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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.

Q.E.D.?


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

  1. 1
    David Wilson says:

    you realize of course that they do not teach geometry anymore, but (grumpy as I am today from a winter cold) your putting Q.E.D. at the end of your article has made me smile, thanks & be well.

  2. 2

    Back in the 1980’s, when the greenhouse effect first reached prominence as an issue, I was a skeptic. I thought if CO2 is the principal driver of global warming, why did most of the 20th century warming happen before 1940, while most of the CO2 accumulation happened after 1940? I figured if there was anything to anthropogenic global warming (AGW) temperatures would continue to rise over the next few decades and the issue would come to a head in the 2000’s.

    Well they did and it has. Given the results of this natural “experiment” and the fact that many laymen are now interested in this issue I decided to look into the science of AGW to see how much I understood and how many results I could obtain for myself using simper models. In the website given above I present my current understanding of AGW in terms of a model that I have implemented on an Excel spreadsheet and which anyone with some math and technical background could do for themselves.

    I bend over backwards to the skeptics by including the cosmic ray mechanism as a central feature of my model. Interestingly, the inclusion of this mechanism *strengthens* the case *for* AGW.

    The reason is that in the absence of the cosmic ray effect the impact of solar is through total solar irradiance (TSI), and is very small. The data I find has a solar cycle size of 1 watt/meter in TSI. With albedo of 0.3 this comes to a 1*(1/4)*(1-0.3) = 0.18 watts/meter impact on average solar insolation which translates to maybe 0.1 C, depending on what you assume for climate sensitivity.

    With the cosmic ray model, the size of this effect rises to ~0.4 C. It cannot be seen directly because of oceanic damping, but it does call for about ~0.3C of warming (instead of ~0.1 C from pure TSI) in the early 20th century based on Lockwood’s solar activity reconstructions. Since solar activity hasn’t risen since the 1950’s, solar contributes zip to recent warming.

    Between 1900 and 1950 the CO2 forcing was about a quarter of the post-1950 forcing, which is capable of producing ~0.7 C of warming. Yet the temperature rise early in the 20th century was not much smaller than the recent rise. With the cosmic ray effect we have ~0.3 C of solar warming combined with ~0.2 of CO2 warming, which is then offset by human-produced aerosols to yield ~0.3 of waring. Since the 1950’s we have ~0 C of solar warming plus ~0.7 C of CO2 warming combined with aerosols to yield ~0.4 C of actual warming.

    Without the cosmic ray solar effect it is harder to explain why the early 20th century temperature rise was so big compared to the post-fifties warming.

    Svensmark and the cosmic ray skeptics have pretty much nailed the case for AGW, despite their intentions.

  3. 3
    Chris S says:

    Loved this post as I am currently studying math (yes In summer) and you mention Logarithims which I’m currently learning. Math makes more sense when it’s related to actual usage rather then numbers on a dry erase board.

  4. 4
    David B. Benson says:

    Q.E.D.

    The six step explaination is most clear. Thank you.

  5. 5
    Aaron Lewis says:

    How significant?

    Arctic sea ice (area) on 7/31/07 was 35% less than on 7/31/1997.

    The North Atlantic is warmer than it was 10 years ago. Therefore, we can reasonably speculate that a warming North Atlantic contributed to the weather patterns that caused flooding in England this summer.

    Does anyone want to argue that global warming in some way mitigated the current flood situation in South-East Asia? Is there a weatherman out there willing to state that the heat content of the oceans had no effect on the monsoon? NO? The only other option is that AGW contributed to the effect. We may not be able to quantify the effect at this time, but AGW added its mite.

    I look at the current warming of the North Pacific, and I expect that heat in the water will cause the Pacific storm tracks to move, and change the weather up and down the West Coast of North America. That is significant.

    It is time for weathermen to STOP saying that they cannot attribute specific weather events to AGW. Weather forecasts are going to fall flat unless they account for global warming. Every honest weather man will start their weather forecast, “Because of global warming. . . . “ Then, the public will pay attention.

    And, Gavin has just reminded us that we have not yet seen the full effects from green house gases already emitted!

  6. 6
    Konstantin says:

    As a physicist I can pretty much follow the science on AGW, and can demonstrate to reasonably open-minded people that it exists and is significant. However, I have very little idea what the effects of AGW on humanity will be beyond the fact that it is an ecological disaster which can kill lots of people in the developing world (excellent reasons to do whatever it takes to get rid of it, in my opinion) and so I have a problem with responding to the argument that we need do nothing because at least as far as the DEVELOPED world is concerned AGW will be at most a nuisance.
    Living in Houston, TX where many people work for oil companies I often hear that “plants/animals are cute, but people come first; no breaking the economy for a few critters”, “ok glaciers are on their way out, but people can always build desalinization plants”, “agriculture may be hurt someplaces but will improve in others” and “no matter what this cannot make or break OUR economy and lives. The rest of the world can go XXXX”. Can sbd give me a few arguments to use on such idiots?

  7. 7
    Steve Reynolds says:

    Aaron Lewis> Does anyone want to argue that global warming in some way mitigated the current flood situation in South-East Asia? Is there a weatherman out there willing to state that the heat content of the oceans had no effect on the monsoon? NO? The only other option is that AGW contributed to the effect.

