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.

Influence of spatial variations of the geoelectric field on geomagnetically induced currents

“…A common approach is to use long geomagnetic data sets to extrapolate indices (Siscoe, 1976;Love et al, 2015;Riley, 2012), or to extrapolate the amplitude of the variation field or its time derivative (Danskin & Lotz, 2015;Love et al, 2016;Thomson et al, 2011). A related possibility is to extrapolate the geoelectric field modelled from magnetic field data (Myllys et al, 2014;Nikitina et al, 2016;Pulkkinen et al, 2012;2015;Wintoft et al, 2016).…”

Space Weather Quarterly Volume 14, Issue 1, 2017

“…In particular, Riley [2012] chose x min = 120, while Love et al [2015] used x min = 63 as a lower bound for |Dst|. Here we use an approach for optimizing the value of x min based on minimizing the Kolmogorov-Smirnov (KS) goodness-of-fit statistic between the model and the data [Clauset et al, 2009].…”

“…Riley [2012] and Love et al [2015] identified the minimum values in severity (x min ) manually and, arguably, somewhat subjectively. In particular, Riley [2012] chose x min = 120, while Love et al [2015] used x min = 63 as a lower bound for |Dst|.…”

“…Then, following Love et al [2015], we identify all contiguous data for which this threshold is exceeded and label that as a single storm. Since it is also possible that Dst may cross the −100 nT threshold one or more times during the same storm; we define a further threshold of −20 nT to identify the start and end times of the storm.…”

“…Love [2012] considered the 10 year occurrence probabilities of rare natural events, including geomagnetic storms, but added the important component of estimating uncertainties, using Poisson parameters to infer confidence-credibility intervals. He found, for example, Love et al [2015] considered the assumption that the data could be adequately described by a power law distribution. Specifically, they tested the idea of whether Dst would be better described by a lognormal distribution rather than a power law distribution.…”