The difference between the northern and southern hemisphere aa indices. The upper two panels are for the classic aa indices, the bottom two panels after correction for secular geomagnetic drift and division by the station sensitivity factors. The left-hand panels are for 3-hourly values, the right-hand panels are for daily means. In each panel the number of samples N is colour-coded as a function of the southern index value (vertical axis) and the northern index value (horizontal axis) and the mauve line is the ideal case where the two are the same for all samples. Note that pixel sizes are increased logarithmically with increased index values. (a) 3-hourly values of classic aa indices, aa _N and aa _S. (b) Daily means of classic aa indices, Aa _N = 〈aa _N〉 _τ=1 day and Aa _S = 〈aa _S〉 _τ=1 day (c) Corrected 3-hourly indices, aa _HN and aa _HS derived using equations (6)–(9). (d) Daily means of corrected indices Aa _HN = 〈aa _HN〉_τ=1 day and Aa _HS = 〈aa _HN〉_τ=1 day. Each panel gives the correlation coefficient, r, between the full sequence (1868–2017) of northern and southern hemisphere values and the r.m.s. fractional deviation of the two from the aa value, δ. For aa _N and aa _S, r is 0.66 and δ is 0.53; for aa _HN and aa _HS, r is increased to 0.79 and δ reduced to 0.45. For Aa _N and Aa _S, r is 0.92 and δ is 0.28; for Aa _HN and Aa _HS, r is (very slightly) increased to 0.93 and δ reduced to 0.22. Note the quantised nature of the classic aa _N and aa _S values in (a), but also the splitting of the allowed values caused by the use of scaling factors to intercalibrate the stations.