    I do not follow your logic. I think that you at least need to show that current weather extremes are outside what is expected from historical variation.

    [Response: Actually no. To demonstrate attribution you don’t need to show that something is unprecedented, merely that it follows consistently. If you take your request to its logical conclusion, we would have to wait until we find ourselves with 10 deg C warming and 100 metres of sea level rise (each of which has happened before) before we could say anything about what was causing it. – gavin]

  8. 8
  9. 9

    A lot of good information. Numbers that I hadn’t seen before. Thank you. I wondered where the coefficient 5.35 came from and I see you point out in part 4., that a doubling of CO2 causes a radiative forcing of 3.7 watts/meter^2 ( within plus or minus .4 w/m^2), then 3.7=Cxln2 or C=3.7/ln2 =5.35 or nearly so.

  10. 10
    danny bee says:

    I hate to say this, but the world needs to stop all car and plane transport right NOW, for a one year test run. To see if we can survive without these co2 machines……the UN should declare a global emergency NOW and ask all member nations to stop all vehicular and plane traffic NOW. For a one year period, and then get together and see what the results are. We are in a major major emergency, and most media are worring about Paris Hilton and Becks. Who cares? Barry Bonds and A-Rod, not important. The Planet is in DIRE DIRE straights….

  11. 11
    Timothy Chase says:

    Konstantin (#6) wrote:

    Living in Houston, TX where many people work for oil companies I often hear that “plants/animals are cute, but people come first; no breaking the economy for a few critters”, “ok glaciers are on their way out, but people can always build desalinization plants”, “agriculture may be hurt someplaces but will improve in others” and “no matter what this cannot make or break OUR economy and lives. The rest of the world can go XXXX”. Can sbd give me a few arguments to use on such idiots?

    Well, by the end of this century, over a billion people in Asia are going to be facing severe water-shortages as the result of the disappearance of the glaciers in the Tibetean Plateau. This will destroy much of the agriculture in the region. This should drive up food prices worldwide.

    But closer to home, you will see a permanent dustbowel begin to form in the US Southwest – and another begin to form in the US Southeast. We aren’t supposed to be able to grow wheat in the continental US much beyond 2080. Wheat. Thats under business as usual.

    Of course, we could have Canada grow things for us – except they are already using their farmland to capacity. But maybe they could start farming in all of that thawing permafrost…? It tends to have a problem holding water. Not much reason to think the chemistry is right, either, but I have only started digging into their soil. Additionally, farming counts on a great deal of infrastructure being in place. So do cities.

    And it already appears that ice melt is a fairly nonlinear process. Under business as usual could greatly exceed the IPCC’s estimates. Several meters by the end of the century seems quite possible, given the various feedbacks. Five meters isn’t entirely out of the question – either in terms of the dynamics (e.g., positive feedback between Greenland and the West Antarctic Peninsula) or the paleoclimate record.

    Please see:

    However, Hansen et al (2007) show that the typical ~6ky time scale for paleoclimate ice sheet disintegration reflects the half-width of the shortest of the weak orbital forcings that drive the climate change, not an inherent time scale of ice sheets for disintegration. Indeed, the paleoclimate record contains numerous examples of ice sheets yielding sea level rise of several meters per century, with forcings smaller than that of the BAU scenario. The problem with the paleoclimate ice sheet models is that they do not generally contain the physics of ice streams, effects of surface melt descending through crevasses and lubricating basal flow, or realistic interactions with the ocean.

    Hansen, J.E., 2007: Scientific reticence and sea level rise. Environ. Res. Lett., 2, 024002, doi:10.1088/1748-9326/2/2/024002.
    http://pubs.giss.nasa.gov/abstracts/2007/Hansen.html

    And it should be remembered that approximately half of the world’s population lives within 100 km of the coasts. According to the USGS, five meters would submerge 3.2 million kilometers of land, displacing more than half a billion people.

    Please see:

    Modeling Sea-Level Rise Effects on Population using Global Elevation and Land-Cover Data
    E. Lynn Usery (2007)
    http://cegis.usgs.gov/pdf/aag-2007.pdf

    Personally, in economic terms and under business as usual, I believe we could see the beginnings of an economic crisis in this century which will dwarf the Great Depression both in terms of its severity and duration.

  12. 12
    Chuck Booth says:

    Re # 6 Konstantin, here is some more ammunition for you:

    Ecosystem Services provide by Mother Earth include:
    1. Provisioning, including food, water, fuel, and fiber.
    2. Regulating, such as the prevention of soil erosion and flooding.
    3. Cultural, including recreation, spiritual values, and a “sense of place.”
    4. Basic support, including soil formation, nutrient cycling, and oxygen from photosynthesis.

