Regression to the Mean of Extreme Geomagnetic Storms

Abstract

Extreme space weather events on Earth occur during intervals of strong solar wind driving. The solar wind drives plasma convection and currents in the near-Earth space environment. For low values of the driver, the Earth's response is linear, estimated by parameters such as the polar cap index based on ground magnetometer activity. Curiously, for extreme solar wind driving, the Earth's response appears not to increase beyond a saturation limit. Theorists have advanced a host of explanations for this saturation effect, but there is no consensus. Here, we demonstrate that the saturation is a manifestation of the regression to the mean effect resulting from random uncertainty in the time and magnitude of solar wind measurements. Our results reveal that data analysis underpinning the saturation theories is non-linearly biased; hence, the theories must be validated against the correct solar wind data. Correcting for the uncertainties reveals that the Earth's response to solar wind driving is linear throughout, and the impact of extreme geomagnetic storms can be twice as large as previously thought. We show that regression to the mean is a fundamental property of the relationship between measurement and the truth, where the truth corresponding to the measurement is closer to the mean. This effect is particularly pronounced for uncertain measurements of extreme values and is likely to manifest across various fields, from extreme climate studies to chronic medical pain.