STATISTICS OF THE LARGEST GEOMAGNETIC STORMS PER SOLAR-CYCLE (1844-1993)

A previous application of extreme-value statistics to the first, secon d 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 i ndex, rather than the half-daily aa index used previously. Values of t he conventional aa index (1868-1993), supplemented by the Helsinki Ak index (1844-1880), provide an almost continuous, and largely homogeneo us, daily measure of geomagnetic activity over an interval of 150 year s. As in the earlier investigation, analytic expressions giving the pr obabilities of the three greatest storms (extreme values) per solar cy cle, as continuous functions of storm magnitude (aa), are obtained by least-squares fitting of the observations to the appropriate theoretic al 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. Si nce the Ale index may not provide an entirely homogeneous extension of the aa index, the statistical analysis is performed separately for tw elve solar cycles (1868-1993), as well as nine solar cycles (1868-1967 ). The results are utilized to determine the expected ranges of the ex treme values as a function of the number of solar cycles. For fourteen solar cycles, the expected ranges of the daily aa index for the first , second and third largest geomagnetic storms per solar cycle decrease monotonically in magnitude, contrary to the situation for the half-da ily a index over nine solar cycles. The observed range of the first ex treme daily aa index for fourteen solar cycles is 159-352 nT and for t welve salar cycles is 215-352 nT. In a group of 100 solar cycles the e xpected 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 cond ition aa < 550 for the largest geomagnetic storm in the next 100 solar cycles. The statistical analysis is used to infer that remarkable con jugate auroral observations on the night of 16 September 1770, which w ere recorded during the first voyage of Captain Cook to Australia, occ urred during an intense geomagnetic storm.