    A few peer-reviewed scientific reports, and summaries of reports, that explain and quantify these services:

    Schröter, D. et al (2005) Ecosystem Service Supply and Vulnerability to Global Change in Europe. Science 25 November 2005, Vol. 310. no. 5752, pp. 1333 – 1337

    Worm, B. et al (2006) Impacts of Biodiversity Loss on Ocean Ecosystem Services. Science 3 November 2006, Vol. 314. no. 5800, pp. 787 – 790

    Stokstad, E. (2005) Taking the Pulse of Earth’s Life-Support Systems
    Science 1 April 2005, Vol. 308. no. 5718, pp. 41 – 43
    Note: This article is an overview of the “Millennium Ecosystem Assessment Synthesis Report,” http://www.maweb.org

    Balvanera, P. et al (2001) Conserving Biodiversity and Ecosystem Services. Science 1 June 2007, Vol. 316. no. 5829, p. 1285

    Kareiva, P. et al (2007)Domesticated Nature: Shaping Landscapes and Ecosystems for Human Welfare. Science 29 June 2007, Vol. 316. no. 5833, pp. 1866 – 1869

  13. 13
    robert davies says:

    Re: 6: Konstantin, I’ve found it effective to point out that, with just another (roughly) 1.5 deg F increase in global ave. temp. (GAT), we will be entering a global climate that the human ecosystem has never seen before. Now note that the most recent IPCC results (Fourth Assessment Report) indicate, with high confidence, a 21st-century temp increase of 3.5-8 deg F. My reading of the paleoclimate data suggests that the last time GAT was 3.5 deg F warmer was roughly 4 million years ago (whereas modern humans came on the scene roughly 150,000 years ago).

    These are knobs on the master control panel that we really don’t want to be twiddling. The full spectrum of the consequences that temp. increases like these – on the timescale of a century – will effect is simply impossible to anticipate. I think that an effective point to make to people is that, from a risk management standpoint, we simply cannot risk the twiddling (“Dad, what does this one do?”). Reading the IPCC working group 3 report one does find some “winners” in the short term, but by century’s end it’s pretty much all bad for human civilization – with strong potential for catastrophically bad.

  14. 14
    Jim Baerg says:

    Re: comment 10 by Danny bee
    It’s often hard to tell if a poster has tongue in cheek, but I’ll assume not in this case.
    Eliminating car & plane transport immediately would be an economic disaster. Over the next few decades shifting much of our road & air traffic to electric rail would be relatively easy. Of course the CO2 emission reductions would be minor unless the electricity is generated by non-fossil (probably nuclear) means.

  15. 15
    Ed Barkley says:

    Another quiet hurricane season this year, huh? And yet “we will see a permanent dust bowl begin to form in the US Southwest – and another begin to form in the US Southeast”

    Pardon me if I don’t trust your rain forecasting.

    The problem you should all be worried about is that the international housing bubble, being substantially more oppressive that this summer’s temperatures, is going to preempt your AGW-derived economic depression by 75 years and steal all of your thunder. Pun intended.

  16. 16
    Mike Donald says:

    Chaps and ladies,

    Here’s a funny discovered on forum-land. Version 2.0 no less (July 24, 2007). I have a strong suspicion this is Moncktonite bull and requires debunking before the clown brigade start quoting it.

    Gerhard Gerlich, Ralf D. Tscheuschner. Falsification of the atmospheric CO2 greenhouse effects within the frame of physics.

    http://xxx.lanl.gov/PS_cache/arxiv/pdf/0707/0707.1161v2.pdf

    Abstract

    The atmospheric greenhouse effect, an idea that authors trace back to the traditional works of Fourier 1824, Tyndall 1861, and Arrhenius 1896, and which is still supported in global climatology, essentially describes a fictitious mechanism, in which a planetary atmosphere acts as a heat pump driven by an environment that is radiatively interacting with but radiatively equilibrated to the atmospheric system. According to the second law of thermodynamics such a planetary machine can never exist. Nevertheless, in almost all texts of global climatology and in a widespread secondary literature it is taken for granted that such mechanism is real and stands on a firm scientific foundation. In this paper the popular conjecture is analyzed and the underlying physical principles are clarified. By showing that (a) there are no common physical laws between the warming phenomenon in glass houses and the fictitious atmospheric greenhouse effects, (b) there are no calculations to determine an average surface temperature of a planet, (c) the frequently mentioned difference of 33 C is a meaningless number calculated wrongly, (d) the formulas of cavity radiation are used inappropriately, (e) the assumption of a radiative balance is unphysical, (f) thermal conductivity and friction must not be set to zero, the atmospheric greenhouse conjecture is falsified

    End of Abstract

  17. 17
    John Carter says:

    I think you lost the readers at step 1! what is sigmaT^4 ?? how is it related to 15C.

    The magical parameters 1-a and S/4 appear from nowhere? what are they?

    [Response: Sorry. I did assume a little knowledge so this isn’t the post for absolute beginners. sigmaT^4 is the upward blackbody radiation (based on stefan-boltzmann) at the surface, ‘a’ is the albedo (reflectivity), so (1-a) is the fraction of incident solar radiation that is absorbed by the planet. And S is the solar constant (1366 W/m2). The factor 1/4 comes from the ratio of the area of the disk to the total surface area of the planet (which takes into account the Earth spherical shape and the difference between day and night). – gavin]

  18. 18
    Valuethinker says:

    6.

    Konstantin

    Read ‘Six Degrees’ by Mark Lynas. A good summary of the latest research on temperature change and the impact on human beings.

    James Lovelock ‘The Revenge of Gaia’ will give you a more extreme view. But Peter Ward’s work on mass extinction (especially the Permian Extinction), see his recent article in Scientific American, is even more extreme still. If we get a giant methane bubble due to permafrost melt, then we die.

