The AR4 attribution statement
Second, the IPCC statement is not a declaration about what the most likely value of ‘x’ is. It states merely that P(x> 50%) is at least 0.9. In the two figures, one has the mean value of x at 80%, while the other has the mean value at 100%. Both fit the IPCC statement equally well. Some people have interpreted the IPCC statement confusing the likelihood of the statement with the actual relative trend (i.e. that the 90% refers to the expected attribution), but that would be a big misreading of the text.
Third, there is certainly a potential for the increase in temperatures due to anthropogenic GHG changes to be greater than the observed trend because we know that there have been both natural (volcanic and solar) and human-caused (reflective aerosols, land use change) factors that are expected to have lead to cooling over the post-1950 period (therefore there is no cut off at 95% of the actual trend). The actual trend will be a function of the warming factors, balanced by the cooling factors. And of the warming factors, the well-mixed greenhouse gas (CO_{2}, CH_{4}, N_{2}O, CFCs) changes are the dominant term (about 75% of the increase in warming factors from 1950, the rest is related to black carbon effects, ozone etc.).
Fourth, the statement clearly encompasses many different estimates of what the actual trends are being driven by and is not therefore a particularly strong conclusion. Myles Allen (Allen, 2011) points out that during the drafting, the text was changed from ‘contributed substantially’ to ‘most’, and focused on greenhouse gases rather than the total anthropogenic effect specifically in order to have a more quantitative conclusion and more justifiable statement.
Now let’s put some real numbers in here. Attribution is fundamentally a modelling task, and the principal models that can be used are the coupled GCMs – at least to start with. What do they estimate the warming trend from the well-mixed GHGs to have been over the last 50 years? The figure below shows this for some of the GISS CMIP5 models (more model data can be downloaded from CMIP5 portal):
The 50 year trends (here, from 1956 to 2005, 5 ensemble members), are 0.84ºC (range [0.79,0.92]) for just greenhouse gas forcing. and 0.67ºC (range [0.54,0.76]) for the all-forcings case (in CMIP3, the envelope of the all-forcing trends is [0.4,1.3], or equivalently 0.74 +/- 0.22ºC (1 sigma spread) using 55 individual model simulations – the wider spread reflecting structural variations in the models and forcings). As in the more recent model simulations, the GISS CMIP3 50 year trends using only well-mixed GHG forcings is around 0.1ºC more than the ‘all-forcing’ case (data here).
The actual observed trend depends a little on the dataset used, but is around 0.6 +/- 0.05ºC (1 sigma uncertainty in the OLS fit). If we then estimate the percentage (as illustrated above), assuming a 0.2ºC sigma in the model spread, ‘x’ is roughly 140% +/- 35% (1 sigma). If we interpreted that range as a Gaussian distribution (not really a good idea, but simple enough for illustration), we’d estimate that P(x<50%) would be less than 1% (even less likely than the IPCC AR4 statement allowed for).
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References
- M. Allen, " In defense of the traditional null hypothesis: remarks on the Trenberth and Curry WIREs opinion articles ", WIREs Clim Change, vol. 2, pp. 931-934, 2011. http://dx.doi.org/10.1002/wcc.145