(Left) Cumulative probability distributions (c.d.f.s) of indices and (right) scatter plots of uncorrected and corrected 3-hourly values. (a) c.d.f.s of classic aa indices aa _N (in red), aa _S (in blue), and aa (in black): the steps for the hemispheric indices show their quasi-quantised nature and note that larger southern hemisphere values are consistently more common than northern hemisphere values for aa < 58 nT, but the opposite is true for aa > 58nT. (b) Scatter plots of aa _HN against aa _N (red points) and of aa _HS against aa _S (blue points). (c) c.d.f.s of corrected aa indices aa _HN (in red), aa _HS (in blue), and aa _H (in black). (d) Scatter plot of aa _H against aa.