    Tim Flannery ‘The Weather Makers’ also has a good intro to the impact of temperature changes.

    The idea that the US will be OK if half of the species on this planet dies is a pretty specious one, if you think about it. When you don’t know which species. The honey bee, maybe?

    Then there is the pine bark beetle, which is destroying the forests of British Columbia. And now, due to the warmer winters, it has hopped the Rockies into Alberta.

    And of course there is West Nile Virus, which is moving north with the warmer weather. Close Central Park, anyone?

    You might mention drought in California (Australia is having the worst drought ever recorded, since the white man arrived, and is considering shutting down agriculture in the Murray-Darling system, which is 90% below its normal water level), or the Dust Bowl conditions in the Great Plains in the 1930s (another 5 year drought), or the collapse of water flow into the Colorado River, or category 6 Hurricanes (Katrina was a 4).

    Massive uncontrollable forest fires might be another consequence in places like Colorado. Greece has lost something like 40% of its forest cover this summer.

    Turning to James Hansen’s latest pieces (the technical piece, and the non technical piece in New Scientist) 40% or more of Florida could be under water by 2100, if Hansen is right about glacial melt (which the IPCC explicitly excluded from its forecast).

  19. 19
    Bob Bergen says:

    Gavin, your six steps would mean nothing to the vast majority of students I taught over 15 years at the community college level. Way too much math for them!

    I taught Earth Science, a survey course at the freshman level which included the basics of Geology, Meteorology, Oceanography and Astronomy. Yea, I know – a brief brush approach. I picked out of each major topic those subtopics which would mean most to my students, most of whom would never ever see another science course.
    And gobal climate change was a major topic.

    But these students often had not even an algebra background. So I was forced to teach “Physics for Poets” when necessary to explain physical phenomena and concepts. An interesting assignment, for sure.

    These same students, incidentally, read around the tenth grade level. I often had to explain specific words and phrases from the textbook, and the meaning of a long paragraph was often beyond them.

    We need your explanations in those terms to talk to virtually anyone chosen randomly from the public: short words, no math.

    [Response: One thing I’ve found over the years of dealing directly and indirectly with high school students is that the direct scientist-student route is not very productive (very different assumptions about what an explanation entails!). However, the scientist-teacher then teacher-student route is much more so. Teachers get the scientific points much faster and are also in a much better position (and have more patience) to lead the students to understanding. Therefore, maybe we could help each other out here. Since you presumably understand the points made above (!), perhaps you’d care to translate it down another level – If so, I’ll post that up as well and we can see if it works better. – gavin]

  20. 20
    Andree Henkel says:

    Re 15

    sigma*T^4 is the amount of (infrared) energy radiated from 1sqm Area earth surface according to Boltzmann´s law
    http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
    sigma is the boltzmann constant; T is absolute temperature in K, the surface temperature (in °C) has to be converted to K (Kelvin – add 273.15K)

    a is the albedo (reflectivity for sunlight) of the earth, it is roughly 0.3 without unit
    http://en.wikipedia.org/wiki/Albedo
    S is the “solar constant”, the amount of solar energy into 1sqm (90° incidence angle) before it enters earths atmosphere, it is roughly 1366W
    http://en.wikipedia.org/wiki/Solar_constant#Solar_constant
    it has to be divided by 4 to account for the area ratio: crossection of a sphere / surface area of a sphere
    (the incident sunlight on earth surface is proportional to the crosssectional area, but the radiated energy is proportional to the surface area)

  21. 21
    Kevin says:

    Thanks for another great post — I really appreciate the efforts you make to make the science behind global warming understandable by the average person. This is a still a bit technical for complete lay people, but generally excellent work.

    Kevin
    http://www.21st-century-citizen.com

  22. 22
    ChrisC says:

    Re: 6: Konstantin

    My favourite places on Earth are coral reefs. These ecosystems are among the most diverse on Earth. They directly support large human populations, and indirectly, through tourism, fisheries and medicinal derivatives, support many more.

    Coral reefs are under extreme threat from climate change. Tropical corals are particularly at risk from bleaching, due to higher than average sea temperature, and from calcium carbonate skeleton dissolution as a result of lowering sea pH. It is estimated that up to 50% of coral may be killed by 2030 under present trends.

    See the Australian Great Barrier Reef Marine Park Authorities web site for more info:

    http://www.gbrmpa.gov.au/corp_site/info_services/science/climate_change/climate_change_and_the_great_barrier_reef

    Cold water corals are also under threat, although much less is known about these very recently discovered ecosystems. Check out Lopelia.org

    http://www.lophelia.org/conservation/threats_cc.htm

    Hope that helps.

  23. 23

    [[I hate to say this, but the world needs to stop all car and plane transport right NOW, for a one year test run. To see if we can survive without these co2 machines……]]

    A recipe for instant worldwide recession, not to mention starvation. Food moves on trains, trucks and ships, you know.

    Are you, by any chance, an agent provocateur working for the denialists?

  24. 24

    [[I think you lost the readers at step 1! what is sigmaT^4 ?? how is it related to 15C.

    The magical parameters 1-a and S/4 appear from nowhere? what are they?]]

