Some Experiments in Extreme‐Value Statistical Modeling of Magnetic Superstorm Intensities

Abstract

Abstract In support of projects for forecasting and mitigating the deleterious effects of extreme space weather storms, an examination is made of the intensities of magnetic superstorms recorded in the Dst index time series (1957–2016). Modified peak‐over‐threshold and solar cycle, block‐maximum samplings of the Dst time series are performed to obtain compilations of storm maximum −Dstm intensity values. Lognormal, upper limit lognormal, generalized Pareto, and generalized extreme‐value model distributions are fitted to the −Dstm data using a maximum‐likelihood algorithm. All four candidate models provide good representations of the data. Comparisons of the statistical significance and goodness of fits of the various models give no clear indication as to which model is best. The statistical models are used to extrapolate to extreme‐value intensities, such as would be expected (on average) to occur once per century. An upper limit lognormal fit to peak‐over‐threshold −Dstm data above a superstorm threshold of 283 nT gives a 100‐year extrapolated intensity of 542 nT and a 68% confidence interval (obtained by bootstrap resampling) of [466, 583] nT. A generalized extreme‐value distribution fit to solar cycle, block‐maximum −DstmBM data gives a nine‐solar cycle (approximately 100‐year) extrapolated intensity of 591 nT. The Dst data are found to be insufficient for providing usefully accurate estimates of a statistically theoretical upper limit for magnetic storm intensity. Secular change in storm intensities is noted, as is a need for improved estimates of pre‐1957 magnetic storm intensities.

Keywords

• extreme events
• magnetic storm intensities
• space weather hazards
• statistical methods