DASP Blog: Hossein Ghadjari on "when the ionosphere misbehaves"
In this DASP blog, Hossein Ghadjari (University of Calgary)
discusses their recent paper on Intermittency in the integrated power of ionospheric density fluctuations. If you
have any questions, reach out to Hossein at hossein.ghadjari@ucalgary.ca
When the Ionosphere Misbehaves: Intermittency, Heavy Tails, and Why It Matters
Every GPS or satellite signal must pass through the ionosphere. Sometimes this layer develops irregular “lumps and gaps” in its electron density that bend, scatter, or briefly block signals. When that happens, a receiver can lose lock on satellites, and navigation can fail. In our study, we used almost ten years of ESA Swarm satellite data after sunset near the magnetic equator to measure how strongly the electron density wiggles at different spatial scales, linking those measurements to real outages, called loss of navigational capability (LNC). LNC means that a receiver can track fewer than four GPS satellites, which is the minimum needed for a position fix.
Two central ideas frame our results: intermittency, where the system is mostly quiet but occasionally produces powerful bursts, and self-organised criticality (SOC), where systems naturally evolve toward a state that yields power-law, heavy-tailed event sizes. Swarm satellite data show that below ~30 km, fluctuation strengths follow a power law, and intermittency spans many scales, confirmed by multifractal analysis. LNC events cluster in the far tail. These findings demonstrate that rare bursts dominate operational risk and occur where statistical patterns predict.
Why heavy tails matter (the intuitive way)
Not all randomness is created equal. In thin-tailed (near-Gaussian) situations, such as human height or age, biology and physics impose hard limits and a characteristic scale. Most values cluster tightly around “typical”, and even exceptional cases deviate by only a few multiples of that scale. A person might be over 2 meters tall or live past 100 years, but you will not meet a 10-meter-tall person or a 1,000-year-old; the system’s constraints forbid orders-of-magnitude extremes.
By contrast, heavy-tailed systems have no single characteristic scale. Event sizes can span many orders of magnitude, and the probability of very large events decays slowly, often like a power law. That is why you can see extraordinarily wealthy individuals or very large earthquakes: the tail is thick enough that outsized events, while still rare, are not ruled out by the system’s statistics. Our ionospheric results look like the second case. The fluctuation strength spans orders of magnitude and is heavy-tailed at small scales. In such regimes, rare, catastrophic bursts are part of the model, not anomalies.
Universality: when very different systems share the same rules
A striking feature of many heavy-tailed, scale-free systems is universality. Near a critical state, the fine details often do not matter; what matters are broad features like symmetries, conserved quantities, and dimensionality. Systems that share these features fall into the same universality class, visible as the same scaling exponents and similar power-law behaviour over many scales.
If ionospheric irregularities and, for example, neuronal avalanches in the brain turn out to share the same exponents and scaling relations, they may belong to the same universality class. Practically, that opens a two-way street for insight. Methods for tail-aware forecasting, cascade modelling, or early-warning indicators that detect when the tail is thickening can transfer from one system to the other with minimal changes. So, progress in pinning down how ionospheric bursts start and grow in principle informs neuroscience, and vice versa. Universality does not claim the mechanisms are identical; it says that near the critical regime, the statistics obey the same rules, and those rules can travel across disciplines.
So what?
For operations, the lesson is straightforward: averages do not protect you when rare extremes dominate risk. Heavy-tail-aware monitoring and nowcasting, altitude- or geometry-aware design margins, and procedures that adapt during bursty regimes are the right tools for a system that is usually quiet and then bursts. Recognising intermittency, heavy tails, and possible universality in ionospheric irregularities reframes the problem, from chasing typical days to planning for the days that matter most.
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| Swarm-C integrated power histograms over nearly 10 years. (a) Scales 30 to 450 km on log-log axes; red circles mark LNC counts per bin; black line is a normal synthetic reference. (b to d) Same as (a) for 15 to 30, 10 to 15, and 7.5 to 10 km |
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