greenhouse effect, as frequently described, requires the repeated absorption and re-emission of LW IR in the atmosphere, sometimes illustrated as happening in layers; this is a reasonable model of a diffusion process, more commonly seen in heat conduction, it results in a negative temperature gradient in the direction of heat flow. If this is indeed the right model for the greenhouse effect, well and good but it is not the only heat transfer process in the atmosphere, convection and advection are also important, a balanced assessment needs to be made to show the dominance of radiation diffusion. This radiation diffusion process also occurs in the sun but only below the convection zone. If these two processes are occurring in the earth’s atmosphere then there has to be a good explanation as to how they can live together in the same place because one takes place in the absence of mixing (turbulance?) and the other relies on mixing.

  30. 180
    Patrick 027 says:

    Re 179 – in a nutshell, when air rises it cools as it expands due to the decrease in pressure. When there is no net heating of the air and no mixing of air of different heat contents, the change in temperature follows a dry adiabat (the process is adiabatic, which means it is isentropic , reversable – the exact reverse temperature changes occur in sinking); if the air cools to a point where relative humidity reaches 100 %, then latent heating occurs as water vapor condenses or freezes, and the temperature follows a moist adiabat (also isentropic (sinking would yeild melting, evaporation) only so long as the condensed moisture is not removed from the air (no precipitation), or mixing with air of different heat and moisture content occurs). — if the environmental lapse rate (the rate of temperature decrease with height) is greater then a dry adiabatic lapse rate, then the air mass is unstable and overturning occurs; if the environmental lapse rate is greater than the moist adiabatic lapse rate, then the air mass is stable to localized vertical convection (there can still be large scale overturning due to horizontal temperature gradients, such as a variation of an idealized Hadley cell, though without constant heating and cooling to maintain the gradient, this motion must eventually halt (as would localized vertical overturing without heating below and cooling above) (coriolis effect adds some complexity to large scale overturing, …)). If the environmental lapse rate is between dry and moist adiabatic lapse rates, then the air mass is conditionally unstable – if some air is forced to rise until condensation occurs and then a little bit more, it can become bouant and continue to rise, with potential energy being converted to kinetic energy. An example is what happens in the upward portion of a Hadley cell (Actually, the horizontal convergence actually tends to destabilize the whole lower air mass as well as push air upward). The Hadley cells can be viewed as being driven by latent heating near the equator (with precipitation) and radiative cooling in the subtropics. (why they don’t extend to the poles is because the horizontal temperature gradient in the midlatitudes is strong enough that leads to significant baroclinic instability that generates baroclinic eddies (extratropical cyclones and anticyclones) which convert the potential energy of the background temperature gradient into the potential energy of the gradients associated with the eddies, some of which is converted into eddy kinetic energy by rising warm air and sinking cooler air …(where the sinking and rising are not generally oriented poleward and equatorward from each other, hence the lack of Hadley cell in the average motion (at least that’s how I understand it))… some of which is converted into the kinetic energy of the background state – while heat is transported poleward, etc.) ———- Anyway, the reason the troposphere exists is because pure radiative equilibrium would lead to an unstable lapse rate. Thus there is a convective adjustment; the troposphere, I think on average, tends to be maintained near a moist adiabat by moist convection. The temperature still falls with height (in most parts – there can be low level inversions with negative lapse rates, typically in polar regions and cold winter areas and sometimes at night if the air is dry and clear); so the radiation emitted upward by the troposphere is still less than the radiation emitted downward by the troposphere to the surface. Heat transported upward by convection from the surface through the troposphere must ultimately be balanced by radiative cooling; as the radiative cooling is distributed in some way and not concentrated at the surface, the radiation is emitted at a cooler temperature then it would have been if it had been emitted from the surface, bypassing convection…

  31. 181
    Patrick 027 says:

    well, actually – “(Actually, the horizontal convergence actually tends to destabilize the whole lower air mass as well as push air upward). ” horizontal convergence by itself cannot completely destabilize a layer but it does reduce the stability.

    – also, the moist adiabatic lapse rate is a function of temperature because at 100 % relative humidity, water vapor partial pressure (and thus mixing ratio at a given total pressure) increases roughly exponentially with increasing temperature; at high temperatures, at saturation, more water vapor must condense per unit drop in temperature. There is greater latent heating per unit height increase at higher temperatures, so moist adiabatic lapse rates are slower at higher temperatures. In very cold air, such as found near the top of the troposphere, there is not much moisture even at 100% relative humidity, and the moist adiabats become similar to the dry adiabats. Global warming tends to decrease the lapse rate of the lower troposphere in the tropics, which is why surface warming in the tropics is less than in the mid-to-upper troposphere (but I think the temperature difference from surface to tropopause may yet increase – the tropopause generally should rise as the troposphere warms while the stratosphere tends to cool). In polar regions, warming tends to be greatest near the surface – I think part of that is because polar regions tend to have more stable air to begin with.