    The “Stefan-Boltzman law” says that a perfect radiator known as a black body emits a flux of so many watts per square meter, depending on the fourth power of the object’s temperature:

    I = σ T4 (1)

    Here, σ is the Stefan-Boltzmann constant, equivalent to about 5.6704 x 10-8 W K-4 m-2 and T is the temperature in °K., I comes out in watts per square meter. For example, Earth’s surface, at a mean global annual temperature of 288° K., radiates 390 watts per square meter. (Or it would if it were a blackbody. Actually, for most objects you have to sandwich in a factor ε called the “emissivity” into the equation above, ε ranging from 0 to 1, and it’s about 0.95 for Earth’s surface.

    The average Solar energy flux falling on the Earth’s surface is

    F = (S / 4) (1 – A)

    Here S is the “Solar constant,” the average flux intercepted by one square meter of space perpendicular to the sun at Earth’s distance from the sun. It has an a canonical value of 1,367.6 watts per square meter. A is the Earth’s “bolometric Bond albedo,” the fraction of solar energy reflected away by the Earth’s surface and atmosphere (mostly by clouds). A for Earth is 0.306 according to NASA. The factor 1/4 arises because Earth intercepts Solar energy on its cross-sectional area — π R2 — but has a spherical surface area — 4 π R2. Or in other words, half the Earth is in darkness and most of it slants away from the Sun.

    Plugging S = 1367.6 and A = 0.306 into the equation above, we find that F is about 237 watts per square meter for the Earth, corresponding to an “equilibrium temperature” (or “emission temperature,” or “effective temperature”) of 254° K. Most formulations use a slightly different S and A and get 255° K. This is actually the temperature you would measure if you tried to calculate Earth’s temperature from a distance. The difference between the 255° K. emission temperature and the 288° K. surface temperature, 33° K., is a measure of the strength of Earth’s greenhouse effect.

  25. 25
    B Buckner says:

    Danny Bee could also help by turning off his computer.

  26. 26
    Gunnar Moller says:

    To 15)

    T and sigma are standard nomenclature used in physics to discuss “black body radiation”, i.e. the thermal radiation emitted by a body at temperature T.

    sigma is the Stefan-Boltzmann constant (see e.g. http://en.wikipedia.org/wiki/Stefan-Boltzmann_constant)

    However, a and S still require some more knowing person’s explanation…

  27. 27
    Hank Roberts says:

    Bob Bergen is right in #19. Once you get the points clear, rewrite in simpler language.

    Simpler than the way a good writer about science can write for smart grade schoolers — write even more simply and clearly for people who may have once been curious but are older and by now tired and barely _care_ about knowing how the world works.

    Writing for smart children is easier than writing for people buried in the everyday noise. Their purchasing power and votes are being trolled for by PR and advertisers every minute. They’re hunkered down and not listening.

  28. 28

    I had the cart before the horse in my earlier post #9. The Coefficient 5.35 in the formula RF=5.35ln(CO2/CO2-orig) comes from basic physical principles based on radiation transfer calculations using complex models, as the note in table 6.2 so clearly shows.
    What I did amounts working backwards from the data.

  29. 29
    DaveS says:

    Could you rewrite 4 to leave out models? That point jumps right into models, and the conclusion relies on it.

    [Response: The conclusion relies on the concept of ‘radiative forcing’, it doesn’t rely on any GCM modelling. The linked post is the simplest explanation of the greenhouse effect that you can write down mathematically, and that is definitely not a GCM. The fundamental point is that if you put more energy into a system, then it will warm up. -gavin]

  30. 30
    sidd says:

    In the article you write:

    “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.).”

    You go on to say:

    “the last glacial period is a good example of a large forcing (~7 W/m^2 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).”

    This deduced 3 C sensitivity then does not just come from the ‘fast feedbacks’ but includes the ‘slow’ (ice sheet and other ) feedbacks as well ? So it is not the ‘classically defined’ sensitivity ?

    Hansen et al. recently (Climate Change and Trace Gases, Proc. Roy. Soc. A, 2007) argues that that an appropriate sensitivity might be twice the currently accepted value of 3/4 C/(W/m^2) once the ‘slow’ effects are put in. Would you care to comment on that estimate ?

    sidd

    [Response: The ice age calculations are taking the ice sheets etc. as fixed boundary conditions that impart a forcing of their own. Therefore we are only considering the fast feedbacks (i.e. ice sheets are not being seen as a feedback). The ‘slow feedback’ sensitivity is likely to be higher (since carbon cycle, methane and ice sheet feedbacks are very likely positive), however, estimating that from paleo is tricky since we are moving into a new regime which hasn’t ever happened before. In particular, the sensitivity of the Laurentide ice sheet to warming (which you can estimate from paleo) is not likely to be the same as for Greenland. I would therefore be a little wary of giving that a number – it’s an interesting point though, and I might explore that in a future post. – gavin]

  31. 31
    Walt Bennett says:

    Quoting today’s New York Times, in an article by Reuter’s:

    “The world experienced a series of record-breaking weather events in early 2007, from flooding in Asia to heatwaves in Europe and snowfall in South Africa, the United Nations weather agency said on Tuesday.

