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

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. Plain Language Summary: Estimating the statistical likelihood of extreme‐value geomagnetic storm intensities depends on the selection of data and models. The data used here are discrete samples of a standard time series that measures geomagnetic disturbance. Different methods are examined for identifying data values that can serve as nonredundant representations of storm maximum intensity. Four different statistical models (two formal models and two physically motivated models) are examined as candidate descriptions of the data. Comparisons and contrasts are made of the goodness of model descriptions of the data. Extrapolations are made to estimate once‐per‐century storm intensities; an upper limit on storm intensity cannot be confidently established; slow secular change is noted in the occurrences of intense storms. General suggestions are made for improving inferences about the future occurrence of intense storms. Results inform projects concerned with forecasting and mitigating the deleterious effects of extreme space weather storms. Key Points: Estimates of 100‐year magnetic storm intensities are affected by limitations of the data and the statistical modelsA model fit to peak‐over‐threshold storm maximum data gives a 100‐year intensity and 68% confidence interval of 542 [466, 583] nTStorm maximum data are about as well fitted by lognormal models as they are by formal extreme‐value models [ABSTRACT FROM AUTHOR]