  32. 182
    Chris Bering says:

    In step 2 you say “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”.

    But isn’t such IR spectra, in reality, atmospheric emission spectra and not absorption spectra ?

    Which gases at which altitudes contributes radiation to the various lines, and in what proportion to each other ?
    What’s the proportion of re-radiation versus radiation from thermalization for each gas at each altitude ?

  33. 183

    In response to post 190, the simple model I have developed makes use of the lapse rate in the atmosphere as it is. Most people know that as you climb in elevation it gets colder. Thus, *anything* “up there” that absorbs IR radiation emitted by the surface is going to radiate less than the surface does because it is colder. One might ask how can atmospheric radiation absorbers absorb more energy than they radiate out into space and not warm up? Rather that describing why this is so, simply ignore it. I compare these absorbers to a radiation shield like a carport or the sheets you put in your tomatoes to prevent frost damage. Higher elevations are simply colder. Stuff in the atmosphere than absorbs IR is going to be colder than the surface, on average and so will radiate less energy than the surface will even it they are blackbodies.

    Unless, the atmosphere is *transparent* to IR, surface emissions will be absorbed and reradiated at lower temperatures. And that explains greenhouse warming.

  34. 184
    Patrick 027 says:

    Re 182. – consider any material with some degree of opacity – how far into it can you see? opacity can be measured in terms of optical depth. Using optical depth as the distance coordinate along which a unidirectional beam of radiation travels, the intensity of that beam (of the original photons in the beam) decays exponentially, by a factor of e per unit optical depth – Intensity = inital Intensity * exp(-optical depth). It turns out that the source of a beam coming out of a material is distributed in the same way – that is, if you look along a path, you see more of what’s in front and less of what’s in back, with the distribution of what you see decaying exponentially going away from you. Now, if we’re talking about thermally emitted radiation, then if the temperature changes through a material, parts will look hotter (brighter) or colder (dimmer). If the cold part is in front, it blocks out some of the hotter part, replacing some brighter radiation with a smaller amount of it’s own dim radiation.

    One way to picture this is with a temperature independent factor – let’s call it W. (PS this is the first time I’ve introduced W to explain this concept.) W is the fraction of visual space from some recieving/veiwing location that can be assigned to a radiation source; the total for W at a given location is always 1; contributions to W are distributed along a path where W per unit optical depth decays exponentially with optical depth away from the viewing point. Translated into another coordinate x such as actual distance (or another coordinate – pressure is an especially handy vertical coordinate in atmospheric science (it simplifies some equations to use pressure instead of geometric height)), if the optical depth per unit x is higher, then the exponential decay of W over x is faster, so that less of W is from far away but at the same time the concentration of W at closer positions is increased. So with the atmosphere, for example, if the optical depth per unit vertical distance x increases, you see more from space of the upper atmosphere and less of the lower atmosphere and surface (PS whatever portion of W which is not in the atmosphere must be at the surface). – unless the optical depth of the atmosphere is small to begin with, in which case, less of the surface is seen from space but the entire atmosphere can be seen better. Conversely, if the atmosphere is very opaque, then what acts as the ‘upper atmosphere’ in the previous statement becomes a much thinner layer.

    Anyway, the intensity (power per unit area per unit solid angle, and that per unit wavelength if it is spectral intensity) seen from along a path is the sum of the products of contributions to W multiplied by a corresponding value, which, if scattering is negligible, is the blackbody radiation intensity Ibb for the temperature at that location (if scattering is not neglible, then it is Ibb*a + Isc*(1-a), where a / (1-a) = emission cross section per unit scattering cross section, Isc is scattered light intensity per unit scattering cross section, although that only works with isotropic scattering – scattering is actually quite complicated – luckilly scattering is a small factor in LW (long wave) radiation, the radiation emitted at Earthly temperatures and involved in the greenhouse effect.)

