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Attribution of 20th Century climate change to CO2

Filed under: — gavin @ 4 October 2006 - (Slovenčina)

The discussion of climate change in public (on blogs, in op-eds etc.) is often completely at odds to the discussion in the scientific community (in papers, at conferences, workshops etc.). In public discussions there is often an emphasis on seemingly simple questions (e.g. the percentage of the current greenhouse effect associated with water vapour) that, at first sight, appear to have profound importance to the question of human effects on climate change. In the scientific community however, discussions about these ‘simple’ questions are often not, and have subtleties that rarely get publicly addressed.

One such question is the percentage of 20th Century warming that can be attributed to CO2 increases. This appears straightforward, but it might be rather surprising to readers that this has neither an obvious definition, nor a precise answer. I will therefore try to explain why.

First of all, ‘attribution’ in the technical sense requires a certain statistical power (i.e. you should be able to rule out alternate explanations with some level of confidence). This is a stricter measure than the word in common parlance would imply (another example of where popular usage and scientific usage of a term might cause confusion). Secondly, attribution (in the technical sense) of an observed climate change is inherently a modelling exercise. Some physical model (of whatever complexity) must be used to link cause and effect – simple statistical correlations between a forcing and a (noisy) response are not sufficient to distinguish between two potential forcings with similar trends. Given that modelling is a rather uncertain business, those uncertainties must be reflected in any eventual attribution. It certainly is an important question whether we can attribute current climate change to anthropogenic forcing – but this is generally done on a probabilistic basis (i.e. anthropogenic climate change has been detected with some high probability and is likely to explain a substantial part of the trends – but with some uncertainty on the exact percentage depending on the methodology used – the IPCC (2001) chapter is good on this subject).

For the case of the global mean temperature however, we have enough modelling experience to have confidence that, to first order, global mean surface temperatures at decadal and longer timescales are a reasonably linear function of the global mean radiative forcings. This result is built in to simple energy balance models, but is confirmed (more or less) by more complex ocean-atmosphere coupled models and our understanding of long term paleo-climate change. With this model implicity in mind, we can switch the original simple question regarding the attribution of the 20th C temperature response to the attribution of the 20th C forcing. That is, what is the percentage attribution of CO2 to the 20th century forcings?

This is a subtly different problem of course. For one, it avoids the ambiguity related to the lags of the temperature response to the forcings (a couple of decades), it assumes that all forcings are created equal and that they add in a linear manner, and removes the impact of internal variability (since that occurs mainly in the response, not the forcings). These subtleties can be addressed (and are in the formal attribution literature), but we’ll skip over that for now.

Next, how can we define the attribution when we have multiple different forcings – some with warming effects, some with cooling effects that togther might cancel out? Imagine 3 forcings, A, B and C, with forcings of +1, +1 and -1 W/m2 respecitively. Given the net forcing of +1, you could simplistically assign 100% of the effect to A or B. That is pretty arbitrary, and so a better procedure would be to stack up all the warming terms on one side (A+B) and assign the atribution based on the contribution to the warming terms i.e. A/(A+B). That gives an attribution to A and B of 50% each, which seems more reasonable. But even this is ambiguous in some circumstances. Imagine that B is actually a net effect of two separate sources (I’ll give an example of this later on), and so B can alternately be written as two forcings, B1 and B2, one of which is 1.5 and the other that is -0.5. Now by our same definition as before, A is responsible for only 40% of the warming despite nothing having changed about understanding of A nor in the totality of the net forcing (which is still +1).

A real world example of this relates to methane and ozone. If you calculate the forcings (see Shindell et al, 2005) of these two gases using their current concentrations, you get about 0.5 W/m2 and 0.4 W/m2 respectively. However, methane and ozone amounts are related through atmospheric chemistry and can be thought of alternatively as being the consquences of emissions of methane and other reactive gases (in particular, NOx and CO). NOx has a net negative effect since it reduces CH4, and thus the direct impact of methane emissions can be thought of as greater (around 0.8 W/m2, with 0.2 from CO, and -0.1 from NOx) . Nothing has actually changed – it is simply an accounting exercise, but the attribution to methane has increased.

