Scatter plots for 1996–2017 (inclusive) of the mid-latitude range indices with the maximum of the SME index, SME_max, seen in the same 3-hour intervals by the SuperMAG global magnetometer network. (a) (grey) 3-hourly SME_max values as a function of 3-hourly am and (orange) 24-hour running means of SME_max as a function of corresponding running means of am, Am*. Black dots are means in 1-percentile ranges of Am* (giving 614 samples in each bin) and the horizontal and vertical error bars are ±1 standard deviation. The mauve line is a fourth-order polynomial fit to the 3-hourly values. The RMS deviation of the observed 3-hourly SME_max values from the fitted polynomial value for the corresponding am, Δ_RMS is given, as is the correlation coefficient r between 3-hourly SME_max and am values. (b) The same as (a) for 3-hourly ap and its 24-hour running mean, Ap*. (c) The same as (a) for 3-hourly aa and its 24-hour running mean, Aa*. In each panel the cyan line is a linear fit to the 3-hourly values for SME_max < 750 nT, and is plotted to gauge the deviation from linearity of the data for larger SME_max.