CO2 is a trace gas, but what does that mean?

Carbon dioxide, methane, nitrous oxide and most other long-lived greenhouse gases (i.e., barring short-lived water vapour), are considered ‘trace gases’ because their concentration in the atmosphere is so low. For instance, at a current level of 389 parts per million, CO2 represents just 0.0389% of the air, by volume. Tiny isn’t it? How could such a small amount of gas possibly be important?

This issue is often raised by media commentators like Alan Jones, Howard Sattler, Gary Hardgrave and others, when arguing that fossil fuel emissions are irrelevant for climate change. For instance, check out the Media Watch ABC TV story (11 minute video and transcript) called “Balancing a hot debate“.

I’ve seen lots of analogies drawn, in an attempt to explain the importance of trace greenhouse gases. One common one is to point out that a tiny amount of cynanide, if ingested, will kill you. Sometimes a little of a substance can have a big impact.  But actually, there’s a better way to get people to understand, and that’s to follow one of the guiding principles of this blog: “Show me the numbers!“.

In response to a recent post by John Cook on George Pell, religion and climate change, commenter Glenn Tamblyn pointed out an interesting fact: Every cubic metre of air contains roughly 10,000,000,000,000,000,000,000 molecules of CO2. In scientific notation, this is 1022 — a rather large number.

A cubic metre is 1000 litres, which is not really that much air:

It’s simple enough to verify this figure. One mole of an ideal gas at standard room temperature and pressure occupies 22.4 litres. A mole, for those not familar with chemistry, is defined as follows:

The mole is a unit of measurement used in chemistry to express amounts of a chemical substance, defined as an amount of a substance that contains as many elementary entities (e.g., atoms, molecules, ions, electrons) as there are atoms in 12 grams of pure carbon-12 (12C), the isotope of carbon with atomic weight 12. This corresponds to a value of 6.022142 × 1023 elementary entities of that substance [Avagadro’s number]. It is one of the base units in the International System of Units, and has the unit symbol mol.

So, 1 cubic metre contains 44.64 moles of gas, of which 0.0389% is CO2 = 0.0174 moles = 10,458,094,447,812,500,000,000 molecules of CO2. We have a match!

Finally, let’s try to get a feel for just how large a number this is. You can write 1022 in words as a ten billion trillion molecules (0r 10 million quadrillion if you prefer).

The number of stars within the 14-billion-light-year radius of the visible universe (Hubble volume) is estimated to be thirty billion trillion (click on image above), i.e., 3 x 1022. Thus, a mere 3 cubic metres of air, which would sit comfortably on most dining tables, contains as many CO2 molecules as there are stars in the vast span of the visible Universe (which includes an estimated 350 billion galaxies the size of our Milky Way spiral, as well as another 7,000 billion dwarf galaxies similar to the Small Magellanic Cloud).

Bearing these mind-boggling numbers in mind, it’s perhaps not quite so hard to understand how trace atmospheric gases in our atmosphere really do a good job at intercepting infrared radiation. Don’t you think?

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55 Comments

  1. In reply to a bare-faced assertion of falsehood, we can afford to make a bare-faced assertion of truth. If the tone is bullying, we match the non-verbals. I find that the text itself has best impact as short sound-bites, but it must be of un-arguable truth.

    For example, “CO2 is only a few parts per million” can be countered with –
    “It’s six kilos per square metre of sky … ”

    and then if you can still be heard above the bellowing,
    “… blocking heat escape into space”

    Those few words may be that the bystanders can absorb, but the matching of intimidation with righteousness goes a long way, too. Check out David Karoly’s style of delivery.

  2. Take a sheet of window glass.
    Look through it the usual way.
    Pretty clear.
    Now hold it edge on and look through it.
    Kind of dark green and dim.
    There are trace amounts in clear glass that absorb some visible wavelengths. What you see is what gets through.

    Now look through the atmosphere the usual way.
    Now look through the atmosphere toward the horizon.

    The conclusion can be reached by almost anyone from this point.

  3. No, it’s not. Read here about scientific notation, Charlie.

    To get to the most basic level, what is meant by a power of 10? Simply put, it is a number that can be arrived at by multiplying 10’s together. Such numbers can be written in the form 10^n, where n is the (integer) number of 10’s used as factors. Thus

    10^3 = 10 x 10 x 10 = 1000.

    Note that 10^n can be written as a 1 followed by n zeros.

  4. @Barry: where did you get the 6 kg of CO2 per square metre of sky?”

