Regression to the mean can explain saturation of geomagnetic storms
By Maria-Theresia Walach (Lancaster University)
submitted on behalf of Nithin Sivadas (Goddard Space Flight Center/Catholic University of America)
The strength of the solar wind that ‘drives’ (transfers energy to) the magnetosphere is different from the measurements made by satellites at L1, upstream of the magnetosphere. This difference is due to random errors resulting from substantial uncertainty in the timing, evolution and structure of the solar wind. We questioned the premise on which the saturation theories were constructed, and wondered whether there is reliable evidence that the saturation effect is real. We therefore set out to understand and calculate how uncertainty in the input of a system (in this case, the solar wind) affects inferences from data about the response of the system (Earth).
Using data from the Wind, THEMIS, MMS, DoubleStar and Cluster spacecraft, we found that random errors in the reported strength of the solar wind that strikes Earth depend on the strength of the solar wind, which has a log normal probability distribution. We used a Monte Carlo error model to calculate the probable ‘true’ value behind each measurement of solar-wind strength. Unexpectedly, we found a saturation of these true values as the measurement values increased, which is similar to the effect observed in the data (Fig. 1a). In other words, the true value regresses to the mean and away from the measurement, owing to the nature of the random error and statistical properties of the solar-wind strength. Correcting for uncertainties in timing and magnitude reveals that the Earth’s response in the polar PCI index to solar wind driving is linear throughout, which means driving of the magnetospheric system can be twice as large as previously thought for extreme geomagnetic storms (Fig. 1b).
References:
Main paper: Sivadas, N., Sibeck, D., Subramanyan, V., Walach, M.-T., Ozturk, D. S., Ferdousi, B., Michotte de Welle, B., Regression to the mean can explain saturation of geomagnetic storms. Nature 655, 1143–1147 (2026). https://doi.org/10.1038/s41586-026-10757-4. https://rdcu.be/fwSqV
For the interested reader, we recommend the Extended Data and Figures sections and the Supplementary Information section, which hold a large proportion of content for this paper. For a quick synopsis, we recommend the editorial summary below.
Research briefing: https://doi.org/10.1038/d41586-026-02245-6
See publication for more details:
Sivadas, N., Sibeck, D., Subramanyan, V., Walach, M.-T., Ozturk, D. S., Ferdousi, B., Michotte de Welle, B., Regression to the mean can explain saturation of geomagnetic storms. Nature 655, 1143–1147 (2026). https://doi.org/10.1038/s41586-026-10757-4. https://rdcu.be/fwSqV and Research Briefing, https://doi.org/10.1038/d41586-026-02245-6

Uncertainty in measurements of solar wind explains the observed saturation of geomagnetic activity. a, Observations from 1995 to 2019 (green) indicate that, on average, the polar cap index (EPC, a measure of Earth’s geomagnetic response to solar wind) saturates at measurements of large solar-wind strength (E*m). The result of our statistical approach, the Monte Carlo error model (pink), predicts the same saturation effect arising from uncertainty in the measurement of solar wind transferring energy to Earth’s magnetosphere, rather than a physical mechanism. X* and X are measured and ‘true’ solar-wind strengths from the error model. b, Correcting the effect of random errors in values of solar-wind strength shows that Earth’s geomagnetic response is linear (pink), where Ecm is the corrected solar-wind strength. Credit: Sivadas, N. et al./Nature (CC BY 4.0) (https://doi.org/10.1038/d41586-026-02245-6)