    Then one has to integrate over angles and then over wavelength to get the total effect, but basically, greenhouse gasses and clouds emit and absorb LW radiation, emission being temperature dependent and increasing with increasing temperature (in a somewhat complex way if taken at particular wavelengths), so in the LW range, at wavelengths where the atmosphere is more opaque, it is do to stronger emissivity and absorptivity, but W will be (even after integration over directions – though it is no longer a simple exponential relationship, but it is qualitatively similar) more concentrated in the upper atmosphere at those wavelengths, so from space, the colder upper troposphere and lower stratosphere are more apparent – they are emitting, but not as much as they are blocking (via absorption) from the warmer layers below. At wavelengths where the atmosphere is less opaque, more of the lower atmosphere and surface (which are warmer) can be seen from space; At a given wavelength, if opacity is lowered, space recieves more LW radiative energy at that wavelength from the Earth and atmosphere. Now, there are some wavelengths where the atmosphere is so opaque that W contributions shift significantly into the warmer upper stratosphere, so that the Earth and atmosphere will appear brighter if opacity is further increased – this does not mean a reverse of the greenhouse effect, however – because the stratosphere is quick to radiatively adjust (emitting more to space, thus cooling off so as to emit less to space)(it is not convectively tied to the thermal inertia of the surface as the troposphere is), and at the tropopause (top of the troposphere), it will still appear colder looking down as opacity increases – if it is still being heated by solar energy at the same rate, it will warm up until it no longer appears colder from above. I’ve glossed over the radiation going in between layers – that is important too – some examples,

    1. a troposphere which emits less upward can also contribute to a cooling stratosphere;

    2. it is the downward emission to the surface that makes an increase in the greenhouse effect tend to reduce the diurnal temperature range;

    3. and, increasing the opacity of the troposphere (when it is already opaque to some amount) tends to slow the net upward radiative energy flux, so the vertical heat transport by convection may concievably increase in response – this effect would be enhanced by the reduction in lapse rate in the tropics in the lower to mid troposphere, reduced in polar regions due to the opposite change in lapse rate (I think), but also, this effect might be altered, partly cancelled or overuled by

    a. the effect of increasing opacity at wavelengths where the troposphere is not so opaque to begin with (that would enhance radiative energy exchange through the troposphere, although it still decreases radiative cooling at the surface) (although where one gas is weak, another may contribute, so if CO2 increases, for example, the increase in optical depth at wavelengths where CO2 is weak may be less, in proportional to optical depth, than it would be where CO2 is stronger, if there is significant contribution by, for example, water vapor)

    b. the increasing temperature (which results in stronger emission overall, and increases net radiation between a warmer and colder body at constant temperature difference, especially at shorter wavelengths in the LW range (at longer wavelengths, not so much)

    c. a change in the distribution of solar radiation absorption (via increased water vapor) (because convection can be thought of as the necessary flow of heat between two mismatched distributions: between the distribution of solar heating through the atmosphere and surface and the distribution of net LW cooling through the atmosphere and surface (including the net cooling from exchange with the surface (a negative contribution, usually) and other parts of the atmosphere, not just to space).

  35. 185
    Dermod O'Reilly says:

    Patrick, in 179 I asked you to consider a diffusion process in comparison with convection. I read 180 & 182 (your reply to 179) carefully and I found them very interest because they increased my understanding of convection mixing, thank you for a nice lesson but you do not comment on absorption and re-emission (diffusion). The problem of the greenhouse proposition is that it relies on absorption/emission occurring, a process that is relatively slow and can only take place in the presence of a temperatute gradient (see 179 or look on line for a mathematical description of heat transfer by a diffusion process). An intuitive response would be to consider it as “heat trapping”, however this trapping is just not going to happen when the alternative heat transport process of convection is available, as you so eloquently describe in 180 & 181. Yes there is a temperature gradient in the atmosphere, the lapse rate but that comes from the pressure gradient, the lapse rate would be there even if there was no CO2 or H2O.

  36. 186

    [[What’s the proportion of re-radiation versus radiation from thermalization for each gas at each altitude ?]]

    There really isn’t such a thing as “re-radiation.” Gases radiate because they have emission lines in their spectra and are hotter than at absolute zero. What caused them to heat up in the first place can be anything; the resulting radiation is indistinguishable.

  37. 187
    Dermod O'Reilly says:

    Re 186, I think Cris Bering (182) should have a more comprehensive answer because he refers to thermalization. The simple model of polar gases (or any other kind actually) treats it as vibrating in isolation, in which case the resonance band is narrow. I suspect Chris knows that thermalization is a term used to decribe how the energy of one vibration mode becomes shared among all the available modes; this sharing is provoked by collisions for example, if the pressure is sufficiently high. Things do not stop there of course, in the case of trace gases most of this acquired energy is transferred to the non-polar gases where it joins the much larger amounts of heat deposited in the atmosphere by evaporation of water or convection from warm landscape to name a few.

