Statistics of the largest geomagnetic storms per solar cycle ( 1844 ± 1993 )

A previous application of extreme-value statistics to the ®rst, second and third largest geomagnetic storms per solar cycle for nine solar cycles is extended to fourteen solar cycles (1844±1993). The intensity of a geomagnetic storm is measured by the magnitude of the daily aa index, rather than the half-daily aa index used previously. Values of the conventional aa index (1868± 1993), supplemented by the Helsinki Ak index (1844± 1880), provide an almost continuous, and largely homogeneous, daily measure of geomagnetic activity over an interval of 150 years. As in the earlier investigation, analytic expressions giving the probabilities of the three greatest storms (extreme values) per solar cycle, as continuous functions of storm magnitude (aa), are obtained by least-squares ®tting of the observations to the appropriate theoretical extreme-value probability functions. These expressions are used to obtain the statistical characteristics of the extreme values; namely, the mode, median, mean, standard deviation and relative dispersion. Since the Ak index may not provide an entirely homogeneous extension of the aa index, the statistical analysis is performed separately for twelve solar cycles (1868±1993), as well as nine solar cycles (1868±1967). The results are utilized to determine the expected ranges of the extreme values as a function of the number of solar cycles. For fourteen solar cycles, the expected ranges of the daily aa index for the ®rst, second and third largest geomagnetic storms per solar cycle decrease monotonically in magnitude, contrary to the situation for the half-daily aa index over nine solar cycles. The observed range of the ®rst extreme daily aa index for fourteen solar cycles is 159±352 nT and for twelve solar cycles is 215±352 nT. In a group of 100 solar cycles the expected ranges are expanded to 137±539 and 177±511 nT, which represent increases of 108% and 144% in the respective ranges. Thus there is at least a 99% probability that the daily aa index will satisfy the condition aa < 550 for the largest geomagnetic storm in the next 100 solar cycles. The statistical analysis is used to infer that remarkable conjugate auroral observations on the night of 16 September 1770, which were recorded during the ®rst voyage of Captain Cook to Australia, occurred during an intense geomagnetic storm.