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Fig. 9

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Variation of the fraction fp of daily means of in one year that are in the top 5% (solid points) and top 1% (open triangles) of all the 12198 available daily means of for the interval 1964–2016, shown as a function of the annual mean (〈τ=1yr/Po). These data use the optimum α of 0.53. The annual fraction fp[〈τ=1day ≥ pc] is shown for two fixed thresholds: pc = 2.38Po (which defines the 95th percentile of the cumulative probability distribution of all available 〈τ=1day values from the interval 1964–2016 which number 12198); and pc = 3.77Po (which defines the 99th percentile of the same cdf). Points for these two thresholds are shown by solid circles and open triangles, respectively. Only the 31 years in which data availability f exceeds 50% are shown which account for 10186 samples out of the available total of 12198 (the other years show the same trend but the smaller number of samples increases the scatter). The solid line is a third order polynomial fit to the data points for pc = 2.38Po and the dashed line is that for pc = 3.77Po. Both reveal that fp shows an increasing trend with the annual mean value, but it is not, in general, linear. The smaller numbers associated with higher percentiles of the cdf mean that the scatter is increased.

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