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. 


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.