    “The World Meteorological Organization (WMO) said global land surface temperatures in January and April were likely the warmest since records began in 1880, at more than 1 degree Celsius higher than average for those months.

    “There have also been severe monsoon floods across South Asia, abnormally heavy rains in northern Europe, China, Sudan, Mozambique and Uruguay, extreme heatwaves in southeastern Europe and Russia, and unusual snowfall in South Africa and South America this year, the WMO said.”

    We’ve spent much of the last year debating the significance of anecdotal evidence. To me, that evidence represents a trend when year-by-year weather fails to swing back toward the previous norm.

    We have begun to see indisputable signs of this. In the U.S. we had, in some places, a cold, dry spring, and there was much ruckus made by those who see weather as ‘constantly changing’ and ‘beyond the influence of man.’ Yet, when we look around the world, we are seeing things that have not been previously observed. Weather volatility, massive shifting of wet/dry regions and seasons, severe events in areas previously untouched by them.

    The world is warming – is there any room left to dispute that? The warming is causing mega-changes in climate and weather patterns – can this, either, be disputed?

    So, we don’t know, where, when, how much and so forth. We don’t know a lot about a lot of things, yet we study them and report the results and subject them to further scrutiny, and we build a body of knowledge.

    Is climate any different than these other areas of human exploration? No, in the sense that this is how knowledge is accumulated. Yes, in the sense that no matter who or what causes these changes, they will affect the entire planet without sympathy. No buying our way out of these effects.

    And yet, don’t we already see that it is the world’s poorest who will be most cataclysmically affected? Those with the least means tend to live in the low lying coastal regions which are most prone to flooding. It occurs to me that these people will be displaced before they are flooded out: conditions will simply become unbearable. Too hot, too humid, too much disease. A human catastrophe is certainly upon us, and in the end the wealth of nations will be severely punished.

    Where will all the dispossessed go?

  32. 32

    Re #23 where Barton wrote:

    [[I hate to say this, but the world needs to stop all car and plane transport right NOW, for a one year test run. To see if we can survive without these co2 machines……]]

    A recipe for instant worldwide recession, not to mention starvation. Food moves on trains, trucks and ships, you know.

    Yes but food doesn’t grow in deserts, or survive under flood water and that is what global warming is bringing.

    Google for ‘Forest Fires’ and see how globally they are on the increase, and they are the first step towards desertification.

    Google for ‘Floods’ and see how they are spraeding around the world. Australia, the US, Asia and Britain are all suffering. And that will cause food shortages there.

    As the environmental effects of global warming increase, the disruption to the economy will be far worse than that caused by banning the use of unnecessary transport.

  33. 33
    Edward Greisch says:

    Konstantin, this will definitely help:
    download from:
    http://www.sciam.com/article.cfm?articleID=00037A5D-
    A938-150E-A93883414B7F0000&sc=I100322
    from the October 2006 issue of Scientific American
    Article: “Impact from the Deep”
    “Strangling heat and gases emanating from the earth and
    sea, not asteroids, most likely caused several ancient mass
    extinctions. Could the same killer-greenhouse conditions
    build once again? ”
    By Peter D. Ward
    The last paragraph of the article says:
    “The so-called thermal extinction at the end of the
    Paleocene began when atmospheric CO2 was just under
    1,000 parts per million (ppm). At the end of the Triassic,
    CO2 was just above 1,000 ppm. Today with CO2 around
    385 ppm, it seems we are still safe. But with atmospheric
    carbon climbing at an annual rate of 2 ppm and expected to
    accelerate to 3 ppm, levels could approach 900 ppm by the
    end of the next century, and conditions that bring about the
    beginnings of ocean anoxia may be in place. How soon
    after that could there be a new greenhouse extinction? That
    is something our society should never find out.”
    The hydrogen sulfide will finally put an end to people who think
    global warming isn’t a problem.

  34. 34
    David York says:

    Pondering how everything might play out, one deep concern I have is the relationship between Global Warming and Global Dimming, or the fact that our air pollution blocks a significant amount of solar energy from reaching the surface. This decreases the effects of the GHGs that we’ve already contributed to the atmosphere. So what is likely to happen if/when we have an economic meltdown and a significant portion of global industry grinds to a halt? Seems to me this should lead to rapidly rising temps, and who knows what else? Of course I’m referring to the study of post-911 temp increases from the airline shutdown. Do that worldwide and it seems to me that we’d be in big trouble in weeks or months, not 100 years.

    Please tell me I’m wrong…

  35. 35
    Jan Janssens says:

    According to the Wikipedia source, the value for earth’s albedo is 0,3 only because clouds are taking into account. The albedo is about a third lower without the clouds (earth’s surface = 70% water).

    Is it allowed to use part of the atmosphere in this kind of calculations?

    Thanks.

