The world’s navigation systems, from GPS to Europe’s Galileo, depend on radio waves passing cleanly through the ionosphere, a charged atmospheric region extending from 80–1 000 km (50–620 miles) above Earth. After sunset, that layer becomes unstable, and navigation accuracy can collapse in seconds.
When sunlight fades, the lower ionosphere loses its charge faster than the upper layers. This imbalance drives plasma bubbles, pockets of low-density charged gas, upward through the atmosphere. As they rise, they scatter radio waves, breaking the steady flow of data between satellites and receivers. The result is a temporary loss of signal lock, a failure that can halt precision navigation.
These disturbances appear strongest over the magnetic equator, where electric and magnetic forces combine most intensely. They are capable of degrading signals across wide regions, affecting aircraft, ships, and other systems that depend on uninterrupted satellite navigation.
Inside Swarm’s decade-long experiment
To understand the mechanics of these events, researchers examined nearly ten years of observations from ESA’s Swarm mission. The three identical satellites, Swarm A, B, and C, have orbited Earth since 2013, tracking changes in the magnetic field and ionospheric plasma.
Swarm A and C travel at altitudes of about 430 to 460 km (267 to 286 miles), while Swarm B flies higher, at roughly 530 km (329 miles). Each carries a Langmuir probe sampling electron density twice per second and a GPS receiver that records when signals are lost. The data were divided into one-minute segments, giving spatial resolution from about 7.5–450 km (4.7–280 miles), based on the spacecraft speed of 7.5 km/s (4.7 mi/s).
Loss-of-navigational-capability (LNC) events were defined as moments when the onboard GPS receiver tracked fewer than four satellites. Over 2013 to mid-2023, the team recorded 265 such events on Swarm A, 86 on Swarm B, and 285 on Swarm C, with most occurring after sunset between −30° and +30° geomagnetic latitude. Swarm B, flying higher, encountered far fewer events, confirming that turbulence is stronger at lower altitudes.
Because Swarm A and C fly side by side just 1.4° apart, many disruptions appeared on both satellites within 150 seconds of each other. In nearly a quarter of all cases, disturbances occurred simultaneously in both hemispheres, suggesting that ionospheric turbulence often spans magnetic conjugate regions.
The hidden power law behind turbulence
When scientists plotted the size and frequency of these events, they found a striking pattern. The strength of electron density fluctuations followed a power law: small disturbances were common, moderate ones less so, and extreme ones rare, but all related by a simple mathematical ratio. This behaviour appeared in three of the four spatial bands studied, those between 7.5–30 km (4.7–18.6 miles), while the largest-scale fluctuations did not follow the same rule.
The team used a statistical approach developed by Baró and Vives in 2012, combining maximum-likelihood fitting with Kolmogorov–Smirnov tests, accepting only results with p-values above 0.1. These tests confirmed that the probability distributions at smaller scales truly matched a power law, a hallmark of complex, self-organising systems.
Spectral slopes clustered around 1.6, close to but slightly below the Kolmogorov value of 5/3 expected for turbulent flows. This slope is consistent with Rayleigh–Taylor instabilities, the main process driving plasma bubbles in the equatorial ionosphere. The finding implies that turbulence in this region behaves much like other natural cascades, where energy transfers smoothly across scales.
Signs of self-organisation in the ionosphere
The discovery fits into a broader concept known as self-organised criticality, where a system naturally evolves toward a critical threshold at which tiny disturbances can trigger large events. The classic analogy is a sand pile: as grains accumulate, the slope steepens until a single grain can cause an avalanche. The ionosphere appears to behave in much the same way.
However, the researchers describe this as a statistical analogy rather than direct proof. They could not measure avalanche durations or spatial scaling because of satellite motion and limited sampling rates. Still, the power-law pattern, combined with heavy-tailed distributions and intermittent bursts of turbulence, provides strong circumstantial evidence that the ionosphere may operate near a critical state.
To explore this further, the team applied multifractal detrended fluctuation analysis. The generalized Hurst exponent, h(q), ranged from about 0.4 to 1.5, with h(2) greater than 0.5, showing that plasma fluctuations are persistent and long-memory in nature. The comparison between 2014, a year of high solar activity, and 2017, a quiet year, revealed similar fractal patterns, meaning that intermittency and multifractality persist under very different solar conditions.
Patterns that mirror earthquakes
Ghadjari and colleagues also compared ionospheric fluctuations with earthquake statistics. The analogy is more than poetic: both systems release energy in bursts that follow power-law relationships. In seismology, this is known as the Gutenberg–Richter law, where small quakes are frequent and large ones are rare. In the ionosphere, the integrated power of plasma fluctuations plays a similar role, with extreme bursts producing the most severe navigation losses.
Just as earthquakes share common spectral slopes but vary in energy release, ionospheric events can have similar frequency characteristics yet differ greatly in strength. The largest fluctuations correspond to loss-of-lock or total outage events. This parallel suggests that the same statistical laws governing tectonic stress may also apply to plasma dynamics in near-Earth space.
What the findings could mean for navigation
Recognising that the ionosphere behaves as a scale-free, self-organising system could help refine how scientists predict its impact on GNSS reliability. Instead of assuming random noise, models may treat plasma turbulence as a structured process that follows measurable probabilities.
The study stops short of claiming that forecasts are now possible, but the statistical framework it establishes may guide the development of probabilistic nowcasting tools for satellite navigation. By knowing the likelihood of extreme ionospheric states, operators could better anticipate when positioning errors or signal losses are most probable.
What the satellites could not see
The research team emphasised important limitations. The Langmuir probes sample at just 2 Hz, meaning they cannot detect small-scale scintillation below about 7.5 km (4.7 miles). The satellites’ constant motion prevents direct observation of temporal avalanche sequences or the true spatial extent of disturbances. In addition, receiver software upgrades made in 2015 and changing solar conditions influence how often events were detected.
Because of these factors, the evidence for self-organised criticality remains statistical rather than definitive. To verify it, future missions will need instruments capable of higher-frequency plasma measurements and static platforms that can capture time-resolved dynamics.
Why it matters for science and society
Finding a universal mathematical law in ionospheric turbulence reshapes how scientists understand the upper atmosphere. It links space weather, earthquakes, and other complex systems through the shared logic of scale-invariant behaviour.
For technology, it points toward better models of when and where GPS disruptions may occur, improving resilience for transport, emergency response, and communication networks.
The Swarm mission, still operating after more than a decade, continues to provide the long data record required for these insights. Its observations are helping to map how Earth’s magnetic and plasma environment behaves not as random noise but as an organised, dynamic system that follows nature’s own mathematics.
References:
1 Intermittency in the integrated power of ionospheric density fluctuations – Hossein Ghadjari et al. – J. Space Weather Space Clim. – July 18, 2025 – https://doi.org/10.1051/swsc/2025026 – OPEN ACCESS
2 Swarm decodes mathematical pattern behind GPS outages – ESA – November 18, 2025