    Classical thermodynamics addresses this situation (proportion of re-radiation, thermalization etc. etc. (there are a lot of energy exchange mechanisms!)) by the copout “it depends on the probability of an event taking place”. But do not give up, further explanation will be found under the titles “Statistical Thermodynamics” and “Statistical Mechanics”. The first and most important conclusion you will draw from studying these thermodynamics of any sort is that, in questions of energy (heat) transfer, no process can be considered in isolation; thus, although statements that refer to “radiative heat balance” can be applied to the solar system where there are only radiative effects, it is utterly unscientific to apply it to the workings a planetary system having a wet atmosphere where evaporation etc. playng a dominant role.

    Frequently proponents of the greenhouse effect cite Arhenius as the founder of their science, I have not found in his calculations any reference to CO2 radiating to outer space or of it coupling heat to other molecules. Basically he appears to assume that CO2 only reflects infrared back to the earth’s surface. Similarly Angstrom sent infrared down a tube; I do not think that this simulates a planetary atmosphere to any useful extent!

  38. 188


    > “The logarithmic form comes from the fact that some particular lines
    > are already saturated and that the increase in forcing depends on the
    > ‘wings’ (see this post for more details).

    Are you sure that the spectral line shape is really needed to explain
    the logarithmic behaviour? If so, then my favored “explanation for dummies”
    is an oversimplification. It goes like this:

    Heat transport outward from the Earth goes by two mechanisms: radiative from
    the Earth surface, and convective + radiative from the tropopause. Looking at
    the IR opacity curve of CO2, one sees that the atmosphere (at sea level
    densities) is opaque for about 20% of the surface area of the Planck curve.
    This means that 80% of radiative cooling comes directly from the surface,
    and 20% from higher up, the tropopause, after convective transport.

    But… the tropopause is at a temperature 50 degrees C less than the Earth
    surface (as your friendly captain will tell you when flying at that level),
    meaning it is only half as effective an IR radiator as the ground. Thus,
    more realistic percentages are 90% / 10%.

    Then, we double the CO2 concentration. As a result, the tropopause (level
    where the air becomes mostly transparent to thermal IR in the wavelength band
    considered) moves up by one scale height, or 5 km. The adiabatic lapse
    rate under it in the troposphere is some 5 degs C per km, meaning that
    the radiative surface cools by 25 degrees.

    This cuts the emissivity from 10% of the total to more like 7%, requiring
    for balance the average global tempature to go up by one-quarter of 3%
    (Stefan-Bolzmann) i.e., 0.75%, or 0.0075 * 272 degs C = 2 degs C. Pretty
    close to the correct value. (But of course we haven’t talked H2O yet ;-)

    This description makes the logarithmic behaviour intuitively obvious: every
    _percentage_ increase of CO2 produces the same _absolute_ uplift of the
    tropopause, the same absolute temperature drop in tropopausal temperature,
    and the same absolute increase in global temperature to compensate.

    And didn’t already Arrhenius derive the logarithmic formula, without knowing
    a lot about spectral line shapes? What did I miss?

  39. 189
    Patrick 027 says:

    Re 185 – if the temperature profile of the atmosphere is held steady as LW opacity increases, then, as described above, LW emission to space, and in particular the net upward LW radiation at the tropopause, will decrease. Convective transport can and will change in response to changing radiative transport within the surface-atmosphere system (although even some slight temperature changes would be required for that); however, this cannot change the initial change in net LW radiation at the tropopause or net LW radiation to space (setting aside cloud feedbacks, other feedbacks) – which I think can be set aside if the temperatures are held steady); the temperature distribution has to change to reset the LW radiation. That or a decrease in solar heating must occur; until balance is restored, the troposphere will tend to warm up – convection’s role couples the surface temperature and the different layers of the troposphere together, so they warm together, as the tropopause will tend to rise, so that, it could be said, the temperature distribution ‘catches up’ with the distribution of the ability to radiatively cool to the lower stratosphere and to space.

    A simple way to illustrate this is by considering two extremes – an atmosphere completely transparent in the LW range (zero gfeenhouse effect) and an atmosphere of infinite optical depth in the LW range.

    In the first case, all emission to space comes from the surface, there is no convection (at least in a one dimensional column model where horizontal temperature gradients are irrevelant – although even if they did exist I my initial expectation is that there would still be very little convection).