    The current value is 391 ppm by volume, that is, in molar proportion. The weight of the atmosphere at sea level is 101.3 N/m2, in round terms 10 tonnes per square metre. Taking the molecular weight of air as 28.5 and CO2 as 44, 391/10^6*44/28.5*10^4 =6.0 kg/m2

    When I have an audience of somebody actually wanting to know, I find it evocative at this point to gesture at the square metre on which I’m standing and then gesture upwards into the cold sky. “If it wasn’t for the usual 4.5 kg/m2 of CO2 in the way, we would be downright cold. However industrial man has put an extra 1.5 kg/m2 in the way of heat escaping, so you and I are going to get hotter.”

    Brief though that explanation is, it is not the soundbite needed to slip in while a denier gasps for breath between shouts. I often add…

    “… and it’s worsening at 30 grams per year! “

  5. Further to Roger Clifton’s comment – 6kg of CO2 at standard temperature & pressure would make a layer of pure CO2 2.1 metres thick over that 1m2 patch of surface.

    Given the existence of abundant demonstrations that CO2 at STP can completely block IR radiation (such as this video, using a tube about 1m long: http://www.youtube.com/watch?v=Ot5n9m4whaw ) then there *shouldn’t* be any argument about this…

  6. Here’s another way … the recommended intake of B12 is about 2 micrograms per day. If you don’t get it, you get sick. If you don’t get it for long enough, very sick. For a person eating half a kilo a day of food, this is 4 parts per billion :) (2e-6/500). Small things can
    indeed have big impacts.

  7. Karl-Friedrich Lenz, cesium-137 is not a good choice. What you want is a very short-lived isotope, that is an alpha emitter and that is well absorbed by the body.

    Cesium-137 has a 30 year half-life and it’s a gamma emitter; that’s no good.

    Various plutonium isotopes have half-lives in the tens of thousands of years and only 10^-4 to 10^-5 of it is absorbed by the stomach lining.

    What you want is something like polonium-210; which is a short-lived alpha emitter and easily absorbed if ingested. The median lethal dose for polonium-210 has been calculated at 50 ng if ingested; Litvinenko got 10 mg.

  8. @Soylent

    “Litvinenko got 10 mg.”

    With 100 g of food, that would amount to 100 ppm. So yes, that would be another “trace element” you would not want there.

    And 10 mg is overkill, the 50 ng median lethal dose would amount to 0.0005 ppm of 100 g of food. Not in the same range as 389 ppm.

    Cesium would probably be a good choice independent of how dangerous it actually is because most people don’t know about actual danger levels and freak out when they hear that word.

    And it probably really is not a good idea to gobble down Cesium in large amounts:

    From the Wikipedia “Cesium” article:

    “Experiments with dogs showed that a single dose of 3.8 millicuries (140 MBq, 4.1 μg of caesium-137) per kilogram is lethal within three weeks;”

    So that would be 328 μg of Cesium for someone weighing 80 kg, or 0.328 mg, which is 328 ppm of 1 kg of food.

    Cesium in your lunch might actually work out as a analogy even if taken literally.

    Or to put all that much shorter, if trace elements of CO2 are no reason to worry, what’s the big deal with trace elements of Cesium and Plutonium?
    MODERATOR
    I understand this is a suggested analogy but think we are getting a little off topic here.

  9. @ Bern, Roger

    Further to Roger Clifton’s comment – 6kg of CO2 at standard temperature & pressure would make a layer of pure CO2 2.1 metres thick over that 1m2 patch of surface.

    Meaning that if all CO2 in the atmosphere were condensed, you could (more or less) have a 2.1 metre thick layer of pure CO2 at Earth’s surface, covering the whole planet?

  10. Short lived radionuclides are very toxic, whereas CO2 is hardly toxic at all. I don’t think it is a good analogue. Neither is cyanide for that reason.

    The amount of carbon atoms in your lunch is also huge. So what? Avogadro’s number is just really big. Numbers are only useful when compared in perspective. Tossing big numbers to impress is a common unscientific media ploy.

    The only thing that matters is how much extra solar energy does the emitted CO2 trap in our atmosphere, and what does that do to the climate and weather.

  11. I don’t think we need to get stuck on the denominator of this quantity. There is only one (derived) unit here, kg/m2, not two. I’m mindful of a segment in a movie, where the owner of a brand-new horseless carriage tries to explain to a child, how, in the space of a single hour, this here machine can travel the incredible distance of would-you-believe, forty whole miles. But the elaborate conceptualisation of the adult, struggling with his preconceptions, is wasted on the child, who is quite directly impressed with the sheer speed of the auto.

    Nothing elegant has happened, this is just the power of SI units. We have taken a quantity expressed in the jargon of physical chemistry, which we hold up as a measure of imminent doom, without actually converting it for ourselves. The jargon isn’t ours, and whoever let it out of the laboratory was too damned lazy, or too damned arrogant, to convert it into international units so that outsiders could understand.

