When you measure something that varies randomly over time like the solar wind, and your measurement contains some error, a strange thing happens at the extremes. If you observe a very high value, the true underlying value is statistically more likely to be somewhat lower than what you measured. Not because you made a mistake, but because extreme values are rare by definition, and measurement errors tend to push ordinary values up into the “extreme” zone more often than they push genuinely extreme values down. This is called regression to the mean, and it has a crucial consequence. If you then compare your noisy, extreme measurement to the Earth’s response which is driven by the true value, the response will look smaller than expected. Repeat this across thousands of measurements, and a fake “ceiling” emerges from the data.
Think of it this way. Imagine measuring ocean waves during a storm. The largest waves you record are not just large because of the ocean itself, they also contain a small element of chance. A wave that is unusually high is more likely to have been helped by a favourable fluctuation. When you measure again, that same boost is unlikely to occur a second time, so the next measurement tends to be closer to the average. The ocean has not changed; the extremes simply become less extreme when viewed again.
That is exactly what the authors argue is happening with geomagnetic storm measurements. The solar wind is not measured right next to the Earth. It is measured 1.5 million kilometres away at L1, and then it has to travel all the way to the magnetosphere, through the bow shock, the point where the solar wind slams into the Earth’s magnetic field and dramatically slows down, and eventually map its effects onto the polar ionosphere.
Three things can go wrong along the way. The travel time from L1 to the Earth is uncertain, sometimes by tens of minutes. The travel time from the bow shock to the polar ionosphere adds further unpredictability. And the solar wind itself physically transforms during the journey: its speed, direction, and magnetic configuration all change as it navigates the turbulent region between L1 and the reconnection site near the Earth.
Crucially, these errors get larger as the solar wind gets stronger. This is the property statisticians call “heteroskedastic” uncertainty, the noise grows with the signal. And it is precisely this property, combined with the fact that, put simply, the solar wind follows a log-normal distribution (skewed toward lower values, with rare but very high peaks), that produces the non-linear, saturation-like bias in the data.