    In the last case, all emission to space comes from the very top of the atmosphere (for the sake of this thought experiment, let’s say there is a top of the atmosphere at some defined location); there is no upper atmosphere any more in the sense of being above the tropopause – the entire atmosphere is tropospheric, and being infinitely opaque, no net upward LW radiative heat flux can occur within the troposphere, hence all heat from wherever solar radiation is initially absorbed must be brought upward to the tropopause entirely by convection, where only then is it radiated to space; thus the surface will be much warmer, and the temperature at the tropopause in this case is the same as the temperature at the surface would be without any greenhouse effect (setting aside horizontal temperature variation for the moment)

    (the above assuming the solar heating is constant – actually, because some solar heating is within the atmosphere, and in particular because some is in the upper atmosphere due mainly to absorption of the shorter wavelengths by ozone and oxygen, this heating would occur within the troposphere in the second case; in the first case it would lead to an entirely thermospheric atmosphere where the atmospheric solar heat gain would be conducted downward (a very slow process requiring a large vertical temperature gradient – a large negative lapse rate) to the surface.

    (this all assumes that no part of the surface (hot in the second case) or atmosphere (hot in the first case) becomes hot enough from solar heating to emit significantly at solar wavelengths (SW radiation)).

    In between these two extremes, both net LW radiation and net convection transport heat generally upward (in polar regions the atmosphere can actually lose heat to the surface even in the daily average) within the troposphere, and net LW radiation transports heat upward within the upper atmosphere above the tropopause (it acts alone in a one-dimensional model meant to be representative of the whole Earth – in three dimensions there is some convection in the stratosphere and mesosphere, but it is not locallized vertical convection, and it is not driven by the potential energy of differential heating as is typical in the troposphere; rather it is driven by kinetic energy coming up from the troposphere)

    Interestingly, in the in between case, because there is significant LW radiational cooling within the troposphere, it is possible for the tropopause (at least parts of it – I’m not sure of the global average off hand) to be colder than the temperature of the surface in the first case or the tropopause in the second case.

    (For variations or more detail on this and previous explanations, See also my comments (not to imply that mine are the best comments or only comments, but I remember my own comments better because I wrote them) at and (where I was just “Pat”, and also where the topic of molecular collisions and local thermodynamic equilibrium came up – speaking of which:)

    Re 187:

    At local thermodynamic equilibrium (which essentially exists in the vast majority of the atmosphere’s mass because collisions are frequent enough), all suffiently large (for statistics) subgroupings of particles in a given location have the same temperature; so, for example, greenhouse gasses are at the same temperature as non-greenhouse gasses (the same also being true of gasses which absorb solar or other energy – except where fluorescence would occur (could the aurora be described properly as fluorescence?)). Thus, when greenhouse gasses (or other gasses absorbing solar energy) radiate more or less energy then they receive, they cool off or heat up, changing temperature (and/or for water vapor and clouds, potentially changing phase, and/or for oxygen and ozone, chemically reacting); but the amount of temperature change per unit heating or cooling (per unit atmosphere, by one or a few components of that unit of atmosphere) is determined by the heat capacity (per unit atmosphere) of all atmospheric components combined because the gain or loss of heat is distributed by collisions.

    PS back to that W thing (which sums to 1 along any one direction) – for integrating over angles (solid angles) to find total W per unit area, for the purpose of illustrating the integration of intensity to find a flux per unit area, (just going downward or upward from that unit area, not both at once), one must weight the W for each direction by the cosine of the angle with the normal to the area (assuming a horizontal area, this is the angle A from vertical – downward, the nadir, upward, the zenith, and then the angle is the zenith angle) and then multiply by the solid angle d(solid angle) (or for numerical integration, a solid angle increment) before integrating over solid angle. For W, the amount per unit area is pi steradians (there are 2 pi steradians in a hemisphere, but the cos(A) factor reduces the integration by half, due to the greater reductions of contributions at higher angles). For finding a radiative flux per unit area F, one finds I (which has units of F per steradian) along each direction as described in comment 184, and then substitute I for W in the above formulation to get F. If F is a function of wavelength and is per unit wavelength, then one must then integrate over wavelength to get the total.

  40. 190
    Dermod O'Reilly says:

    Re 189, going backwards through your post. I think your “PS” is for something else. Your “Re 187” Yes, that is the process for radiative heating of the atmosphere but the atmosphere is mainly heated by the water evaporation cycle, on this point the IPCC quoting Kiehl & Trenberth are probably correct (see Fig1 p4/96), but they have one interesting thing in this diagram, the net radiative power from the ground to the atmosphere is only 26W/M2 (390 – 324 – 40) compared with 67W/M2, 24W/M2 and 78W/M2 for absorbed insolation, ground thermals and water cycle, 170W/M2 in total. The IPCC is clearly of the opinion that radiation from the ground plays a very small role in heating the atmosphere and I agree.