Is there any way to calculate an attribution of the warming factors robustly so that the attributions don’t depend on arbitrary redefinitions? Unfortunately no. So we are stuck with an attribution based on the total forcings that can exceed 100%, or an attribution based on warming factors that is not robust to definitional changes. This is the prime reason why this simple-minded calculation is not discussed in the literature very often. In contrast, there is a rich literature of more sophisticated attribution studies that look at patterns of response to various forcings.

Possibly more useful is a categorisation based on a seperation of anthropogenic and natural (solar, volcanic) forcings. This is less susceptible to rearrangements, and so should be less arbitrary and has been preferred for more formal detection and attribution studies (for instance, Stott et al, 2000).

Forcing estimates 1750-2000, Hansen et al, 2005

What does this all mean in practice? Estimated time series of forcings can be found on the GISS website. As estimated by Hansen et al, 2005 (see figure), the total forcing from 1750 to 2000 is about 1.7 W/m2 (it is slightly smaller for 1850 to 2000, but that difference is a minor issue). The biggest warming factors are CO2 (1.5 W/m2), CH4 (0.6 W/m2, including indirect effects), CFCs (0.3), N2O (0.15), O3 (0.3), black carbon (0.8), and solar (0.3), and the important cooling factors are sulphate and nitrate aerosols (~-2.1, including direct and indriect effects), and land use (-0.15). Each of these terms has uncertainty associated with it (a lot for aerosol effects, less for the GHGs). So CO2‘s role compared to the net forcing is about 85% of the effect, but 37% compared to all warming effects. All well-mixed greenhouse gases are 64% of warming effects, and all anthropogenic forcings (everything except solar, volcanic effects have very small trends) are ~80% of the forcings (and are strongly positive). Even if solar trends were doubled, it would still only be less than half of the effect of CO2, and barely a fifth of the total greenhouse gas forcing. If we take account of the uncertainties, the CO2 attribution compared to all warming effects could vary from 30 to 40% perhaps. The headline number therefore depends very much on what you assume.

Recently, Roger Pielke Sr. came up with a (rather improbably precise) value of 26.5% for the CO2 contribution. This was predicated on the enhanced methane forcing mentioned above (though he didn’t remove the ozone effect, which was inconsistent), an unjustified downgrading of the CO2 forcing (from 1.4 to 1.1 W/m2), the addition of an estimated albedo change from remote sensing (but there is no way to assess whether that was either already included (due to aerosol effects), or is a feedback rather than a forcing). A more appropriate re-calculation would give numbers more like those discussed above (i.e. around 30 to 40%).

But this is game anyone can play. If you’re clever (and dishonest) you can take advantage of the fact that many people are unaware that there are cooling factors at all. By showing that B explains all of the net forcing, you can imply that the effect of A is zero since there is nothing apparently left to explain. Crichton has used this in his presentations to imply that because land use and solar have warming impacts (though he’s simply wrong on the land use case), CO2 just can’t have any significant effect (slide 18). Sneaky, eh?

But does the specific percentage attribution really imply much for the future? (i.e. does it matter that CO2 forced 40% or 80% of 20th Century change?). The focus of the debate on CO2 is not wholly predicated on its attribution to past forcing (since concern about CO2 emissions was raised long before human-caused climate change had been clearly detected, let alone attributed), but on its potential for causing large future growth in forcings. CO2 trends are forecast to dominate trends in other components (due in part to the long timescales needed to draw the excess CO2 down into the deep ocean). Indeed, for the last decade, by far the major growth in forcings has come from CO2, and that is unlikely to change in decades to come. The understanding of the physics of greenhouse gases and the accumulation of evidence for GHG-driven climate change is now overwhelming – and much of that information has not yet made it into formal attribution studies – thus scientists on the whole are more sure of the attribution than is reflected in those papers. This is not to say that formal attribution per se is not relevant – it is, especially for dealing with the issue of natural variability, and assessing our ability to correctly explain recent changes as part of an evaluation of future projections. It’s just that precisely knowing the percentage is less important than knowing that that the observed climate change was highly unlikely to be natural.

