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

Jeffrey J. Love·E. Joshua Rigler·Antti Pulkkinen·Pete Riley
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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 − D s t 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, − D s t ≥ 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 − D s t ≥ 880 nT (greater than Carrington) but a wide 95% confidence interval of [490, 1187] nT.

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Jeffrey J. Love, E. Joshua Rigler, Antti Pulkkinen, Pete Riley. 2015-08-19. On the lognormality of historical magnetic-storm intensity statistics: Implications for extreme-event probabilities. https://doi.org/10.1002/2015gl064842

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