    Now to your response, “Re 185”. In your 2nd par. “A simple way” in the first case (no GH gases) there would still be convection since the earth is a globe and the sun heats it according to the cosine law, this gives a temperature gradient along the surface, a one-dimensional model will not show this. However, in the absence of GH gases the atmosphere would still spread heat about as it does now.

    Re “the last case”, LW opaque atmosphere. According to the IPCC the “top of the atmosphere” radiation is 195W/M2 (they have 30W/M2 from clouds) with only 40W/M2 direct from the surface, this situation is not too far from your last case. Thus, on this lovely planet on which we live, the so-called GH gases are responsible for cooling the atmosphere but not for heating it.

    With regard to gases cooling the atmosphere it is useful to consider radiative transfer in a more general way. Radiative transfer is an optical effect from a surface For example, gold coating is used to help define the temperature of satellite parts because of its low emissivity but the emissivity for a mirror finish is much lower than that for a matt finish. The gold surface radiates (or in this case fails to radiate) whatever heat comes from underneath it, the same applies to gassy planets; the top of the earth’s atmosphere radiates heat into deep space from polar gases, it does not matter a damn how the heat gets there, in the case of the earth convection and water cycle are far more powerful heat transfer processes than any possible thermal diffusion.

    So why does the earth’s surface temperature appear to be warmer than radiative equilibrium would dictate? The answer lies with the IPCC’s diagram, the radiative balance does not concern the surface temperature but the temperature somewhere at the top of the troposphere. The surface is, thermally speaking, a long way from the top of the troposphere.

    The surface temperature is governed by the thermal energy in the atmosphere. The second law of thermodynamics states that “entropy tends to maximise”, frequently this is interpreted as “heat flows from hot to cold” and this is true for gases in the absence of gravity. In the presence of gravity a better view is “the energy density (Joules/kg) tends to uniformity”. In this case the temperature throughout the atmosphere can no longer be uniform, it becomes inversely proportional to the pressure (height), it is this that causes the temperature difference between the rocky/watery surface and the radiation zone at the top of the troposphere.

    Have a nice day!

  41. 191
    Bryan White says:

    Re #124: Camp and Tung — if the claims that cosmic radiation is important to water droplet nucleation and cloud formation have merit, then the modulation of the cosmic ray flux by the 11 year solar cycle would lead to more cloud cover at solar min (hence colder) and less at solar max (hotter).

    This relative perturbation of albedo would lead to Camp and Tung producing an estimate for forcing that is biased high, would it not? By how much, I wonder?

    Also, the use of “average” temperatures in the discussions concerns me. Since radiation is T^4, and regional (land surface) temperatures range about 10% of T, how is the graininess of the radiation treated?

  42. 192
    Patrick 027 says:

    Re 190,

    paragraph 2 – I was hesitant about convection without a GH effect because it occured to me that while, from some initial conditions, convection would certainly occur, it might halt or nearly halt as some equilibrium state is reached. As air descends in the polar regions, it would become as warm (or warmer, if precipitation occured during rising in the tropics) as it was when it rose in the tropics (being unable to radiatively cool itself). Actually, I guess that the air would be cooled by contact with the surface at the poles and also by evaporation, so some convection could be sustained – although I expect it would be rather weak (it would only cool one very thin layer of air at a time); if there is any direct solar heating of the atmosphere, as there is now (such as by UV radiation), the lapse rate will be negative (thermals would be inhibited). But solar heating of the atmosphere itself could help contribute to a Hadley cell type circulation – but it would have to be balanced, again, by cooling by contact with the cold regions of the surface, and by evaporation, suggesting it would slow.

    – – – – – –

    paragraph 1:

    Yes, it is true that a majority of vertical convective heat transport from the surface is the latent heat of water vapor – as that water vapor is eventually condensed/frozen and precipitated (sometimes with some intermediate steps re-evaporation, re-condensation, remelting and refreezing), that heat goes into the atmosphere as sensible heat, which, along with sensible heat directly from the surface, can be transported upward even farther.

    In terms of (globally averaged or globally representative) upward vertical heat fluxes (a downward flux is a negative upward flux) (W/m2) as a function of height, the net convective flux at any level is the sum of the net latent heat flux and the net sensible heat flux (except in a very thin layer hugging the surface, where some sensible heat flux is via conduction). The net convective flux declines with height – this is a flux convergence, which means that the atmosphere is being heated (which happens to be balanced by radiative cooling). The net latent heat flux decreasing with height may be partly balanced by a contribution to increasing net sensible heat flux with height; the rest would be balanced by increasing net radiative flux with height. Whether the net sensible heat flux increases or decreases with height would depend on the combination of changes with height in net latent heat flux and net radiative flux; my guess is that the net sensible heat flux grows with height near the surface (if the net latent heat flux declines faster than net radiative flux grows) and declines with height farther up (if the reverse is true at that level). At the tropopause, the net convective flux goes to zero and remains at zero going into the upper atmosphere.