  36. 36
    Richard Ordway says:

    I don’t want to hijack the thread, but the cover page of the Newsweek article on oil, coal, gas and transportation industry funding of deniers and the responses to it are amusing and indicative of what is going on politically and why. Sorry if someone has already mentioned it:

    Newsweek front page article:
    http://www.msnbc.msn.com/id/20122975/site/newsweek/page/0/

    Response from a denier with utterly no scientific proof whatsoever:

    http://epw.senate.gov/public/index.cfm?FuseAction=Minority.Blogs&ContentRecord_id=38d98c0a-802a-23ad-48ac-d9f7facb61a7

  37. 37
    Steve Searls says:

    # Konstantin Says:
    6 August 2007 at 7:33 PM

    As a physicist I can pretty much follow the science on AGW, and can demonstrate to reasonably open-minded people that it exists and is significant. However, I have very little idea what the effects of AGW on humanity will be beyond the fact that it is an ecological disaster which can kill lots of people in the developing world (excellent reasons to do whatever it takes to get rid of it, in my opinion) and so I have a problem with responding to the argument that we need do nothing because at least as far as the DEVELOPED world is concerned AGW will be at most a nuisance.
    Living in Houston, TX where many people work for oil companies I often hear that “plants/animals are cute, but people come first; no breaking the economy for a few critters”, “ok glaciers are on their way out, but people can always build desalinization plants”, “agriculture may be hurt someplaces but will improve in others” and “no matter what this cannot make or break OUR economy and lives. The rest of the world can go XXXX”. Can sbd give me a few arguments to use on such idiots
    ?

    I can give you a real quick answer Konstantin: Katrina and Rita. I’d also refer them to this story by Reuters: LINK, which details that the first 6 months of 2007 had some of the severest weather on record.

  38. 38
    George Peabody says:

    Probably off-topic, but I’d like to nominate Timothy Chase’s (#11) “permanent dustbowel in the [U.S.] Southwest” for typo of the month! It suggested a number of perfectly atrocious puns, all of which I was able to resist…

  39. 39
    Hank Roberts says:

    Answering David York in #34: You’re not wrong. Sorry!
    http://scrippsnews.ucsd.edu/Releases/?releaseID=761

    “… After correctly predicting in 1980 that global warming would be detected by 2000, Ramanathan observed at the end of the 20-year period that the amount of warming was roughly half what he’d predicted. The stifling of the warming trend is generally attributed to a counteracting cooling effect caused by global dimming, an inference that has since been supported by data collected by Ramanathan and others from a number of field campaigns.

    But what will happen when the counterbalance is eliminated? Already Western nations have been successful in reducing particulate pollution and Ramanathan believes emerging nations, most importantly in south Asia, will soon follow suit. As one form of pollution is eliminated, the mask concealing the true impact of global warming will be stripped away. He predicts an acceleration of warming trends to take place in coming decades but what that means for cloud formation, hydrological cycles and other events that affect albedo is unknown.

    “We’re sort of in uncharted territory when it comes to what happens 30 or 40 years from now,” Ramanathan said.

    Related to AGU Fall Meeting 2006 “Bjerknes Lecture: Global Dimming and Its Masking Effect on Global Warming”

  40. 40
    Chuck Booth says:

    The following article (and web site) might be of interest to RealClimate readers. I can’t vouch for the scientific accuracy/validity of the content (It does not seem to have undergone standard peer review, except by the editors. The author is a research scientist at the Institute of Environmental Physics / Remote Sensing (iup/ife) at the University of Bremen, Germany). But, the animations are kinda cool. Perhaps someone more qualified than I can comment?

    Visualization of the global distribution of greenhouse gases using satellite measurements, by Michael Buchwitz. The Encyclopedia of Earth. Posted July 31, 2007
    http://www.eoearth.org/article/Visualization_of_the_global_distribution_of_greenhouse_gases_using_satellite_measurements

  41. 41
    Michael Farinha says:

    Is there a statistical breakdown anywhere of what percentage of human behavior causes Global Warming?

    eg.

    Carbon Dioxide
    20% Automobiles
    15% Aircrafts
    30% coal power plants
    … etc

    Methane
    40% Bovine emittance
    20% Something else
    … etc

    Sorry but I’m a complete layman to what most of this site discusses as far as the science. I see a lot of knee-jerk reaction to what ‘we’ should to to combat Global Warming. I think it would be more prudent to at least focus the public on fixing the worst offenders.

  42. 42
    Timothy Chase says:

    Chuck Booth (#37) wrote:

    Visualization of the global distribution of greenhouse gases using satellite measurements, by Michael Buchwitz. The Encyclopedia of Earth. Posted July 31, 2007
    http://www.eoearth.org/article/Visualization_of_the_global_distribution_of_greenhouse_gases_using_satellite_measurements

    You can find more at:

    University of Bremen IUP/IFE SCIAMACHY WFM-DOAS: Main page
    http://www.iup.uni-bremen.de/sciamachy/NIR_NADIR_WFM_DOAS/

  43. 43
    DaveS says:

    Michael F Is there a statistical breakdown anywhere of what percentage of human behavior causes Global Warming?

    How could they answer that when no one even knows how much of the warming is due to CO2 or methane and when there is absolutely no way to account for all of the various feedbacks (notably, of course, including the ones that they haven’t thought of or don’t know about)?

    It would be a bit like asking the hurricane forecasters how many of the 19 named storms last year were due to factor X. Both rely HEAVILY on theoretical models which give ballpark figures, and which, obviously, can be dramatically inaccurate. They’re lucky if they are usably accurate, let alone able to account for the effects of particular trace gases.

