A. Are the IPCC Projections Accurate?

The IPCC in its 2013 Assessment Report gave numerous projections of temperatures and CO2 content under various scenarios.  The table below displays the temperature anomaly (°C), the actual temperature (°K), and the CO2 concentration in ppmv.   Table 4 below is a presentation of the data taken from the IPCC Figure 12.40 at page 1100 and Figure 12.42 on page 1103 using RCP8.5 for the business as usual scenario. 

Figure-CC-Table4

With this data, the numbers were plotted on a graph and an equation generated matching the data with a particular curve.  This is shown in Figure 2 in Section B below.  The best equation that fits the curve based on the above data is set forth as:

Y = 5.9906 ln(x) +251.35.

Where Y is the temperature in degrees Kelvin and X is the CO2 concentration in ppmv.  The curve fits the data with a remarkable 99.73% R squared relationship.  R squared is a measure of the precision that the two plotted variables are the only variables, i.e. a 100% R squared means that the X variable and Y variable are the only variables.  A 99.73% R squared is exceptional and eliminates essentially all but temperature and CO2. 

Because the above formula is not 100% exact match, it is likely there is a very minor variable missing.  It is possible that the IPCC formula was modified to include a minor effect from other greenhouse gases such as methane, nitrous oxides etc.   As shown in Question 9, section A, the concentration of these other greenhouse gases is less than 1 percent of CO2, i.e. 0.49%.  This is a possible reason why the above equation was not a 100% fit.