    Upward flux decreasing (increasing) with height => Upward flux convergence (divergence) => heating (cooling)

    The net radiative flux is the sum of the net LW flux and the net SW (solar) flux, the latter being negative as the net SW flux is downward toward SW absorption, a majority of which occurs at the surface.

    The net radiative flux will average to zero above the tropopause if the climate is in equilibrium; this is the sum of a positive LW flux and a negative SW flux. The net radiative flux thus becomes negative in the troposphere to balance the positive convective flux. The SW flux decreases with height (negative with increasing magnitude) from SW absorption in the atmosphere; going down it rises sharply to zero at the surface (well, not quite so sharply in the ocean).

    The net fluxes are the upward minus downward fluxes – for example, there is some downward convective flux as descending air is not at absolute zero temperature and is not devoid of all water vapor; there is some upward SW flux from reflection and scattering. The net LW flux is generally positive because looking up, one sees colder air and space (the higher up one goes, more and more of that is space); looking down, one sees warmer air and an even warmer surface (on average) (the higher up one goes, less and less of that is the surface). Divergence or convergence of the net LW flux is due to an imbalance between LW absorption and LW emission within a layer (which can be further seperated into absorption of upward LW flux, emission downward, emission upward, and absorption of downward LW flux; alternatively one can divide the net LW flux into upward and downward fluxes first, then the divergence or convergence of each of those is related to imbalances in absorption of LW from below and emission upward, and absorption of LW from above and emission downward). That at equilibrium, the divergence of the net LW flux must match the convergence of net SW and net convective fluxes, places a constraint on how the temperature varies with height. An imbalance will tend to heat or cool a layer – above the tropopause, the most direct effect is a temperature change that alters emission of LW radiation, and thus changes the divergence of LW radiation within that layer. Below the tropopause, convection also adjusts. (SW also adjusts if feedbacks affect SW absorption and albedo.) Near the tropopause, there is a potential (depending on the nature of the imbalance) for convection to become important above or to cease being important immediately below, causing movement of the tropopause. Within the troposphere, the potential for convection to occur tends to maintain a lapse rate (a relationship between temperatures at different levels, not directly by itself does it maintain the temperature itself) that will constrain the LW fluxes, and then the convective fluxes will adjust.

    While the net convective flux is larger than the net LW flux at the surface, this does not mean LW fluxes are less important (I’m not saying they’re more important, just that both are important). For example, if the atmosphere were to become colder with no other changes, both convection and the net LW flux at the surface would increase to heat the the atmosphere, as the atmosphere would be radiating less LW flux downward. It would also be radiating less upward; it would still absorb as much from the surface, so there would be less LW radiating to space; except for SW feedbacks, there would thus be an imbalance that tends to heat the system back up. Consider also that the LW flux downward from the atmosphere to the surface is larger than SW heating at the surface – the larger the LW flux downward to the surface, the less relative effect that temporal variations in SW flux to the surface have – so the diurnal temperature range tends to get smaller.

    paragraph 3:

    It is true that greenhouse agents act directly to radiatively cool the atmosphere. But they decrease the LW radiative cooling of the surface, the cooling balances convective heating, they reduce the LW flux to space, in particular from below the tropopause, and thus indirectly make the troposphere warmer than it would otherwise be.

    paragraph 6 – Within the troposphere, convection tends to maintain some lapse rate, because there is a distribution of radiative heating and cooling that tends to make the lower atmosphere unstable to convection. But above the tropopause, this is not so; stable layers exist where the lapse rate is not so great as to allow convection (in a one dimensional model representative of the average – there is some overturning driven by kinetic energy from below.) – There is essentially no a priori limit to how stable the air can be – how strongly negative the lapse rate can become.

  43. 193
    Patrick 027 says:

    – oh, and you have a nice day too!

  44. 194
    Patrick 027 says:

    Re 190 paragraph 2 – So what I’m picturing (for zero greenhouse effect) is an atmosphere with small horizontal temperature gradients at most levels except very near the surface; there would be a very strong but thin (surface-hugging) inversion near the poles that would weaken towards the tropics. Within that layer there would be a tendency for convection. Not much heat would actually be transported owing to the thinness of the layer. The layer might be so thin that friction with the surface would be significant or perhaps dominant? relative to pressure gradient and coriolis forces.

