Attribution of 20th Century climate change to CO₂

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).

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…