    If we try to elaborate on the quantity of “6 kg/m2″ to a modern schoolkid, he or she will think we’re loony. After all, the quantity is expressed in a derivative of familiar units, so there is no deeper meaning than that.

    But let’s go back to the invitation presented in this thread. Let’s discuss tactics defending AGW, for the next occasion when you or I are under attack by the likes of “Alan Jones, Howard Sattler, Gary Hardgrave and others”.

    For example: How would you answer in three seconds, the jibe, “the stuff is natural, plants use it as fertiliser”? Remember, after three seconds, you’ll be shouted down.

  12. @ Tom Keen points out that Bern’s calculation of the CO2 content as equivalent to a layer of 2.1 m of CO2 gas, amounts to a lot when that layer is covering the entire planet.

    That mass of CO2 in the air column makes it difficult for satellite surveillance of CO2 emitters on the ground — but not impossible. The OCO satellite was intended to “play a valuable role in treaty enforcement”. However it crashed in 2009, and I haven’t heard of its replacement yet.

  13. How about this one: “A hundred times more water in the air makes a much stronger GHG than CO2″ is another jibe.

    My suggestion to reply is …
    “… there’s more CO2 than water at the top of the atmosphere…”
    then …
    “… where the heat escapes from …
    and
    “… stratosphere is so dry that water is less than 4 ppmv , but CO2 is still 390-odd ppmv, a hundred times MORE than water…”

  14. @Soylent + @Roger Clifton: your two arguments go against each other, unfortunately. If the total column of GHG matters, as Soylent suggests, water is clearly much more important than CO2. If only the amount in the stratosphere matters, as Roger Clifton suggests, Soylent needs to divide his numbers by 1000 (relative air pressure in stratosphere compared to see level), rather diminishing their impact.

  15. but the climate has always changed, naturally

    My car heats “naturally” every morning and cools every night, but I pay serious attention if it doesn’t stop heating and starts making funny noises.

  16. Zdenek, I don’t see why the whole atmospheric column wouldn’t matter but the situation is obviously not equivalent to a 2 meter blanket of CO2 at 1 bar pressure(e.g. convection would be massively more important in such a tiny column of gas).

    Water is a much more important greenhouse gas than CO2; but it is a feedback, not a forcing. It follows temperature and the residence time for water in the atmosphere is a mere two weeks. You effectively can’t change the water vapour without changing the temperature.

    Without ANY greenhouse gases, not even water vapour; the earth’s average temperature would be about 33 degrees C colder than todays average temperature. It would be an uninhabitable snowball devoid of life.

  17. @Zdenek apparent contradiction…

    The sunlight that we receive has a spectrum that starts in the visible and trails away into the infrared, because the hydrogen, oxygen and nitrogen above that level in the solar atmosphere is transparent to it and opaque to anything harder. Similarly, our atmosphere lets the visible radiation in to heat up the sea and ground and air before it escapes back out into space more slowly, as infrared.

    Because it’s transparent, we can discount nitrogen and oxygen and hydrogen in our own atmosphere. And argon and helium as they too are transparent. The remaining molecules, H2O, CO2, N2O, CH4 etc, have many atoms to wiggle and wriggle and vibrate, so they absorb and emit at different wavelengths across the infrared. The more there is of these gases, the slower heat percolates upwards. That’s the greenhouse effect.

    In the bottom of the atmosphere where we get our weather, water makes up most of the remainder. In wide bands across the infrared, the wet atmosphere appears as we would see a bright white fog, where photons can only so far before they are absorbed again. It’s not that humid areas are getting more heat, is just that they are slower to shed it — upwards.

    But at the very top of the atmosphere there is almost no water at all, so there it is CO2 that dominates the greenhouse effect. There, CO2 absorbs from below and emits in all directions, so the banked-up heat which has trickled its way upwards escapes to space.

    To put that in three seconds: “it’s the cork in the bottle, if the heat can’t get out at the top, we cook at the bottom”

  18. A curly one was tried out on Tim Flannery: “if we all stopped emitting tomorrow, how long would it take to see an effect?”

    (I watched in pain as he tried to answer as if it were an honest question. Of course it wasn’t an honest question, because we wouldn’t see an effect, only the absence of an effect, for the questioner to pounce on and say, so why bother?

    I think an insincere question like this one is better dealt with in the parry-and-thrust style used by turnages, above, which ripostes a rhetorical question.)

    Anyone want to try for a 3-second riposte?