In summary, I hope I’ve shown that there is too much ambiguity in any exact percentage attribution for it to be particularly relevant, though I don’t suppose that will stop it being discussed. Maybe this provides a bit of context though…

114 Responses to “Attribution of 20th Century climate change to CO2

  1. 101
    Jeff says:

    CO2 levels appear to have risen steadily only since the 1920’s … So what caused the temperature increase from 1900 – 1920’s ? and what caused the temperature DECREASE from 1940 – 1970 … Until you explain either situation forget about convincing anyone that CO2 is the main forcing agent …

  2. 102
    Dan says:

    re: 101. Goodness, all you have to do is type “1940-1970 cooling” in the search box at the top of the page to see the scientific explanation for that cooling trend! Is it that hard to do? Until you make the simple effort to look for clear results to your basic questions, forget about convincing anyone that CO2 is not the main forcing agent.

  3. 103
    Hank Roberts says:

    “Jeff” — what’s your source for your belief that “CO2 levels appear to have risen steadily only since the 1920’s” — you wrote that at 3:40 am ?

    I can’t find a source for that, searching the web. Who’s your source? And, why do you believe your source? Are you looking at a picture or table in a publication? Or did someone you trust tell you that’s a fact?

  4. 104
    David donovan says:


    You could even check out

    It seems more-or-less accurate to me.

  5. 105
    Hank Roberts says:

    I don’t find Stocker with the search tool; has this been discussed?

    Broecker, W.S., T.F. Stocker, 2006, The Holocene CO2 rise: Anthropogenic or natural? EOS Transactions of the American Geophysical Union 87, 27-29. PDF (0.4 MB)

  6. 106
    Jack Cregan (Layman) says:

    This is perhaps a little off-topic, but I would very much appreciate a response.

    If the level of our emissions of carbon dioxide does not fall below the biosphere’s capacity to absorb it, is there any way that the concentration of carbon dioxide in the atmosphere can fall?

    The 2001 IPCC Report states that carbon dioxide stays in the atmosphere for around 200 years. What happens to it after that?

    My reason for asking these questions is that, in his latest book – “Heat: How to stop the planet burning” – George Monbiot tells us that the current concentration of greenhouse gases in the atmosphere is a carbon dioxide equivalent of 440 or 450ppm, as well as asserting (based on research from the Potsdam ICI) that this concentration must not exceed 440ppm in 2030 if we are to stand a good chance of avoiding a 2 degrees centrigrade rise in the average global temperature.

    With my very basic understanding of the issues, if what he says is true it would seem to me that – to avoid a 2 degree rise – we cannot afford to emit any more carbon dioxide than the biosphere will absorb, and we may need to emit less than it will absorb. Monbiot proposes nothing so drastic.

    Am I missing something?

    [Response: See – gavin]

  7. 107
    Lawrie Boxall says:

    Dear Gavin
    As a layman I would appreciate your comments on the opinions of Lubos Motl on his Physics Blog which I reproduce below – specifically that the forcing response of CO2 has a reducing (1-exp) component.

    Motl says this:
    You should realize that the carbon dioxide only absorbs the infrared radiation at certain frequencies, and it can only absorb the maximum of 100% of the radiation at these frequencies. By this comment, I want to point out that the “forcing” – the expected additive shift of the terrestrial equilibrium temperature – is not a linear function of the carbon dioxide concentration. Instead, the additional greenhouse effect becomes increasingly unimportant as the concentration increases: the expected temperature increase for a single frequency is something like

    1.5 ( 1 – exp[-(concentration-280)/200 ppm] ) Celsius

    The decreasing exponential tells you how much radiation at the critical frequencies is able to penetrate through the carbon dioxide and leave the planet. The numbers in the formula above are not completely accurate and the precise exponential form is not quite robust either but the qualitative message is reliable. When the concentration increases, additional CO2 becomes less and less important.

