On the lognormality of historical magnetic storm intensity statistics: Implications for extreme-event probabilities

Abstract

An examination is made of the hypothesis that the statistics of magnetic storm maximum intensities are the realization of a lognormal stochastic process. Weighted least squares and maximum likelihood methods are used to fit lognormal functions to -Dst storm time maxima for years 1957-2012; bootstrap analysis is used to established confidence limits on forecasts. Both methods provide fits that are reasonably consistent with the data; both methods also provide fits that are superior to those that can be made with a power-law function. In general, the maximum likelihood method provides forecasts having tighter confidence intervals than those provided by weighted least squares. From extrapolation of maximum likelihood fits: a magnetic storm with intensity exceeding that of the 1859 Carrington event, -Dst ≥ 850 nT, occurs about 1.13 times per century and a wide 95% confidence interval of [0.42, 2.41] times per century; a 100 year magnetic storm is identified as having a -Dst ≥ 880 nT (greater than Carrington) but a wide 95% confidence interval of [490, 1187] nT.