  19. Roger:

    “If you are overweight and want to lose 20 kg to reduce your future health risks, you need to diet for more than a day.”

    That is probably only 3 seconds — one could elaborate on the fact that it will take maybe 6-12 months to achieve your goal, but it doesn’t mean that you shouldn’t start immediately on cutting those kilojoules, as it will make a real difference over time…

  20. @Roger Clifton:

    “The warming’s like a monstrous tanker. It’d take 40 years to stop, another 40 to turn it round.”

    or

    “Well, we’ve dug ourselves a pretty big hole. We need to stop digging, but we also need to climb out.”

  21. Denialist: “But the climate has always changed, naturally!”

    Riposte by Nick Palmer: “Millions of species have been made extinct by prehistoric natural climate changes – is it sane to create a man made version?

    — It sure is crazy. Ian Plimer has said, according to (link) that extinctions are an entirely normal part of the Earth’s evolution. An urgent reply to that one is “sure, but no humans have survived one“.

    I am inclined to say “we are shaped by this environment, and will vanish with its passing“, but I suspect it’s a bit highbrow for the drunken tone we have to match. Perhaps we could paraphrase Douglas Adams , ” we have all the conceit of a puddle, marvelling at a hot wind of our own making”

  22. Denialist: “if we all stopped emitting tomorrow, how long would it take to see an effect?

    @Barry, paraphrased: if you have to lose 20 kg … you’ll have to diet for a lot more than a day.

    Quite right! (However, I imagine myself rehearsing this one over and over, and then slipping it in what seems to be just the right moment — to find that my three seconds of fame has turned into two more seconds of dead silence as all eyes turn towards me and the enormous fat guy I have said it to.)

    @turnages suggested: “warming’s like a monstrous tanker. It’d take 40 years to stop, another 40 to turn it round.”

    Turnages gaves us another good one! Looming juggernaut with an enormous momentum, with helpless humans struggling at the wheel. Instability and its terrible burden could be invoked too: ” if it runs aground and something tips, it will destroy us all”

  23. There’s also the “but man-made CO2-emissions are only 3%[7% etc.] of the total”. Usually decorated with epithets front, middle and center.

    The idea here is that natural sources of CO2, such as the oceans and forests and things, emit a ridiculous amount of CO2, so how can our puny emissions have any impact? But of course, oceans and forests and things also absorb a ridiculous amount of CO2; they are not net emitters of CO2. If you count every molecule of CO2 that leaves solution you get a big meaningless number for the “emissions” of the ocean. If you count all the CO2 emitted by rotting vegetation you get a big meaningless number for the CO2 emitted by of plants. Human emissions may only be a few percent of gross emissions, but gross emissions are meaningless, we are ~150% of net emissions(oceans are a net sink and absorb about a third of the CO2 emitted as they reach an equilibrium with the new CO2 concentration).

    A brief answer to this one is: If you keep spending 3%[7% etc.] more than you earn you will eventually default. The planet is not too big to fail, it is too big to bail out.

  24. (This comment and your two prior to this have been deleted)
    MODERATOR
    As you already know, BNC no longer posts comments from those sceptical of the scientific consensus of AGW/CC. When Barry implemented the new policy you elected to opt out. If you have forgotten the reasoning behind this change to BNC’s agenda please re-read the Comments Policy on the About page.

  25. if we all stopped emitting tomorrow, how long would it take to see an effect?

    The question I think you are referring to and have merely paraphrased is the one which Tim Flannery was asked by Andrew Bolt. Given Bolt asks his question all the time Flannery had every reason to be prepared. Unfortunately it isn’t a question many are prepared to answer seriously. And if you think the question isn’t an honest one then you are kidding yourself. The Bolt question was rated the number one question regarding the carbon tax in an online poll of Age readers.

    The fairest version of the question asks if the world does nothing what will be the temperature difference in 2100 (or some other date) if Australia adopts the carbon tax (or ETS equivalent) versus if we don’t.

    This is not a question about whether AGW is real or otherwise. In fact it assumes AGW is real. It is a question regarding the benefit of one particular action.

    The carbon tax will have costs. It will have benefits. The costs are modest. It is fair enough to ask what the benefits are and to expect experts to embrace that question with seriousness. Yet if you google the question you don’t readily find answers by proponents of the tax, but plenty by opponents. An example calculation by an opponent follows:-

    http://joannenova.com.au/2011/03/carbon-tax-australia-welcome-to-futility-island/

    I have tried to get various bloggers who support the tax to put up their own answers to the question. There are of course reasonable assertions that Australia won’t be acting alone, or that we will move to a higher price later. And these are of course part of the intent. However on the cost side of the ledger extra action will also mean extra costs.

