A preprint reports an empirical relationship for estimating maximum geomagnetically induced currents, or GIC—the current measurements recorded at monitoring sites during geomagnetic storms. Its central question was whether one relationship could be applied across a range of storms, using solar-wind conditions and site-specific scaling factors. The equations describe an association in the observations, not a demonstrated cause for any particular current.
The primary modeling database covered 67 sites across nine storms. For each storm period, it stored the maximum GIC, two solar-wind extrema and site-specific α and β factors. The analysis combined the storm measures with those local scaling factors, rather than using storm inputs alone. The GIC records came from NERC for all nine storms, with additional TVA data for the May 2024 Gannon storm.
To prepare the fit, the response was logarithmically transformed. A Breusch-Pagan test at the 0.05 level found no statistically significant heteroscedasticity after transformation; in plain language, the test found no statistically significant evidence that the spread of errors changed in a way detected by that check. Candidate equations were compared with best-subset selection using the coefficient of determination and corrected AICc, a score used here to reduce overfitting.
What the mean model captured
That process selected a six-parameter model for the mean maximum GIC. Its reported Pearson correlation was 0.73, and its uncentered coefficient of determination was 0.54. The figures indicate that the fitted values captured part of the variation in the observations, but not all of it.
An influence check tested whether the result depended too heavily on one event: when each storm was left out in turn, the analysis concluded that no single storm disproportionately drove the regression. All summed Cook's distances were well below one. Confidence intervals for the reported fit were not provided in the supplied analysis.
A deliberate limit on the high end
For high-end estimates, the researchers selected a seven-parameter quantile-regression equation for the upper 80% bound of maximum GIC. Quantile regression is used here to estimate a chosen point in the upper part of the observed range, rather than the mean.
The choice was shaped by sparse data at the extreme end. An upper-95% equation predicted values exceeding 10,000 amperes but had only about seven supporting observations. The upper-80% fit had about 29 supporting observations, so the analysis retained that bound; even then, the upper-tail estimate remains sensitive to the limited data.
A statistical shape for scenario analysis
The paper also carried out a secondary distribution analysis. It identified 39 storms since 1995 from events with Kp of at least 8 and included lead and trailing periods with Kp of at least 6.
Across all sites tested, a lognormal distribution—a statistical way to describe the spread of positive values—had acceptable goodness of fit under Kolmogorov-Smirnov, or K-S, tests at the 0.05 level. Gamma and Weibull fits were rejected at many sites. Equations for the lognormal shape, location and scale parameters matched the fitted results closely, with Pearson r of 0.99 and a coefficient of determination of 0.98. K-S statistics and confidence intervals were not reported.
What the equations do not settle
The results remain tied to the database used to build the equations: 67 sites across nine storms. The supplied analysis reports no independent external validation set and no uncertainty intervals for the fitted equations. That caution is especially important at the upper end, where the 95% fit had sparse support and was not retained.
The paper states that its data are provided in Appendix A and that its Python analysis code is available at Thomas (2026). The authors declare no conflicts of interest for the manuscript.
The work was supported by NSF RAPID Grant 2434136, with USGS and NRCan acknowledged for funding and operational magnetometer data. The document is posted as an arXiv preprint.
Paper data and sources
Original title: Empirical Relationship for Geomagnetically Induced Currents (GIC) and Solar Wind Conditions
Authors: Dean Thomas, Lucy A. Wilkerson, Robert S. Weigel et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text