  45. 195
    Hank Roberts says:

    Patrick, have you looked at Ray Pierrehumbert’s website (via the Contributors links, on right side of page)? He has an article on “Science Fiction Atmospheres” that I found helped me understand this.

  46. 196
    Dermod O'Reilly says:

    Re 192your par.6 “Within the troposphere, convection tends to maintain some lapse rate” this gives me problems, the lapse rate derives from the pressure gradient which is due to gravity, ja oder nein? I have seen it said that the lapse arises because the sun heats the surface, if you are of this persuasion then this is not the place to resolve the matter!

    [Response: 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]

    Re 195. I have examined Ray Pierrehumbert’s new (draft) book, it is indeed a formidable work but it gives rise to horrendous problems, he should re-examine his description of the 2nd law of thermodynamics and try to reconcile all the methods of heat transport in the earth’s atmosphere before piling everything on to radiation.

  47. 197
    Hank Roberts says:

    Patrick, stand outside of the planet and look at it whole: radiation _is_ all that’s going in and out. The other forms of heat transport are internal rearrangement.

  48. 198
    Dermod O'Reilly says:

    Thanks Hank. One is the weather and the other is …. oh I am going to bed, the sun went down a few hours ago

  49. 199
    Steele says:

    The CO2 theory has a major inherent fallacy. Let me start with the summary of the CO2 lag effect by RealClimate:

    “The 4200 years of warming make up about 5/6 of the total warming. So CO2 could have caused the last 5/6 of the warming, but could not have caused the first 1/6 of the warming.”
    (they have edited out a previous statement that CO2 probably caused about 50% of the warming)
    “From studying all the available data (not just ice cores), the probable sequence of events at a termination goes something like this. Some (currently unknown) process causes Antarctica and the surrounding ocean to warm. This process also causes CO2 to start rising, about 800 years later. Then CO2 further warms the whole planet, because of its heat-trapping properties. This leads to even further CO2 release.”

    However the AGW scientists never address the “sequence of events” for a falling temperature. It is implied by CO2 theory that a certain concentration of CO2 will lead to higher temperatures and thus more CO2. The logical conclusion is that we will get runaway heating. But we didn’t . And why we didn’t never is addressed or explored.

    For illustrative purposes let’s label ocean temperature at 0 degrees during the glacial and 20 degrees at the height of the interglacial.(Studies have shown differences of 20 degrees). Being conservative, lets use the claim that CO2 only causes 50% of the interglacial warming. So the sun raises the ocean temperatures to 10 degrees and causes a release of CO2. Then in accordance with RealClimate’s above summary, a feedback mechanism results where the CO2 traps heat which causes additional release of CO2 and thus more heat trapping.

    I assume you would agree with this scenario. So why does the temperature peak and fall? Lets assume the the cycles of the sun’s orbit now wanes causing the temperature to drop back to 10 degrees and accounting for its full 50% of the warming. But at 10 degrees we still have higher concentrations of CO2 than we had a the glacial minimum I labeled 0. And at 10 degrees the CO2 theory says that there is enough CO2 to trap more heat and release more CO2. We are right back to raising the temperature towards the interglacial maximum. Thus my contention that CO2 theory predicts that CO2 will counteract cooling forces and logically we would never return to the 0 degress of the glacial. Then logic dictates that to reach the observed glacial minimums, the climate must be sensitive to something more powerful than CO2.

    Or else you must argue that there are mechanisms that pull CO2 out of the atmosphere and allow the temperatures to fall. However if your argue that processes that store CO2 like
    photosynthesis or oceanic carbonate formation help lower the CO2 and thus the
    temperature, we are left with another question. At any given temperature such CO2 sinks should be active and thus just as likely to prevent the rising temperatures of the approaching
    interglacial as stimulate the falling temperatures of the approaching glacial
    period. We can not argue that at 10 degrees CO2 causes additional warming during an approaching interglacial, but at 10 degrees CO2 is absorbed by sinks to allow cooling. You can not have it both ways, and this is the inherent fallacy of the CO2 model.

    [Response: Rather than ‘never [being] addressed or explored’ we addressed the reason why you don’t see a runaway effect here: and it’s easy to show that the observed T/CO2 regression and the radiative forcing calculations don’t come any where close to providing enough response to ‘runaway’ (which is good). It does work both ways though and your postulated example is flawed (do a simple mathematical model with an external forcing and a CO2 feedback). – gavin]

  50. 200
    Steele says:

    “It does work both ways though and your postulated example is flawed (do a simple mathematical model with an external forcing and a CO2 feedback). – gavin”

    I did just give a very simple mathematical model. Perhaps you could show me how it is flawed vs just saying it is flawed.

    [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]