Comment on AR5’s FAQ2.2 Figure 1

While studying the IPCC 5^th assessment report AR5, the author noted FAQ2.2 Figure 1 that was used to argue warm days and nights have increased and cold days and nights have decreased for period 1981-2010 as compared with period 1951-1980. 

Firstly, the figure has obviously misplaced major tick numbers of “10” and “5” for the abscissa; supposedly this is a simple typo.

Secondly, label for the ordinate “Probability” does not appear correct.  It should be “Probability Density.”  Label “Probability” is correct for discrete probability graphs, which are usually displayed using bar graphs.  The graphs in Figure 1 are all in a fashion of continuous probability distribution function.  Probability for any interval is expressed by the area size under the probability density curve over the interval.  The X-axis is of temperature anomaly (°C) instead of the Z-values, a more precise label for the Y-axis in this case can be “Probability Density (1/°C)”.

Thirdly, we know logically that: for discrete probability bar graphs, summing up all the probability numbers leads to 1; for continuous probability curve graphs, total area size under the probability density curve must equal 1.

The graphs in FAQ2.2 Figure 1 were digitised, and area size under the graphs was integrated.  The area size is found to be an illogical number approximately 0.5 instead of 1.0.  An example with the graph for 1951-1980 daily minimum temperature is shown in the figure below.  This fact shows that there must be something incorrect in data handling and/or production of the graphs.