  44. 44
    Timothy Chase says:

    George Peabody (#38) wrote:

    Probably off-topic, but I’d like to nominate Timothy Chase’s (#11) “permanent dustbowel in the [U.S.] Southwest” for typo of the month! It suggested a number of perfectly atrocious puns, all of which I was able to resist…

    Much appreciated!

    Unfortunately spelling was never one of my strengths – and my wife tells me that I took German just long enough for it to mangle my English grammar… In contrast, my wife lost a spelling “B” on account of reading too many British novels as a child – but she probably would have done just fine in Great Britain.

  45. 45
    Timothy Chase says:

    RE David York (#34)…

    How about BAU with carbon dioxide buildup partially masked by aerosol-induced global dimming, building climate crisis leading to a major economic recession? No more global dimming – followed by the full effects of several more decades of high levels of CO2 emissions.

  46. 46
    Michael Farinha says:

    I’m not saying to get numbers to show that 10% of x causes global warming. But rather since carbon dioxide, for example, is generally accepted as one of the leading causes of Global Warming we should be able to come up with a somewhat accurate estimate of where all the carbon dioxide comes from.

    I’m not trying to debunk anything. It just gets me when people like Danny Bee say “the world needs to stop all car and plane transport right NOW, for a one year test run,” I shake my head.

    If car & plane transport causes, lets say, 5% of the worlds ‘carbon footprint’ and coal plants are 40% of the carbon footprint. Then focusing solely on cars & planes would be folly.

    [Response: The data are available at the Energy information Administration, and are roughly for CO2 30% power stations, 30% transportation, and 30% industrial and residential. However, you really need to break it down by sector and include the other greenhouse gases – there is a nice graphic of this in a paper I saw recently, I’ll see if I can’t find it and post it here…. – gavin]

  47. 47
    DocMartyn says:

    “This means that there is an upward surface flux of LW around (~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.

    A more useful factor gives ~0.75 ºC/(W/m2).”
    —————————————————————————————–
    From Stefan-Boltzmann we get an Earth temperature with no greenhouse gasses;-

    T4 = [1,368 W/m2 x (0.69)]/4s ; so T = 254 K or -19° Celsius

    So the 150 W/m2 , we calculate that the Earths temperature is 150*0.75 + -19° Celsius. That is the earths average temperature is 93.5° Celsius. However, this is not the case.
    With an average temperature of 15° Celsius, forcing is going to be 15+19/150 ºC/(W/m2) or 0.225 ºC/(W/m2); 2*CO2 could maximally give 5 W/m2 gives a max of 1 ºC.

    ——————————————————————————————

    [Response: You can’t take any value that has the same units as the radiative forcing and multiply it by the sensitivity and expect to get anything sensible. For one thing, the 150 W/m2 net LW absorption includes all feedbacks already, secondly expecting climate sensitivity to be linear from no greenhouse gases to today’s level is rather optimistic. Bottom line, you can’t estimate sensitivity from the mean conditions today – you need to look at a climate change. – gavin]

  48. 48
    Michael Farinha says:

    DaveS –
    How are we as a society supposed to curb our ‘carbon footprint’ if we don’t have at least a moderate grasp as to which parts of our society/lifestyles is to blame? When I see people like Danny Bee suggest “the world needs to stop all car and plane transport right NOW, for a one year test run,” I shake my head. That is not a solution to this problem. If someone were actually able to impose such a restriction I can guarantee you that the death toll across the world from a lack of food and resources would far outweigh any benefit (for mankind) it would cause in the reduction of Global Warming.

    With all the politicking around Global Warming I think it would behoove us to know which culprits to focus our efforts on first. Otherwise it will be like taking a stab in the dark… and we don’t want to stab ourselves in the process.

    Chuck B –
    Thanks for the link but just knowing that the USA is responsible for xx% of greenhouse gases doesn’t help me as a citizen make an informed decision on how I can best help. If you could say, for example, the USA is responsible for 40% of the worlds greenhouse gases with 4% from automobiles, 6% from aircraft, 35% from coal power plants, etc… then I, and society, can focus on the worst offenders first.

    Supposing that my above statistics are correct It would be more prudent for society to rally around reforming our coal power plants more so than around car’s and airplanes.

    I was a business major so my line of thinking is more on a return on investment wavelength. :-) Put most of your effort where you will be most effective.

  49. 49
    N Leaton says:

    My understanding is the CO2 effect is small. It is then amplified by increased water vapour in the atmosphere resulting from the warming caused by the CO2.

    What’s the CO2 effect alone at current CO2 levels in degrees C rise?

    What evidence is there that the amplification only works for CO2 produced warming, and not some other small warming?

    [Response: Feedbacks work for everything. That’s why the ‘radiative forcing’ concept works – it doesn’t matter if the initial push is from greenhouse gases or the sun. The change in temperature you’d need to balance a forcing of 4 W/m2 with no feedbacks is around 1.2 ºC and the difference between that and the real sensitivity (around 3 ºC) is a measure of how strong the net feedbacks are. – gavin]

  50. 50
    David B. Benson says:

    Re #48: Michael Farinha — I recommend you follow

    http://biopact.com

    to discover where many billions of $$ are being usefully spent to provide biomass derived energy sources, for the benifit of many peoples.

    You’ll also find that the blog authors have opinions about which strategies are useful and which are less so…


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