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

Abstract

Abstract. 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 `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.

Supermagnetic Storms: Hazard to Society

“…One can therefore assign accurate probabilities to flares and storms for only the lower energies where the number of observed events is statistically significant. Willis et al [1997] have applied extreme-value statistics to the first, second, and third largest geomagnetic storms per solar cycle for 14 solar cycles (1844-1993) using the daily aa index. They predict 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.…”

Long-term biases in geomagnetic &lt;i&gt;K&lt;/i&gt; and &lt;i&gt;aa&lt;/i&gt; indices

“…Love (jlove@usgs.gov) The aa index has been widely used in the analysis of a number of inter-related issues, including: (1) magnetic-storm occurrence statistics and time-series analysis (Courtillot et al, 1977;Gonzalez et al, 1990;Willis et al, 1997), (2) spaceweather hazards (Boteler et al, 1998;Thomson et al, 2010), (3) solar-terrestrial interaction (Russell, 1975;Legrand and Simon, 1989;Pulkkinen et al, 2001;Lockwood, 2005), (4) solar activity and its prediction (Thompson, 1993;Hathaway et al, 1999;Fröhlich and Lean, 2004), (5) terrestrial climate change (Cliver et al, 1998;Friis-Christensen, 2001; Le Mouël et al, 2005), (6) atmospheric ozone depletion (Jarvis, 2005), and (7) cosmic rays and atmospheric radionuclide production (Stuiver and Quay, 1980;Beer et al, 1990).…”

A note on the statistics of the largest geomagnetic storms per solar cycle

“…Beginning with Siscoe (1976), extreme value statistics have been used to model the intensity of large geomagnetic storms (e.g., Silbergleit, 1997;Willis et al, 1997). As described below, in these analyses, extreme value distributions of the Gumbel type are fit to measures of the intensity of the most intense geomagnetic storms that occurred in each of the recent solar cycles.…”