How robust is Figure 10 in AR5-SPM ?

The new AR5 iconic graph is Figure 10 in the Summary for Policy Makers.   Myles Allen appeared on the BBC with 10 lumps of coal on a table to explain how we had already burned 5 of them leaving  just  5 left to burn if we want to avoid a catastrophe. It is a simple powerful message understandable by policy makers – but is it actually correct ?

Fig 10 from SPM. The Hadcrut4 data points are shown in cyan. CO2 is taken from Mauna Loa data and scaled up by 2.3 to because 43% of anthropogenic emissions remain in atmosphere. Gtons of anthropogenic CO2 are calculated relative to 1850. The blue curve is a logarithmic fit to the data because CO2 forcing is known to depend on the logarithm of CO2 concentration.

Figure 1: Overlayed on figure 10 from the SPM are Hadcrut4 data points shown in cyan where  CO2 is taken from Mauna Loa data.  Gtons of anthropogenic CO2 are calculated relative to 1850 and scaled up by a factor 2.3 because 43% of anthropogenic emissions remain in atmosphere. The blue curve is a logarithmic fit to the Hadcrut4 data. This is  because CO2 forcing is known to depend on the logarithm of CO2 concentration and is certainly not linear.  This is derived in Radiative forcing of CO2

Figure 2: A clearer version of the comparison with Figure 10 is this one taken from the slides of the cabinet presentation by Prof. Walport. The overlay with the data is good showing consistency of carbon counting. I left out many of the 19th century points due to poor knowledge of CO2 levels.

Figure 2: A clearer version of the comparison with Figure 10 is this one taken from the slides of the cabinet presentation made by Prof. Walport. The overlay with the data is good showing consistency of carbon counting between my data and AR5. I left out many of the 19th century points due to poor knowledge of CO2 levels. Overlaid at the point where doubling of CO2 in the atmosphere since 1850 occurs (560ppm) are the “extremely confident” estimates from AR5 of ECS and TCR.

When I saw the graph from Fig 10. I thought there must be a mistake because it showed that all RCP emission scenarios simulated by  CMIP5 models result in a simple linear dependence on anthropogenic CO2. This cannot be correct because it is well known  that CO2 radiative forcing increases logarithmically with concentration – not linearly.  So I decided to investigate.

The novel feature of the SPM  presentation is that the x-axis is not time but instead cumulative anthropogenic carbon emissions. Different emission scenarios result in different lengths along essentially the same trajectory. I therefore took the HADCRUT4 annual temperature anomalies scaled to 1860 -1880 and smoothed CO2 concentrations from Mauna Loa in order to map the temperature data onto Gtons of increase of atmospheric CO2 since 1850. It also well known that just 43% of anthropogenic emissions remain airborne annually in the atmosphere, so the actual carbon emissions by man are a factor 2.3 higher  than those inferred from CO2 data.

The resultant temperature anomalies are plotted in cyan in figure 1 and purple in figure 2. Previously I have shown that  a good fit to the last 163 years of temperature data can be made with logarithmic and natural variability. A logarithmic temperature dependence for TCR is to be expected because CO2 forcing increases logarithmically and temperature is a response to forcing. Therefore I made a new fit to the data as a function of Gtons of CO2. This fit is shown in blue and I maintain that this is a more realistic extrapolation into the future than  linear projections.  Even with the most pessimistic emission scenarios RCP8.5 temperatures remain at most ~2C in 2100.

The real intention of this plot seems to have been  more  political than scientific. It draws the viewer onto the scary red linear line and does not show any of the large uncertainty in the models highlighted elsewhere in the WG1.  Compare it for example with AR5 Figure 1.4 showing huge  uncertainties.  It is also incompatible with its own statements regarding climate sensitivity especially TCR:

ECS is likely between 1.5°C to 4.5°C (medium confidence) and extremely unlikely less than 1.0°C”

This assessment concludes with high confidence that the transient climate response (TCR) is likely in the range 1°C to 2.5°C

The TCR limits are shown overlaid on Figure 1. Both TCR and ECS limits are shown in figure 2.

In my opinion the graph is not scientifically correct because a) it hides model uncertainties and b) it portrays a linear dependence on carbon emissions whereas it should logically be logarithmic.

Update: Frank points out correctly that my fit to the Hadcrut4 data really only applies to transient climate response(TCR). It is not clear whether the IPCC projections are for equilibrium temperature after 2100 or the transient temperatures at 2100. If the former then my curve would rise up around 30% but it would still be logarithmic.

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