The true meaning of numbers

Gavin has already discussed John Christy’s misleading graph earlier in 2016, however, since the end of 2016, there has been a surge in interest in this graph in Norway amongst people who try to diminish the role of anthropogenic global warming.

I think this graph is warranted some extra comments in addition to Gavin’s points because it is flawed on more counts beyond those that he has already discussed. In fact, those using this graph to judge climate models reveal an elementary lack of understanding of climate data.

Fig. 1. Example of Christy’s flawed evaluation taken from Comparing models to the satellite datasets.

Different types of numbers

The upper left panel in Fig. 1 shows that Christy compared the average of 102 climate model simulations with temperature from satellite measurements (average of three different analyses) and weather balloons (average of two analyses). This is a flawed comparison because it compares a statistical parameter with a variable.

A parameter, such as the mean (also referred to as the ‘average’) and the standard deviation, describe the statistical distribution of a given variable. However, such parameters are not equivalent to the variable they describe.

The comparison between the average of model runs and observations is surprising, because it is clearly incorrect from elementary statistics (This is similar statistics-confusion as the flaw found in the Douglass et al. (2007)).

I can illustrate this with an example: Fig. 2 shows 108 different model simulations of the global mean temperature (from the CMIP5 experiment). The thick black line shows the average of all the model runs (the ‘multi-model ensemble’).

Global mean temperature from ensemble simulations (CMIP5) and the HadCRUT4 (baseline: 1961-90).

Fig. 2. Global mean temperature from ensemble simulations (CMIP5) and the NCEP/NCAR reanalysis 1 (baseline: 1961-90). (Figure source code)

None of the individual runs (coloured thin curves) match the mean (thick black curve), and if I were to use the same logic as Christy, I could incorrectly claim that the average is inconsistent with the individual runs because of their different characters. But the average is based on all these individual runs. Hence, this type of logic is obviously flawed.

To be fair, the observations shown in Cristy’s graph were also based on averages, although of a small set of analyses. This does not improve the case because all the satellite data are based on the same measurements and only differ in terms of synthesis and choices made in the analyses (they are highly correlated, as we will see later on).

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