    What the Bolt question says is show us the numbers. It is a fair question. Proponents of the tax that dismiss the question discredit their side of the debate. If the critics have the right number then proponent should make the case why the low number is worth the cost. If the number is wrong then show us better numbers. It really is no different to the argument with wind farm proponents. Numbers, numbers, numbers.

    p.s. I like the kg per sq meters of sky metric and also the video.

    MODERATOR
    Off topic on this thread and likely to divert the discussion back to the carbon tax. Please re-post on the Carbon Tax thread. Commenters please do not reply on this thread.

  26. Barry, can you explain, or direct me to a good introductory level source, that describes how a CO2 molecule traps heat?

    You’ve shown here that there are a lot of molecules per cubic meter air, but for CO2 to make a difference is that it actually traps an IR photon. Suppose that these molecules, although plenty in number, if small enough, appear non-existent to radiation. So, how does a CO2 molecule trap IR? I assume this has something to do with the IR wavelength, dipole molecule structure of CO2 and it’s radius? I guess I’m looking for the IR trapping cross section of a CO2 molecule?

  27. “If we all stopped emitting, how long would it take to see an effect?”

    Thousand years. That’s the time frame global warming is locked into at whatever level of CO2 is reached before stopping.

    Solomon, Irreversible climate change due to carbon dioxide emissions,

    http://k-lenz.de/a013

    And no, that answer is not a reason to think the problem is less urgent.

  28. Barry, I’m sorry if my question was vague or not specific enough (not a native English speaker), but:

    I’ve read the CO2 history by Spencer Weart many times and reference it often. It’s interesting stuff and contains many, many links to literarture. But it doesn’t describe *how* CO2 traps heat and neither does the RealClimate article you link. They only describe the evidence that it does via the band absorption. Weart, RC and Soylent’s link are showing there are plenty of laboratory measurements as well as satellite and landbased measurements that show that CO2 traps heat and more CO2 widens (or deepens) the wings of the absorption bands so that even more IR is trapped.

    I know all that and I’m not trying to deny any of that, in any case you are thinking that. It also isn’t what I was trying to ask you about. Please let my try again:

    Your article explains nicely that a trace gas still involves many molecules per unit air, but molecules are small as are photons, so my question is:
    How do CO2 molecules trap IR photons? Following from that: How big is the IR trapping cross-section of an CO2 molecule and following from that: How far can an IR photon -emitted from the earths surface- travel on average before it is intercepted by a CO2 molecule?

    I’m just trying to complete the argument you set out here and hope you or anyone else can point me to a good source. Thanks.

  29. cynicus, your questions on gas vibrations and stretch/bend of greenhouse gas molecules are explained very well by David Archer, here. CO2 cross-sections for IR are given here: http://vpl.astro.washington.edu/spectra/co2.htm (and this image). The typical wavelength of an IR photon spans 0.74 to 300 micrometres. As this chart shows, water vapor is inactive in the 4 micron region, while CO2 provides 100% absorption at 4.3 microns. CO2 augments the water vapor spectra in the 15 micron region to fully absorb IR. As per above, 1 cubic metre is 10^18 cubic micrometres, containing 10^22 molecules of CO2, or a density of ~10,000 CO2 molecules per cubic micrometre. Thus, there will are plenty of chances for interception of IR by CO2 and other GHGs.

  30. Thanks Barry! That is what I was trying to find (perhaps I should’ve suspected that David Archer would be able to provide the answer).

    Looks like I have some reading to do… :D

    Thanks again.

  31. Barry, don’t forget that the 1 cubic metre contains about 1% water which calculates out to 2.65×10^23 ! Considering that water vapour is responsible for 70% of the known absorption of incoming sunlight, particularly in the infrared region, and about 60% of the atmospheric absorption of thermal radiation so we need to seriously look at ways of reducing water vapour in the atmosphere. Using Mars as an example, it has an atmosphere containing 95% CO2 but contains little water vapour and look, no problem with runaway warming !

  32. Gordon, yes, of course water vapour is an important GHG. No doubt, as I mentioned in my response to cynicus. However, it is a feedback (a very important one), but not a forcing. Without the long-lived GHGs, the water vapour would rain/snow out of the atmosphere (and not return) within days.

  33. Just clarifying for any student readers – infrared light of certain wavelengths is very strongly absorbed by CO2 in the atmosphere. Water and ozone absorb at other wavelengths. (See: transmission spectrum)

    However infrared light at wavelengths in between these are able to penetrate right through the atmosphere. Satellites that look back at the earth, such as Landsat 8 make imagesof the Earth using this light.

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