    The formula above simply does not allow you more than 1.5 Celsius degrees of warming from the CO2 greenhouse effect. Similar formulae based on the Arrhenius’ law predicts a decrease of the derivative “d Temperature / d Concentration” to be just a power law – not exponential decrease – but it is still a decrease.

    He goes on to say:

    When you substitute the concentration of 560 ppm (parts per million), you obtain something like 1 Celsius degree increase relatively to the pre-industrial era. But even if you plug in the current concentration of 380 ppm, you obtain about 0.76 Celsius degrees of “global warming”. Although we have only completed about 40% of the proverbial CO2 doubling, we have already achieved about 75% of the warming effect that is expected from such a doubling: the difference is a result of the exponentially suppressed influence of the growing carbon dioxide concentration.

    Many thanks for your time in advance
    Lawrie Boxall

    [Response:If the temperature-CO2 relation were as simple as Lubos suggests, all would indeed be simple. But it isn’t, as he knows full well. That the T-CO2 relation is approximately logarithmic is no surprise, its why future T increases tend to be approximately linear when CO2 increases exponentially – see for example – William]

  8. 108
    Tim Hughes says:

    moderator – this is actually about another article “Tropical Glacier Retreat”

    I regard myself as a skeptic, but I don’t have a “skeptic press”, and grouping me in with people whose work I have never even read is slightly offensive.

    ANyway, I thought all scientists were skeptics and skeptics are your friends.

    My thoughts are that it would be better if your articles did not mention works that you disapprove of, as they are not relevant. Perhaps you should have articles devoted just to those works that you disapprove of.

  9. 109
    Blair Dowden says:

    Re #107: I think there is some confusion here between the direct radiative effect of adding carbon dioxide to the atmosphere, and actual effect felt on Earth because of various feedbacks.

    Lubos correctly points out (confirmed by William) that the effect of greenhouse gases, including carbon dioxide, is logarithmic. That means each doubling of greenhouse gas levels produces the same forcing (ie. rise in temperature). It does not mean the greenhouse effect is limited to 1.5 degrees – it seems our physicist is incapable of elementary math.

    He does (sort of) correctly state that the direct forcing due to a doubling of carbon dioxide is 1 degree (actually 1.2 degrees C). He leaves out the fact that feedbacks will amplify this by a factor of two or there (exactly how much is called “climate sensitivity”, and is still a matter of debate). So the amount of warming so far includes these feedbacks, and is not inconsistent with current theory. The future warming from more carbon dioxide that will be “exponentially suppressed” is relatively small.

    His implication that the potential for greenhouse warming is almost all used up makes no sense. There have been much higher levels of carbon dioxide and global temperatures in the distant past, which would not be possible if he was correct.

  10. 110
    Tom Fiddaman says:

    Re 107, 109

    Actually Lubos incorrectly points out the logarithmic effect, because he concludes that at 380ppm ~75% of the 2x effect has been achieved. Using his own formula, it’s 52%, not 75%, unless there’s a typo. If you calculate it logarithmically, LN(380/280)/LN(560/280) = 44%.

    Second, the language is misleading. Most will read “75% of the warming effect” as 75% of the temperature change, when in fact it’s only 75% (or 44-52%) of the direct forcing that’s been achieved. Taking account of the large thermal mass of the system, the temperature change seen today is an even smaller fraction of the potential, even if you don’t believe in feedbacks (as he apparently does not).

  11. 111
    Blair Dowden says:

    Re #110: Well, Tom, he correctly says the effect is logarithmic but incorrectly calculates it. The language is certainly and deliberately misleading. By my calculation, before any feedbacks, a CO2 rise from 270 ppm (the pre-industrial level) to 370 ppm (near today’s levels) gives a forcing of 0.45 degrees, while a rise from 440 ppm to 540 ppm (double pre-industrial levels) gives 0.29 degrees. So it is less, but it does not vanish into nothing as Lubos claims.

    You are right that thermal inertia is delaying the effect of the greenhouse gas increases so far. But that will continue to be the case as long as greenhouse gas levels are increasing.

  12. 112

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